Optimal probability density function control for NARMAX stochastic systems

This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output probability density function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.

[1]  John F. Forbes,et al.  Regulatory control design for stochastic processes: shaping the probability density function , 2003, Proceedings of the 2003 American Control Conference, 2003..

[2]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[3]  David Clarke,et al.  Advances in model-based predictive control , 1994 .

[4]  Francis J. Doyle,et al.  Control of particle size distribution described by a population balance model of semibatch emulsion polymerization , 2000 .

[5]  Hong Wang,et al.  Bounded Dynamic Stochastic Systems: Modelling and Control , 2000 .

[6]  E. Lavretsky,et al.  Greedy optimal control , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[7]  Jian-Qiao Sun,et al.  Non-linear stochastic control via stationary response design , 2003 .

[8]  Lei Guo,et al.  PID controller design for output PDFs of stochastic systems using linear matrix inequalities , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[9]  Ian R. Petersen,et al.  Minimax optimal control of stochastic uncertain systems with relative entropy constraints , 2000, IEEE Trans. Autom. Control..

[10]  P. Dupuis,et al.  Minimax optimal control of stochastic uncertain systems with relative entropy constraints , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[11]  H. Wang,et al.  Control of conditional output probability density functions for general nonlinear and non-Gaussian dynamic stochastic systems , 2003 .

[12]  Hong Wang,et al.  Minimum entropy control of closed-loop tracking errors for dynamic stochastic systems , 2003, IEEE Trans. Autom. Control..

[13]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..