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distributed model predictive control for consensus of nonlinear systems via parametric sensitivity

ISA TRANSACTIONS 2025年 156卷 87-98页

作者： Yu, Tianyu Zhao, Fei Xu, Zuhua Zhao, Jun Chen, Xi Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China

To handle the nonlinear consensus problem, a distributed model predictive control (DMPC) scheme is developed via parametric sensitivity. A two-stage input computation strategy is adopted for enhancing optimization efficiency. In the background stage, each agent first establishes its next-step optimization problem based on communication topology, and then performs distributed optimization to calculate the future inputs. In the online stage, all the agents build their sensitivity equations based on new information. Three variants of sensitivity equation are developed based on the level of communication load capacity, and the corresponding computation strategies are proposed. After solution, the background inputs are corrected and implemented. The optimality and robustness of the proposed algorithm are rigorously derived. Finally, the superiority of this DMPC scheme is demonstrated in the multi-vehicle system with two different topologies.

关键词： Consensus problem distributed model predictive control Nonlinear programming Parametric sensitivity

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

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART D-JOURNAL OF AUTOMOBILE ENGINEERING 2025年第2-3期239卷 615-634页

作者： Wang, Yiping Wang, Shixuan Su, Chuqi Li, Xueyun Zhang, Qianwen Zhang, Zhentao Tian, Mohan Wuhan Univ Technol Hubei Key Lab Adv Technol Automot Components Wuhan Peoples R China Wuhan Univ Technol Hubei Collaborat Innovat Ctr Automot Components Te Wuhan Peoples R China Wuhan Univ Technol Hubei Technol Res Ctr New Energy & Intelligent Con Wuhan Peoples R China Wuhan Univ Technol Sch Automot Engn 205 Luoshi Rd Wuhan 430070 Hubei Peoples R China

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.

关键词： Cooperative adaptive cruise control model predictive control distributed model predictive control platoon control vehicle platooning distance fluctuation

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Dynamic Self-Triggered Robust distributed model predictive control for Coupled Nonlinear Systems

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2025年

作者： Guo, Rui Feng, Jianwen Wu, Xiaoqun Wang, Jingyi Huang, Tingwen Zhu, Haibin Shenzhen Univ Sch Math Sci Shenzhen 518060 Guangdong Peoples R China Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen 518060 Guangdong Peoples R China Shenzhen Univ Adv Technol Fac Comp Sci & Control Engn Shenzhen 518055 Peoples R China Nipissing Univ Dept Comp Sci & Math North Bay ON P1B 8L7 Canada

This article proposes a dynamic self-triggered distributed model predictive control algorithm for coupled nonlinear systems facing external disturbances and constraints on state and input variables. A dynamic self-triggered mechanism that combines the advantages of event-triggered and self-triggered strategies is designed to simultaneously reduce the frequencies of both sampling and solving optimization problems. Particularly, the triggering threshold is adaptively adjusted using a dynamic variable, which can effectively balance control performance and computational resources. Furthermore, through the construction of a two-model optimal control problem and the analysis of input-to-state practical stability for the overall system, a single-mode distributed model predictive control framework is established for each subsystem within the proposed algorithm, which enables a fully distributed implementation. Sufficient conditions for recursive feasibility and robust stability are investigated, and conservatism is reduced by eliminating the requirement for the system state to reach the terminal region in finite time. Finally, the effectiveness of the developed algorithm is validated through two numerical examples with comparisons.

关键词： Heuristic algorithms Event detection predictive control Prediction algorithms Electronic mail Trajectory Economic indicators Couplings Computer science Circuit stability Coupled nonlinear systems distributed model predictive control dynamic self-triggered mechanism

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Event-triggered distributed model predictive control for PWA systems

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR control 2025年第2期35卷 435-451页

作者： Ma, Aoyun Li, Dewei Xi, Yugeng Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Minist Educ China Key Lab Syst Control & Informat Proc Shanghai Peoples R China Shanghai Engn Res Ctr Intelligent Control & Manage Shanghai Peoples R China

The online computational burden and control performance are two main issues in implementing distributed model predictive control for piecewise affine systems. In the previous research, many methods have been proposed to solve these issues, such as a one-step distributed model predictive control method that was proposed to reduce the heavy online computational burden. However, its control performance is limited because of the one-step prediction horizon. This article proposes an event-triggered distributed model predictive control algorithm for such systems. The online computational burden is alleviated within the distributed framework through the use of an event-triggered mechanism and a variable prediction horizon approach. These strategies not only reduce the number of optimization problems requiring online resolution and simplify them, but also allow for a balance between the control performance and the online computational burden by adjusting event-triggering thresholds. The algorithm utilizes state tubes and terminal sets that are tailored to the characteristics of the piecewise affine systems, thereby rigorously establishing the recursive feasibility of the optimization problems and the stability of the closed-loop system. The simulation results validate the effectiveness of the proposed algorithm.

