Reference Tracking using a Non-Cooperative Distributed Model Predictive Control Algorithm

On distributed model predictive control for vehicle platooning with a recursive feasibility guarantee

Stability and Convergence Analysis of a Distributed MPC Scheme Based on Communication and Iterative Calculation of Control Action

This paper presents a distributed model predictive control (DMPC) algorithm for heterogeneous vehicle platoons with unidirectional topologies and a priori unknown desired set point. The vehicles (or nodes) in a platoon are dynamically decoupled but constrained by spatial geometry. Each node is assigned a local open-loop optimal control problem only relying on the information of neighboring nodes, in which the cost function is designed by penalizing on the errors between predicted and assumed trajectories. Together with this penalization, an equality based terminal constraint is proposed to ensure stability, which enforces the terminal states of each node in the predictive horizon equal to the average of its neighboring states. By using the sum of local cost functions as a Lyapunov candidate, it is proved that asymptotic stability of such a DMPC can be achieved through an explicit sufficient condition on the weights of the cost functions. Simulations with passenger cars demonstrate the effectiveness of proposed DMPC.

In this study, an approach to design robust distributed model predictive control (MPC) is proposed for polytopic uncertain networked control systems with time delays. To reduce the computational complexity and improve the flexibility, the entire system is decomposed into multiple smaller dimensional subsystems. For each subsystem, the proposed robust distributed MPC algorithm requires solving multiple linear matrix inequality optimisation problems to minimise an upper bound on a robust performance objective. An augmented polytopic uncertainty description is invoked to handle the input delays. The conservativeness of distributed MPC algorithm is reduced by utilising a sequence of feedback control laws. An iterative on‐line algorithm for robust distributed MPC is developed to coordinate the distributed MPC controllers. Convergence and robust stability of the proposed distributed MPC are investigated. A numerical example is carried out to demonstrate the effectiveness of the proposed algorithm.

SummaryIn this paper, a distributed output feedback model predictive control (OFMPC) algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. Compared with the intensively applied state feedback control in MPC, the OFMPC is more feasible to the real world because the system states are often unmeasurable. With taking both actuator saturation and packet loss into account, the presented OFMPC algorithm is more practical. Moreover, by splitting the controller inputs into two independent parts, the presented dynamic output feedback control (DOFC) strategy provides more freedom to the controller design. With the global system decomposed into some subsystems, the computation complexity is reduced, thus the online designing time can be saved. By defining the estimation error function and forming an augmented system to handle the DOFC and by transforming the nonlinear feedback law into a convex hull of linear feedback laws, the distributed controllers are obtained by solving a linear matrix inequality (LMI) optimization problem. Finally, some simulation examples are employed to show the effectiveness of the techniques proposed in this paper. Copyright © 2015 John Wiley & Sons, Ltd.

In this study, a distributed model predictive control algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. The global system is decomposed into several subsystems, and a novel distributed controller model is established to account for both the actuator saturation and packet loss in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. By transforming the non‐linear feedback law into a convex hull of linear feedback laws, the distributed controllers for subsystems are obtained by solving a linear matrix inequality (LMI) optimisation problem. Finally, two simulation examples are employed to show the effectiveness of the techniques proposed in this study.

This paper presents a distributed model predictive control (DMPC) algorithm for multiple unmanned aerial vehicle (Multi-UAV) formation tracking. This algorithm takes into account the rapidly formation and maintenance of multi-UAV formation, and each UAV only needs to accept the information of neighbor nodes (UAVs) for real-time online rolling optimization. The DMPC scheme enables all followers to form the desired formation while tracking the leader. The Lyapunov function is constructed by the sum of local cost functions, and it is proved that the asymptotic stability can be guaranteed under the conditions of satisfying the proposed terminal constraints and weights. Finally, the effectiveness of the proposed algorithm is illustrated by simulation.

In this paper, a multi-agent formation control strategy with collision avoidance and obstacle avoidance in complex environments is proposed. Under a virtual leader structure, the multi-agent formation is realized through path planning and formation control. In path planning, a transitional region based on prediction horizon is used to replan reference trajectories and avoid obstacles in advance. The virtual-leader alternation strategy and feasible state searching strategy are adopted to avoid one side obstacles and crowded obstacles, respectively. Then the path planning optimization problem is formulated by mixed-integer quadratic programming (MIQP) to calculate trajectories collision-free with obstacles. In formation control, a distributed model predictive control (DMPC) algorithm is developed to form and maintain formation. In DMPC optimization problem, the non-convex obstacle avoidance constraints are replaced with deviation constraints and linear constraints to design terminal invariant set and reduce online computation burden. Under the whole formation control strategy, the tasks of obstacle avoidance and collision avoidance are both achieved and the agents maintain the formation as much as possible. Finally, the example with different obstacle situations is discussed to illustrate the effectiveness of the proposed strategy.

