Studies On Synthesis Approaches Of Robust Predictive Control

Predictive control is a kind of computer control algorithm, which appeared in late 70s and has been applied in industries widely. In the development of predictive control theory, how to reduce the online computation burden and improve the feasibility have always been the hotspots. How to better handle the constraints in the system model attracts people all the time. In the past studies about output feedback predictive control, most of the researchers have not considered the observation error for stability, which is not rational in our point. In this paper the above problems are emphasized. The main contents including:1. It surveys the history for application of LMI in control theory, emphasizing the principle of LMI and the importance for its application in synthesis approaches of predictive control. An example is given to show the application of LMI in a synthesis approach of robust predictive control. This paper can serve as a reference for applying LMI in robust predictive control and carrying out robust predictive control algorithm on microcomputer.2. It gives a new approach to constrained robust regulation for systems with polytopic description. This is motivated by two previous techniques. The new method off-line constructs a series of N-step perturbed reachable set, each corresponding to an ellipsoidal terminal constraint set. On-line, when the state lies in a different perturbed reachable set, the corresponding terminal constraint set is applied and a partial closed-loop optimization problem is constructed. By solving such an optimization problem in a receding horizon way, the formulated controller stabilizes the closed-loop system. The simulation shows the effectiveness of the new method.3. It designs an output feedback robust predictive control for systems with polytopic description, based-on a performance cost constructed upon the estimator state. Firstly, we derive some matrix inequalities that restrain the estimator state invariant, and the estimation error contractive, within an ellipsoid. Then, we off-line set up a series of such ellipsoids corresponded to a control law sequence, and give the rule for selecting the real-time control law from the sequence. The closed-loop stability is guaranteed for this kind of controller. The simulation shows the effectiveness of the new method.