Stochastic adaptive control using multiple estimation models

The use of multiple models for adaptively controlling an unknown continuous-time linear system was proposed in [1] and discussed in detail in [2]. 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 [3]. 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 objective of the paper is to demonstrate that the convergence of these schemes can be treated in a unified manner. Simulations are included to indicate the improvement in performance that can be achieved using such schemes.