Robust adaptive systems and self stabilization

A methodology for the global stability analysis and, consequently, for the design of robust deterministic and stochastic adaptive control, filtering, and prediction is introduced. The methodology represents a mathematical formalization of the self-stabilization mechanism which is a natural characteristic of every properly designed adaptive system. The underlying idea is the construction of a suitable Lyapunov function for different periods of adaptation. 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 unmodeled dynamics does not depend on the algorithm gain, and it is specified in terms of the corresponding H^∞ norm. In order to establish goal stability, persistency exciting conditions are not required in the present results