Distributed Model Predictive Control Method Research Articles

Distributed Model Predictive Control Based on Bus Voltage Derivative and SoC Dynamic Model for Shipboard DC Microgrids

State-of-charge (SoC) consistency and bus voltage regulation are two major control objectives of shipboard DC microgrids. To achieve these objectives, this paper presents a novel distributed model predictive control (DMPC) strategy with multiple cost functions. Firstly, based on the bus voltage derivative and SoC dynamic model, the voltage and SoC control equations in discrete form are established. Subsequently, considering the safe operation of battery energy storage systems (BESSs), a DMPC taking the energy storage current as the control set is designed. Finally, the average voltage compensation is taken to achieve precise control of the average voltage. The proposed method can avoid the complex process of adjusting weight coefficients, thereby simplifying controller design. Furthermore, the robustness and practicality of the proposed DMPC method are verified through MATLAB/Simulink 2021a simulations and hardware-in-the-loop (HiL) experiments.

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 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.

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.

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.

Distributed Model Predictive Control via Separable Optimization in Multiagent Networks

We present a distributed model predictive control method which enables a group of agents to compute their control inputs locally, while communicating with their neighbors over a communication network. While many distributed model predictive control methods require a central station for some coordination or computation of the optimization variables, our method does not require a central station, making our approach applicable to a variety of communication network topologies. With our method, each agent solves for its control inputs without solving for the control inputs of other agents, allowing for efficient optimization by each agent, unlike some other distributed methods. Further, our method attains linear convergence to the optimal control inputs in convex model predictive control problems, improving upon the sub-linear convergence rates provided by some other distributed methods such as dual decomposition methods. Moreover, our algorithm provides a closed-loop controller for convex model predictive control problems with affine constraints. We demonstrate our method in both convex and non-convex model predictive control problems in wireless transceiver alignment and satellite deployment, where we show robustness of our method to time delays.

DMPC-based load frequency control of multi-area power systems with heterogeneous energy storage system considering SoC consensus

The energy storage system (ESS) has been widely used for the load frequency control (LFC) of power systems. The heterogeneous ESS (HESS) consisting of various types of energy storage units (ESUs) with different regulation characteristics creates many difficulties in designing a high-performance LFC strategy for a multi-area power system. To obtain the satisfied dynamic response of the LFC scheme against load disturbances and keep the state of charge (SoC) balance of the HESS, this paper proposes a distributed model predictive control (DMPC) method to design the LFC strategy. Firstly, the dynamic model of the power system with HESS is established. Then, the distributed predictive model for LFC design is formulated by considering the LFC objective, the SoC balance requirement, and the operational constraints of the generators and the HESS. Subsequently, the optimal LFC strategy is obtained by solving the distributed predictive model based on the linear quadratic programming (LQP) method. Finally, we make case studies to validate the effectiveness of the proposed method. Compared with the PI-based LFC, the proposed DMPC-based LFC performs better in stabilizing the system frequency, narrowing the area control error (ACE), and keeping the SoC of all the ESUs consistent.

Trajectory Tracking Control of Transformer Inspection Robot Using Distributed Model Predictive Control.

To overcome the difficulty in tracking the trajectory of an inspection robot inside a transformer, this paper proposes a distributed model predictive control method. First, the kinematics and dynamics models of a robot in transformer oil are established based on the Lagrange equation. Then, by using the nonlinear model predictive control method and following the distributed control theory, the motion of a robot in transformer oil is decoupled into five independent subsystems. Based on this, a distributed model predictive control (DMPC) method is then developed. Finally, the simulation results indicate that a robot motion control system based on DMPC achieves high tracking accuracy and robustness with reduced computing complexity, and it provides an effective solution for the motion control of robots in narrow environments.

