A Unified Approach to Robust Stochastic and Deterministic Adaptive Control

This paper presents a new methodology for the global stability analysis, and consequently, for the design of robust deterministic and stochastic adaptive control, filtering and prediction. The methodology advocated herein represents a mathematical formalization of the self-stabilization mechanism which is a natural characteristic of every properly designed adaptive system. The effectiveness of the proposed approach is demonstrated by solving the robust deterministic and stochastic adaptive control problems. It is shown that very small algorithm gains ¿, may produce very large signals in the adaptive loop, which are unacceptable for practical applications. The intensity of the admissible unmodelled dynamics does not depend on the algorithm design parameters and it is specified in terms of the corresponding H^¿ norm.