Distributed Model Predictive Control Controller Research Articles

Ensuring Secure Platooning of Constrained Intelligent and Connected Vehicles Against Byzantine Attacks: A Distributed MPC Framework

This study investigates resilient platoon control for constrained intelligent and connected vehicles (ICVs) against F-local Byzantine attacks. We introduce a resilient distributed model-predictive platooning control framework for such ICVs. This framework seamlessly integrates the predesigned optimal control with distributed model predictive control (DMPC) optimization and introduces a unique distributed attack detector to ensure the reliability of the transmitted information among vehicles. Notably, our strategy uses previously broadcasted information and a specialized convex set, termed the “resilience set”, to identify unreliable data. This approach significantly eases graph robustness prerequisites, requiring only an (F + 1)-robust graph, in contrast to the established mean sequence reduced algorithms, which require a minimum (2F + 1)-robust graph. Additionally, we introduce a verification algorithm to restore trust in vehicles under minor attacks, further reducing communication network robustness. Our analysis demonstrates the recursive feasibility of the DMPC optimization. Furthermore, the proposed method achieves exceptional control performance by minimizing the discrepancies between the DMPC control inputs and predesigned platoon control inputs, while ensuring constraint compliance and cybersecurity. Simulation results verify the effectiveness of our theoretical findings.

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.

Two-Layer Robust Distributed Predictive Control for Load Frequency Control of a Power System under Wind Power Fluctuation

The frequency stability of interconnected power systems becomes quite challenging when incorporating renewable energy sources (mostly wind power). Distributed model predictive control (DMPC) is an effective method to maintain stable grid frequency and realize power system load frequency control (LFC). This paper proposes a two-layer robust DMPC for the LFC of an interconnected power system. In the scheme, the wind power penetrating the power grid is largely affected by the environment condition, and it is taken as an uncertain disturbance to the power system. The two-layer robust DMPC consists of a nominal DMPC controller and an ancillary DMPC controller. The nominal DMPCs coordinate with each other in achieving the systemwide LFC objective, where the systemwide objective is a strict convex combination of the local LFC objectives. The nominal optimization problems are solved supposing the wind power fluctuation is zero. The ancillary DMPC generates the actual control signal for each generation unit based on signals which are transmitted from the nominal DMPC controller. The simulation on a four-area interconnected power system demonstrates the effectiveness of the proposed algorithm in alleviating the frequency deviation caused by varying the load and uncertain wind power fluctuation.

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.

Barrier-function-based distributed predictive control for operational safety of nonlinear processes

This article focuses on the design of distributed model predictive control (DMPC) systems for nonlinear processes with input constraints using a Control Lyapunov-Barrier Function (CLBF) to achieve simultaneous closed-loop stability and process safety. Specifically, we first use a constrained CLBF to design explicit control laws for each subsystem and to characterize a set of initial conditions, starting from which the closed-loop states of the overall nonlinear system are guaranteed to converge to the operating steady-state under the CLBF-based control laws while avoiding unsafe regions in state space. We then propose the CLBF-based DMPC, and prove its feasibility and effectiveness in ensuring the stability and avoidance of unsafe regions under sample-and-hold implementation of DMPC control actions. The CLBF-based DMPC is applied to both sequential and iterative DMPC designs in the general sense, and a modification to the DMPC formulation is presented for special cases of systems where the coupling between subsystems is in a one-way cascading manner. The proposed CLBF-DMPC method is demonstrated via a nonlinear chemical process example consisting of two subsystems.

Distributed Model Predictive Coordinated Control for Combined Heat and Power Load of an Integrated Energy System

Due to the strong coupling and multiple constraints of combined heat and power (CHP) generation in an integrated energy system (IES), the model predictive control (MPC) is widely adopted as the lower layer coordination controller. However, with the upgrade of capacity and the expansion of scale, centralized MPC (CMPC) is no longer capable of dealing with heavy-data, high dimensional IES optimization problem. To address this concern, distributed MPC (DMPC) is applied to coordinate the energy supply of CHP-IES. In view of the characteristics of CHP-IES, DMPC should be endowed with the capability of offset-free tracking and disturbance rejection. Hence, the disturbance augmentation method and the modification of objective function have been applied to facilitate each DMPC controller with the required abilities. Through simulation comparison with CMPC on the same theoretical model, the performance of modified cooperative DMPC (CDMPC) is on par with CMPC, while the computational burden is drastically relieved.

