In this paper, an online temporal differences (TD) learning approach is proposed to solve the robust control problem for discrete-time Markov jump linear systems (MJLS) subject to completely unknown transition probabilities (TP). The TD learning algorithm consists of two parts: policy evaluation and policy improvement. In the first part, by observing the mode jumping trajectories instead of solving a set of coupled algebraic Riccati equations, value functions are updated and approximate the TP related matrices. In the second part, new robust controllers can be obtained until value functions converge in the previous part. Moreover, the convergence of the value functions is proved by initializing a feasible control policy. Finally, two examples are presented to illustrate the effectiveness of the proposed approach by comparing with existing results.

In the present study, a temporal difference (TD) learning algorithm is proposed to solve the H∞ optimal control problem for semi‐Markov jump linear systems (S‐MJLSs). The proposed scheme is TP‐free so that it can be applied in cases without pre‐known transition probabilities of embedded Markov chain. Coupled algebraic Riccati equations (CAREs) implied with the analytical solution of control gains are derived by utilizing a S‐MJLS augmented with maximum sojourn time, which contributes to develop the TD learning algorithm. It is proved that for sufficiently rich enough jumping modes and jumping numbers observed online, the value function in TD algorithm converges to CAREs solutions. Finally, an example is carried out to evaluate the learning capability of TD algorithm and the effectiveness of the proposed control method.