Stochastic adaptive control using multiple models for improved performance in the presence of random disturbances (Q2719855)

Multiple models for the adaptive control of an unknown continuous-time linear system have been proposed by \textit{K. S. Narendra} and \textit{J. Balakrishnan} [IEEE Trans. Autom. Control 39, 1861-1866 (1994; Zbl 0816.93049)]. Their methods have been recently extended by \textit{L. S. Narendra} and \textit{C. Xiang} [IEEE Trans. Autom. Control 45, 1669-1686 (2000; Zbl 0988.93042)] to discrete-time linear systems in the presence of a stochastic disturbance, and convergence of the adaptive scheme and the asymptotic behaviour of the overall system have been proved for both the deterministic (noise-free) and the stochastic case. Motivated by the fact that the nature of the underlying disturbance may not be known, which makes the a priori choice of the appropriate estimation method difficult, the authors of the present paper study the adaptive control problem when structurally different procedures are used simultaneously to estimate the parameters of the plant. They show that the multiple model switching and tuning approach can be chosen to select the best estimation method. In particular, they provide a framework to analyse convergence and stability of stochastic adaptive control problems using multiple estimation models. Finally, computer simulation results are included to illustrate the advantages of using different estimation procedures in the adaptive control problem.