Engineering Tripos Part IIB, 4F7: Statistical Signal Analysis, 2020-21
Module Leader
Lecturer
Timing and Structure
Michaelmas term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3F3; Useful 3F1 and 3F8
Aims
The aims of the course are to:
- Continue the study of statistical signal processing techniques from the basics studied in 3F3.
- Introduce time-series models, in particular State-space models and hidden Markov models; understand their role in applications of signal processing.
- Develop techniques for fitting statisical modes to data and estimating hidden signals from noisy observations.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand state-space models and hidden Markov models including their mathematical characterisation, strengths and limitations.
- Understand how to execute all the necessary computational tasks involved in fitting the models to data, to estimate unobserved quantities and make future predictions.
- Understand the computational methodology employed, their mathematical derivation, their strengths and weaknesses, how to execute them, and their use more generally in Statistical and data-centric engineering problems.
Content
This course is about fitting statistical models to data that arrives sequentially over time. Once an appropriate model has been fit, tasks like predicting future trends or estimating quantities not directly observed can be performed. The statistical modelling and computational methodology covered by this course is widely used in many applied areas. For example, data that arrives sequentially over time is a common occurrence in Signal Processing (Engineering), Finance, Machine Learning, Environmental statistics etc.
The model that most appropriately describes data that arrives sequentially over time is a time-series model, an example of which is the ARMA model (studied in 3F3.) However, this course will look at more versatile models that incorporate hidden or latent state variables as these are able to account for richer behaviour. Also, models that aim describe how many really physical processes evolve over time often necessarily have to incorporate unobserved hidden states that form a Markov process.
- Introduction to state-space models and optimal linear filtering; the Kalman filter; exemplar problems in signal processing.
- Introduction to hidden Markov models: definition; inference/estimation aims; exact computation of the conditional probability distributions.
- Importance sampling: introduction; weight degeneracy; statistical properties.
- Sequential importance sampling and resampling (also known as the particle filter): application to hidden Markov models; filtering; smoothing.
- Calibrating hidden Markov models: maximum likelihood estimation and its implementation.
- Exemplar problems in Signal Processing.
- Examples Papers.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 01/09/2020 10:38
Engineering Tripos Part IIB, 4F7: Statistical signal and network models, 2024-25
Module Leader
lecturers
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3F1, 3F3, 3F8 recommended. 3M1 useful.
Aims
The aims of the course are to:
- Introduce time-series models, in particular State-space models and hidden Markov models; understand their role in applications of signal processing.
- Develop techniques for fitting statisical models to data and estimating hidden signals from noisy observations.
- Introduce network models, graph algorithms, and techniques to analyse large scale relational data
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand state-space models, hidden Markov models, and network models including their mathematical characterisation, strengths and limitations.
- Execute the necessary computational tasks involved in fitting the models to data, to estimate unobserved quantities and make future predictions.
- Understand the computational methodology employed, their mathematical derivation, their strengths and weaknesses, how to execute them, and their use more generally in Statistical and data-centric engineering problems.
Content
This course is about fitting statistical models to data that arrives sequentially over time and across network structures. Once an appropriate model has been fitted, tasks such as predicting future trends or estimating quantities not directly observed can be performed. The statistical modelling and computational methodology covered by this course is widely used in many applied areas. For example, data that arrives sequentially over time is a common occurrence in Signal Processing (Engineering), Finance, Machine Learning, Environmental statistics etc.
The model that most appropriately describes data that arrives sequentially over time is a time-series model, an example of which is the ARMA model (studied in 3F3.) However, this course will look at more versatile models that incorporate hidden or latent state variables as these are able to account for richer behaviour. Also, models that aim describe how many really physical processes evolve over time often necessarily have to incorporate unobserved hidden states that form a Markov process.
Besides changing over time, many data are distributed over different individuals or sites. For example, users of a social media platform will each have different properties. Networks (graphs) provide a simple formalism to analyse distributed systems composed of small but interrelated parts.
State space models and time series:
The model that most appropriately describes data that arrives sequentially over time is a time-series model, an example of which is the AR model (studied in 3F3). However, this course will look at more versatile stochastic (random) state-space models that incorporate hidden or latent state variables as these are able to account for richer behaviour. Also, models that aim describe how many really physical processes evolve over time often necessarily have to incorporate unobserved hidden states that form a Markov process.
-
Introduction to state-space models and optimal linear filtering; the Kalman filter; exemplar problems in signal processing.
-
Introduction to hidden Markov models: definition; inference/estimation aims; exact computation of the conditional probability distributions.
