Parametric method for optimal model reference output tracking with markov jump parameters

This paper deals with the optimal model output tracking problem where the reference model is a class of Morkov jump system, which the aim is to make the output of the linear system track the output of a given reference model with Markov jumps. A new succinct general complete parametric expression for the tracking controller is established. The characteristic of this paper is to introduce the Markov jump inputs into the linear time-invariant system. By introducing linear quadratic index with Markov jumps, the dynamic characteristics of the closed-loop system have a jump property; By introducing reference model with Markov jump features, the system output tracks the jumping output of the reference model. The above two points have a good prospect in some applications such as the anti-tracking control problems of spacecraft, it can make the specific trajectory of the spacecraft unpredictable, which can effectively increase the difficulty for hostile target to track and increase the survivability against hostile target. For certain systems, the proposed algorithm has the extra degree of freedom in parametric design which can be used to achieve some additional performance. Through the illustrative example we can see the effectiveness of the method.