Self-Tuning Sup Regulators for Discrete Systems

The problem of controlling systems with a bound on the increment of their disturbances and with constant but unknown parameters is considered. A new modified least squares (MLS) algorithm is presented to estimate the parameters for the above systems. A self-tuning sup regulator algorithm based on MLS algorithm and the sup regulator, which minimizes the supremum of the absolute output of the system for all time and all disturbances to which the system is subjected, is presented and analyzed. Under the assumption that the plant to be controlled is stably invertible, the global convergence analysis shows that the closed-loop system is stable and the properties of the self-tuning sup regulator asymptotically converge to those of the sup regulator.