Distributed Model Predictive Control Scheme Research Articles

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.

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.

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.

Rolling self-triggered distributed MPC for dynamically coupled nonlinear systems

The mutual influences caused by dynamic couplings in large-scale systems increase the difficulty in the design and analysis of distributed model predictive control (DMPC), and require information exchange among subsystems which calls for a scheduling strategy to save communication resources in communication-limited environments. To circumvent the two problems, we design a rolling self-triggered DMPC strategy for large-scale dynamically coupled systems with state and control input constraints. First, the optimal control problem where the cost is subject to the coupled dynamic and the constraints are subject to the uncoupled counterpart is proposed, forming the dual-model DMPC that is simple in design and analysis but yields good control performance. Second, the information exchange only occurs at some specified triggering instants determined by a rolling self-triggered mechanism, saving communication resources more significantly. The effectiveness of the designed strategy is verified by numerical simulations.

SVD-Based Robust Distributed MPC for Tracking Systems Coupled in Dynamics With Global Constraints.

This article presents a novel singular value decomposition (SVD)-based robust distributed model predictive control (SVD-RDMPC) strategy for linear systems with additive uncertainties. The system is globally constrained and consists of multiple interrelated subsystems with bounded disturbances, each of whom has local constraints on states and inputs. First, we integrate the steady-state target optimizer into the MPC problem through the offset cost function to formulate a modified single optimization problem for tracking changing targets from real-time optimization. Then, the concept of constraint tightening is utilized to enhance the robustness and ensure robust constraint satisfaction in the presence of interferences. On this basis, the SVD method is introduced to decompose the new optimization problem into several independent subsystems on the orthogonal projection space, and a distributed dual gradient algorithm with convergence proved is implemented to obtain the control of each nominal subsystem. The recursive feasibility is then ensured and the tracking ability of the strategy is analyzed. It is verified that for a target, the system can be steered to a neighborhood of the closest possible steady setpoint. At last, the effectiveness of the raised SVD-RDMPC strategy is established in two simulations on building temperature control and load frequency control.

Distributed Control of an Ill-Conditioned Non-Linear Process Using Control Relevant Excitation Signals

Efficient control schemes for ill-conditioned systems, such as the high-purity distillation column, can be challenging and costly to design and implement. In this paper, we propose a distributed control scheme that utilizes well-designed excitation signals to identify the system. Unlike traditional systems, we found that a summation of correlated and uncorrelated signals can yield better excitation of the plant. Our proposed distributed model predictive control (MPC) scheme uses a shifted input sequence to address loop interactions and reduce the computational load. This approach deviates from traditional schemes that use iteration, which can increase complexity and computational load. We initially tested the proposed method on the linear model of a highly coupled 2 × 2 process and compared its performance with decentralized proportional-integral-derivative (PID) controllers and centralized MPC. Our results show improved performance over PID controllers and similar results to centralized MPC. Furthermore, we compared the performance of the proposed approach with a centralized MPC on a nonlinear model of a distillation column. The results for the second study also demonstrated comparable performance between the two controllers with the decentralised control slightly outperforming the centralised MPC in some cases. These findings are promising and may be of interest to practitioners that are more comfortable with tuning decentralised loops.

Distributed Predictive Secondary Control With Soft Constraints for Optimal Dispatch in Hybrid AC/DC Microgrids

Hybrid AC/DC microgrids (H-MGs) are a prominent solution for integrating distributed generation and modern AC and DC loads. However, controlling these systems is challenging as multiple electrical variables need to be controlled and coordinated. To provide flexibility to the control system, these variables can be regulated to specific values or within secure bands. This paper proposes a set of distributed model predictive control schemes for the secondary control level to control certain variables to specific values and other variables within secure pre-defined bands into H-MGs. Specifically, optimal dispatch of active and reactive power is achieved while frequency and voltages are regulated within secure bands in H-MGs. Dynamic models of AC generators, DC generators and interlinking converters along with their novel multi-objective cost functions are developed in constrained distributed predictive optimisation problems to simultaneously achieve the aforementioned objectives via information sharing. Extensive simulation work validates the performance of this proposal.

