Dynamical Systems (AM3.2)

LECTURER : R.M. Adams

Prerequisites

Linear algebra, Advanced calculus. Further exposure to differential equations and/or mechanics would be advantageous.

Description

This course is an elementary introduction to modern linear control from an application-oriented mathematical perspective. Control theory deals with dynamical systems which can be controlled; to control a dynamical object means to influence its behaviour in order to achieve a desired goal. Typically, the dynamics of a (deterministic, finite dimensional, differentiable) control system is described by a set of ordinary differential equations (the so-called state equations) with the controls as parameters. Control systems with outputs constitute natural extensions. Linear control systems (with outputs)  form an important class of control systems.

Topics

Mathematical formulation of the control problem; Linear dynamical systems; Linear control systems : controllability, observability, linear feedback, and realization; Stability and control; Optimal control : Pontryagin's principle, linear regulators with quadratic costs.

Textbook

None prescribed. Complete course notes will pe provided.

Tutorials

ONE tutorial per week.

Tests/Exams

TWO class tests and ONE final examination.