Problems of adaptive optimal control of discrete-time systems under bounded disturbance and linear performance indexes

We present some problems of adaptive optimal robust control of linear discretetime systems under uncertainty and bounded external disturbance in which the optimal or guaranteed value of the performance index is a linear or linear-fractional function of unknown parameters of the system and set-membership estimation based on the method of recurrent objective inequalities reduces to recurrent updating of polyhedral estimates of unknown parameters. In such problems, computing current optimal estimates becomes a recurrent linear programming problem which is computationally tractable on modern computers for systems with a small number of estimated parameters.