Adaptive linear quadratic Gaussian control of Markov jump linear systems

The adaptive linear quadratic problem of continuous-time linear jump systems with unknown jump parameter and stochastic disturbance is concerned in this paper, and jumping parameters can be described by finite-state Markov processes. A sufficient condition characterizing the stabilizability of the system is obtained, which hinges on the existence of a set of algebraic coupled Riccatic equations. A constructive method for designing stabilizing feedback laws is provided in this paper. The index difference between the adaptive LQ control and the conventional LQ optimal control is asymptotically bounded by a constant depending on the estimation step and priori information of the parameter set.