This book considers the development of new analysis and control techniques for special classes of hybrid systems: piecewise affine systems and max-plus-linear systems. Among different existing control methods we chose the optimal control framework and its receding horizon implementation referred to as model predictive control. We derived an efficient solution to a class of finite-horizon robust optimal control problems for constrained max-plus-linear systems based on convexity of the underlying optimization problem. Using the optimal control framework, novel model predictive control schemes are designed for piecewise affine and max-plus-linear systems that make use of their special structure and that incorporate conditions to guarantee a priori closed-loop asymptotic stability.

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