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Optimal probability density function control for NARMAX stochastic systems. (English) Zbl 1149.93350
Summary: 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.
MSC:
93E20Optimal stochastic control (systems)
93C10Nonlinear control systems
93E15Stochastic stability