Stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems using stochastic maximum principle

A stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems is proposed based on the stochastic averaging method, stochastic maximum principle and stochastic differential game theory. First, the partially completed averaged Itô stochastic differential equations are derived...

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Bibliographic Details
Published inStructural and multidisciplinary optimization Vol. 49; no. 1; pp. 69 - 80
Main Authors Hu, R. C., Ying, Z. G., Zhu, W. Q.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2014
Springer Nature B.V
Subjects
Computational Mathematics and Numerical Analysis
Control systems
Control theory
Differential equations
Engineering
Engineering Design
Game theory
Hamiltonian functions
Maximum principle
Minimax technique
Optimal control
Optimization
Parameter uncertainty
Performance indices
Research Paper
Strategy
System effectiveness
Theoretical and Applied Mechanics
Nonlinear quasi-Hamiltonian system
Stochastic optimal control
Parameter uncertainty
Stochastic averaging
Stochastic maximum principle
Minimax control
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Summary:A stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems is proposed based on the stochastic averaging method, stochastic maximum principle and stochastic differential game theory. First, the partially completed averaged Itô stochastic differential equations are derived from a given system by using the stochastic averaging method for quasi-Hamiltonian systems with uncertain parameters. Then, the stochastic Hamiltonian system for minimax optimal control with a given performance index is established based on the stochastic maximum principle. The worst disturbances are determined by minimizing the Hamiltonian function, and the worst-case optimal controls are obtained by maximizing the minimal Hamiltonian function. The differential equation for adjoint process as a function of system energy is derived from the adjoint equation by using the Itô differential rule. Finally, two examples of controlled uncertain quasi-Hamiltonian systems are worked out to illustrate the application and effectiveness of the proposed control strategy.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-013-0958-x