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Piecewise Linear Optimal Controllers for Hybrid Systems


F. Borrelli

American Control Conference, Chicago, IL, USA

In this paper 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 (MPC), which is based on the minimization of a weighted l_1/infinity-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 (mp-MILP), which avoids solving mixed-integer programs on-line (Bemporad, Morari, 1999). As the resulting control law is piecewise affine, on-line computation is drastically reduced to a simple linear function evaluation.

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