Distributed Model Predictive Control Algorithm Research Articles

Dynamic event-triggering-based distributed model predictive control of heterogeneous connected vehicle platoon under DoS attacks

This paper is concerned with the distributed model predictive control (DMPC) for heterogeneous connected vehicle platoon (CVP) under denial-of-service (DoS) attacks. Firstly, a dynamic event-triggering mechanism (DETM) based on the information interaction between vehicles is proposed to reduce the communication and computational burdens. Due to the fact that the triggering moment for each vehicle cannot be synchronized and DoS attacks can break the communication between vehicles, a packet replenishment mechanism is designed to ensure the integrity and effectiveness of information interaction. Then, the effect of external disturbance is handled by adding robustness constraints to the DMPC algorithm. In addition, the recursive feasibility of the DMPC algorithm and input-to-state practical stability (ISPS) of the CVP control system are demonstrated. Finally, the effectiveness of the algorithm is verified by simulation and comparison results.

Resilient distributed model predictive control of state‐delayed linear parameter varying systems with quantitative communication against denial of service attacks

AbstractThis work presents a resilient distributed model predictive control (MPC) method for linear parameter varying (LPV) systems with state delays and attacks in communication networks. Coordinations are required for distributed MPC (DMPC) to achieve the global performance of centralized MPC (CMPC). However, control performance can be severely degraded by unreliable communication networks, for example, with denial of service (DoS) attacks. A resilient control framework is derived to address the unreliable communications in DMPC. A global system is divided into subsystems for the distributed control purpose. To deal with the model uncertainties and state delays, a “min‐max” DMPC algorithm is presented with a buffer to ensure resilience against DoS attacks. A quantization scheme is introduced to quantize the control information exchanged between subsystems. An iterative interaction scheme is proposed to exchange feedback control laws among subsystems. The stability of the closed‐loop system under the proposed algorithm is ensured by using a Lyapunov function method. The effectiveness of the proposed DMPC is demonstrated through two simulation examples.

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.

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.

Parallel distributed collision avoidance with intention consensus based on ADMM

This paper presents an approach to the problem of collaborative collision avoidance of autonomous inland ships. We propose a distributed model predictive control algorithm that allows ships to negotiate their intention to collaboratively avoid collisions directly. Furthermore, a new method is introduced to better shape ships’ behavior in order to follow Traffic regulations. The simulation results illustrate that the proposed algorithm could significantly increase ship safety navigation. Moreover, it also shows that the solution proposed by our algorithm complies with waterway Traffic regulations except in complex situations when other safe solutions are negotiated.

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.

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

Distributed model predictive control of vehicle platoons under switching communication topologies

Abstract This paper studies the control problem for vehicle platoons under switching communication topologies, where the Predecessor-Following (PF)-failure topology is allowed. Firstly, we design a local optimization problem for each vehicle by using the state information of itself and its neighbouring vehicles, and then present Algorithm 1 based on Distributed Model Predictive Control (DMPC). By constructing a common Lyapunov function defined by the joint neighbourhood set, we derive sufficient conditions with respect to the weight matrices in the open-loop optimization problem and the switching topologies for ensuring the stability of the closed-loop system under Algorithm 1. Furthermore, we propose Algorithm 2 by introducing novel constraints into the local optimization problem for each vehicle, which utilize shrinking historical position errors to cope with PF-link failures, such that the string stability of the vehicle platoon is ensured. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed DMPC algorithms for the vehicel platoon under switching communication topologies.

A Distributed Multiparticle Precise Stopping Control Model Based on the Distributed Model Predictive Control Algorithm for High-Speed Trains

