Synthesis of optimal controllers for piecewise affine systems with sampled-data switching

Authors:
Shun-Ichi Azuma;Jun-Ichi Imura
Affiliations:
Department of Systems Science, Graduate School of Informatics, Kyoto University, Uji, Kyoto 611-0011, Japan;Department of Mechanical and Environmental Informatics, Graduate School of Information Science and Engineering, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

This paper discusses the optimal control problem of the continuous-time piecewise affine (PWA) systems with sampled-data switching, where the switching action is executed based upon a condition on the state at each sampling time. First, an algebraic characterization for the problem to be feasible is derived. Next, an optimal continuous-time controller is derived for a general class of PWA systems with sampled-data switching, for which the optimal control problem is feasible but whose subsystems in some modes may be uncontrollable in the usual sense. Finally, as an application of the proposed approach, the high-speed and energy-saving control problem of the CPU processing is formulated, and the validity of the proposed methods is shown by numerical simulations.