Design of Nonlinear Adaptation and Adaptive Identification Algorithms by Using Nonsearching Self-Adjusting Systems (NSAS) with a Reference Model

Abstract

The paper is concerned with the adaptive control of a continuous linear nonstationary multidimensional plant all of whose states are observable. The coefficients of the controller are tuned by parameter adjustment loops in an open (adaptive identification) or closed (USAS with a reference model) cycle. The adaptation and identification algorithms are designed by the direct Lyapunov method with Lyapunov function which is the sum of the quadratic form of generalized adaptation errors and the quadratic forms of a special types of parametric misalignments between plant and model. New classes of adaptation and identificational algorithms are suggested which are nonlinear vector functions of bilinear forms of the system states and coordinate adaptation errors.