Hierarchical distributed MPC method for hybrid energy management: A case study of ship with variable operating conditions

The energy management (EM) strategy, power controller, and local controller of the EM system are coupled, and together affect hybrid power system performance. To achieve coordinated control and multi-objective optimisation of a hybrid power system, a hierarchical distributed control method was proposed, and a validation study was conducted based on model-in-the-loop simulations (MILs) and hardware-in-the-loop simulations (HILs). First, a real-time EM strategy based on a combination of forward dynamic programming (FDP) and model predictive control (MPC) methods was proposed to optimise the power allocation for multiple energy sources. Second, a distributed controller based on a consistency algorithm was proposed to coordinate the differences in the characteristics of multiple energy sources. A dynamic virtual impedance-based droop controller was designed for dynamic tracking of the reference power. The performance of the three-layer control structure was comprehensively validated through MILs and HILs. The results show that the dynamic virtual impedance-based droop control method can track the nonlinear reference power with control deviation within 5 %. The distributed controller is able to keep the bus voltage stable. The global control accuracy of the DC bus voltage is improved by 18.08 %, and the battery current global fluctuations is reduced by 17.4 %. The real-time FDP-MPC-based EM strategy can achieve 99.89 % energy savings and emissions reduction compared to the global DP-MPC-based method, with greater robustness, real-time performance. The results demonstrate that the proposed method is effective for real-time applications and can achieve hierarchical and multi-objective optimal control of the hybrid power system.

A Multirobot Distributed Collaborative Region Coverage Search Algorithm Based on Glasius Bio-Inspired Neural Network

There are many constraints for a multi-robot system to perform a region coverage search task in an unknown environment. To address this, we propose a novel multi-robot distributed collaborative region coverage search algorithm based on Glasius bio-inspired neural network (GBNN). Firstly, we develop an environmental information updating model to represent the dynamic search environment. This model converts the environmental information detected by the robot into dynamic neural activity landscape of GBNN. Secondly, we introduce the distributed model predictive control method in search path planning to improve search efficiency. In addition, we propose a distributed collaborative decision-making mechanism among the robots to produce several dynamic search sub-teams. Within each sub-team, collaborative decisions are made among the robot members to optimize the solution and obtain the next movement path of each robot. Finally, we conduct experiments in three aspects to verify the effectiveness of the proposed method. Compared with three algorithms in this field, the experimental results demonstrate that the proposed algorithm exhibits good performance in a multi-robot region coverage search task.

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.

DMPC-based string stable platoon control with robustness against communication delays

Communication delays are inevitable in vehicle platoons and may inhibit control performance. To address this issue, existing delay compensation strategies often resort to a greater time headway based on the delay upper bound, which compromises the benefits on traffic throughput. Moreover, it remains a major challenge to strictly ensure string stability with delays for distributed model predictive control (DMPC)-based controller. This paper presents a DMPC method for the cooperation of heterogeneous platoons subject to time-varying communication delays and greatly improves robustness against communication delays by improving the DMPC mechanism. A third-order heterogeneous vehicle dynamics model is integrated into the proposed method to improve control precision when implemented in the field. A synchronization mechanism is designed and the constant spacing policy is applied, which eliminates the delay dependence of the time headway selection and may thus improve traffic throughput. By incorporating a dual-mode scheme, a robustness constraint and a string stability constraint in the optimization problem, feasibility, closed-loop stability, and string stability are theoretically proved. A sufficient condition on the controller parameters is derived to guarantee closed-loop stability under communication delays. Numerical simulations are conducted to demonstrate the effectiveness of the proposed delay-compensating DMPC controller. The results reveal that the proposed controller outperforms the traditional DMPC controller and delay-involved linear controller on string stability, tracking performance and desired spacing selection.