Distributed model predictive control based on neighborhood optimization for thickness and tension control system in tandem cold rolling mill

The control precision of thickness and tension is a crucial indicator for evaluating a tandem cold rolling control system. However, the control mode for field application cannot meet the actual quality requirements. Therefore, a distributed model predictive control (DMPC) strategy combined with neighborhood optimization is proposed to decrease the strip thickness deviation and tension change in this paper. First, a cold rolling model describing the relationship among the process parameters is established for the multi-stand cold rolling system. Then, according to the neighborhood optimization theory, the state evolution equation of the output system on each stand is derived. Furthermore, through proper consideration of the input and state information during optimization, optimal control variables are obtained using the proposed performance index to improve the system performance. A series of simulations were carried out with actual rolling data to analyze and validate the capability of the designed control system. The statistical data show that as roll speed disturbance occurs, the thickness and tension deviations can be controlled within respective ranges of 6 × 10 −5mm and 0.012 kN with the DMPC control strategy. In addition, each scan cycle calculation only takes 0.0085 s in such a strategy. Compared with the conventional control method, the thickness and tension DMPC control system provides excellent performance and can effectively enhance the strip product quality.

Distributed MPC-Based Secondary Control for Energy Storage Systems in a DC Microgrid

In this paper, a novel distributed model predictive control (DMPC) strategy based on voltage observer for multiple energy storage systems (ESs) is firstly proposed to achieve a tradeoff between voltage regulation and power sharing. In order to reduce the impact of communication delay on voltage observer, an improved DMPC consensus algorithm is proposed. This scheme improves the robustness of the system to the delay. Besides, a small-signal dynamic model of a DC microgrid with the improved DMPC controllers is established to analyze its dynamic performance. The time-domain simulation results are presented to verify that, under the constraints of the DC bus voltage, a flexible trade-off between voltage regulation and power distribution can be achieved. Besides, the communication delay problems can be reduced.

Resilient distributed MPC for systems under synchronous round-robin scheduling

This paper is concerned with the resilient dynamic output-feedback (DOF) distributed model predictive control (DMPC) problem for discrete-time polytopic uncertain systems under synchronous Round-Robin (RR) scheduling. In order to alleviate the computation burden and improve the system robustness against uncertainties, the global system is decomposed into several subsystems, where each subsystem under synchronous RR scheduling communicates with each other via a network. The RR scheduling is adopted to avoid data collisions, however the updating information at each time instant is unfortunately reduced, and the underlying RR scheduling of subsystems are deeply coupled. The main purpose of this paper is to design a set of resilient DOF-based DMPC controllers for systems under the consideration of polytopic uncertainties and synchronous RR scheduling, such that the desirable performance can be obtained at a low cost of computational time. A novel distributed performance index dependent of the synchronous RR scheduling is constructed, where the last iteration information from the neighbor subsystems is used to deal with various couplings. Then, by resorting to the distributed RR-dependent Lyapunov-like approach and inequality analysis technique, a certain upper bound of the objective is put forward to establish a solvable auxiliary optimization problem (AOP). Moreover, by using the Jacobi iteration algorithm to solve such a problem online, the distributed feedback gains are directly obtained to guarantee the convergence of system states. Finally, two examples including a distillation process example and a numerical example are employed to show the effectiveness of the proposed resilient DMPC strategy.

