Robust output feedback time optimal decomposed controllers for linear systems via moving horizon estimation

This paper studies the robust output feedback time optimal control (TOC) problem for linear discrete-time systems with state and input constraints. Bounded state disturbances are assumed. The moving horizon estimation (MHE) technique combined with a Luenberger observer is used to design a state estimator with which the state estimation error converges to and remains in some disturbance invariant set. A novel approach is proposed to reduce the computational complexity of TOC, in which the terminal controller comprises several predetermined local linear feedback laws, resulting in a large terminal set. Starting from this relatively large terminal set, a large domain of attraction of the proposed TOC controller can be obtained by using a short horizon, which consequently leads to a low on-line computational effort. A correction term, the output of the observer subtracted from the output of the plant and then multiplied by a design matrix, is added to the TOC controller, which aims at further correcting estimates of the state based on the present estimation error. Furthermore, by formulating a suitable cost function, as time evolves the TOC controller reaches the desired controller to obtain a good asymptotical behavior. A case study is used to illustrate the proposed approach.