Adaptive authority allocation for shared steering control considering social behaviours: a hybrid fuzzy approach with game-theoretical vehicle interaction model

In a typical traffic scenario, automated vehicles are required to interact with surrounding traffic participants, e.g. human-driven vehicles, pedestrians, etc. In this paper, a novel adaptive authority allocation strategy considering the social behaviours of surrounding vehicles is proposed for the shared steering control (SSC) of automated vehicles. First, a Koopman-based potential-field-driven distributed model predictive control (K-PF-DMPC) method is proposed for the modelling of vehicle interaction to describe surrounding vehicle's social behaviour. This method effectively deals with the nonlinearity embedded in the non-cooperative game-based vehicle interaction model, so that the analytical form of Nash equilibrium can be derived for a fast online solution. Then, the SSC system of the automated vehicle is implemented by a weighted summation method. To balance the driving performance and intervention degree while considering the surrounding vehicles' social behaviours, a hybrid fuzzy strategy (HFS) is proposed for allocating the control authority between the driver and automation. The value of authority allocation coefficient is calculated by fusing the outputs from two shared fuzzy controllers, i.e. the enhanced and weakened shared fuzzy controllers, in accordance to the belief of the surrounding vehicle's type. Several numerical simulations and driver-in-the-loop simulator experiments are conducted for validation. Results show that the proposed strategy can provide appropriate steering intervention to the driver owing to the consideration of the surrounding vehicle's social behaviour and obtains the best driver-automation collaboration performance compared with the comparative groups.

Robust tube‐based distributed MPC for PWA systems

AbstractA robust tube‐based distributed model predictive control method is proposed for spatially interconnected systems with constraints and disturbances. The system contains multiple discrete‐time piecewise affine subsystems, which are coupled to each other through states. The predictive states of each subsystem are dependent on its states, inputs, and neighbouring states, and shrinking constraints are constructed to deal with the disturbances and the model mismatches. The differences between the predicted states at the current time instant and the optimal states at the previous time instant are constrained, which improves the accuracy of the predicted model and enhances the control performance. The conditions which ensure the recursive feasibility of optimization problems and the asymptotic stability of closed‐loop system are obtained. The effectiveness of the proposed method is verified by the simulation results.

Distributed Model Predictive Control Method for Spacecraft Formation Flying in a Leader–Follower Formation

This paper presents a Distributed Model Predictive Control (DMPC) algorithm for a scenario of spacecraft formation flying, namely spacecraft platooning in a leader-follower formation. This spacecraft formation application can be regarded as a cooperative system composed of several spacecraft with a common goal, for which a relative translational model is considered connecting the different agents. A distributed algorithm is proposed that solves a 1-hop optimization problem in order to estimate the optimal control action sequence, including also relevant constraints to protect and deal with the overall system. The algorithm is then analyzed in terms of uniqueness and convergence of the optimal control action. The proposed methods are validated with realistic simulation results, showing that all vehicles demonstrate reliable performance following a given trajectory or goal in a formation, while satisfying all the considered constraints.

Distributed tube model predictive control for string stability of heterogeneous vehicle platoons

This article develops a distributed tube model predictive control method to guarantee the string stability of the heterogeneous vehicle platoon under external disturbance and controller saturation. The error model of each vehicle is proposed based on the desired distance and velocity, where the coupled factor between vehicles is treated as a random disturbance. The linear feedback controller is devised to reject disturbances by keeping the actual trajectory within a tube around the nominal trajectory, and a model predictive controller is proposed by treating the input saturation and string stability as state constraints in the optimization problem. Compared with previous results, the proposed control strategy achieves a better performance of disturbance rejection and greatly reduces the online computation burden, which would be more favorable in engineering applications. The method proposed in this article is illustrated to be effective by simulation.

Hierarchical and Distributed Eco-Driving Approach for Mixed Vehicle Clusters at Unsignalized Intersections

To improve the driving efficiency and energy-saving characteristics for large-scale mixed traffic flows under different market penetration rates (MPRs) of intelligent and connected vehicles (ICVs) at unsignalized intersections, considering the cooperative eco-driving performance between ICVs and human-driven vehicles (HDVs) with time-varying speed characteristics, the hierarchical and distributed cooperative eco-driving architecture is first established in this paper, consisting of a cloud decision layer and a vehicle control layer. For the cloud decision layer, the multivehicle model-free adaptive predictive cooperative driving (MFAPCD) method is designed by using only the driving data of the HDVs and ICVs formation based on compact form dynamic linearization (CFDL) technique, thereby improving traffic efficiency. Furthermore, the CFDL integral terminal sliding mode predictive control (CFDL-ITSMPC) scheme is utilized to predict the time-varying driving speed of HDVs, and then, the CFDL predictive control (CFDL-PC) scheme is utilized to predict the expected control variables of ICVs formation. For the vehicle control layer, based on the anticipated driving speed obtained from the cloud decision layer, the nonlinear distributed model predictive control (NDMPC) method is utilized for distributed optimal control of each vehicle formation, to achieve optimization in terms of energy saving. Simulation results show that, compared with the signal time assignment strategy, the method can increase the average velocity by about 15.22% and decrease the average fuel consumption by about 36.43% under different MPRs and traffic volumes.