-
Importance sampling: introduction; weight degeneracy; statistical properties.
-
Sequential importance sampling and resampling (also known as the particle filter): application to hidden Markov models; filtering; smoothing.
-
Calibrating hidden Markov models: maximum likelihood estimation and its implementation.
-
Exemplar problems in Signal Processing.
-
Examples Papers.
Networks modelling:
Besides changing over time, many data are distributed over different individuals or sites. For example, users of a social media platform will each have different properties. Networks (graphs) provide a simple formalism to analyse distributed systems composed of small but interrelated parts. We will cover:
-
· Fundamentals, basic graph theory and algorithms.
-
· Metrics: centrality (e.g. PageRank), assortativity, clustering, diameter ("six degrees of separation").
-
· Models of networks: Erdős–Rényi, small-world and scale free.
-
· Models on networks: Spreading, reliability and percolation.
-
· Community detection and stochastic block models.
-
· Graph spectra and their applications.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 18/09/2024 13:21
Engineering Tripos Part IIB, 4F7: Statistical signal and network models, 2025-26
Module Leader
lecturers
Timing and Structure
Michaelmas term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3F1, 3F3, 3F8 recommended. 3M1 useful.
Aims
The aims of the course are to:
- Introduce time-series models, in particular State-space models and hidden Markov models; understand their role in applications of signal processing.
- Develop techniques for fitting statisical models to data and estimating hidden signals from noisy observations.
- Introduce network models, graph algorithms, and techniques to analyse large scale relational data
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand state-space models, hidden Markov models, and network models including their mathematical characterisation, strengths and limitations.
- Execute the necessary computational tasks involved in fitting the models to data, to estimate unobserved quantities and make future predictions.
- Understand the computational methodology employed, their mathematical derivation, their strengths and weaknesses, how to execute them, and their use more generally in Statistical and data-centric engineering problems.
Content
This course is about fitting statistical models to data that arrives sequentially over time and across network structures. Once an appropriate model has been fitted, tasks such as predicting future trends or estimating quantities not directly observed can be performed. The statistical modelling and computational methodology covered by this course is widely used in many applied areas. For example, data that arrives sequentially over time is a common occurrence in Signal Processing (Engineering), Finance, Machine Learning, Environmental statistics etc.
The model that most appropriately describes data that arrives sequentially over time is a time-series model, an example of which is the ARMA model (studied in 3F3.) However, this course will look at more versatile models that incorporate hidden or latent state variables as these are able to account for richer behaviour. Also, models that aim describe how many really physical processes evolve over time often necessarily have to incorporate unobserved hidden states that form a Markov process.
Besides changing over time, many data are distributed over different individuals or sites. For example, users of a social media platform will each have different properties. Networks (graphs) provide a simple formalism to analyse distributed systems composed of small but interrelated parts.
State space models and time series:
The model that most appropriately describes data that arrives sequentially over time is a time-series model, an example of which is the AR model (studied in 3F3). However, this course will look at more versatile stochastic (random) state-space models that incorporate hidden or latent state variables as these are able to account for richer behaviour. Also, models that aim describe how many really physical processes evolve over time often necessarily have to incorporate unobserved hidden states that form a Markov process.
-
Introduction to state-space models and optimal linear filtering; the Kalman filter; exemplar problems in signal processing.
-
Introduction to hidden Markov models: definition; inference/estimation aims; exact computation of the conditional probability distributions.
-
Importance sampling: introduction; weight degeneracy; statistical properties.
-
Sequential importance sampling and resampling (also known as the particle filter): application to hidden Markov models; filtering; smoothing.
-
Calibrating hidden Markov models: maximum likelihood estimation and its implementation.
-
Exemplar problems in Signal Processing.
-
Examples Papers.
Networks modelling:
Besides changing over time, many data are distributed over different individuals or sites. For example, users of a social media platform will each have different properties. Networks (graphs) provide a simple formalism to analyse distributed systems composed of small but interrelated parts. We will cover:
-
· Fundamentals, basic graph theory and algorithms.
-
· Metrics: centrality (e.g. PageRank), assortativity, clustering, diameter ("six degrees of separation").
-
· Models of networks: Erdős–Rényi, small-world and scale free.
-
· Models on networks: Spreading, reliability and percolation.
-
· Community detection and stochastic block models.
