Distributed Model Predictive Control Research Articles

Iterative distributed model predictive control for nonlinear systems with coupled non‐convex constraints and costs

AbstractThis paper proposes a distributed model predictive control (DMPC) algorithm for dynamic decoupled discrete‐time nonlinear systems subject to nonlinear (maybe non‐convex) coupled constraints and costs. Solving the resulting nonlinear optimal control problem (OCP) using a DMPC algorithm that is fully distributed, termination‐flexible, and recursively feasible for nonlinear systems with coupled constraints and costs remains an open problem. To address this, we propose a fully distributed and globally convergence‐guaranteed framework called inexact distributed sequential quadratic programming (IDSQP) for solving the OCP at each time step. Specifically, the proposed IDSQP framework has the following advantages: (i) it uses a distributed dual fast gradient approach for solving inner quadratic programming problems, enabling fully distributed execution; (ii) it can handle the adverse effects of inexact (insufficient) calculation of each internal quadratic programming problem caused by early termination of iterations, thereby saving computational time; and (iii) it employs distributed globalization techniques to eliminate the need for an initial guess of the solution. Under reasonable assumptions, the proposed DMPC algorithm ensures the recursive feasibility and stability of the entire closed‐loop system. We conduct simulation experiments on multi‐agent formation control with non‐convex collision avoidance constraints and compare the results against several benchmarks to verify the performance of the proposed DMPC method.

A Distributed Model Predictive Control Strategy for Constrained Multi-Agent Systems: The Uncertain Target Capturing Scenario

In this paper, a distributed control architecture is presented for addressing the target capturing problem of a multi-agent system whose dynamics is described by double integrator models subject to bounded disturbance effects. Starting from novel kinematic models used as reference trajectories, the aim consists in driving the multi-agent system within the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">containment</i> region without entering the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distancing</i> one and, whenever necessary, there remaining confined. The underlying control problem has been tackled by means of model predictive control arguments. In particular, two different distributed strategies have been developed, and adequately switched to each other, in order to guarantee constraint satisfaction within the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">capturing</i> region despite any disturbance realization. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes a methodological solution for dealing with the capturing problem for multi-agent systems operating in uncertain environments where the target is defined by the ring resulting from the distancing and containment ellipsoids. Differently from the existing literature, the proposed approach combines into a unique framework properties coming from potential fields theory and distributed model predictive control philosophy. It is interesting to put in light that the underlying control strategy allows the users to face surveillance and rescue operations, to cite a few, in computational affordable way due to the required memory resources because most of computations can be straightforwardly moved in the off-line phase.

Learning-Based Distributed Model Predictive Control Approximation Scheme With Guarantees

Learning-Based Distributed Model Predictive Control Approximation Scheme With Guarantees

Distributed multi-horizon model predictive control for network of energy hubs

The increasing penetration of renewable energy resources has transformed the energy system from a traditional hierarchical energy delivery paradigm to a distributed structure. Local energy hubs activates synergies among energy carriers rendering flexibility to the system and gives rise to possible energy trading among networked local energy hubs. Joint operation of such hubs and peer-to-peer trading between them can improve energy efficiency and support the integration of renewable energy resources. However, for such complex systems involving multiple stakeholders, both computational tractability and privacy concerns need to be accounted for. In this work, a novel multi-horizon distributed MPC framework is introduced for the control of energy hub networks. The multi-horizon approach increases the prediction horizon for MPC without compromising the time discretization or making the problem computationally intractable. The distributed scheme is based on a consensus alternating direction method of multipliers algorithm. It combines the superior performance of the centralized approach with the privacy preservation of the decentralized approach. A benchmark three-hub network is used to investigate the performance of the proposed method in simulation and compare it to the decentralized, centralized and standard model predictive control (MPC) approaches. The results show superior performance of the distributed multi-horizon MPC in terms of total cost, computational time, and robustness to demand and prices variations. Finally, the performance was also experimentally validated in real time by implementing the controller on a real energy hub system.

