Constrained Stochastic Distribution Control for Nonlinear Stochastic Systems with Non-gaussian Noises

In this paper, a stochastic distribution control (SDC) algorithm is presented for nonlinear and non-Gaussian stochastic systems with constraints on control inputs. A generalized entropy optimization criterion is constructed based on the probability density function (PDF) of the tracking error. An optimal control law is then obtained using the penalty function method. Stability analysis for this closed loop system is formulated. Finally, the comparative simulation results are presented to show that the proposed SDC algorithm is superior to PID controller. The contributions of the paper are threefold: 1) the principle of preservation of probability is introduced to deduce the PDF of tracking error under a relaxed assumption on the controlled systems; 2) the mathematical expectation of the squared error is included in the performance index to reduce the tracking error; 3) penalty function method is adopted to solve the SDC problem for nonlinear and non-Gaussian stochastic systems with constraints on control inputs.