JUMP LINEAR QUADRATIC GAUSSIAN CONTROL IN CONTINUOUS-TIME

This paper is concerned with the optimal quadratic control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes. The systems are also subject to Gaussian input and measurement noise. In this paper, the optimal solution for the jump linear quadratic Gaussian (JLQG) problem is given. This solution is based on a separation theorem. The optimal state estimator is sample path dependent (it may depend upon past as well as the current values of the jump parameter). If the plant parameters are constant in each value of the underlying jumping process, then the controller portion of the compensator converges to a time invariant control law. However, the filter portion of the optimal infinite time horizon JLQG compensator is not time invariant. Thus, a suboptimal filter which does converge to a steady-state solution (under certain conditions) is derived and a time-invariant compensator is obtained.