Multi-UAV DMPC Cooperative Guidance with Constraints of Terminal Angle and Obstacle Avoidance

This paper studies the salvo attack problem for multiple unmanned aerial vehicles (UAVs) against a maneuvering target, and a guidance scheme based on distributed model predictive control (DMPC) is presented to achieve cooperative interception with constraints of terminal impact angle and no-fly zone (or obstacle) avoidance. Firstly, for guaranteeing the synchronization of UAVs in calculating their acceleration commands, the assumed predictive trajectories are introduced, whose deviation from the actual state trajectories is limited by the designed compatibility constraints. Secondly, based on the velocity-obstacle model, the obstacle avoidance constraints are presented, and for guaranteeing the convergence of impact time and impact angles, the auxiliary controller and terminal ingredients are developed, which complete the design of DMPC cooperative guidance scheme. Subsequently, the rigorous proof for the convergence of the proposed guidance scheme is provided. Based on the above design, a complete implementation process of the guidance scheme is presented, in which each UAV uses the particle swarm optimization algorithm to solve the preprocessed local optimization problem, and only the shared information among neighbors is utilized for calculation. Finally, the numerical simulations are conducted under diverse cases, which demonstrate the effectiveness of the proposed guidance scheme when solving cooperative interception problems with terminal angle and obstacle avoidance constraints.

Receding optimal synthesis of robust consensus for multi-agent systems with limited communication

ABSTRACT A novel strategy based on the robust distributed model predictive control (DMPC) is proposed in this paper to address the consensus of multi-agent systems subjected to unknown-but-bounded disturbances with limited communication range. The proposed strategy utilises the formulation of the tube-based predictive control and has the ability to handle the explicit input constraints and achieve the bounded consensus with initial communication topology preserved under the disturbances. In this proposed strategy, a novel constraint is designed to guarantee the connectivity of the system under the disturbances, and the synthesis methods are proposed for the controller. Meanwhile, it is proved that the proposed algorithm in this paper is recursively feasible, the connectivity can always be preserved and the system can finally reach bounded consensus under the disturbances. A simulation example is provided to demonstrate the proposed robust DMPC-based strategy.

Game Theory-Based Interactive Control for Human–Machine Cooperative Driving

To address the safety and efficient driving issues of human–machine shared control vehicles (HSCVs) in future complex traffic environments, this paper proposes a game theory-based interactive control method between HSCVs and surrounding autonomous vehicles (SVs) and involves considering different driving behaviors. In HSCV, a comprehensive driver model integrating steering control and speed control is designed based on the brain emotional learning circuit model (BELCM), and the control authority between the driver and the automation system is dynamically allocated through the evaluation of the driving safety field. Factors such as driving safety and travel efficiency that reflect personalized driving style are considered for modeling the uncertain behavior of SVs. In the interaction between HSCVs and SVs, a method based on game theory and distributed model predictive control (DMPC) that considers the uncertainty of SVs’ driving behavior is established and is finally integrated into a multi-objective constraint problem. The driver control input in an HSCV will also be introduced into the solution process. To demonstrate the feasibility of the proposed method, two test scenarios considering the driving characteristics of different SVs are established. The test results show that automation control systems can promptly stop the human driver’s dangerous operations in an HSCV and safely interact with multiple AVs with different driving characteristics.

A Multi-Timescale Coordinated Optimization Framework for Economic Dispatch of Micro-Energy Grid Considering Prediction Error

The integration of a large number of renewable energy sources (RES) into the micro-energy grid (MEG) brings certain challenges to its optimal dispatching, especially the impact of RES and load prediction error on optimal dispatching. Therefore, this paper proposes a multi-timescale coordinated optimization framework for economic dispatch of MEG considering prediction error, including three stages: day-ahead economic dispatch, intra-day rolling optimization and real-time adjustment. In the day-ahead and intra-day stages, the device's output is solved with the objective of optimal system economy. The MEG is divided into three subsystems in the real-time adjustment stage using distributed model predictive control (DMPC). The subsystems cooperate to correct the intra-day device output, which reduces the complexity of solving system optimization problems. Meanwhile, considering that the prediction horizon in DMPC usually remains constant during the optimization, which affects the control performance of DMPC. This paper analyzes the impact of the prediction horizon and control horizon on the control performance of DMPC. Then a DMPC method with adaptive adjustment of the prediction horizon according to the prediction errors of RES and loads power is proposed, which can balance the stability and prediction accuracy of the system. Finally, the case studies verify the feasibility of the proposed strategy.

Incorporating Control Barrier Functions in Distributed Model Predictive Control for Multirobot Coordinated Control

Incorporating Control Barrier Functions in Distributed Model Predictive Control for Multirobot Coordinated Control

Distributed Model Predictive Control for Consensus of Multi-Agent Systems With Connectivity Maintenance

Distributed Model Predictive Control for Consensus of Multi-Agent Systems With Connectivity Maintenance

Sensitivity-based distributed model predictive control: synchronous and asynchronous execution compared to ADMM

Abstract This paper presents synchronous and asynchronous formulations of a sensitivity-based algorithm for solving distributed continuous-time nonlinear optimal control problems with a neighbor-affine structure. Sensitivities are defined in an optimal control context and utilized to ensure coordination between agents. By using delayed data in the asynchronous formulation, idle times of agents are reduced and faster execution of the algorithm is achieved. The convergence behavior w.r.t. topology and coupling strength is investigated in a numerical simulation and the execution time is evaluated on distributed hardware with communication over TCP in comparison to the alternating direction method of multipliers (ADMM) algorithm.

