ADAPTIVE CONTROL VIA FINITELY-CONVERGENT ALGORITHMS

A short review of the method of finitely-convergent algorithms in the theory of adaptive systems is presented. The method was proposed in (Yakubovich, V.A., Recurrent Finite-convergent Algorithms to Solve the Systems of Inequalities, Dokl. Akad. Nauk SSSR, 1966, vol. 166, no. 6, pp. 1308–1311. English translation in Soviet Math. Dokl., 1966, vol. 7, pp. 300–304). The method consists of reduction of an adaptive control problem to a countable system of inequalities. A procedure of their solution plays a role of adaptation algorithm. It should converge in a finite time in a closed loop system. The method often allows to obtain suboptimal (in the minimax sense) adaptive control systems.Basic ideas and achievments of the method as well as some recent results are considered. Among them are adaptive control of sampled systems with time delay which is not a multiple of the sampling period. In this relation a problem of limiting zeros of sampled systems with delay arise. It is shown that limiting values of the sampling zeros have the same properties as zeros of Euler polynomials.