Optimal control of mode transition rates/probabilities for Markovian jump systems

In this paper, we investigate the optimal control of mode transition rates/probabilities for continuous-time/discrete-time Markovian jump systems, respectively. Unlike the traditional state feedback control, the control variable with respect to mode transition rates/probabilities is introduced into mode indicator equation, which describes the jump dynamics in Markovian jump systems. Since mode transition rates/probabilities indicate the mode jumping rule among subsystems, the control of transition rates/probabilities is perceived as an effective way to improve the system performance. Base on this, the optimal control of mode transition rates/probabilities is given to minimize the system performance, which is including mode cost and control expenditure. Simultaneously, for the sake of ensuring the system stability, the constraint condition about the control variable is dissused before the optimal controller design. And numerical examples are provided to illustrate the results.