Multiple-model adaptive control for jump-linear stochastic systems

The problem of stochastic control is considered for linear discrete-timesystemswith Markovian jump parameters, where the parameters are included in both state and observation models and their evolutions are not observed. When applying a multiple-model adaptive control (MMAC) strategy to the problem, we need in general mN sequences of control gains, where m is the number of Markov-chain states and N is a final time. This approach is clearly impractical for large N. A suboptimal control method is proposed to alleviate the computational loads of the MMAC approach. Algorithms for the elemental control gains are obtained in terms of a set of m coupled Riccati-like equations, while a generalized pseudo-Bayes algorithm (GPBA) is used for the elemental filter mechanism.Simulation results are included to illustrate the effectiveness of the proposed method by comparing with some MMACs using other elemental filtering techniques.