Robust Control of Constrained Systems

Eric Kerrigan (CUED)

Most systems are subject to state and control constraints and the design of controllers for such systems is a very active area of research. A fundamental control problem is that of determining the subset of the state space which can be steered via an admissible control sequence to any given target set, while guaranteeing that the state constraints will be satisfied for all allowable disturbance sequences. This can be seen as a more general interpretation of the classical reachability and controllability problems of linear, unconstrained systems.

In particular, invariant set theory has been shown to be crucial in understanding the behaviour of constrained systems, since constraints can be satisfied if and only if the initial state is contained in a set which is positively invariant for the closed-loop system.

The first part of this talk will be concerned with giving a review of robust set invariance theory in a general, nonlinear setting. The concepts of robust controllable, stabilisable and invariant sets will be introduced.

The second part will focus on the application of set invariance theory in analysing and synthesising robust predictive controllers for systems with state and control constraints, subject to unknown-but-bounded disturbances.

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