A comparative look at two formation control approaches based on optimization and algebraic graph theory

This paper takes a novel look at formation control by comparing control setups based on two very different frameworks. These are applied to the distributed control of communicating omnidirectional mobile robots. One framework, which is possibly the most common approach to formation control, is based on algebraic graph theory, whereas the other, namely distributed model predictive control (DMPC), is based on distributed optimization, representing a rather uncommon view on the task. In this study, formation control is understood as the task of attaining and maintaining a specific relative positioning between robotic agents while moving the formation through the environment. While interesting on its own, formation control can serve as the basis for superordinate tasks like cooperative transportation. For an encompassing treatment of the task, two different control goals are considered, resulting in different setups for each control framework. One goal consists of moving the formation’s geometric center to a specific position, whereas the other aims at letting the whole formation move with the desired velocity. In both cases, the involved robots are subject to input constraints. Already during control design, some qualitative differences between the two frameworks become apparent, with the DMPC controller exhibiting characteristic beneficial qualities in exchange for its higher computational demand. Results from various simulation scenarios confirm these observations. Considerations on the practical implementation of the two schemes, as well as hardware experiments with tailor-made mobile robots, provide valuable insight for robotics practitioners, and highlight the applicability of the two frameworks.

Distributed model predictive control of multi-vehicle systems with switching communication topologies

Vehicle-to-vehicle (V2V) communication-enabled cooperation of multiple connected vehicles improves the safety and efficiency of our transportation systems. However, the joining and leaving of vehicles and unreliability of wireless communication channels will cause the switching of communication topology among vehicles, thus affecting the performance of multi-vehicle systems. To address this issue, a distributed model predictive control (DMPC) method is proposed for multi-vehicle system control under switching communication topologies. First, an open-loop optimization problem is formulated, within which neighbor-deviation and self-deviation penalties and constraints are incorporated to ensure stability. Then, a DMPC algorithm is designed for multi-vehicle systems subject to switching communication topologies. For the closed-loop system, the convergence of predicted terminal states is proved based on the neighbor-deviation constraint. After that, closed-loop system stability is analysed based on a common Lyapunov function (CLF) defined using a joint neighbor set. It is proved that asymptotic stability of the closed-loop system can be achieved through a sufficient condition on the weight matrices of the open-loop optimization problem. Numerical simulations are conducted to demonstrate the effectiveness of the proposed DMPC controller.

Distributed model predictive control of positive Markov jump systems

This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design.

A linear framework on the distributed model predictive control of positive systems

This paper investigates the distributed model predictive control (DMPC) for positive systems with interval and polytopic uncertainties, respectively. Different from the traditional quadratic DMPC, a new linear DMPC framework is established for positive systems. First, a linear cooperative cost function (performance index function) is introduced for the DMPC of positive systems. Accordingly, some linear constraint conditions are imposed on the systems. Then, a linear co-positive Lyapunov function is constructed. Using the linear Lyapunov function, the DMPC controllers are designed for interval positive systems and polytopic positive systems, respectively. The controller of each subsystem contains not only the state information of the subsystem but also the state information of other correlated subsystems. Linear programming based optimization algorithm is addressed to compute the controller parameters. To guarantee the feasibility and stability of the systems, a cone invariant set is proposed. Finally, two case studies are provided to illustrate the effectiveness of the theoretical findings.

Sequential and Iterative Distributed Model Predictive Control of Multi-Motor Driving Cutterhead System for TBM

In this paper, we investigate the robust control of multi-motor driving cutterhead system for tunnel boring machines (TBMs) with distributed model predictive control (MPC). By analyzing the working procedures of the induction motor, coupling, reduction gear box, and spur gear, a dynamical model of cutterhead system is established. The model is then represented into a state-space model with additional loads. A sequential and iterative distributed MPC algorithm is established for optimizing the input torques for the driving motors. To design the distributed MPC, the whole system is decomposed into several subsystems according to the distribution of input torques. The future system outputs are predicted by using the system model and the distributed MPC optimizes the input sequence at each time instant in a recursive fashion. The model errors are corrected by comparing the actual outputs and predicted outputs. A sequential and iterative algorithm is proposed to coordinate the distributed MPC controllers. Finally, simulations are carried out to validate the distributed MPC algorithm on torque optimization of cutterhead system in TBMs.