Adaptive distributed MPC based load frequency control with dynamic virtual inertia of offshore wind farms

AbstractThe penetration of offshore wind farms (OWFs) in city‐close power systems is rapidly increasing. System inertia will be further reduced. Active frequency support of wind power is essential to solve the load frequency control (LFC) problem. Here, the dynamic virtual inertia control (VIC) method is employed to enhance frequency stability within the permitted operating states of OWFs. An adaptive distributed model predictive control (DMPC) method is proposed and applied to an interconnected power system. The dynamic VIC‐based LFC model is derived and used to construct the predictive model of DMPC. To expand the adaptation of the analytical linearized model of OWFs in different operating points, the adaptive law is further designed to dynamically adjust the parameters of DMPC. The simulation results demonstrate the effectiveness of the proposed control method. The frequency fluctuations can be well‐restrained under different disturbances.

Model predictive coordinated cooperative control mechanism for multiagent systems based on priority negotiation

Aiming at the control requirements in complex industrial processes and the problem of poor decision-making flexibility of agents in state/output difference-based consensus strategies, a novel model predictive coordinated cooperative control mechanism is proposed using multiagent systems as the computational paradigm. The proposed mechanism considers the global state of the system, the interaction of control actions among agents, the constraints of the process, and energy consumption. According to the proposed coordinated cooperative control mechanism, each agent must accomplish three tasks at each time step. First, each agent proposes its own “winner-takes-all” control scheme and calculates its payoff. Then, adjacent agents determine their own priorities at the current time step according to the payoffs of the “winner-takes-all” scheme by using a designed pairwise game mechanism. Next, each agent, in order of priority, calculates its sequence of actual optimal control input increments by applying the dynamic predictive control approach based on the dynamic model of the system. Finally, the effectiveness of the proposed coordinated cooperative control mechanism is verified by comparing it with the networked coordination-based distributed model predictive control approach and the centralized model predictive control approach based on the temperature control process of heating an alumina ceramic block in a high-power microwave reactor with six microwave sources.

Coalitional Distributed Model Predictive Control Strategy with Switching Topologies for Multi-Agent Systems

Controlling multi-agent systems (MASs) has attracted increased interest within the control community. Since the control challenge consists of the fact that each agent has limited local capabilities, our adopted solution is tailored so that a group of such entities works together and shares resources and information to fulfill a given task. In this work, we propose a coalitional control solution using the distributed model predictive control (DMPC) framework, suitable for a multi-agent system. The methodology has a switching mechanism that selects the best communication topology for the overall system. The proposed control algorithm was validated in simulation using a homogeneous vehicle platooning application with longitudinal dynamics. The available communication topologies were specifically tailored taking into account the information flow between adjacent vehicles. The obtained results show that when the platoon’s string stability is risked, the algorithm switches between different communication topologies. The resulting coalitions between vehicles ensure an increase in the overall stability of the entire system and prove the efficacy of our proposed methodology.

Asynchronous ADMM for nonlinear continuous‐time systems

AbstractThis paper presents synchronous as well as asynchronous formulations of the alternating direction method of multipliers (ADMM) for solving continuous‐time nonlinear distributed model predictive control (DMPC) problems. It is shown that the optimal control problems of certain system classes can be transformed to fit the consensus‐based ADMM variant problem formulation. The arising subproblems are solved locally on the agent level while the consensus step is solved centrally by a coordinator. Furthermore, the convergence of the synchronous and asynchronous ADMM algorithms to their respective first‐order optimality conditions is presented in a continuous‐time setting. The algorithm is applied to different example systems for which the convergence behavior and influence of the individual algorithmic parameters are investigated. The computation time of the agents remains unaffected by the system size and thus demonstrates the applicability to high‐scaled systems. Moreover, results show that the asynchronous algorithm performs better in terms of execution time when compared to its synchronous counterpart.

