An overview of sensitivity-based distributed optimization and model predictive control

Designing a stabilized distributed model predictive control (DMPC) with constraints is an open and important problem for a class of large-scale distributed systems, which are composed by both weakly and strongly coupled subsystems. This paper proposes a design of DMPC network to stabilize this class of large-scale systems. A coupling degree-based clustering method is first designed to classify subsystems into some middle-scale subsystems (M-subsystem) off-line according to the adjacent matrix, so that these M-subsystems are weakly coupled with each other. Then, each M-subsystem is controlled by a virtual model predictive control (MPC), which is realized by several individual controllers with running iterative cooperative DMPC algorithm, since the solution of cooperative DMPC is able to converge to a fixed point without coupling constraints. Each MPC communicates with the corresponding interacted M-subsystems’ MPCs once in a control period for exchanging future state evolution estimation. All the subsystem-based MPCs are composed of the proposed peer-to-peer DMPC network. In addition, an additional consistency and stabilization constraints are added to guarantee the recursive feasibility and stability of the overall system. The convergence of the iterative DMPC algorithm for each M-subsystem and the stabilization analysis of the overall system are provided. The simulation results show the efficiency of the proposed method. Note to Practitioners —The proposed method is designed for the systems, which are composed of both strong and weak coupling subsystems and are controlled in a distributed structure. The aim of this method is to design a distributed model predictive control (MPC) network for the operational optimization of entire system. The designed control structure and the distributed MPC algorithm with the proposed method could guarantee the recursive feasibility and asymptotic stability of the entire system. To apply this method, the first step is to obtain the models of each subsystem. Then, design the distributed MPC network structure according to the proposed cluster algorithm, which determines the set of subsystems that each virtue MPC controls. Next step is to configure the network information exchanging among these subsystems and construct the optimization problem of each subsystem. Finally, use the existing quadratically constrained quadratic program solvers to calculate the optimal control laws and apply these optimal control laws to the corresponding subsystems. This method can be used in large-scale chemical processes, air conditioner systems for multizone buildings, distributed energy generation systems, and so on.

Partitioned Based Cooperative Distributed Model Predictive Control for Large-Scale Nonlinear Systems

Unlike steady-state optimization and linear model predictive control, dynamic optimization and nonlinear model predictive control is underway to industry application. This paper discusses the implementation issues of two-level control strategy integrated dynamic real-time optimization and nonlinear model predictive control of a heat-integrated distillation column system. To realize this scheme, four nonlinear programming problems: economic operation optimization, data reconciliation and state estimation, parameter estimation and nonlinear model predictive control, are considered based on system rigorous dynamic model. The economic operation optimization is to minimize the cost of the plant. The unmeasured states are estimated by measurements of temperatures, pressures and flow rates. Time-variant parameters such as tray efficiencies and feed composition are updated on-line. The sequential quadratic programming and orthogonal collocation are used to solve the dynamic nonlinear optimization problems.

To solve dynamic multi-optimization problems, optimization algorithms are required to converge quickly in response to changes in the environment without reducing the diversity of the found solutions. Most Multi-Objective Evolutionary Algorithms (MOEAs) are designed to solve static multi-objective optimization problems where the environment does not change dynamically. For that reason, the requirement for convergence in static optimization problems is not as time-critical as for dynamic optimization problems. Most MOEAs use generic variables and operators that scale to static multi-objective optimization problems. Problems emerge when the algorithms can not converge fast enough, due to scalability issues introduced by using too generic operators. This paper presents an evolutionary algorithm CONTROLEUM-GA that uses domain specific variables and operators to solve a real dynamic greenhouse climate control problem. The domain specific operators only encode existing knowledge about the environment. A comprehensive comparative study is provided to evaluate the results of applying the CONTROLEUM-GA compared to NSGAII, ∊-NSGAII and ∊-MOEA. Experimental results demonstrate clear improvements in convergence time without compromising the quality of the found solutions compared to other state-of-art algorithms.

Recent results have suggested that online Model Predictive Control (MPC) can be computed quickly enough to control fast sampled systems. High-speed applications impose a hard real-time constraint on the solution of the MPC problem, which generally prevents the computation of the optimal controller. In current approaches guarantees on feasibility and stability are sacrificed in order to achieve a real-time setting. In this paper we develop a real-time MPC scheme based on robust MPC design that recovers these guarantees while allowing for extremely fast computation. We show that a simple warm-start optimization procedure providing an enhanced feasible solution guarantees feasibility and stability for arbitrary time constraints. The proposed method can be practically implemented and efficiently solved for dynamic systems of significant problem size. Implementation details for a real-time robust MPC method are provided that achieves computation times equal to those reported for methods without guarantees. A 12-dimensional problem with 3 control inputs and a prediction horizon of 10 time steps is solved in 2msec with a performance deterioration less than 1% and thereby allows for sampling rates of 500Hz.

