Abstract
The optimal control problem for hybrid (discrete-continuouis) system is considered in the case when the continuous behavior can be controled and discontinuities arise when the system achives the boundary of some set. We suppose that discontinuities can be considered as a result of some impulsive inputs, which can be represented in feedback form as the intermediated conditions. Meanwhile, variuos types of irregulariries such as: nonextandability of solution or sliding mode can arise. However, if the jumps of solution are described by some shift operator, as for hybrid system satisfying the robustness condition, one can reduce this problem to the standard problem of nonsmooth optimization and the representation of solution by differential equation with a measure and the existence theorem for optimal solution can be obtained.
This work was supported in part by National Science Foundation of USA grant CMS 94-1447s and International Association for the Promotion of Cooperation with Scientists from the Independent States of the Former Soviet Union (INTAS) grants 94–697 and 93–2622.
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Miller, B.M. (1998). Optimization of generalized solutions of nonlinear hybrid (discrete-continuous) systems. In: Henzinger, T.A., Sastry, S. (eds) Hybrid Systems: Computation and Control. HSCC 1998. Lecture Notes in Computer Science, vol 1386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64358-3_49
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DOI: https://doi.org/10.1007/3-540-64358-3_49
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