It will be shown how recent results can be used for the robust and optimal control of uncertain, discrete-time, piecewise affine systems which are subject to constraints on the input and state. The first part of the talk will concentrate on the problem of robust, time-optimal control to a given target set. The equivalent problem of computing the reachable set of states of the system will be described and a geometric solution will be given. The second part of the talk will show how dynamic and parametric programming can be used to give an explicit solution to the problem of robustly steering the system to a given target set, while minimising the worst-case cost on the input and state trajectory.
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