-
· Graph spectra and their applications.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 04/06/2025 13:30
Engineering Tripos Part IIB, 4F7: Statistical Signal Analysis, 2021-22
Module Leader
Lecturer
Timing and Structure
Michaelmas term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3F3; Useful 3F1 and 3F8
Aims
The aims of the course are to:
- Continue the study of statistical signal processing techniques from the basics studied in 3F3.
- Introduce time-series models, in particular State-space models and hidden Markov models; understand their role in applications of signal processing.
- Develop techniques for fitting statisical modes to data and estimating hidden signals from noisy observations.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand state-space models and hidden Markov models including their mathematical characterisation, strengths and limitations.
- Understand how to execute all the necessary computational tasks involved in fitting the models to data, to estimate unobserved quantities and make future predictions.
- Understand the computational methodology employed, their mathematical derivation, their strengths and weaknesses, how to execute them, and their use more generally in Statistical and data-centric engineering problems.
Content
This course is about fitting statistical models to data that arrives sequentially over time. Once an appropriate model has been fit, tasks like predicting future trends or estimating quantities not directly observed can be performed. The statistical modelling and computational methodology covered by this course is widely used in many applied areas. For example, data that arrives sequentially over time is a common occurrence in Signal Processing (Engineering), Finance, Machine Learning, Environmental statistics etc.
The model that most appropriately describes data that arrives sequentially over time is a time-series model, an example of which is the ARMA model (studied in 3F3.) However, this course will look at more versatile models that incorporate hidden or latent state variables as these are able to account for richer behaviour. Also, models that aim describe how many really physical processes evolve over time often necessarily have to incorporate unobserved hidden states that form a Markov process.
- Introduction to state-space models and optimal linear filtering; the Kalman filter; exemplar problems in signal processing.
- Introduction to hidden Markov models: definition; inference/estimation aims; exact computation of the conditional probability distributions.
- Importance sampling: introduction; weight degeneracy; statistical properties.
- Sequential importance sampling and resampling (also known as the particle filter): application to hidden Markov models; filtering; smoothing.
- Calibrating hidden Markov models: maximum likelihood estimation and its implementation.
- Exemplar problems in Signal Processing.
- Examples Papers.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 20/05/2021 07:49
Engineering Tripos Part IIB, 4F2: Robust and Nonlinear Control, 2024-25
Module Leader
Lecturer
Timing and Structure
Lent term. 14 lectures + 2 computer lab sessions. Assessment: 100% coursework
Prerequisites
3F2 assumed.
Aims
The aims of the course are to:
- introduce fundamental concepts from nonlinear dynamic systems
- introduce techniques for the analysis and control of nonlinear and multivariable systems.
Objectives
As specific objectives, by the end of the course students should be able to:
- apply standard analysis and design tools to multivariable and nonlinear feedback systems.
- appreciate the diversity of phenomena in nonlinear systems.
Content
Part I. ROBUST CONTROL (7L + 1 Computer Lab session, Prof F Forni)
1. Uncertainty and Nonlinearity in control systems: simple models.
2. Signal spaces and system gains.
3. The small-gain theorem and the passivity theorem. Phase versus gain uncertainties
4. Dissipativity theory
5. Robust stability and performance. Stability margins.
6. An introduction to H-infty control.
7. Gap metrics
PART 2: NONLINEAR SYSTEMS (7L + 1 computer lab session, Prof F Forni)
1. Small and large signal analysis. Contractive systems. Fading memory operators.
2. State-space analysis and Nyquist. Differential stability. Differential dissipativity. Differential circle criterion.
3. Feedback systems: simple models.
4. Phase portrait analysis.
5. Analysis and design of switches and clocks. Robust differential control.
6. Monotone systems. Scale relative graphs (SRGs). Applications in biology.
7. Describing function analysis.
Further notes
ASSESSMENT
Coursework only.
Coursework
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 Robust control of haptic interfaces Coursework 1 brief description Learning objective:
|
Individual Report anonymously marked |
28 February 2025 [30/60] |
|
[Coursework activity #2 Feedback oscillations control ] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
28 March 2025 [30/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D1
Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 19/01/2025 18:26
Engineering Tripos Part IIB, 4F2: Robust and Nonlinear Control, 2025-26
Module Leader
Lecturer
Timing and Structure
Lent term. 14 lectures + 2 computer lab sessions. Assessment: 100% coursework
Prerequisites
3F2 assumed.
Aims
The aims of the course are to:
- introduce fundamental concepts from nonlinear dynamic systems
- introduce techniques for the analysis and control of nonlinear and multivariable systems.
Objectives
As specific objectives, by the end of the course students should be able to:
- apply standard analysis and design tools to multivariable and nonlinear feedback systems.