Fast Distributed Model Predictive Control Method for Active Suspension Systems

In order to balance the performance index and computational efficiency of the active suspension control system, this paper offers a fast distributed model predictive control (DMPC) method based on multi-agents for the active suspension system. Firstly, a seven-degrees-of-freedom model of the vehicle is created. This study establishes a reduced-dimension vehicle model based on graph theory in accordance with its network topology and mutual coupling constraints. Then, for engineering applications, a multi-agent-based distributed model predictive control method of an active suspension system is presented. The partial differential equation of rolling optimization is solved by a radical basis function (RBF) neural network. It improves the computational efficiency of the algorithm on the premise of satisfying multi-objective optimization. Finally, the joint simulation of CarSim and Matlab/Simulink shows that the control system can greatly minimize the vertical acceleration, pitch acceleration, and roll acceleration of the vehicle body. In particular, under the steering condition, it can take into account the safety, comfort, and handling stability of the vehicle at the same time.

Multi-time scale optimization scheduling of microgrid considering source and load uncertainty

With the increase of renewable energy penetration in microgrid and the stochasticity of customer load, microgrid faces new difficulties in maintaining the smooth power of contact lines and system economy when achieving optimal scheduling. In order to balance the accuracy, economy and robustness of microgrid scheduling better, a multi-time scale optimal scheduling strategy for microgrids considering the uncertainty of source and load is proposed. In the day-ahead scheduling stage, a two-stage distributionally robust optimal scheduling model is established with the objective of minimizing the comprehensive day-ahead scheduling cost of the microgrid, and the optimal day-ahead scheduling solution is found under the probability distribution of the worst scenario. In the intra-day scheduling stage, based on the prediction value of source and load with higher accuracy, a distributed model predictive control method is used to build an intra-day rolling optimization and real-time adjustment optimal scheduling model, which ensures the effective implementation of the day-ahead plan and fully suppresses power fluctuation of the contact line. The simulation results show that the proposed multi-time scale optimal scheduling method can not only maintain the smooth power of contact lines, but also achieve robust and economic operation of the microgrid.

Distributed Model Predictive Control for Heterogeneous Vehicle Platoon With Inter-Vehicular Spacing Constraints

This paper proposes a distributed control scheme for a platoon of heterogeneous vehicles based on the mechanism of model predictive control (MPC). The platoon composes of a group of vehicles interacting with each other via inter-vehicular spacing constraints, to avoid collision and reduce communication latency, and aims to make multiple vehicles driving on the same lane safely with a close range and the same velocity. Each vehicle is subject to both state constraints and input constraints, communicates only with neighboring vehicles, and may not know a priori desired setpoint. We divide the computation of control inputs into several local optimization problems based on each vehicle’s local information. To compute the control input of each vehicle based on local information, a distributed computing method must be adopted and thus the coupled constraint is required to be decoupled. This is achieved by introducing the reference state trajectories from neighboring vehicles for each vehicle and by employing the interactive structure of computing local problems of vehicles with odd indices and even indices. It is shown that the feasibility of MPC optimization problems is achieved at all time steps based on tailored terminal inequality constraints, and the asymptotic stability of each vehicle to the desired trajectory is guaranteed even under a single iteration between vehicles at each time. Finally, a comparison simulation is conducted to demonstrate the effectiveness of the proposed distributed MPC method for heterogeneous vehicle control with respect to normal and extreme scenarios.