Course overview
This course will provide training in system modelling using state-space equations and applying optimal state estimation and optimal control techniques to state-space models. It will provide thorough understanding and knowledge of theory and design of estimation in signal processing. Content includes: Model multivariable systems using state-space equations and linearisation techniques; Linear algebra for state-space methods; Concepts of controllability, stabilizability, observability, detectability, duality, canonical/Kalman decomposition; Design state-feedback controllers and Luenberger observers, and from them derive output-feedback controllers through the separation principle; Design optimal output-feedback controllers; Estimation Theory; Signal parameter estimation: e.g., maximum likelihood estimation;
Signal waveform estimation: Wiener Filters; Spectral Estimation.
Course learning outcomes
- Determine a linear state-space model for a multivariable multibody system analytically and computationally, in continuous time and discrete time. (PLO 1, 4, 5) (EA 1.1-1.3, 2.1-2.3)
- Analyse the controllability, observability and stability of a multivariable linear time-invariant system. (PLO 1, 4, 5) (EA 1.1-1.3, 2.1-2.3)
- Design optimal output-feedback controllers using linear quadratic regulation and Bayesian estimation. (PO 1, 4, 5) (EA 1.1-1.3, 2.1-2.3)
- Apply model predictive control to linear plants with input/output/state constraints, with a clear understanding of the underlying theory and implementation challenges. (PLO 1, 4, 5) (EA 1.1-1.3, 2.1-2.3)
- Perform multidomain modeling and simulation, control system design and analysis using industry-standard tools. (PLO 1, 2, 4, 5) (EA 1.1-1.4, 3.4)
- Discuss the mathematical theory and recent trends in modern control. (PLO 1, 2, 7, 9) (EA 1.1-1.5, 3.2, 3.4)