Distributed Dual Closed-Loop Model Predictive Formation Control for Collision-Free Multi-AUV System Subject to Compound Disturbances

This paper focuses on the collision-free formation tracking of autonomous underwater vehicles (AUVs) with compound disturbances in complex ocean environments. We propose a novel finite-time extended state observer (FTESO)-based distributed dual closed-loop model predictive control scheme. Initially, a fast FTESO is designed to accurately estimate both model uncertainties and external disturbances for each subsystem. Subsequently, the outer-loop and inner-loop formation controllers are developed by integrating disturbance compensation with distributed model predictive control (DMPC) theory. With full consideration of the input and state constraints, we resolve the local information-based DMPC optimization problem to obtain the control inputs for each AUV, thereby preventing actuator saturation and collisions among AUVs. Moreover, to mitigate the increased computation caused by the control structure, the Laguerre orthogonal function is applied to alleviate the computational burden in time intervals. We also demonstrate the stability of the closed-loop system by applying the terminal state constraint. Finally, based on a connected directed topology, comparative simulations are performed under various control schemes to verify the robustness and superior performance of the proposed scheme.

Event-Based Distributed Predictive Approach for the Cooperation of Networked Mobile Manipulators

This article presents an event-triggered distributed model predictive control strategy for the cooperation of networked mobile manipulators to save communication and computational resources effectively. First, based on the nonlinear feedback technique, an auxiliary model with bounded disturbances is established, and a model predictive controller is designed for each mobile manipulator considering the system constraints. Then, an event-triggering mechanism involving the difference between the actual state and its optimal prediction is developed to reduce the frequency of communication and computation of the networked mobile manipulators. The optimization problem is solved, and information is exchanged only when the event-triggering condition is satisfied. Moreover, sufficient conditions for guaranteeing the feasibility of the proposed algorithm and the stability of the closed-loop system are formulated, respectively. Finally, the simulation results show that the proposed strategy works well.

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.

Compound Event-Triggered Distributed MPC for Coupled Nonlinear Systems.

This article investigates the event-triggered distributed model predictive control (DMPC) for perturbed coupled nonlinear systems subject to state and control input constraints. A novel compound event-triggered DMPC strategy, including a compound triggering condition and a new constraint tightening approach, is developed. In this event-triggered strategy, two stability-related conditions are checked in a parallel manner, which relaxes the requirement of the decrease of the Lyapunov function. An open-loop prediction scheme to avoid periodic transmission is designed for the states in the terminal set. As a result, the number of triggering and transmission instants can be reduced significantly. Furthermore, the proposed constraint tightening approach solves the problem of the state constraint satisfaction, which is quite challenging due to the external disturbances and the mutual influences caused by dynamical coupling. Simulations are conducted at last to validate the effectiveness of the proposed algorithm.

Energy Balance in a Standalone PV Battery Hybrid Generation System on Solar-Powered Aircraft Using the Model Predictive Control Method

This paper proposes a battery state of charge (SOC)-based energy management strategy using hierarchical distributed model predictive control (HDMPC) for a standalone microgrid on solar-powered long-endurance aircraft. The microgrid was innovatively designed as a two-layer structure in which the first layer consists of a photovoltaic generation and battery storage system named the PV battery module (PBM). The second layer, named the microgrid subsystem (MGSS), consists of several PBMs, each of which supplies power to a specific DC load on the aircraft. The control system is divided into two levels: the grid-level model predictive control (MPC) and the converter-level MPC. The grid-level MPC adopts a distributed model predictive control strategy to obtain the reference power of each module. The converter-level MPC calculates the control variables of converters using a supervisory model predictive control (SMPC) strategy. The new microgrid structure and the proposed control strategy have improved the reliability of the energy system and increased its energy utilization rate.

Distributed Model Predictive Control and Coalitional Control Strategies—Comparative Performance Analysis Using an Eight-Tank Process Case Study

Complex systems composed of multiple interconnected sub-systems need to be controlled with specialized control algorithms. In this paper, two classes of control algorithms suitable for such processes are presented. Firstly, two distributed model predictive control (DMPC) strategies with different formulations are described. Afterward, a coalitional control (CC) strategy is proposed, with two different communication topologies, i.e., a default decentralized topology and a distributed topology. All algorithms were tested on the same simulation setup consisting of eight water tanks. The simulation results show that the coalitional control methodology has a similar performance to the distributed algorithms. Moreover, due to its simplified formulation, the former can be easily tested on embedded systems with limited computation storage.