Combined environmental and economic dispatch of smart grids using distributed model predictive control

This paper concerns a distributed model predictive control (DMPC) strategy in which each controller views the signals from other subsystems as disturbance inputs in its local model. The DMPC controllers exchange predictions on the bounds of their state trajectories and incorporate this information into their local DMPC problems. They also impose their own predicted state bounds as constraints in subsequent DMPC iterations to guarantee their subsystem satisfies the bounds broadcast to the other controllers. Each controller solves a local min-max problem on each iteration to optimize performance with respect to worst-case disturbances. Parameterized state feedback is introduced into the DMPC formulation to obtain less conservative solutions and predictions. The paper presents sufficient conditions for feasibility and stability. The approach is illustrated with an example.

ABSTRACTIn this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

In this paper, we study the distributed model predictive control (MPC) of polytopic uncertain systems with quantised communication and packet dropouts. The model of the whole plant is divided into a certain number of incomplete subsystems. Due to the nature of the distributed control structure, there is generally a lack of information about the state of the overall system. Each subsystem shares its information with neighbour subsystems via reliable connection. Distributed MPC controllers are designed for each subsystem by solving the linear matrix inequalities optimisation problem. The distributed state feedback laws are quantised and transmitted via communication network. An iterative algorithm is presented to make coordination among distributed state feedback laws. The communication is assumed to be affected by random packet dropouts in a representation of Bernoulli distributed white sequences with known conditional probabilities. A case study is carried out to demonstrate the effectiveness of the proposed distributed MPC technique.

This work focuses on a class of nonlinear control problems that arise when new control systems which may use networked sensors and/or actuators are added to already operating control loops to improve closed‐loop performance. In this case, it is desirable to design the pre‐existing control system and the new control system in a way such that they coordinate their actions. To address this control problem, a distributed model predictive control method is introduced where both the pre‐existing control system and the new control system are designed via Lyapunov‐based model predictive control. Working with general nonlinear models of chemical processes and assuming that there exists a Lyapunov‐based controller that stabilizes the nominal closed‐loop system using only the pre‐existing control loops, two separate Lyapunov‐based model predictive controllers are designed that coordinate their actions in an efficient fashion. Specifically, the proposed distributed model predictive control design preserves the stability properties of the Lyapunov‐based controller, improves the closed‐loop performance, and allows handling input constraints. In addition, the proposed distributed control design requires reduced communication between the two distributed controllers since it requires that these controllers communicate only once at each sampling time and is computationally more efficient compared to the corresponding centralized model predictive control design. The theoretical results are illustrated using a chemical process example. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Managing spatio-temporal complexity in Hopfield neural network simulations for large-scale static optimization

A distributed model predictive controller (MPC) shows its higher efficacy than a centralized MPC scheme, especially when the number of controlled agents increases. In the smart grid, to realize load regulation using the demand side management idea, we present a distributed MPC scheme for controlling the aggregated power output of thermostatically controller appliances (TCAs) to provide this service. Minimum ON/OFF time constraints, which are converted from logic conditions into inequalities, are modelled inherently in the optimization problem. A simulation using realistic data reveals the feasibility and efficacy of the proposed distributed MPC scheme.

Fil: Giovanini, Leonardo Luis. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingenieria y Ciencias Hidricas. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional; Argentina

Optimal chiller loading in a district cooling system with thermal energy storage

In this chapter we discuss the ant colony optimization meta-heuristic (ACO) and its application to static and dynamic constraint satisfaction optimization problems, in particular the static and dynamic maximum satisfiability problems (MAX-SAT). In the first part of the chapter we give an introduction to meta-heuristics in general and ant colony optimization in particular, followed by an introduction to constraint satisfaction and static and dynamic constraint satisfaction optimization problems. Then, we describe how to apply the ACO algorithm to the problems, and do an analysis of the results obtained for several benchmarks. The adapted ant colony optimization accomplishes very well the task of dealing with systematic changes of dynamic MAX-SAT instances derived from static problems.