We propose a procedure for synthesizing piecewise linear optimal controllers for discrete-time hybrid systems. A stabilizing controller is obtained by designing a model predictive controller, which is based on the minimization of a weighted l/sub 1///spl infin/-norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a multiparametric mixed-integer linear program, which avoids solving mixed-integer programs online. As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluation.
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Bemporad et al. (2000) studied this question.
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