ECE 686: Filtering and control of stochastic linear systems
Instructor: Andrew Heunis
Email: heunis@uwaterloo.ca
Phone: 519-888-4567 x32083
Location: EIT 3115
Course objectives:
This is a course on state estimation and control in stochastic linear dynamical systems, in both discrete and continuous-time settings. State estimation in linear systems is shown to be equivalent to projection onto a closed subspace, generated by an observation process, in a Hilbert space of random variables. This formulation of state estimation allows one to obtain representations for state estimators in the form of the Kalman filter equations under very general conditions. The discrete-time Kalman filter and dynamic programming are used to study the discrete linear stochastic optimal control problem with quadratic cost function.
Pre-requisites for this course are a familiarity with elementary probability theory at the level of ECE 316, linear system theory at the level of ECE-682, and a willingness to adapt to new mathematical arguments. The necessary real analysis, dynamic programming etc., will be covered as part of the course.
Contents:
1. Elements of metric space theory and Hilbert spaces.
2. The geometric theory of linear filtering.
3. Discrete-time linear filtering and the discrete-time Kalman filter.
4. Discrete-time stochastic optimal control with complete and partial observations.
5. Elements of the theory of continuous-time stochastic processes.
6. The Wiener integral and linear stochastic differential equations.
7. The innovation theorem of Kailath and representation formulae for continuous-time linear filters.
8. The continuous-time Kalman filter.
Text:
Course notes will be provided.