Nonlinear one-step-ahead predictive mean control of bounded dynamic stochastic systems with guaranteed stability

Following the recently developed algorithms for the modelling and control of the shape of the output probability density functions of bounded dynamic stochastic systems, a nonlinear one-step-ahead predictive mean controller with a guaranteed closed loop stability is proposed. At first, the B-spline neural network-based square-root model is used to represent the output probability density functions. The mean controller design of the output distribution is then studied by transferring the design procedure to a solution of a nonlinear optimization problem. The Levenberg–Marquardt modification for gradient search approach is adopted in the optimization phase and a Lyapunov-based stability analysis is carried out for the closed loop system. This leads to a sufficient condition for the asymptotic stability of the closed loop system. Robustness analysis is performed when the system is subjected to random noises and modelling errors. It has been shown that the closed mean control loop system is still locally asymptotically stable and the tracking errors are bounded. Simulation examples are used to demonstrate the use of the algorithm and encouraging results have been obtained.