Adaptive control system with a variable adjustment law gain based on the recursive least squares method

The aim of the present paper is to synthesize an adaptive control system with variable adaptation-loop gain to compensate for the plant parametric uncertainty. In contrast to the existing ones, such a system simultaneously (1) includes an algorithm for the automatic calculation of the parameter adjustment law gain in the controller, which operates in proportion to the current regressor value, thus permitting one to obtain an adjustable upper bound for the rate of convergence of the plant output-controller parameter errors to zero (subject to the condition of persistent excitation of the regressor); (2) does not require knowing the signs or values of the entries of the plant gain matrix. The Lyapunov second method and the recursive least squares method are used to synthesize such a control system. For this system, the stability and the boundedness of the above-mentioned error values are proved, and estimates for the rate of their convergence to zero are obtained. The efficiency of our approach is demonstrated by mathematical modeling of an example of a plant corresponding to the statement of the research problem.