Stochastic minimax optimal time-delay state feedback control of uncertain quasi-integrable Hamiltonian systems

Ju Feng, Zu-Guang Ying, Yong Wang, Wei-Qiu Zhu

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

A stochastic minimax optimal time-delay state feedback control strategy for uncertain quasi-integrable Hamiltonian systems is proposed. First, a stochastic optimal state feedback control problem of uncertain quasi-integrable Hamiltonian system with time delay in feedback control subjected to Gaussian white noise is formulated. Then, the time-delayed state feedback control forces are approximated by the control forces without time delay and the original problem is converted into a stochastic optimal state feedback control problem of an uncertain system without time delay. After that, by following a procedure based on the stochastic averaging method and stochastic differential game, the worst-case disturbances and the optimal controls are obtained from solving a Hamiltonian–Jacobi–Isaacs (HJI) equation. As an example, the stochastic minimax optimal state feedback control of a Duffing oscillator with parametric disturbances and time-delayed feedback control is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy.
Original languageEnglish
JournalActa Mechanica
Volume222
Issue number3-4
Pages (from-to)309-319
ISSN0001-5970
DOIs
Publication statusPublished - 2011
Externally publishedYes

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