Adaptive l1-optimal control for SISO plant

An adaptive minimax control problem is stated for a general SISO plant in which the disturbance is assumed to belong to a given convex set of sequences and arbitrary otherwise. Unlike the standard stochastic approach there is no identification procedure or minimization of a performance index. It is replaced by the requirement to provide a value of the performance index not greater than the game value for any compatible model in the given class of adaptation. A general algorithm is described which reduces the adaptive control problem to the optimal control problem with fixed parameters followed by one minimization procedure. For the linear systems with disturbances defined by local constraints an algorithm for the optimal LTI compensator design is proposed. This gives a solution to the adaptive control problem for these systems. The standard l¹-control problem is a special case of the minimax problems considered