Abstract
AbstractThis paper considers the worst‐case optimal control of discontinuous piecewise affine (PWA) systems, which are subjected to constraints and disturbances. We seek to pre‐compute, via dynamic programming, an explicit control law for these systems when a PWA cost function is utilized. One difficulty with this problem class is that, even for initial states for which the value function of the optimal control problem is finite, there might not exist a control law that attains the infimum. Hence, we propose a method that is guaranteed to obtain a sub‐optimal solution, and where the degree of sub‐optimality can be specified a priori. This is achieved by approximating the underlying sub‐problems with a parametric piecewise linear program. Copyright © 2008 John Wiley & Sons, Ltd.
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