Linear Quadratic Optimal Control for Discrete-time Markov Jump Linear Systems

This paper mainly investigates the optimal control problem for the linear discrete-time Markov jump system. The general case for the finite-horizon optimal control is considered, where the input weighting matrix in the performance index is just required to be positive semi-definite. This relaxes the constraint imposed on the control problem greatly. A necessary and sufficient condition for the existence of the optimal controller is developed for the first time based on a set of coupled difference Riccati equations (CDRE), which is easily verifiable. And an explicit solution to the controller is given. One of the key techniques is to solve a forward and backward Markov jumping difference equation (FBMJDE) by the relationship between the state and the costate.