Decentralized Model Predictive Control For Singular Large-scale Systems

Decentralized predictive control is a kind of process control method, which combinesdecentralized control with predictive control. This method can not only simplify the information oflarge-scale system to reduce the size and complexity of the problem, but also use the projectionpredictive strategy to handle the information shortage problem caused by the limited informationstructure. Decentralized predictive control is the effective method in the study of large-scale systemcontrol.In this paper, the predictive control is introduced into the decentralized control of singularlarge-scale system. The decentralized model predictive control for singular large-scale systems isdiscussed by Lyapunov method and linear matrix inequality (LMI) method. And the design methodof decentralized predictive controller is given. In addition, the stability is guaranteed.The main contents in this paper include:(1)For the singular large-scale system with input constraints, a decentralized predictive controlalgorithm is studied when the states are measurable. Using the Lyapunov function and LMI method,the decentralized state feedback predictive control law and the algorithm of controller design aregiven. It is proved that the stability is guaranteed by the initial feasible solutions of the optimizationproblem, and the regular and the impulse-free of the system are also held. The numerical simulationexample shows the effectiveness of the algorithm.(2)With the singular large-scale system with interconnected subsystems, the problem ofdecentralized robust output feedback predictive control is investigated when the states areunmeasurable. Using the Lyapunov function of parameter independent and LMI method, thedecentralized robust output feedback predictive control law and the algorithm of controller design aregiven. It is proved that the robust stability is guaranteed by the initial feasible solutions of theoptimization problem, and the regular and the impulse-free of the system are also held. Theeffectiveness of the algorithm is shown by two numerical simulation examples.(3)In the view of interconnected singular large-scale system, the algorithm of decentralized robustpredictive control is studied. This method puts the correlation between subsystems as an externaldisturbance. Namely, the decentralized predictive control problem of the large-scale system withexternal disturbance is solved. And the specific design method of decentralized robust predictivecontroller is proposed by making use of the nominal model and comparison model.(4)Considering polytopic uncertain singular systems with input constraints, an offline robust predictive control algorithm using LMI and Ellipsoidal Invariant Sets is given. The part of the onlinecalculating is translated into offline design when affected by the input constraints. So the calculationof online optimization problems is reduced through the offline design in this paper. A numericalsimulation results prove the feasibility and effectiveness of the algorithm.