On feasibility, stability and performance in distributed model predictive control

In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the solution algorithm, i.e. the amount of communication between subsystems, as small as possible. At the same time, the number of iterations must be enough to give a feasible solution to the optimization problem and to guarantee stability of the closed loop system. In this paper, a stopping condition to the distributed optimization algorithm that guarantees these properties, is presented. The stopping condition is based on two theoretical contributions. First, since the optimization problem is solved using dual decomposition, standard techniques to prove stability in model predictive control (MPC), i.e. with a terminal cost and a terminal constraint set that involve all state variables, do not apply. For the case without a terminal cost or a terminal constraint set, we present a new method to quantify the control horizon needed to ensure stability and a prespecified performance. Second, the stopping condition is based on a novel adaptive constraint tightening approach. Using this adaptive constraint tightening approach, we guarantee that a primal feasible solution to the optimization problem is found and that closed loop stability and performance is obtained. Numerical examples show that the number of iterations needed to guarantee feasibility of the optimization problem, stability and a prespecified performance of the closed-loop system can be reduced significantly using the proposed stopping condition

Distributed model predictive control of steam/water loop in large scale ships

In modern steam power plants, the ever-increasing complexity requires great reliability and flexibility of the control system. Hence, in this paper, the feasibility of a distributed model predictive control (DiMPC) strategy with an extended prediction self-adaptive control (EPSAC) framework is studied, in which the multiple controllers allow each sub-loop to have its own requirement flexibility. Meanwhile, the model predictive control can guarantee a good performance for the system with constraints. The performance is compared against a decentralized model predictive control (DeMPC) and a centralized model predictive control (CMPC). In order to improve the computing speed, a multiple objective model predictive control (MOMPC) is proposed. For the stability of the control system, the convergence of the DiMPC is discussed. Simulation tests are performed on the five different sub-loops of steam/water loop. The results indicate that the DiMPC may achieve similar performance as CMPC while outperforming the DeMPC method

Distributed Model Predictive Control for Reconfigurable Large-Scale Systems

Large-scale Systems are gaining more importance in the modern world requiring flexible techniques capable of handling interactions. This thesis is concerned with the development of suitable algorithms based on Model Predictive Control (MPC) that guarantee stability, recursive feasibility and constraint satisfaction. In the first part of this thesis, the main properties and control challenges for controlling an Large-Scale System are brought together, and the main distributed approaches for solving these problems are surveyed. Also, two novel Distributed MPC algorithms are presented. A non-centralised approach to the output-feedback variant of tube-based model predictive control of dynamically coupled linear time-invariant systems with shared constraints. A tube-based algorithm capable of handling the interactions–not rejecting them– that replaces the conventional linear disturbance rejection controller with a second MPC controller, as is done in tube-based nonlinear MPC. Following this, a smart-grids application of the developed algorithm is presented to solve the load frequency control for a power network. The approach achieves guaranteed constraint satisfaction, the recursive feasibility of the MPC problems and stability while maintaining on-line complexity similar to conventional MPC. The second part of the thesis covers reconfigurable distributed MPC. Two novel approaches are considered: a nominal MPC methodology that incorporates information of external disturbances, and a coalitional approach for robust distributed MPC. The first approach uses available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a disturbance, which may change from time step to time step, is resent in the model and on the system. We show how standard stabilising terminal conditions may be modified to account for the use of disturbances in the prediction model. Robust stability and feasibility are established under the assumption that the disturbance change across sampling instances is limited. The proposed coalitional approach to robust Distributed MPC aims to tackle the existing trade-off between communication and performance in Large-Scale System by exploiting the different network topologies of system dynamics. The algorithm employs a method to switch between topologies using a multi-rate control approach. The optimal topology selection problem is solved using a consensus approach appropriately constrained to reduce the effects of any combinatorial explosion. The robust control algorithm is capable of recomputing the necessary parameters online to readjust to new partitions. Robust constraint satisfaction, recursive and stability are guaranteed by the proposed algorithm

Distributed model predictive control of linear systems with persistent disturbances

This article presents a new form of robust distributed model predictive control (MPC) for multiple dynamically decoupled subsystems, in which distributed control agents exchange plans to achieve satisfaction of coupling constraints. The new method offers greater flexibility in communications than existing robust methods, and relaxes restrictions on the order in which distributed computations are performed. The local controllers use the concept of tube MPC – in which an optimisation designs a tube for the system to follow rather than a trajectory – to achieve robust feasibility and stability despite the presence of persistent, bounded disturbances. A methodical exploration of the trades between performance and communication is provided by numerical simulations of an example scenario. It is shown that at low levels of inter-agent communication, distributed MPC can obtain a lower closed-loop cost than that obtained by a centralised implementation. A further example shows that the flexibility in communications means the new algorithm has a relatively low susceptibility to the adverse effects of delays in computation and communication

Distributed Model Predictive Control for Building Temperature Control

This thesis and technical report concentrates on distributed control using a distributed model predictive scheme. The model of a two room house and three room houses is build and a distributed model predictive control (MPC) algorithm is implemented in order to reach specified room temperatures with minimized energy effort in each room. For reference tracking Target Calculation and the delta input scheme are used. The MPC optimization problem is solved at each time step through an iterative method, where the number of iterations is reduced through a stopping criterion guaranteeing stability and a prespecified amount of performance and feasibility. The optimization problem is divided up into subproblems, where each subproblem takes less computational effort than the central optimization problem. Due to the possibility of coupling between subsystems, communication between the subsystems is needed. The reference values are reached and iterations needed to solve the optimization are reduced with the stopping condition. This method saves computing time and gives privacy to each subsystem, since only required information is communicated. Also the subsystems get less susceptible to the failure of one coupled subsystem, since if one subsystem fails, the others could go on. But, due to the needed communication, t h i s method is more suitable for large systems with sparse coupling. For a small system, or too much coupling the communication effort will get to high

Distributed Learning Model Predictive Control for Linear Systems

This paper presents a distributed learning model predictive control (DLMPC) scheme for distributed linear time invariant systems with coupled dynamics and state constraints. The proposed solution method is based on an online distributed optimization scheme with nearest-neighbor communication. If the control task is iterative and data from previous feasible iterations are available, local data are exploited by the subsystems in order to construct the local terminal set and terminal cost, which guarantee recursive feasibility and asymptotic stability, as well as performance improvement over iterations. In case a first feasible trajectory is difficult to obtain, or the task is non-iterative, we further propose an algorithm that efficiently explores the state-space and generates the data required for the construction of the terminal cost and terminal constraint in the MPC problem in a safe and distributed way. In contrast to other distributed MPC schemes which use structured positive invariant sets, the proposed approach involves a control invariant set as the terminal set, on which we do not impose any distributed structure. The proposed iterative scheme converges to the global optimal solution of the underlying infinite horizon optimal control problem under mild conditions. Numerical experiments demonstrate the effectiveness of the proposed DLMPC scheme

Distributed Model Predictive Control Using a Chain of Tubes

A new distributed MPC algorithm for the regulation of dynamically coupled subsystems is presented in this paper. The current control action is computed via two robust controllers working in a nested fashion. The inner controller builds a nominal reference trajectory from a decentralized perspective. The outer controller uses this information to take into account the effects of the coupling and generate a distributed control action. The tube-based approach to robustness is employed. A supplementary constraint is included in the outer optimization problem to provide recursive feasibility of the overall controllerComment: Accepted for presentation at the UKACC CONTROL 2016 conference (Belfast, UK