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Optimal Control of Hybrid Systems


T. Geyer

Nordborg, Denmark, Danfoss A/S

Hybrid systems are heterogeneous systems that exhibit both continuous dynamics (difference or differential equations) and discrete dynamics (automata, logic transitions and switching, piecewise linear mappings, quantized commands, etc.). At present, there is a wealth of practical problems of this type which can only be handled by trial and error, thus requiring excessive development time. Our ultimate goal is to provide tools which automatically generate controllers guaranteed to satisfy the designers' specifications for such complex situations in much less time. In this seminar I will first summarize our theoretical efforts by introducing a modelling framework for hybrid systems that is directly tailored to the synthesis of stabilizing model predictive controllers based on combinatorial optimization and multi-parametric programming. We show that optimal control laws for hybrid systems can be computed in closed-form and that they are piecewise affine state-feedback functions, a very attractive feature for fast-sampling applications. In a second part, I will show how to solve the optimal control problem of a fixed frequency switch-mode DC-DC converters, and derive the state-feedback control law, which can be directly implemented in hardware in terms of a look-up table. This example is particularly meant to illustrate the design flow and the various tools available to effectively design optimal controllers for hybrid systems.


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