Optimal Vibration Control for Structural Quasi-Hamiltonian Systems with Noised Observations

A structural control system with smart sensors and actuators is considered and its basic dynamic equations are given. The controlled stochastically excited and dissipative Hamiltonian system with a noised observation is obtained by discretizing the nonlinear stochastic smart structure system. The estimated nonlinear stochastic system with control is obtained in which the optimally estimated state is determined by the observation based on the extended Kalman filter. Then the dynamical programming equation for the estimated system is obtained based on the stochastic dynamical programming principle. From this the optimal control law dependent on the estimated state is determined. The proposed optimal control strategy is applied to two nonlinear stochastic systems with controls and noised observations. The control efficacy for stochastic vibration response reductions of the systems is illustrated with numerical results. The proposed optimal control strategy is applicable to general nonlinear stochastic structural systems with smart sensors smart actuators and noised observations.