A scheme of speed gradient and its application in problems of adaptive control

The paper is concerned with a scheme for design of adaptive control algorithms whereby motion is organized in the space of parameters to be adjusted along the gradient of the speed of change of a single functional. This scheme, initially formulated by A. A. Krasovskiy for the identification problem covers many well-known adaptation and identification algorithms synthesized by the direct Lyapunov method. General conditions for stability of such systems are obtained. Ways are suggested to regularize algorithms so as to make the systems insensitive to unmonitor able disturbances and to the digital nature of the adaptation algorithms. Examples are given of applying the scheme to design of adaptation algorithms in a number of problems of adaptive control for dynamic plants.