Joint Estimation and Control of Jump Linear Systems With Multiplicative Noises

Abstract

Jump Linear Quadratic Gaussian systems are considered in the presence of state-and control-dependent noises. Assuming that the jumps of the model parameters are perfectly observed, it is possible to formulate and solve an optimal input synthesis problem. It is found that the optimal solution does not present the certainty equivalence property, so that the estimation and control synthesis must be treated simultaneously. Optimal equations for the filter and regulator gains are obtained in terms of a set of coupled nonlinear matrix differential equations.