Stochastic adaptive control using multiple models for improved performance in the presence of random disturbances

The use of multiple models for adaptively controlling an unknown continuous‐time linear system was proposed in Narendra and Balakrishnan (IEEE Transactions on Automatic Control 1994; 39(9):1861–1866). and discussed in detail in Narendra and Xiang (IEEE Transactions on Automatic Control 2000, 45(9):(1669–1686) Technical Reports 9801 and 9803, Centre for System Science, Yale University, 1998). Recently, the same concepts were extended to discrete‐time systems, both for the noise free case as well as when a stochastic disturbance is present, and the convergence of the algorithms was established. In this paper we consider structurally different estimation models, and use the multiple models approach to select, on‐line, the one that results in the best performance of the overall system for the given disturbance characteristics. The principal objective of the paper is to demonstrate that the convergence of these schemes can be treated in a unified manner. Simulations are included towards the end of the paper to indicate the improvement in performance that can be achieved using such schemes. Copyright © 2001 John Wiley & Sons, Ltd.