Adaptive suboptimal systems with a variable dimension of the vector of adjustable parameters

A short review is presented of the methods of recurrent aim inequalities, which is the trend developed by V.A. Yakubovich in the theory of adaptive systems. Two new problems are also considered of the suboptimal (in the minimax sense) adaptive control of minimum-phase discrete and continuous objects of the unknown order with delay. In passing, a solution is found of the suboptimal problem for continuous objects with known parameters and a criterion is defined of the minimum phasing of the discrete model for a continuous object in the case when the delay is not a multiple of the discretization period. As an adaptive algorithm, the finite-convergent algorithm shows up for the solution of the counting system of recurrent aim inequalities with a variable number of adjustable parameters, which stabilizes only on completion of transient processes.