Optimal control of multisolution ordinary differential equations in the absence of convexity |
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| Authors: | Shu Luan Hang Gao |
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| Institution: | (1) Siemens Power Transmission and Distribution Inc., 10900 Wayzata Blvd., Minnetonka, MN 55305, USA;(2) Department of Automation, Tsinghua University, Beijing, 100084, People’s Republic of China;(3) Department of Electrical and Computer Engineering, Oregon State University, Corvallis, OR 97330, USA |
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| Abstract: | In this paper, the authors study an optimal control problem governed by a class of multistate ordinary differential equations
in the absence of convexity. To overcome the difficulty that the corresponding approximate optimal control problem may have
no solution, relaxed controls are introduced. With the help of relaxation theory, Pontryagin’s maximum principle for the optimal
pairs of the original control problem is obtained. In the end of this paper, the authors discuss the application of the maximum
principle by an example. |
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