Optimal stochastic control for performance- and stability-robustness

A design method for discrete-time control systems that maintain stability with minimum performance degradation in the presence of a variety of deterministic and stochastic perturbation/disturbances is presented. Deterministic perturbation and modeling errors are represented by maximum deviations from a nominal linear discrete-time system, and stochastic perturbations are modeled by generalization of the sector-bound nonlinearity concept to the stochastic case. Based on the given bounds on deterministic and stochastic perturbations an upper bound on the quadratic performance index, which is useful in assessing the performance deterioration according to the feedback gain used, is found. Then the optimal feedback gain which minimizes this bound on the performance index is derived. In the time-invariant case the existence of a stabilizing property of the bound-optimal controller, which is obtained by minimizing an average cost per stage, is shown