ADMM-based Distributed Model Predictive Control

Distributed model predictive control(DMPC)can effectively deal with various constraints because of its perfect control performance,fault tolerance and flexible structure.Thus,it is widely used in complex industrial process control,and its theoretical research has also received much attention.In recent years,research on distributed model predictive control in system stability analysis and online optimization algorithms has achieved certain results.At the same time,the coupling exists extensively in large-scale complex systems,and the existence of the coupling part under the distributed structure makes the optimization problem of the subsystem unable to be effectively solved.Therefore,how to deal with the problem of updating and optimizing the coupling part has become the key to distributed model predictive control.At the same time,how to design the terminal set and the constraints of each subsystem,and reduce both the system communication cost and the amount of online calculations;how to ensure the iterative feasibility and closedloop stability in the optimization process are also difficult research issues.In this paper,we focus on global coupling constraint based DMPC problem,the DMPC problem with the coupled cost,and the decoupling of DMPC problem with state-to-system correlations and the improvement of related optimization algorithms.The main content of the article is summarized as follows:First,we briefly introduce the research background of DMPC,and some necessary preliminaries,including the basic concepts and theorems of model predictive control and convex optimization.In Chapter 2,we mainly consider the distributed model predictive control problem for discrete-time linear systems with local(uncoupled)and global(coupled)constraints.We first focus on the dual problem of overall system-based control problem,then convert the problem into a consensus problem of dual and auxiliary variables,and finally apply Augmented Lagrangian method-based parallel and partially parallel splitting algorithms to solve related optimization problems.Based on reasonable assumptions on the feasible set of system parameter variables,control input variables,and state variables,the stability and iterative feasibility of the system can be guaranteed.Numerical simulation of distributed optimization algorithms is given at the end of this chapter.In Chapter 3,our research is mainly based on multi-agent systems.We consider the control problems of multiple discrete linear time-invariant systems which have different dynamic models with coupled cost and constraints between the systems.Different from the Chapter 2,the coupled constraints in this chapter are in norm form.The design of both terminal set and weight matrixes of the terminal cost based on Lyapunov stability and satisfying the coupled constraints are given in this chapter.Also,the distributed optimization problem is solved by ALM-based parallel split algorithm,and the iterative feasibility and the stability of the overall system are guaranteed.The distributed model predictive control algorithm is verified in numerical simulation experiments.The results show that the distributed algorithm shortens the optimization time and reduces the communication cost while ensuring the system performance.In Chapter 4,our research mainly considers the coupled state-based distributed model predictive control problems of multiple discrete linear time-invariant systems with different dynamic models.In this chapter,we first complete the decoupling between systems based on the idea of “frozen”;then,we propose distributed Alternating Direction Method of Multipliers(ADMM)based on independent performance indicatorsindependent prediction models for the decoupled system and solve the optimization problem.Also,we successfully achieve the stable control goal of the system.Finally,the validity of the distributed algorithm is verified by numerical experiments.