Guaranteed cost control and guaranteed error estimation of stochastic systems with uncertain parameters

The idea of guaranteed cost control can be easily extended to stochastic systems with uncertain parameters in plant dynamics. By a slight modification, the guaranteed error estimation can be formulated as a problem of guaranteed cost control. The system considered in this paper is described by a stochastic differential equation with an additive random input and a noisy measurement. The noise processes are assumed to be Gaussian, zero mean, independent with know variances. Furthermore the controlled plant has large parameter uncertainties known to be in some bounded sets. It is shown that with reasonable bounds on uncertain terms, the overall performance bounds are asymptotically tight in the sense that the solutions reduce to the optimal ones when uncertainties vanish.