Multi-objective PID control for non-Gaussian stochastic distribution system based on two-step intelligent models

A new method for controlling the shape of the conditional output probability density function (PDF) for general nonlinear dynamic stochastic systems is proposed based on B-spline neural network (NN) model and T-S fuzzy model. Applying NN approximation to the measured PDFs, we transform the concerned problem into the tracking of given weights. Meanwhile, the complex multi-delay T-S fuzzy model with exogenous disturbances, parametric uncertainties and state constraints is used to represent the nonlinear weight dynamics. Moreover, instead of the non-convex design algorithms and PI control, the improved convex linear matrix inequality (LMI) algorithms and the generalized PID controller are proposed such that the multiple control objectives including stability, robustness, tracking performance and state constraint can be guaranteed simultaneously. Simulations are performed to demonstrate the efficiency of the proposed approach.