Robust Distributed Model Predictive Control for Formation Tracking of Nonholonomic Vehicles

Robust Distributed Model Predictive Control for Formation Tracking of Nonholonomic Vehicles

Observer‐based event‐triggered distributed model predictive control for a class of nonlinear interconnected systems

AbstractIn this paper, an observer‐based event‐triggered distributed model predictive control method is proposed for a class of nonlinear interconnected systems with bounded disturbances, considering unmeasurable states. First of all, the state observer is constructed. It is proved that the observation error is bounded. Second, distributed model predictive controller is designed by using observed value. Meanwhile, the event‐triggered mechanism is set by using the error between the actual output and the predicted output. The setting of event‐triggered mechanism not only ensures the error between the actual output and the predicted output within a certain range, but also reduces the calculation amounts of solving the optimization problem. The states of each subsystem enter the terminal invariant set by distributed model predictive control, and then are stabilized in the invariant set under the action of output feedback control law. In addition, sufficient conditions are given to ensure the feasibility of the algorithm and the stability of the closed‐loop system. Finally, the numerical example is given, and the simulation results verify the effectiveness of the proposed algorithm.

Coordinated Operation of Virtual Coupling High-Speed Trains Under a Novel Sequential Model Predictive Control Framework

This paper deals with the coordinated control problem of the multiple high-speeds operating under the virtual coupling mode with special consideration of the coupled safety inter-train distance constraints and other independent constraints affecting train dynamics. Considering the inertial lag phenomenon within longitudinal dynamics, this study employs a third-order nonlinear control model to characterize train motion. To cope with the intricate running constraints explicitly, a centralized constrained model predictive (MPC) control problem is formulated for the regulation of the trains. Within the framework of sequential solving approach, a novel distributed model predictive control (DMPC) algorithm is designed based on a distributed train running information exchange mechanism. The algorithm decomposes the centralized MPC problem into a sequence of local problems, allowing for sequential computation and meeting the real-time control requirements. Notably, the algorithm mitigates solution conservatism arising from the distributed optimization mechanism by accounting for potential hypothetical control policies among a train’s topological neighbors when designing its control policy. The feasibility and effectiveness of the proposed results are rigorously confirmed through theoretical analysis and illustrated by numerical experiment results.

Car-following stability improvement of cooperative adaptive cruise control based on distributed model predictive control

To solve the problem of large fluctuation of vehicle following distance in cooperative adaptive cruise control (CACC), a distributed model predictive control (DMPC) strategy is proposed. The idea of hierarchical control is performed to control the CACC system. The controller is divided into an upper controller and a lower controller. The upper controller calculates the expected acceleration of the vehicle according to the platooning state, and the lower controller controls the throttle and braking system pressure of the vehicle according to the expected acceleration. Firstly, the longitudinal dynamic model of vehicle platooning is established. Secondly, the objective function is designed according to the control objectives, so that the platooning can obtain the optimal control quantity at the current time. Meanwhile, the robust design is used to improve the controller performance, and the optimization of reference trajectory and the extension of feasible domain are used to improve the stability of the controller. Car-following Stability therefore can be improved. Then the lower controller is designed based on a reverse engine model and a reverse braking model. Finally, the effectiveness of the designed control strategy is verified by the co-simulation of Carsim and MATLAB/Simulink. The results show that DMPC can reduce the peak value, the standard deviation, and the root mean square of vehicle following distance error and improve the following stability.

Robust distributed MPC for disturbed nonlinear multi-agent systems based on a mixed differential–integral event-triggered mechanism

The cooperation of multi-agent systems (MAS) based on distributed model predictive control (DMPC) is a current research hotspot, and how to more effectively handle additive disturbances and reduce resource consumption are two difficult problems that need to be solved. In view of this, this paper aims to design a more effective DMPC strategy for MAS, so as to effectively deal with the above problems without loss of the control performance. Firstly, a finite-horizon constrained optimization problem is established for MAS, in which a robustness constraint is designed to effectively handle additive disturbances. Then, a new efficient event-triggering condition is designed, which is established by considering the mixed information of differential and integral of the state error. Furthermore, based on the dual-mode control, an event-triggered robust DMPC algorithm is proposed to further reduce the resource consumption of the system. In addition, theoretical results are provided through analysis and deduction to ensure the iterative feasibility of the algorithm, stability of the closed-loop system and Zeno-free behavior. Finally, the proposed algorithm is applied to two examples for simulation and comparison to verify its effectiveness. The simulation results show that compared to DMPC and classical event-triggered DMPC methods, the proposed algorithm can reduce the average resource consumption of MAS by more than 81% and 36%, respectively, which indicates that the proposed strategy can effectively reduce the computation and communication burden of MAS without affecting the control performance.