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- Title
Stochastic Minimax Vibration Control for Uncertain Nonlinear Quasi-Hamiltonian Systems with Noisy Observations.
- Authors
Zu-guang Ying; Rong-chun Hu; Rong-hua Huan
- Abstract
A stochastic minimax control strategy for uncertain nonlinear quasi-Hamiltonian systems with noisy observations under random excitations is proposed based on the extended Kalman filter and minimax stochastic dynamical programming principle. A structure system with smart sensors and actuators is modeled as a controlled, excited and dissipative Hamiltonian system with noisy observations. The differential equations for the uncertain nonlinear quasi-Hamiltonian system with control and observation under random excitation are given first. The estimated nonlinear stochastic control system with uncertain parameters is obtained from the uncertain quasi-Hamiltonian system with noisy observation. In this case, the optimally estimated state is determined by the observation based on the extended Kalman filter. The dual dynamical programming equation for the estimated uncertain system is then obtained based on the minimax stochastic dynamical programming principle. The worst-case disturbances are determined for bounded uncertain parameters and the optimal control law is determined for the worst case by the programming equation. The proposed minimax control strategy is applied to two uncertain nonlinear stochastic systems with controls and noisy observations. The control effectiveness for the stochastic vibration response reductions of the systems is illustrated with numerical results. The proposed minimax control strategy is applicable to general uncertain nonlinear multi-degree-of-freedom structure systems with noisy observations under random excitations.
- Subjects
NONLINEAR systems; NONLINEAR dynamical systems; STOCHASTIC systems; UNCERTAIN systems; NONLINEAR control theory; NONLINEAR differential equations; STOCHASTIC programming
- Publication
International Journal of Acoustics & Vibration, 2019, Vol 24, Issue 4, p707
- ISSN
1027-5851
- Publication type
Article
- DOI
10.20855/ijav.2019.24.41446