Abstract The fixed-point stopping of high-speed trains in stations is generally accomplished through manual operation in China. This situation often leads to a failure to stop at fixed-point signs and causes a fluctuation in the longitudinal acceleration due to the lack of experience of the drivers. To achieve precise, stable, and automatic stopping, a distributed multiparticle precise stopping control model based on the distributed model predictive control (MPC) algorithm is developed in this paper. A two-level hierarchical control structure for the subcontroller of each vehicle is adopted to bring itself to a controlled stop. In the upper control of subcontroller, the MPC algorithm is designed in turn based on the multiparticle mechanism model of the train. In the lower control of subcontroller, the target input from the upper control is converted and distributed. The controlled object, a comprehensive numerical computing model including the spatial dynamic model of the train and its electropneumatic blending braking model, is established and controlled by the corresponding subcontroller and employed to verify the performance of the controller. The influence of the model control parameters on the stopping performance is discussed, and the optimal combination of control parameters is selected. The proposed control model using the optimization parameters is tested and verified through the comprehensive numerical computing model. The results indicate that the stopping error is 0.0075 m, which is much less than the accuracy requirements for fixed-point stopping. The computing time of each subcontroller in real-time is stable at 0.09 s. The coupler impact force between two adjacent vehicles can also be effectively inhibited and eliminated. Its control performance outperforms a proportional–integral–derivative (PID) algorithm. The proposed precise stopping model and comprehensive numerical computing model provide references for the application and algorithm optimization of automatic train operation technology in high-speed trains.

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.

Distributed model predictive control for heterogeneous vehicle platoon with unknown input of leading vehicle

In this paper, a distributed model predictive control (DMPC) algorithm for a platoon of heterogeneous vehicles is proposed. The leading vehicle is allowed to be driven by a non-zero and time-varying input, rather than traveling at a constant velocity. Except for individual state and input constraints for each vehicle, all vehicles are coupled via state-coupled inter-vehicular spacing constraints and state-coupled cost functions, which maintain the unidimensional platoon formation with satisfactory transient performance. Each vehicle communicates with its neighboring vehicles, and may not know the leading vehicle’s kinetic status information. The control input of each following vehicle is computed by a local optimization problem established by each vehicle’s local information and the assumed state information from its neighbors. By designing distributed terminal control laws for following vehicles, dividing each state-coupled set into several specific subsets, and then forcing each following vehicle to optimize its state constrained in the assigned subsets, the coupled constraints and cost functions can be decoupled, and thus a distributed and parallel computing method can be adopted to compute the control inputs of all following vehicles. Based on the tailored terminal equality constraints together with the tailored terminal control laws, the recursive feasibility of local MPC optimization problems is achieved at all time steps and the asymptotic stability of each vehicle is also guaranteed. The effectiveness of the proposed DMPC method is demonstrated in simulation, and the advantage of the proposed DMPC dealing with the leading vehicle’s non-zero, inaccessible, and time-varying input is highlighted by a comparison simulation for heterogeneous vehicle platoon with a continuously changing leading vehicle velocity.

Robust distributed model predictive control of connected vehicle platoon against DoS attacks

This paper investigates the robust distributed model predictive control (DMPC) of connected vehicle platoon (CVP) systems subject to denial-of-service (DoS) attacks. The main objective is to design a DMPC algorithm that enables the CVP system to achieve exponential tracking performance. First, a switched system model is proposed for the networked CVP system in the presence of DoS attacks. Then the sufficient conditions for the exponential stability of tracking the performance of the CVP control system under DoS attacks are obtained by constructing a specific Lyapunov function and using the topological matrix decoupling technique. In our paper, the DoS attack phenomenon is handled by introducing the frequency and duration parameters, and a quantitative relationship between the exponential decay rate of the CVP system and the DoS attacks parameters is established based on the conditions proposed in the system design, and the critical value of the DoS attack duration ratio is also derived. Finally, the effectiveness of the proposed algorithm is verified through a simulation of a CVP system consisting of one leading vehicle and three following vehicles.

Dynamic consensus of linear multi-agent system using self-triggered distributed model predictive control

This article discusses self-triggering algorithm using distributed model predictive control (DMPC) to achieve dynamic consensus in linear multi-agent systems (MASs). The iterative computations and communications required at each time step in traditional consensus algorithms cause escalation of the energy consumption and shorten the life span of the MAS. An attempt to solve this problem is made by proposing a sequential self-triggering consensus algorithm, where each agent computes its own triggering instants. A Laguerre based DMPC design is adopted that notably reduces the computational complexity of conventional DMPC. The proposed self-triggered DMPC algorithm optimizes the control input and triggering interval while guaranteeing the dynamic consensus of the agents. By virtue of the Laguerre function based control architecture, the additional computations owing to the self-triggered algorithm do not impose stress on the controller; yet reduce the load on communication resources. The equality constraint on the terminal state of the agents is utilized along with Lyapunov criteria to establish the closed loop stability of the MAS. The proposed scheme achieves a considerable drop in controller design computations as well as data transmissions among agents, and the same is established by comparing these traits of existing schemes while achieving comparable performance. The proposed algorithm is verified through simulation of platoon configuration of vehicles, each of which is modeled as a linear multi-input multi-output (MIMO) system.

Distributed model predictive control based on the alternating direction method of multipliers for branching open canal irrigation systems

Most studies of open canal automation concentrated on the control of single canal pool or cascaded multiple canal pools, neglecting the hydraulic coupling effects between the main canal and lateral canals. Low transmission efficiency and poor equity of agriculture water delivery may be caused in the practical application of large-scale irrigation networks. Considering the high computation and communication requirements for large-scale operating systems, a distributed model predictive control (DMPC) algorithm based on the alternating direction method of multipliers (ADMM) is developed for the branching open canal irrigation systems (BOCISs). A simplified BOCIS example, originating from Test case 2 proposed by the American Society of Civil Engineers, is used for control tests. Moreover, for control performance comparisons and evaluations, centralized model predictive control (CMPC) is employed by modifying the state space of the integrator delay (ID) model. The results show that the control performance of the proposed DMPC converges to the global optimal solution of the CMPC under the normal scenario, and the degradation is less than 0.35 %. The communication and coordination process of DMPC contributes to more powerful robustness and interference immunity than CMPC. Furthermore, in case of sudden accidents occurring in some subsystems, the proposed DMPC is more convenient and timely to execute fault isolation. The improvements on water level oscillations and overshoots can reach 20.3 % and 52.1 % in the other subsystems which need normal water delivery, respectively. Equipped with outstanding control characteristics, the proposed ADMM-based DMPC framework enables the water authorities of large-scale BOCISs to promote surface water distribution in a practicable, flexible, and secure way, showing great potential in developing intelligent irrigation districts.

Distributed MPC based on robustly controllable sets for PWA systems

The optimization problem in model predictive control (MPC) algorithm for piecewise affine (PWA) systems often contains substantial logic variables, which requires extensive computing power for online implementation. This paper proposes a one-step distributed MPC algorithm for spatially interconnected PWA systems with both input and state constraints, where the algorithm is based on a series of r-step robustly controllable sets. Algorithms for offline computing terminal sets and a series of r-step robustly controllable sets are developed using the step-by-step backward approach. The states that lie in the robustly controllable sets are steered into the terminal set in finite steps and ultimately converge into a robustly positively invariant set. The proposed algorithm is demonstrated to significantly reduce the online computational burden. Simulation results are provided to showcase the effectiveness of the algorithm.

Optimal Operation of a Benchmark Simulation Model for Sewer Networks Using a Qualitative Distributed Model Predictive Control Algorithm

This article presents a distributed model predictive control algorithm including fuzzy negotiation among subsystems and a dynamic setpoint generation method, applied to a simulated sewerage network. The methodology considers WWTP as an additional objective of control. To improve the performance of a DMPC using a hydraulic model for prediction, a more detailed model has been considered including suspended solids concentration (TSS). The results obtained with the proposed methodology have been validated on a benchmark simulation model for sewer systems developed to test and compare methodologies, showing good performance.

Cooperative predictive control for arbitrarily mixed vehicle platoons with guaranteed global optimality

AbstractThis paper studies the cooperative control problem of a mixed vehicle platoon, which is composed of connected autonomous vehicles (CAVs) and human‐driven vehicles (HDVs) in an arbitrary order. An alternating direction method of multipliers (ADMM) based distributed model predictive control (DMPC) algorithm is proposed for CAVs to lead the mixed vehicle platoon travelling in a string with anticipated inter‐vehicle spacing and a desired velocity. First, the mixed vehicle platoon is divided into multiple interrelated sub‐platoons with any two adjacent sub‐platoons having a common CAV, and then a generic model is constructed for each sub‐platoon based on the intelligent driver model for HDV and the kinematic model for CAV, respectively. Second, a local MPC controller is designed for each sub‐platoon to optimize the control inputs of CAVs with the objective of minimizing the position and velocity errors of all vehicles in the sub‐platoon, and then the ADMM is utilized to obtain the global optimal solution among local MPC controllers of all sub‐platoons. Finally, numerical simulations and experiments are carried out to verify the effectiveness of the proposed DMPC algorithm, the results of which reveal that it can reduce the computation cost significantly and ensure the control performance comparable to the centralized MPC algorithm.

