Active Year - 2022 - 2023

The aim of this module is to introduce students to techniques and approaches to construct mathematical models of dynamical systems, particularly relating to data-based modelling. 

Topics: The following session topics are indicative and may change to adjust for external factors.


Week 1: General introduction & motivation. Definition of identification, parameter estimation & filtering. White, grey & black-box modelling approaches. Steps of identification procedure. 

Week 2: ARX model structure. Properties of noise. Least squares for static and dynamic systems. Estimation and validation data sets. Model assessment criteria.

Week 3: Parameter estimate bias vs. consistency. Properties of LS estimator. Estimation of noise variance. Model order selection. Over- vs. underparametrised models.

Week 4: Recursive least squares algorithm. General structure of recursive algorithms. Derivation and algorithm initialisation.

Week 5: Linear dynamic model structures. Instrumental variables estimator. Recursive instrumental variables.

Week 6: Pseudo-linear regression. Predictors.

Week 7: Time-varying linear systems. Forgetting factors. Covariance reset. Adaptivity vs. noise sensitivity. 

Week 8: Introduction to Kalman filtering. Kalman filter tuned for parameter estimation. 

Week 9: Introduction and identification of bilinear systems and block-oriented nonlinear systems such as Hammerstein, Wiener and additive NARMAX systems.

Week 10: Practical aspects of identification, i.e. choice of model structure, complexity,  sampling time etc. In-class Test.

Week 11: Coursework Revision

Week 12: The final lecture will be used to close any outstanding topics.

Topics: The following session topics are indicative and may change to adjust for external factors.


Week 1: Motivation, definition and classification of Adaptive Control System 

Week 2: Introduction to Model Reference Adaptive Control (MRAC). MIT Rule

Week 3: MRAC: MIT rule, determination of adaptation gain

Week 4: Lyapunov stability theory

Week 5: MRAC design based on Lyapunov Theory

Week 6: Self Tuning Control: Pole placement, indirect self tuning

Week 7: Self Tuning Control: Direct self tuning, comparison

Week 8: Optimisation: Definitions, mathematical modelling, dynamic programming

Week 9: Solving optimisation problems with MATLAB

Week 10: In-class Test

Week 11: Multi-objective optimisation: Examples and solutions

Week 12: Extremum Seeking Control: MPPT design for PV panels

Topics: The following session topics are indicative and may change to adjust for external factors.


Week 1: Introduction to nonlinear control, the importance of nonlinear control, some nonlinear phenomena

Week 2: Mathematical Preliminaries: Norm definition, positive definite functions, comparison functions

Week 3: Phase Plane Analysis: Phase plane analysis, the concept of an equilibrium, singular points

Week 4: Lyapunov stability I: Definition of stability, asymptotic stability

Week 5: Lyapunov stability II: Indirect method

Week 6: Structures on nonlinear systems, applications, various cotrol techniques to deal with particular structures

Week 7: Design I: Dissipativity and Passivity

Week 8: Design II: Feedback linearisation

Week 9: Design III: Backstepping

Week 10: In-class Test

Week 11: Design IV: Backstepping cont.

Week 12: Design V: Sliding Mode Control

Automatic Control Lecture Notes


Previous Years

XX: Year, F: Fall, S: Spring

Undergraduate Level: 

Graduate Level: