Adaptive control of discrete-time systems using multiple models

The adaptive control of a linear time-invariant discrete-time system using multiple models is considered in this paper. Both the deterministic (noise free) case and the stochastic case when random disturbances are present are discussed. Based on the prediction errors of a finite number of fixed and adaptive identification models, a procedure is outlined for switching between a finite number of controllers to improve performance. The principal contributions of the paper are the proof of global stability of the overall system and the convergence of the tracking error signal to zero in the deterministic case and the proof of convergence of the minimum variance control problem. Computer simulation results are included to complement the theoretical results.