Cooperative distributed model predictive control for robot in-hand manipulation

PurposeThis study aims to process multi-agent system with kinds of limitations and constraints, and consider the robot in-hand manipulation as a problem of coordination and cooperation of multi-fingered hand.Design/methodology/approachA cooperative distributed model predictive control (MPC) algorithm is proposed to perform robot in-hand manipulation.FindingsA cooperative distributed MPC approach is formulated for robot in-hand manipulation problem, which enables address complex limitation and constraint conditions in object motion planning, and realizes tracking trajectory of the object more than tracking position of the object.Originality/valueThis method to implement the moving object task uses the kinematic parameters without the knowledge of dynamic properties of the object. The cooperative distributed MPC scheme is designed to guarantee the movement of the object to a desired position and trajectory at algorithmic level.

A MAS-Based Hierarchical Architecture for the Cooperation Control of Connected and Automated Vehicles

Complex traffic scenarios pose a challenge to the cooperation control of connected and automated vehicles (CAVs). Conventional platoon control or advanced driver-assistance systems only provide an isolated solution due to their inadequacies in systematic perspective. To this end, a multi-agent system (MAS) based distributed control architecture together with a hierarchical controller is proposed for the CAVs cooperation control system. The upper layer considers the potential states of a CAV in the platoon evolution (i.e., vehicle-cruising maneuver and vehicle-following maneuver) and elaborates the transition rules for discrete maneuvering behaviors. The lower layer includes the corresponding motion controller for each CAV. Artificial potential field (APF) combined with the distributed model predictive control algorithm is adopted to realize the integrated longitudinal, lateral and yaw motion control of CAVs. Next, inspired by the Pareto-optimal method for tackling the MAS-cooperation system, an optimal solution strategy is introduced to solve the CAVs cooperation problem from the viewpoint of the control theory. Furthermore, multi-constraints are designed to ensure a safety inter-vehicle spacing between CAVs, while the vehicle stability can also be guaranteed. The simulation results demonstrate that the MAS-based hierarchical control architecture can effectively handle the cooperation control of CAVs in the typical traffic scenarios. The real-time implementation of the proposed controller also proves the feasibility.

Coordinated AGC control strategy for an interconnected multi-source power system based on distributed model predictive control algorithm

The erratic and random characteristics of wind power and wind-thermal replacement significantly degrade the performance of AGC in an interconnected, multi-source power system. For the lack of cooperation between wind power and thermal plants in AGC of interconnected power system as well as the heavy computational burden and inflexible information interaction of centralized AGC architecture, a novel coordinated AGC control strategy for an interconnected multi-source power system based on distributed model predictive control (DMPC) algorithm is proposed in this research. Under the DMPC architecture, the dimension of centralized AGC problem is reduced in each subsystem, and the overall AGC performance can be enhanced through inter-area communication between subsystems. In the meantime, based on the proposed coordinated control strategy, the active AGC response capability of wind farms and energy storage in the interconnected system is exploited to realize the dynamic cooperation between the wind generation and thermal AGC plants, and the overall AGC control performance can be further improved. In this paper, local DMPC controllers are deployed in each subsystem to address the drawbacks of a centralized control architecture by exchanging forecast and state measurement information with neighboring subsystems. In addition, considering the current operating status of multiple kinds of energy sources with different features, a fuzzy-based coordinated control strategy is designed for the purpose of dynamically allocating the AGC demand inside the wind-storage system, and the wind farm’s reliability for AGC response in diverse operation scenarios can be guaranteed. Finally, comparative analysis with existing works has been conducted on a three-area power system, and numerical results demonstrate that the proposed coordinated AGC control strategy has better performance in AGC performance and the dynamic cooperation can be achieved between wind power and thermal plants in AGC response through the designed wind-storage system and coordinated DMPC AGC control strategy.