On the synthesis of adaptive multiparameter control systems by the Lyapunov method

Adaptive automatic control systems become very frequently of use in technical practice. They are especially applied in automatic control systems of the flying bodies despite of higher expenses like the variable aerodynamic configuration of an aircraft and the application of a computer in autopilot circuits. Model reference adaptive control systems constitute an important group of adaptive systems. At present, the synthesis of model reference adaptive control systems is made more perfect by the Lyapunov stability theory. The design by means of Lyapunov method simultaneously guarantees the stability of the whole adaptive system. The published papers [1; 2; 3] deal only with the Lyapunov design of adaptive algorithms for one-parameter control systems. The objective of this paper is to formulate adaptive algorithms in more general and simpler form than in the cited papers. The derived relations are suitable for multiparameter control systems, too. In addition, it is recommended to avoid the use of derivative members of higher order by a suitable choice of state variables and of a reference model.