Distributed Model Predictive Control Problem Research Articles

Distributed Model Predictive Formation Control for a Group of UAVs With Spatial Kinematics and Unidirectional Data Transmissions

This paper proposes a distributed model predictive control (DMPC) algorithm for the formation flight of a group of UAVs modeled by six degree-of-freedom (6-DoF) spatial kinematics. The formation system has a leader-follower structure with the leader cruising at a constant linear velocity during the flight, and the UAVs transmit data in a unidirectional order. The DMPC algorithm utilizes the unidirectional structure through the reception and transmission of an assumed output sequence as the reference trajectory, which is constructed from the solutions to the local DMPC problem and the prediction model. Based on the interactions between UAVs, convergence and stability of the multi-UAV formation are ensured by the terminal constraints and recursive feasibility of the DMPC optimization. Simulations involving time-delays, packet drops and turbulence effect are conducted to verify the effectiveness of the proposed algorithm. Comparisons with non-unidirectional data transmissions further demonstrate that the unidirectional structure plays a critical role in the convergence performance

Multiple Subformulae Cooperative Control for Multiagent Systems Under Conflicting Signal Temporal Logic Tasks

This paper studies the temporal logic problem for multi-agent systems, where each agent is subject to signal temporal logic (STL) tasks with multiple sub-tasks. In the distributed framework, due to the existence of coupling sub-tasks, the satisfaction of the conjunction of all sub-tasks may be conflicting. A two-step distributed model predictive control (DMPC) strategy is proposed to maximize the amount of the satisfied sub-tasks and minimize the violation degree of those failed sub-tasks. In step one, a novel robustness metric of STL is proposed to measure whether each sub-task is satisfied or not, and is directly incorporated into the DMPC optimization problem to determine the satisfiability of each sub-task. Based on the planning results of step one, a DMPC optimization problem with a short planning horizon is designed in step two to minimize the violation degree of the unsatisfiable sub-tasks while ensuring the satisfaction of those satisfiable ones. All agents solve their two-step DMPC problems sequentially to realize the satisfaction verification of the coupled sub-tasks at each time instant. Further, the soundness and feasibility of the two-step DMPC algorithm are formally guaranteed. Simulations and experiments illustrate the effectiveness of the proposed algorithm.

DMPC based distributed voltage control for unbalanced distribution networks with single-/three-phase DGs

This paper proposes a distributed voltage control scheme for unbalanced distribution networks (DNs) with single-/three-phase distributed generations (S/T-DGs) based on distributed model predictive control (DMPC). The active and reactive power outputs of each phase of DG units are optimally coordinated to regulate three-phase voltages of all buses to be close to the nominal value and mitigate voltage fluctuations. According to the operation conditions of three-phase DNs, two control modes are designed: preventive and corrective modes. In the preventive mode, the measured voltages of each phase are within the predefined limits, only the reactive power outputs of DG units are optimally adjusted to minimize the voltage deviations of each phase of all critical buses from the nominal value and mitigate the reactive power variations; while in the corrective mode, both the active and reactive power outputs of DG units are optimized to minimize the voltage deviations and the curtailed active power of DGs. The relationship between voltage variation of each phase and power injection is determined using an efficient analytical sensitivity calculation method. The DG controller only exchanges information with adjacent controllers and solves the local DMPC problem. A modified Finnish distribution network with 6 SDGs and 2 TDGs was used to verify the control performance of the proposed distributed voltage control scheme.© 2017 Elsevier Inc. All rights reserved.

Robust Longitudinal Distributed Model Predictive Control of Connected and Automated Vehicles With Coupled Safety Constraints

This paper deals with robust cooperative control of connected and automated vehicles (CAVs) with special consideration of the coupled safety inter-vehicle distance constraints. To address the hard constraints caused by the vehicle physical limitations and the coupled safety constraints among adjacent vehicles explicitly, the distributed model predictive control (DMPC) problem for CAVs is formulated. By virtue of the Lagrangian multiplier method and the dual decomposition technique, the DMPC problem subject to coupled constraints is recast into a distributed dual variable consensus optimization problem comprised of a series of subsystems with local copies of the dual variables, which is then cooperatively solved in parallel based on the alternating direction method of multiplier (ADMM) under the distributed information exchange mechanism. In addition, the disturbance is dynamically mitigated by the feedback control, and its influence on the vehicle status is quantified by the associated robust positively invariant set. Robust cooperative control protocols are proposed to regulate the cooperative operations of CAVs, and the recursive feasibility and the closed-loop stability are theoretically proved. Numerical experiments are carried out to illustrate the effectiveness of the proposed method.

Distributed model predictive control with priority coordination for limited supply multi-zone HVAC systems

The conventional multi-zone HVAC (Heating Ventilation and Air Conditioning) system includes a lot of Variable Air Volume (VAV) boxes to regulate the corresponding zone temperature, and centralized equipment (air supply fans and ducts, etc.) to supply conditioned air in the air-side. With the limitation of the total supply air mass rate in centralized equipment and the priority of zones’ requirement, it becomes a question of resource allocation and schedule on how to coordinate air mass rate to each zone. It is also intricate to control each zone’s temperature in a fully distributed fashion due to this global constraint. In this paper, a distributed model predictive control (DMPC) with priority coordination is proposed for multi-zone HVAC systems. This strategy is composed of a priority coordinated layer and a lower DMPC layer. In the coordinated layer, a thermal bound calculation mechanism with priority is presented to adjust thermal bounds for DMPC to resolve the resource allocation problem when the subsystems are competing for the resource. In DMPC, an operational cost-saving controller is put forward, and the global resource limit is guaranteed by transforming the optimization problem into a consensus problem, which is running in a fully distributed way. In this control scheme, the original infeasible DMPC problem is relaxed, and the entire system is functioning well with specified performance compromise. The effectiveness of the proposed scheme is proved by simulation examples.

