Adaptive suboptimal stabilization of discretetime minimumphase plant under output uncertainty

The paper addresses the problem of adaptive suboptimal stabilization of linear, time-invariant discrete-time minimum-phase plant under output uncertainty and bounded exogenous disturbance. The control criterion is taken in the form of the worst-case upper limit of the absolute value of the plant output. The parameters of the plant, the upper bound on the disturbance, and the induced norm of the uncertainty are assumed to be not known to the designer. Conventional gradient or projection type estimation algorithms are of no use in this problem in view of the non-identifiability of the unknown parameters of the plant as well as the upperbounds on the disturbance and the uncertainty. The statement of the problem is based on the known results in the theory of robust control in the ℓ1 setup, and the solution of the problem is based on set-membership approach and optimal estima-tion where the identification criterion is taken in the form of the control criterion. The control criterion in the specific problem under consideration is a linear-frac-tional function of the upper bounds on the disturbance and the uncertainty. This peculiarity enables use of simple cone estimates composed of p linear inequalities with respect to p estimated parameters and reduces online optimal estimation to the selection of the best estimate among p candidate estimates. Cone estimates arebased on the method of recurrent objective inequalities and additionally provide online model validation.