Advanced Control S10
Module aims
This module builds on your knowledge of linear control to give insights into nonlinear control and optimization-based methods for robust and data-driven control.
Core concepts include nonlinear stability theory, Lyapunov functions, optimal control, robust control, and an introduction to model predictive control. You will gain an appreciation of how optimization concepts such as Linear Matrix Inequalities (LMIs), Semi-Definite Programming (SDP) and constrained optimization can be used to design controllers for optimal and robust performance, for both known and unknown systems.
The module is highly relevant to modern applications including flight control systems, robotics, and control of wind turbines. The optimization-based approach will give insights into how data-driven tools can play a key role in control design.
Learning outcomes
On successfully completing this module, you should be able to:
1. Derive and assess conditions to demonstrate stability and boundedness of trajectories for linear and nonlinear dynamical systems.
2. Formulate and solve classical control problems (e.g. related to optimal control and disturbance attenuation) involving linear and nonlinear dynamical systems.
3. Compose Linear Matrix Inequalities (LMIs) or Semi-Definite Programmes (SDPs) that yield the solution of certain control design problems.
4. Synthesise data-driven control methods for unknown dynamical systems utilising LMIs and SDPs.
5. Devise approximate solutions of constrained or unconstrained optimal control problems using Model Predictive Control.
Module syllabus
The module will cover stability theory for linear and nonlinear systems, via the introduction of Lyapunov equations and (control) Lyapunov functions. Classes of static optimisation problems involving positive definite matrices, such as Linear Matrix Inequalities (LMIs) and Semi-Definite Programmes (SDPs), and the method of Lagrange multipliers for constrained optimization; common control problems with objectives that go beyond ‘simple’ stability (optimal control and robust control), including the translation of hard constraints into soft constraints (and suitable ‘tuning’); control design via model-based/data-driven LMIs or SDPs for known/unknown dynamical systems; an introduction to dynamic programming for nonlinear systems; an introduction to MPC as a tool to solve optimal control problems with and without constraints.
Teaching methods
The module will be delivered primarily through large-class lectures, introducing the key concepts and methods, supported by a variety of delivery methods (e.g. using traditional methods, technological tools for active learning, and elements of flipped classroom approaches). The content will be presented via a combination of slides, whiteboard and visualizer.
Learning will be reinforced through tutorial question sheets, worked examples and quizzes.
Assessments
This module presents opportunities for both formative and summative assessment.
You will be formatively assessed through progress tests and tutorial sessions.
You will have additional opportunities to self-assess your learning via tutorial problem sheets.
You will be summatively assessed by a written closed-book examination at the end of the module.
You will receive feedback on examinations in the form of an examination feedback report on the performance of the entire cohort.
You will receive feedback on your performance whilst undertaking tutorial exercises, during which you will also receive instruction on the correct solution to tutorial problems.
Further individual feedback will be available to you on request via this module’s online feedback forum, through staff office hours and discussions with tutors.
| Assessment type
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Assessment description
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Weighting
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Pass mark
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Must pass?
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| Examination
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Closed book written examination
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100%
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50%
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N
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Reading list
Module leaders
Dr Thulasi Mylvaganam