A novel distributed model predictive control method based on a substructuring technique for smart tensegrity structure vibrations

This paper considers distributed model predictive control (DMPC) for the vibrations of smart tensegrity structures with input saturation. A distributed control strategy is necessary to enable the autonomy in the individual subsystems, reduce the computational burden of centralized control, and enhance the fault tolerance of control systems. In this work, the dynamic model for smart tensegrity structures equipped with active piezoelectric actuators is generated first by the finite element method. Then, based on the substructuring technique, the entire tensegrity structure system is decomposed into a series of multilevel subsystems. For each subsystem, the continuous-time predictive model equations are discretized by the explicit form of the Newmark-β algorithm. Finally, based on the parametric variational principle, the DMPC problem with input saturation is transformed into a series of linear complementarity problems. The proposed method provides a simple, unified and flexible multilevel distributed control framework for solving the vibration control problems of smart tensegrity structure systems. Numerical experiments illustrate that the proposed DMPC method is effective and exhibits performance comparable to that of a typical centralized model predictive control (CMPC) method. In addition, the constraints of the control input saturation for the proposed DMPC method can be satisfied.

A nonlinear distributed model predictive scheme for systems based on Hammerstein model

A distributed model predictive control (DMPC) scheme for systems based on the Hammerstein structure is proposed in this work. To deal with the nonlinearity of the Hammerstein model, the DMPC problem is reduced to an optimization problem on the intermediate variable and, subsequently, the inverse of the nonlinear block is considered to find the corresponding control inputs. Also, a sub-optimality bound of the method is presented. To illustrate our approach, we consider a nonlinear system controlled in a distributed manner by two agents that exchange information and make cooperative decisions. The efficiency of the proposed DMPC is demonstrated through a simulation example where it is compared to the corresponding centralized approach.

Relaxed hybrid consensus ADMM for distributed convex optimisation with coupling constraints

In this study, the solution of a convex distributed optimisation problem with a global coupling inequality constraint is considered. By using the Lagrange duality framework, the problem is transformed into a distributed consensus optimisation problem and then based on the recently proposed Hybrid Alternating Direction Method of Multipliers (H-ADMM), which merges distributed and centralised optimisation concepts problems, a novel distributed algorithm is developed. In particular, the authors offer a reformulation of the original H-ADMM in an operator theoretical framework, which exploits the known relationship between ADMM and Douglas–Rachford splitting. In addition, the authors' formulation allows us to generalise the H-ADMM by including a relaxation constant, not present in the original design of the algorithm. Moreover, an adaptive penalty parameter selection scheme that consistently improves the practical convergence properties of the algorithm is proposed. Finally, the convergence results of the proposed algorithm are discussed and moreover, in order to present the effectiveness and the major capabilities of the proposed algorithm in off-line and on-line scenarios, distributed quadratic programming and distributed model predictive control problems are considered in the simulation section.

Optimal Economic Schedule for a Network of Microgrids With Hybrid Energy Storage System Using Distributed Model Predictive Control

In this paper, an optimal procedure for the economic schedule of a network of interconnected microgrids with hybrid energy storage system is carried out through a control algorithm based on distributed model predictive control (DMPC). The algorithm is specifically designed according to the criterion of improving the cost function of each microgrid acting as a single system through the network mode operation. The algorithm allows maximum economical benefit of the microgrids, minimizing the degradation causes of each storage system, and fulfilling the different system constraints. In order to capture both continuous/discrete dynamics and switching between different operating conditions, the plant is modeled with the framework of mixed logic dynamic. The DMPC problem is solved with the use of mixed integer linear programming using a piecewise formulation, in order to linearize a mixed integer quadratic programming problem.

Nash-optimization distributed model predictive control for multi mobile robots formation

This paper investigates the distributed model predictive control (DMPC) problem for multi mobile robots. The distributed system model is obtained by the kinematic model of single mobile robot. By including the coupling terms in the cost function, cooperation between subsystems can be incorporated in the distributed control problem. Then, each robot has its own optimal control problem, and neighboring subsystems can exchange information with one another by using wireless communication. The distributed model predictive control problem is formulated by the local cost function and solved by using Nash-optimization algorithm. The convergence condition of the proposed algorithm is presented. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.

Distributed Control of Multi-Agent Systems through Model Predictive Control with Stability

This paper deals with the distributed model predictive control problem in multi-agent systems under fixed interaction topologies. we propose a distributed model predictive control schemes with guaranteed closed-loop stability. In this distributed structure, the problem is decomposed into a set of distributed optimal control problems. Simulation results show that the proposed scheme is effective under fixed interaction topologies among subsystems.

An improved distributed version of Han's method for distributed MPC of canal systems

Recently, we have introduced a distributed version of Han's method that can be used for distributed model predictive control (DMPC) of dynamically coupled linear systems, under coupling constraints (Doan et al., 2009). Some DMPC problems of water networks can be cast into this type. In this paper, we propose an improved version of this method and apply it to a canal system. The simulation results show that the modifications lead to faster convergence of the method, thus making it more practical in control of water networks.