关键词： distributed model predictive control event-triggered mechanism piecewise affine systems variable prediction horizon

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Sensitivity-Based distributed model predictive control for Non-Linear Systems Under Inexact Optimization

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OPTIMAL control APPLICATIONS & METHODS 2025年第0期

作者： von Esch, Maximilian Pierer Voelz, Andreas Graichen, Knut Friedrich Alexander Univ Erlangen Nurnberg Chair Automat Control Erlangen Germany

This paper presents a distributed model predictive control (DMPC) scheme for non-linear continuous-time systems. The underlying distributed optimal control problem is cooperatively solved in parallel via a sensitivity-based algorithm. The algorithm is fully distributed in the sense that only one neighbor-to-neighbor communication step per iteration is necessary and that all computations are performed locally. Sufficient conditions are derived for the algorithm to converge towards the central solution. Based on this result, stability is shown for the suboptimal DMPC scheme under inexact minimization with the sensitivity-based algorithm and verified with numerical simulations. In particular, stability can be guaranteed with either a suitable stopping criterion or a fixed number of algorithm iterations in each MPC sampling step, which allows for a real-time capable implementation.

关键词： distributed model predictive control networked systems non-linear systems real-time sensitivities sensitivity-based distributed optimal control stability

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Time-Coordinated Motion Planning for Multiple Unmanned Vehicles Using distributed model predictive control and Sequential Convex Programming

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR control 2025年第8期35卷 3240-3255页

作者： Liu, Xiaoming Wu, Fuchun Deng, Yunshan Wang, Ming Xia, Yuanqing Beijing Inst Technol Sch Automat Beijing Peoples R China North Automat Control Technol Inst Taiyuan Peoples R China Zhongyuan Univ Technol Zhengzhou Peoples R China

This paper introduces an integrated approach for time-coordinated motion planning of multiple unmanned vehicles using distributed model predictive control (DMPC) and sequential convex programming (SCP). This approach employs a unified framework that integrates trajectory planning and tracking into a single optimization problem, effectively expanding the domain of attraction for the MPC controller and addressing the challenge of time-coordination among multiple vehicles. Non-uniform discrete time scales are introduced to mitigate the dimensionality of the optimization problem, thereby enhancing computational efficiency. By combining the ability of DMPC to distribute computational efforts across multiple vehicles with the iterative convexification method of SCP, our approach efficiently handles the complexities of non-linear optimization. Theoretical analysis has confirmed the feasibility and stability of the proposed method. Based on this approach, the time-coordinated sequential convex programming-based distributed model predictive control (TC-SCP-DMPC) algorithm is proposed. Numerical simulations are conducted to validate the effectiveness and efficiency of the proposed algorithm in achieving time-coordinated control of multiple unmanned vehicles.

关键词： distributed model predictive control multi-vehicle motion planning sequential convex programming time-coordinated control

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

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ASIAN JOURNAL OF control 2025年第2期27卷 728-740页

作者： Zhong, Aiping Lu, Wanlin Zhang, Langwen South China Univ Technol Sch Automat Sci & Technol Guangzhou Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou Peoples R China South China Univ Technol Guangdong Prov Key Lab Tech & Equipment Macromol A Key Lab Autonomous Syst & Networked Control Minist Educ Guangzhou Peoples R China

This 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.