A robust distributed model predictive control algorithm

This article investigates denial-of-service (DoS) attacks and bandwidth limitations in vehicle platooning, addressing the demand for resilient security solutions in connected vehicle electronics. To this end, a dynamic event-triggered distributed model predictive control (DMPC) algorithm with a disturbance compensation mechanism is proposed. Specifically, a disturbance observer is integrated into the DMPC problem to actively compensate for state prediction deviation caused by external disturbances. Meanwhile, a novel dynamic event-triggered mechanism that accommodates DoS attacks is developed to determine whether to solve the DMPC problem. The proposed event-triggered mechanism can dynamically adjust the threshold parameter to reduce the communication and computational overheads. Particularly, considering the incompleteness of information interaction and the limited horizon of neighboring state predictions caused by DoS attacks and asynchronous communication, an information prediction strategy is established. The feasibility of the optimization problem and the stability of the platoon system are strictly analyzed. Finally, the effectiveness of the proposed algorithm is demonstrated through simulation and comparison results.

To address the overvoltage problem caused by the reverse flow of current when a high proportion of distributed photovoltaic (PV) is connected to the distribution network, this paper proposes a grid-connected voltage regulation control strategy based on the cluster division of the Distributed Model Predictive Control (DMPC) algorithm. Firstly, the overvoltage responsibility of each node is calculated using the Shapley value method. This is combined with k-means clustering to achieve effective cluster division, enabling dynamic adjustment of the active and reactive power of photovoltaic power generation units to stabilize regional voltage. Secondly, a group grid-connected voltage control strategy is introduced. This strategy controls the active and reactive power outputs by integrating real-time power output and voltage information from PV generating units in the region with the DMPC algorithm, ensuring overall voltage stability of the grid-connected system. Finally, actual overvoltage data from a 10 kV distribution line in the Dingxi power grid, Gansu Province, is used to verify that under the proposed control strategy, PV grid-connected overvoltage nodes are maintained within 1.06 p.u. The control effect is improved by a margin of 0.05 compared to traditional control methods. This demonstrates the effectiveness of the grouped grid-connected voltage regulation control strategy, achieving smoother voltage regulation performance in distributed PV grid-connected systems.

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.

We consider the problem of steering a multi-agent system to consensus in their outputs. The agents' dynamics are assumed to be heterogeneous, linear, discrete-time and subject to local convex state and input constraints. We present a sequential distributed model predictive control algorithm that asymptotically steers the agents to consensus in their outputs. In their respective model predictive control problems, the agents minimise the distance of a local target output to those of their neighbours while simultaneously tracking the corresponding target steady-state and input pair. We only require the exchange of these target outputs in the scheme whereas the current state and entire predicted trajectories are not shared.

In this paper, a novel cooperative constrained distributed model predictive control algorithm is proposed to control the nonlinear interconnected constrained large-scale systems. In this algorithm, a novel reduced-order cooperative optimisation approach is proposed which is its main contribution that reconstructs and improves the global cost function of any local controller. In proposed algorithm, each local controller computes its optimal control by minimising the corresponding global cost function which is a combination of its own and its neighbouring subsystems’ cost functions. The sufficient conditions are derived to guarantee the recursive feasibility and closed-loop stability specifications to ensure the convergence of the overall states into the positive region which is the neighbourhood of origin. The performance of the proposed algorithm is illustrated via simulation results of a nonlinear large-scale cart-spring-damper system.

In order to reduce the heavy communication burden of cooperative distributed model predictive control (DMPC), A DMPC algorithm based on event-trigger is proposed to balancing the control performance and communication burden through optimizing the interconnection structure of subsystems. An event-trigger using the system Lyapunov function is constructed to avoid solving the introduced MINLP optimization directly, the optimal interconnection structure will be updated only when the event-trigger is triggered. The feasibility of the proposed algorithm in system performance and communication burden decrease is validated by the load frequency control (LFC) problem simulation of interconnected power system.