Abstract
Publisher Summary The parameter-adaptive control problem consists in stabilizing and, if possible, optimizing the behavior of a system with unknown parameters. The contribution of the self-tuning regulator to discrete time parameter stochastic control stimulated a great amount of theoretical and practical work in adaptive control. This chapter presents rigorous proofs of the stabilizing properties of various adaptive control algorithms for linear, time invariant, and finite dimensional systems. The principal motivation for adaptive control is the stabilization and optimization of systems whose parameters are unknown and vary in time (deterministically or stochastically). The chapter presents a set of results concerning the adaptive, asymptotically optimal, control of linear autoregressive system with moving average exogenous control inputs and uncorrelated disturbances (called ARX systems) with random autoregressive (AR) parameters. It discusses the conditions required for the parameter estimates generated in the adaptive control algorithm to be strongly consistent. The the adaptive control algorithm asymptotically stabilizes the system and asymptotically achieves minimum mean-square tracking error.
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