OPTIMAL CONTROL OF MULTISOLUTION ORDINARY DIFFERENTIALEQUATIONS IN THE ABSENCE OF CONVEXITY

Shu LUAN;Hang GAO

Journal of Systems Science & Complexity ›› 2010, Vol. 23 ›› Issue (2) : 321-333.

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Journal of Systems Science & Complexity ›› 2010, Vol. 23 ›› Issue (2) : 321-333. DOI: 10.1007/s11424-010-8237-z
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OPTIMAL CONTROL OF MULTISOLUTION ORDINARY DIFFERENTIALEQUATIONS IN THE ABSENCE OF CONVEXITY

  • Shu LUAN(1), Hang GAO(2)
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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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Multisolution / ODEs / optimal control / Pontryagin's maximum principle / relaxed controls.

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Shu LUAN , Hang GAO. OPTIMAL CONTROL OF MULTISOLUTION ORDINARY DIFFERENTIALEQUATIONS IN THE ABSENCE OF CONVEXITY. Journal of Systems Science and Complexity, 2010, 23(2): 321-333 https://doi.org/10.1007/s11424-010-8237-z
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