Linear Quadratic Tracking Control of Hidden Markov Jump Linear Systems Subject to Ambiguity

The linear quadratic tracking control problem is studied for a class of discrete-time uncertain Markov jump linear systems with time-varying conditional distributions. The controller is designed under the assumption that it has no access to the true states of the Markov chain, but rather it depends on the Markov chain state estimates. To deal with uncertainty, the transition probabilities of Markov state estimates between the different operating modes of the system are considered to belong in an ambiguity set of some nominal transition probabilities. The estimation problem is solved via the one-step forward Viterbi algorithm, while the stochastic control problem is solved via minimax optimization theory. An optimal control policy with some desired robustness properties is designed, and a maximizing time-varying transition probability distribution is obtained. A numerical example is given to illustrate the applicability and effectiveness of the proposed approach.