Model Predictive Control Of Singular Systems With External Disturbances And Input Constraints

Singular systems, also called descriptor systems, differential and algebraic equationsystems, or generalized systems, have widely applications in practical modeling such aselectrical power systems,economical systems,robotic systems, chemical processes andothers. Singular large scale systems are a class of systems which are coupled with anumber of singular subsystems and also have extensive practical background. Then theresearch on control of singular systems and singular large scale systems are of greatsignificance.Model predictive control (MPC) was firstly conceived by industry. Due to the capacityin handing the strong constraints and the nonlinear factors of systems, it has been themost widely used method of modern control. However, practical production processesare often subject to uncertainties, such as parameter uncertainties, unmodeled dynamics,external disturbances, etc. In the other word, the model used to describe the dynamics ofcontrolled systems always have some uncertainties, then the stability performance ofsystems will not very good guaranteed. To this end, the robust MPC is developed toensure the performance of systems which combines the method of robust control withthe receding moving horizon predictive control, and has become an important researchdirection of MPC. Decentralized MPC could make up the limited information structureand information shortage problem in decentralized control, and has become the widelyused approach of the control problem of large scale systems.In the dynamic systems such as electrical power systems, aerospace systems and soon are often influenced by external disturbances and constraints. In this paper, theresearch on robust model predictive control is concerned for a class of singular systemsand singular large scale systems with external disturbances and input constraints. Themain contents are stated as follows:1. The synthesis method of robust quasi-min-max model predictive control ispresented for discrete-time singular systems with persistent disturbances and inputconstraints. To deal with the persistent disturbances, we introduce the notion ofinput-to-state stability (ISS) of discrete-time singular systems for the first time, and asufficient condition is presented to ensure the ISS of discrete-time singular systems. Theoptimal control can be obtained by solving a semi-definite programming problem of a quasi-min-max finite horizon cost function. On the basis of the proposed dual-modeMPC approach, it can be proved that the closed-loop discrete-time singular system isISS, regular and causal.2. The decentralized model predictive control problem is considered fordiscrete-time singular large scale systems subject to external disturbances and controlconstraints. To deal with disturbances input, we choose the H_∞performance. Takinginto account a fully decentralized information structure and the effect of interconnectionas uncertainties, a decentralized robust H_∞MPC controller is designed by solving theonline optimization problem. Furthermore, the designed decentralized MPC approachcan ensure the closed-loop system stable, regular and causal.