论文信息 - OPTIMAL CONTROL IN HYBRID SYSTEMS: AN EFFICIENT DECISION MAKING TOOL

OPTIMAL CONTROL IN HYBRID SYSTEMS: AN EFFICIENT DECISION MAKING TOOL

Hybrid systems evolve simultaneously in continuous and discrete state spaces. An illustration of practical interest is realized by continuous systems for which decisions have to be made at discrete times. We set this problem as an optimal control problem, whereby the decisions become controls that are implemented in order to optimize a certain desired outcome. Due to the intertwining between continuous and discrete dynamics, the derivation of the adjoint and optimality systems is different from the purely continuous or discrete cases. We obtain the necessary optimality conditions and, for a few typical illustrations, we obtain also explicit expressions for the optimal controls.

V. Protopopescu | S. Lenhart | S. Lenhart | V. Protopopescu

[1] L. S. Pontryagin,et al. Mathematical Theory of Optimal Processes , 1962 .

[2] G. Thompson,et al. Optimal Control Theory: Applications to Management Science and Economics , 2000 .

[3] Jiongmin Yong,et al. Optimal Control Theory for Infinite Dimensional Systems , 1994 .

[4] M. L. Juncosa,et al. Non-Monotonicity, Chaos and Combat Models , 1996 .

[5] Abbott,et al. New paradoxical games based on brownian ratchets , 2000, Physical review letters.

[6] John Geweke,et al. Decision making under risk and uncertainty : new models and empirical findings , 1992 .

[7] Tapan Biswas. Decision-Making under Uncertainty , 1997 .

[8] Karen Rudie,et al. A survey of modeling and control of hybrid systems , 1997 .

[9] Damien Challet,et al. Optimal combinations of imperfect objects. , 2002, Physical review letters.

[10] J. Lions. Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[11] Michelle Girvan,et al. Optimal design, robustness, and risk aversion. , 2002, Physical review letters.

[12] M. Petit. Dynamic optimization. The calculus of variations and optimal control in economics and management : by Morton I. Kamien and Nancy L. Schwartz. Second Edition. North-Holland (Advanced Textbooks in Economics), Amsterdam and New York, 1991. Pp. xvii+377. ISBN0-444- 01609-0 , 1994 .

[13] S Lenhart,et al. Modeling and Analysis in Support of Decision Making for Technological Investment , 2003 .