Research On Robust Model Predictive Control Based On Polytope

Predictive control is a receding horizon optimizaiton computer method, which is attracting more attention for its ability to solve all kinds of contraints flexibility. After many years development, many modern predicitve control strategies have been proposed. On the other hand, robust predictive control is an important branch of predicitve control as many models have uncertainty and external disturbance, and many control methods have been designed, but the online computation, stability and control performance all need further rearch.For the robust predicitive control, it is depended on the online computation that if the control stratety can be applied into the high order or fast parameter varying system. In this dissertation, we focused on the reducing the online computation and reduce the conservetive for the uncertain systems which including the uncertain polytope system, linear parameter varying system and nonlinear system, and the main work can be summerized as follows1. First, the background and significance of the predictive control is introduced,followed with the overviews of robust predictive control methods for many systems including the linear parameter varying system, output feedback control and nonlinear system, and the main problems still needed to be solved is put forward. The research status at home and abroad is presented, followed with the introduce of the theory of invariety set and linear matrix inequality. The development and standard problem of the linear matrix inequality are all presented, and the research content and background of this dissertation are introduced at last.2. The shrinking ellipsoid set is proposed, that is, if the state is in the set, it must be in the smaller ellipsoid set at the next step, and then the geometric proportion shrinking ellipsoid is designed. Based on the shrinking ellipsoid set and linear matrix inequality, we design the different control laws correspoinding to the different ellipsoid sets for the system with polytope or/and disturbance uncertain, and propose a control strategy with almost zero online computation followed with its proof of the closed system’s stability.3. For the linear parameter varying system, a small conservativeness control method is proposed based on the shrinking ellipsoid set. As the current states and parameters are known and the future states and parameters are unknown, the performance index can be divided into the current and future parts, and only the future part is described by the polytope, so it reduces the system’s conservativeness.4. For the polytope system with unknown states, it is designed the state estimator for the system with the same disturbance or the different disturbance using quadratic boundness. Based on the designed state estimator, the output feedback control strategy is proposed for the aforementioned system.5. For the nonlinear system, a predictive control strategy is designed based on the local linear method. The designed control law not only can select the control law automatically online, but also can assure the closed system’s stability.6. The control and synchronization methods are proposed for the discrete chaotic system based on the active control and robust model predictive control. The effecitiveness of the proposed method is varified through the simulation of the Henon map and the general Henon map.In conclusion, the main innovative achievements for the robust predicitve control in this paper as follows:1. The concept of shrinking ellipsoid set is put forward followed with the given of the condition of satisfying fixed shrinking rate, and based on it a new robust predictive control strategy is proposed for the discrete time polytope uncertainty system;2. Based on the gain schedule scheme, a robust predicitve control scheme is put forward for a linear parameter varying system;3. Using quadratic boundary, a state estimator is designed for the polytope system with disturbance, and based on it an output feedback predictive control is researched;4. It is proposed an automatic nonlinear robust predicitve control using the local linearization method.