Reconfigurable Model Predictive Control For Networked Distributed System

In industrial process,global information of the control object can be hardly obtained owing to factors such as the spatial distribution and system constraints.In this case,a distributed control structure based on smart meters,sensors,and fieldbus technologies has gradually formed in industrial process.With higher control requirements,during the operation of industrial systems,the production process may require to be adjusted and changes in production materials may occur.As a result,the physical structure of the networked system changes.Due to the coupling relationship among subsystems,changes in the physical structure of the system may lead to infeasibility of existing controller.For such a control problem,this paper proposes a reconfigurable distributed model predictive controller design strategy for networked system where the physical structure may change.The specific contents are as follows:(1)For a class of networked system where the amount of exchanged information in each control cycle is limited,this paper proposes a non-iterative reconfigurable distributed predictive control algorithm,where reference trajectory of specific subsystems is optimized and adjusted online,such that switch in physical structure can be completed as soon as possible.In the proposed control strategy,each subsystem adopts reference trajectory as approximation of actual future state trajectory,and solves local optimization problem by exchanging the reference trajectory,in order to obtain real-time control input.Under this control scheme,the sudden change of the reference trajectory caused by the change in system physical structure is also the main reason that causes the infeasibility of some local controllers.For such a control problem,specific optimization problems are proposed for each local controller to adjust its reference trajectory.Under the premise that all optimization problems are feasible,the convergence rate of specific subsystem is accelerated and state of system can be transitioned to a state point where the physical structure can be switched without causing infeasibility.(2)For a class of networked system with high communication performance,where the time for communication can be ignored in the control cycle,this paper proposes an iterative reconfigurable distributed predictive control algorithm,where steady state and steady input are introduced as relaxed variables,in order to expand the feasible region of the optimization problem and avoid the infeasibility of local controllers due to changes in the physical structure of the system.In the proposed strategy,the terminal invariant set is adopted to ensure the asymptotic stability of the controlled system.When the physical structure of the system changes,the terminal invariant set in the controller under the original physical structure can be unreachable during the predictive horizon for system state under new physical structure,which may cause the infeasibility of controller.For such a problem,this paper introduces relaxed variables of optimization problem,and obtains a centrally variable terminal invariant set,which expands the feasible region of problem to be solved and guarantees real-time switch of system physical structure.To ensure asymptotic convergence of the system state,a deviation term between the steady point and the origin is added to the performance index of the optimization problem.(3)In the algorithms proposed in this paper,the invariant set is used to ensure the asymptotic stability of the controlled system.Such design requires that the controlled system can be stabilized by a block-diagonal state feedback gain matrix,thus it is not suitable for the control of some networked systems with strong coupling.In order to expand the applicable range of the algorithms and improve the global performance of the controlled system,this paper also proposes a method to design a stabilizable invariant set,which does not require the existence of a block-diagonal state feedback gain matrix that stabilizes the entire system.In this method,the real-time control law is composed of the state feedback of subsystem itself and the state feedback of neighboring subsystem.And then,the constraints satisfied by the state feedback gain matrix and parameters of the invariant set are transformed into linear matrix inequalities to be solved.Such method for calculation of invariant set can be applied to the algorithms introduced in the previous contents.In order to verify the effectiveness of the proposed design method of invariant set based on non-block-diagonal state feedback gain matrix,such method is applied in a fully decentralized model predictive control algorithm,and corresponding analyses and simulation results are provided.