Optimal control strategy for discrete-time MJLS with controllable Markov chain and Gaussian white noise

This paper investigates a new optimal control strategy for discrete-time Markovian Jump Linear Systems (MJLSs) with controllable Markov chain and Gaussian white noise. Meanwhile, this MJLS is established under a scalar condition, i.e., state variable, input variable and output variable is scalar. For this system, the optimal control strategy is a combination of output-feedback controller to govern system state and decision which means the artificial action to govern MTPM. Motivated by this, a new joint cost function is put forward to evaluate system performance which is a combination of traditional JLQG cost and additional decision cost. Differing from traditional cost function, this joint cost function means a trade-off between control cost and decision cost and can be further minimized by optimal control strategy. To minimize this joint cost function, the designing of the optimal control strategy is deduced to the seeking of the optimal decision, and the optimal decision can be obtained by an iterative algorithm. Numerical examples illustrate the validity of the proposed optimal control strategy.