PDF shaping control for non-Gaussian stochastic distribution systems with time-delay

In this paper, the novel probability density function (PDF) shaping control problem is studied for a class of non-Gaussian stochastic system with time-delay and multi-uncertainties. After the B-spline expansion is applied to approach the output PDF, the PDF shaping control problem is transformed to the control of dynamical weights vector. Furthermore, the PI tracking control algorithm is proposed for weighting systems with time delay and multi-uncertainties, such that the dynamic system can satisfy multi-objective delay-dependent control demands including stability, robustness, tracking performance and state constraint. Compared with previous works, the method weakens the conservative performance and improves the robustness of the system based on L₁ performance index. A simulation example is presented to illustrate the effectiveness of the proposed approach.