On the Stability Analysis of an Adaptive Control System with a Simplified Control Procedure

This paper presents the results on the stability analysis of computer-based control systems with the simplified adaptation procedure implemented through look-up tables and special selection rules. The simplified procedure implies the development of a number of controllers during the system design, representation of the controllers by a look-up table, and implementation of a procedure for the selection of the appropriate entry of a look-up table during the system operation. Systems, implementing the procedure, can be considered as systems with nonlinearity so that some specific stability problems have to be investigated. The paper presents the analysis of the transient processes in the system causes by the controller change, and the selection of the admissible difference between the alternative controllers in the look-up table. The analytical technique employed to the stability problem in the paper is based on Liapunov's second method. Since the considered nonlinearity type meets Aizerman's conditions, a Liapunov function in so-called "Quadratic Plus Integral" was used. Following the general procedure of Liapunov's method, the absolute stability conditions were formulated for the considered type of control systems.