Optimal vibration control for stochastic discrete-time systems

The problem of optimal disturbance rejection control (ODRC) with zero steady-state error to sinusoidal disturbances for stochastic discrete-time systems is considered. Based on the internal model principle, external sinusoidal disturbance is compensated by constructing a disturbance compensator. Then, an optimal linear quadratic Gaussian (LQG) controller with an infinite-time horizon cost functional is designed. The state estimator from measurements of the output makes the dynamic ODRC law physical reliable and the convergence of the cost functional can be guaranteed. A simulation example shows the approach proposed is effective.