- appreciate the diversity of phenomena in nonlinear systems.
Content
Part I. ROBUST CONTROL (7L + 1 Computer Lab session, Prof F Forni)
1. Uncertainty and Nonlinearity in control systems: simple models.
2. Signal spaces and system gains.
3. The small-gain theorem and the passivity theorem. Phase versus gain uncertainties
4. Dissipativity theory
5. Robust stability and performance. Stability margins.
6. An introduction to H-infty control.
7. Gap metrics
PART 2: NONLINEAR SYSTEMS (7L + 1 computer lab session, Prof F Forni)
1. Small and large signal analysis. Contractive systems. Fading memory operators.
2. State-space analysis and Nyquist. Differential stability. Differential dissipativity. Differential circle criterion.
3. Feedback systems: simple models.
4. Phase portrait analysis.
5. Analysis and design of switches and clocks. Robust differential control.
6. Monotone systems. Scale relative graphs (SRGs). Applications in biology.
7. Describing function analysis.
Further notes
ASSESSMENT
Coursework only.
Coursework
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 Robust control of haptic interfaces Coursework 1 brief description Learning objective:
|
Individual Report anonymously marked |
28 February 2025 [30/60] |
|
[Coursework activity #2 Feedback oscillations control ] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
28 March 2025 [30/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D1
Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 04/06/2025 13:30
Engineering Tripos Part IIB, 4F2: Robust & Nonlinear Systems & Control, 2018-19
Module Leader
Lecturers
Prof MC Smith and Dr I Lestas
Timing and Structure
Lent term. 14 lectures + 2 examples classes. Assessment: Exam only
Prerequisites
3F2 assumed.
Aims
The aims of the course are to:
- introduce fundamental concepts from nonlinear dynamic systems
- introduce techniques for the analysis and control of nonlinear and multivariable systems.
Objectives
As specific objectives, by the end of the course students should be able to:
- apply standard analysis and design tools to multivariable and nonlinear feedback systems.
- appreciate the diversity of phenomena in nonlinear systems.
Content
PART 1: MULTIVARIABLE FEEDBACK SYSTEMS (7L + 1 example class, Prof M.C. Smith)
- Performance measures for multi-input/multi-output systems.
- Stabilization: stability conditions, all stabilizing controllers, small gain theorem.
- Models for uncertain systems.
- Robust stability and performance. Loop shaping design.
- Design of multivariable systems.
PART 2: NONLINEAR SYSTEMS (7L + 1 example class, Dr I Lestas)
- Linear and Nonlinear systems; feedback circuits.
- Differential equations and trajectories.
- Multiple equilibria, limit cycles, chaos and other phenomena.
- Examples from biology and mechanics.
- State space stability analysis:
- The theorems of Lyapunov, LaSalle invariance principle.
- Stability of nonlinear circuits and neural behaviors.
- State-space tools for robustness analysis.
- Input/output stability analysis:
- Describing functions
- Small gain theorems, circle and Popov criteria, passivity.
Further notes
ASSESSMENT
Lecture Syllabus/Written exam (1.5 hours) - Start of Easter Term/100%
Booklists
Please see the Booklist for Group F Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D1
Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 03/01/2019 11:00
Engineering Tripos Part IIB, 4F2: Robust and Nonlinear Control, 2021-22
Module Leader
Lecturers
Prof R Sepulchre and Dr F Forni
Timing and Structure
Lent term. 14 lectures + 2 computer lab sessions. Assessment: 100% coursework
Prerequisites
3F2 assumed.
Aims
The aims of the course are to:
- introduce fundamental concepts from nonlinear dynamic systems
- introduce techniques for the analysis and control of nonlinear and multivariable systems.
Objectives
As specific objectives, by the end of the course students should be able to:
- apply standard analysis and design tools to multivariable and nonlinear feedback systems.
- appreciate the diversity of phenomena in nonlinear systems.
Content
Part I. ROBUST CONTROL (7L + 1 Computer Lab session, Prof R. Sepulchre)
1. Uncertainty and Nonlinearity in control systems: simple models.
2. Signal spaces and system gains.
3. The small-gain theorem and the passivity theorem. Phase versus gain uncertainties
4. Dissipativity theory
5. Robust stability and performance. Stability margins.
6. An introduction to H-infty control.
7. Gap metrics
PART 2: NONLINEAR SYSTEMS (7L + 1 computer lab session, Dr F Forni)
1. Small and large signal analysis. Contractive systems. Fading memory operators.
2. State-space analysis and Nyquist. Differential stability. Differential dissipativity. Differential circle criterion.
3. Feedback systems: simple models.
4. Phase portrait analysis.
5. Analysis and design of switches and clocks. Robust differential control.
6. Monotone systems. Contraction of cones. Polyhedral cones. Applications in biology.
7. Describing function analysis.
Further notes
ASSESSMENT
Coursework only.