关键词： denial of service attacks distributed model predictive control linear parameter varying quantized communication state-delayed

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Self-Triggered distributed model predictive control via Path Parameter Synchronization

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR control 2025年第6期35卷 2027-2042页

作者： Chen, Qianqian Li, Shaoyuan Shanghai Jiao Tong Univ Dept Automat Shanghai Peoples R China Shanghai Jiao Tong Univ Key Lab Syst Control & Informat Proc Shanghai Peoples R China

This paper investigates the formation tracking problem for multiple mobile robots via self-triggered distributed model predictive control (DMPC) strategy and path-parameter communication manner. To ensure the robots follow the desired formation structure along the predefined paths, we establish appropriate tracking error models that form a multi-agent system. At triggered instants, each agent exchanges a sequence of path parameters representing the robot's position, resolves the optimal control problem (OCP) and subsequently determines the open-loop phase. Different from existing coordination methodology, the proposed scheme exhibits two essential merits in environments where resources are particularly limited: (1) The tracking task of robots is achieved by designing an appropriate OCP under the DMPC scheme, and the formation task of robots is achieved through the synchronization of one-dimensional path parameters instead of the multi-dimensional state information, which demands less communication load;(2) The incorporation of the self-triggered scheduler acquires the desired control performance with less calculation time, thereby relieving the computational and communication costs. Sufficient conditions are proposed to guarantee the recursive feasibility of the OCP and the closed-loop stability. Simulation results illustrate the validity of the proposed control algorithm.

关键词： distributed model predictive control formation tracking control multi-agent systems self-triggered control

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Motion planning of multiple unmanned vehicles using sequential convex programming-based distributed model predictive control

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR control 2025年第1期35卷 141-167页

作者： Liu, Xiaoming Wu, Fuchun Deng, Yunshan Wang, Ming Xia, Yuanqing North Automat Control Technol Inst Taiyuan Peoples R China Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China Zhongyuan Univ Technol Zhengzhou 450007 Peoples R China

This article tackles the complex challenge of multi-vehicle motion planning by presenting the novel Sequential Convex Programming-based distributed model predictive control (SCP-DMPC) algorithm. Existing methods often struggle with the nonconvex nature of optimization in multi-vehicle motion planning, frequently compromising on computational efficiency. SCP-DMPC innovatively combines the predictive control of DMPC with the optimization prowess of SCP to address these issues efficiently, while adhering to both physical and operational constraints. To ensure precise attainment of target poses, a three-stage control strategy is introduced, with theoretical analysis on its recursive feasibility and asymptotic stability, enhancing the reliability of the algorithm. Moreover, a heuristic-based deadlock resolution scheme is devised to prevent vehicle stalling, a common issue in cooperative motion. Validated through simulations in challenging scenarios, including symmetric position swapping and obstacle-laden formation transition, SCP-DMPC demonstrates superior adaptability, precision, and efficiency. These results underscore its potential for robust, real-time unmanned vehicle applications, suggesting new directions for future research and development in the field.

关键词： collision avoidance distributed model predictive control multi-vehicle motion planning sequential convex programming

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A robust distributed model predictive control strategy for Leader-Follower formation control of multiple perturbed wheeled mobile robotics

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EUROPEAN JOURNAL OF control 2025年 81卷

作者： Nguyen, Thanh Long Mai, Xuan Sinh Dao, Phuong Nam Hung Yen Univ Technol & Educ Hung Yen Vietnam Hanoi Univ Sci & Technol Sch Elect & Elect Engn Hanoi Vietnam

This article studies the formation and trajectory tracking control of multiple mobile robots with kinematic sub-systems. We proposed an effective design of robust distributed model predictive control (MPC) strategy for Leader-Follower formation control scheme in a group of multiple perturbed Wheeled Mobile Robotics (WMRs) with the consideration of tracking performance in not only the position but also the orientation, as well as the distance between the center and head in each WMR. Furthermore, the relation between formation control objective and non-holonomic property in each agent is also discussed. For the purpose of achieving the desired formation, according to trajectory of leader WMR, the barycentric of the formation requirement is known as corresponding virtual followers, and a distributed tube-MPC scheme is applied to each follower WMR for tracking a reference trajectory with not only the position but also its orientation. In addition, the stability and the performance tracking of multiple perturbed WMRs are investigated by employing Lyapunov stability theory with the indirect comparison method to be implemented by pointing out precisely the proposed terminal controller and the equivalent terminal region. Comprehensive simulation results in several scenarios demonstrate the validity of the proposed control scheme.

关键词： distributed model predictive control Leader-Follower formation control Wheeled mobile robotics (WMRs) Optimal control Lyapunov stability theory

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