Statistic tracking strategy for non-Gaussian systems based on PID controller structure and LMI approach

In this paper, the robust PID tracking control problem is considered for stochastic systems with non-Gaussian variable. The tracked objective is the statistic information of a given target probability density function (PDF), rather than a deterministic signal. Following B-spline expansion approximation for the measurable integrated performance function, the statistic tracking control problem can be reduced to a tracking problem for the nonlinear weighting dynamics. A robust control strategy with PID structure is proposed for the nonlinear weighting system in the presence of exogenous disturbances, and the improved convex LMI algorithms are provided to compute the controller gains. Furthermore, in order to enhance the robust performance, the peak-to-peak measure is applied to optimize the tracking performance. Rigorous stability and performance analysis are developed via the use of Lyapunov stability criterion.