Coursework
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 Robust control of haptic interfaces Coursework 1 brief description Learning objective:
|
Individual Report anonymously marked |
25 February 2022 [30/60] |
|
[Coursework activity #2 Feedback oscillations control ] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
25 March 2022 [30/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D1
Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 27/09/2021 09:29
Engineering Tripos Part IIB, 4F2: Robust & Nonlinear Systems & Control, 2019-20
Module Leader
Lecturers
Prof RJCPM Sepulchre and Dr I Lestas
Timing and Structure
Lent term. 14 lectures + 2 examples classes. Assessment: Exam only
Prerequisites
3F2 assumed.
Aims
The aims of the course are to:
- introduce fundamental concepts from nonlinear dynamic systems
- introduce techniques for the analysis and control of nonlinear and multivariable systems.
Objectives
As specific objectives, by the end of the course students should be able to:
- apply standard analysis and design tools to multivariable and nonlinear feedback systems.
- appreciate the diversity of phenomena in nonlinear systems.
Content
PART 1: MULTIVARIABLE FEEDBACK SYSTEMS (7L + 1 example class, Prof R. Sepulchre)
- Performance measures for multi-input/multi-output systems.
- Stabilization: stability conditions, all stabilizing controllers, small gain theorem.
- Models for uncertain systems.
- Robust stability and performance. Loop shaping design.
- Design of multivariable systems.
PART 2: NONLINEAR SYSTEMS (7L + 1 example class, Dr I Lestas)
- Linear and Nonlinear systems; feedback circuits.
- Differential equations and trajectories.
- Multiple equilibria, limit cycles, chaos and other phenomena.
- Examples from biology and mechanics.
- State space stability analysis:
- The theorems of Lyapunov, LaSalle invariance principle.
- Stability of nonlinear circuits and neural behaviors.
- State-space tools for robustness analysis.
- Input/output stability analysis:
- Describing functions
- Small gain theorems, circle and Popov criteria, passivity.
Further notes
ASSESSMENT
Lecture Syllabus/Written exam (1.5 hours) - Start of Easter Term/100%
Booklists
Please see the Booklist for Group F Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D1
Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 19/09/2019 10:14
Engineering Tripos Part IIB, 4F2: Robust and Nonlinear Control, 2020-21
Module Leader
Lecturers
Prof R Sepulchre and Dr F Forni
Timing and Structure
Lent term. 14 lectures + 2 computer lab sessions. Assessment: 100% coursework
Prerequisites
3F2 assumed.
Aims
The aims of the course are to:
- introduce fundamental concepts from nonlinear dynamic systems
- introduce techniques for the analysis and control of nonlinear and multivariable systems.
Objectives
As specific objectives, by the end of the course students should be able to:
- apply standard analysis and design tools to multivariable and nonlinear feedback systems.
- appreciate the diversity of phenomena in nonlinear systems.
Content
Part I. ROBUST CONTROL (7L + 1 Computer Lab session, Prof R. Sepulchre)
1. Uncertainty and Nonlinearity in control systems: simple models.
2. Signal spaces and system gains.
3. The small-gain theorem and the passivity theorem. Phase versus gain uncertainties
4. Dissipativity theory
5. Robust stability and performance. Stability margins.
6. An introduction to H-infty control.
7. Gap metrics
PART 2: NONLINEAR SYSTEMS (7L + 1 computer lab session, Dr F Forni)
1. Small and large signal analysis. Contractive systems. Fading memory operators.
2. State-space analysis and Nyquist. Differential stability. Differential dissipativity. Differential circle criterion.
3. Feedback systems: simple models.
4. Phase portrait analysis.
5. Analysis and design of switches and clocks. Robust differential control.
6. Monotone systems. Contraction of cones. Polyhedral cones. Applications in biology.
7. Describing function analysis.
Further notes
ASSESSMENT
Coursework only.
Coursework
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 Robust control of haptic interfaces Coursework 1 brief description Learning objective:
|
Individual Report anonymously marked |
24 February 2021 [30/60] |
|
[Coursework activity #2 Feedback oscillations control ] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
24 March 2021 [30/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D1
Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 21/01/2021 09:14
Pages