Event-triggered robust distributed output feedback model predictive control for nonlinear MASs against false data injection attacks

In this paper, an event-triggered distributed output feedback model predictive control scheme for the nonlinear disturbed multiagent systems with sensor–controller channel false data injection attacks is proposed. To provide valid system states to the controller in the event of cyber attacks, a robust multivariate observer is designed to realize the estimation and separation of uncompromised system states, false data injection attacks, and measurement disturbances, simultaneously. Based on these reconstructed signals and a newly-designed linear robustness constraint, the distributed predictive controller is established to achieve smooth cooperative stabilization among agents. Meanwhile, an event-triggered mechanism is applied to save computing resources, and it restricts the error of predictive states and estimated states to guarantee the feasibility of the optimization control problem. Theoretical analyses on robustness and security for the nonlinear multiagent systems under event-triggered distributed output feedback model predictive control are presented. Finally, a simulation on two pairs of one-link flexible joint manipulator systems verifies the theoretical results.

An ADMM-based algorithm for stabilizing distributed model predictive control without terminal cost and constraint

The stability assurance is not straightforward for distributed model predictive control (DMPC), since the well-known terminal cost and constraint technique cannot be readily adapted to the distributed schemes. An alternative method to the complicated procedure of splitting the terminal cost function and constraint set to achieve stability, is to calculate a minimum length for the DMPC prediction horizon. It is known that the DMPC cost will then have a relationship to the infinite-horizon cost, which is determined by a so-called performance factor. Moreover, the stopping condition of the distributed optimization algorithm, which for the sake of smooth handling of the coupling constraints is usually a duality-based algorithm, can be formulated using two scalars: an upper bound for the cost of the next sampling period and a lower bound for the optimal cost of the current one. For the duality-based algorithms, feasibility can only be guaranteed in the limit of iterations, thus the constraint tightening technique should be employed to determine the former scalar. The tightening technique, however, impinges upon calculation of the latter one. This problem is already addressed in the literature for gradient-based methods. By contrast, the consensus form of alternating direction method of multipliers (ADMM) is employed in this paper to stabilize the DMPC scheme. Simulation results reveal that this method outperforms the existing gradient-based approaches in terms of the required number of communications.

Cooperative distributed MPC via decentralized real-time optimization: Implementation results for robot formations

Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While the stability analysis of DMPC is quite well understood, there exist only limited implementation results for realistic applications involving distributed computation and networked communication. This article approaches formation control of mobile robots via a cooperative DMPC scheme. We discuss the implementation via decentralized optimization algorithms. To this end, we combine the alternating direction method of multipliers with decentralized sequential quadratic programming to solve the underlying optimal control problem in a decentralized fashion with nominal convergence guarantees. Our approach only requires coupled subsystems to communicate and does not rely on a central coordinator. Our experimental results showcase the efficacy of DMPC for formation control and they demonstrate the real-time feasibility of the considered algorithms.

Neurodynamics-based distributed model predictive control of a low-speed two-stroke marine main engine power system

This article studies a steady operation optimization problem of a low-speed two-stroke marine main engine (LTMME) power system including a cooling water subsystem, a fuel oil subsystem and a main engine subsystem with input and state constraints. Firstly, a distributed model with coupling inputs and states is established for the LTMME power system according to laws of thermodynamics and kinetics. Further, an optimization problem of the LTMME power system is formulated to ensure the system to operate steadily, subjected to constraint conditions of the distributed model and the input and state bounds. Moreover, the optimization problem is rewritten as a quadratic programming problem, and an iterative distributed model predictive control (DMPC) scheme based on a primal–dual neural network (PDNN) method is used to obtain the optimal inputs within the constrained range. Finally, based on the actual data from an underway ocean vessel named Mingzhou 501 with an LTMME power system, a group of simulations are carried out to verify the effectiveness of the proposed approach.

Event‐triggered distributed model predictive control scheme for temperature regulation in multi‐zone air conditioning systems with improved indoor thermal preference indicator

SummaryDriven by the increasing needs in multi‐zone buildings for reducing the air conditioning (A/C) system related energy consumption and increasing the occupants' thermal comfort, an event‐triggered distributed model predictive control (DMPC) scheme for building temperature regulation with improved indoor thermal preference indicator is proposed. To this end, a temperature‐energy model of the A/C system in a zone which considers multiple types of heat transfer, and the system model of the multi‐zone A/C system are derived first. On this basis, an improved indoor thermal preference indicator that trades off the A/C systems related energy consumption with the aggregate thermal comfort of the occupants is proposed for the multi‐zone A/C system, then the optimal indoor temperature set‐points for each zone are determined by using the distributed consensus algorithm. It is followed by an event‐triggered DMPC scheme by adjusting the A/C systems to arrive at the optimal indoor temperature set‐points for all the zones with lower communication and computation load. The performance and effectiveness of the proposed methods are demonstrated through a case study on an actual multi‐zone A/C system.

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.