Aims & Learning Objectives: Aims: Four concepts underpin control theory: controllability, observability, stabilizability and optimality. Of these, the first two essentially form the focus of the Year 3/4 course on linear control theory. In this course, the latter notions of stabilizability and optimality are developed. Together, the courses on linear control theory and nonlinear & optimal control provide a firm foundation for participating in theoretical and practical developments in an active and expanding discipline.
Objectives:
To present concepts and results pertaining to robustness, stabilization and optimization of (nonlinear) finitedimensional control systems in a rigorous manner. Emphasis is placed on optimization, leading to conversance with both the BellmanHamiltonJacobi approach and the maximum principle of Pontryagin, together with their application.
Content: Topics will be chosen from the following:
Controlled dynamical systems: nonlinear systems and linearization. Stability and robustness. Stabilization by feedback. Lyapunovbased design methods. Stability radii. Smallgain theorem. Optimal control. Value function. The BellmanHamiltonJacobi equation. Verification theorem. Quadraticcost control problem for linear systems. Riccati equations. The Pontryagin maximum principle and transversality conditions (a dynamic programming derivation of a restricted version and statement of the general result with applications). Proof of the maximum principle for the linear timeoptimal control problem.