Constrained Optimization and Distributed Model Predictive Control-Based Merging Strategies for Adjacent Connected Autonomous Vehicle Platoons

Vehicle platooning has been a major research topic in recent years because of its ability to reduce fuel consumption, enhance road traffic safety and utilize the road more efficiently. A practical and applicable platoon merging maneuver is the key to forming new platoons while ensuring safety and economy. This study proposes merging strategies that consider both safe space and acceleration limitations for two adjacent platoons comprising connected autonomous vehicles (CAVs). The distributed model predictive control (DMPC) algorithm is adopted to design a DMPC 2 controller, which includes 1) a space-making DMPC controller that controls the vehicles in one platoon, i.e. the target platoon, to make space for the vehicles in a second platoon, i.e. the merge platoon, and 2) a DMPC platoon controller that controls the merging vehicles to fill in the space in the target platoon. The former considers the explicit acceleration constraint of the vehicle, making the generated trajectory more feasible, and the latter controls the merge platoon to perform an overall mergence, which reduces the complexity of the merge problem. The low computation load of DMPC makes online computing and real-time control possible in practical scenarios. A simulation study is conducted with different scenarios and parameters, and the results demonstrate that the proposed strategy is more feasible and efficient, and less time-consuming than the existing state-of-the-art methods and have the advantages of taking safety distance and control input constraints into account.

A distributed approach to model-predictive control of radiant comfort delivery systems in office spaces with localized thermal environments

This paper introduces a new multi-agent system approach to optimal control of high performance buildings and presents algorithms for both distributed system identification and distributed model predictive control (DMPC). For the system identification, each thermal zone is divided into sub-systems, and a parameter set for each sub-system is first estimated individually, and then integrated into an inverse model for the whole thermal zone using the dual decomposition algorithm. For the DMPC, a distributed optimization algorithm inspired by the Proximal Jacobian Alternating Direction Method of Multipliers (PJ-ADMM) is deployed and multiple MPCs run iteratively while exchanging control input information until they converge. The developed algorithms are tested using field data from an occupied open-plan office space with a radiant floor system with distributed sensing, control, and data communication capabilities for localized comfort delivery. With this tractable approach, agents solve individual optimization problems in parallel, through information exchange and broadcasting, with a smaller scale of the input and constraints, facilitating optimal solutions with improved efficiency that are scalable to different building applications. Using a data-driven model and weather forecast, the DMPC controller is implemented to optimize the operation of an air-cooled chiller while providing different operative temperature bounds for each radiant floor loop. The radiant comfort delivery system with predictive control is capable of providing localized thermal environments while achieving significant energy savings. For the system and climate under consideration, results from the building operation during the cooling season, show 27% reduction in electricity consumption compared to baseline feedback control.

Distributed Model Predictive Control and Implementation for Vehicle Active Suspensions

This paper proposes a distributed model predictive control (DMPC) method for a half-vehicle system with active suspensions. First, the half-vehicle system is divided into three subsystems to reduce the system dimension. Considering the distribution characteristics of suspension control systems, a DMPC controller is designed for each suspension subsystem in order to inhibit the vehicle vertical and pitch motion. To evaluate the proposed control system, controllers with low cost micro-control units (MCU) are implemented, where a fast MPC method for real-time optimization based on continuation/general minimum residual (C/GMRES) method is realized and in-vehicle network FlexRay is used to exchange control information among these controllers. Finally, the implementation of DMPC controllers in MCUs is finished and the results show that vehicle comfortability can be improved by the proposed controllers.

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

ABSTRACTIn this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

Distributed model predictive control with saturated inputs by a saturation‐dependent Lyapunov function

SummaryIn this paper, distributed model predictive control (MPC) problems are considered for input‐saturated polytopic uncertain systems by a saturation‐dependent Lyapunov function approach. The actuator saturation is processed by the transformation into the linear convex combination form. By the decomposition of the control input, distributed MPC controllers are designed in parallel for each subsystems. The Lyapunov Function we select is saturation dependent, which is less conservative than the general Lyapunov Function approach. An invariant set condition is provided and min–max distributed MPC is proposed based on the invariant set. The robust distributed MPC controllers are determined by solving a linear matrix inequality (LMI) optimization problem. To reduce the conservatism, we present a robust distributed MPC algorithm, which is not only saturation dependent but also parameter dependent. A Jacobi iterative algorithm is developed to coordinate the distributed MPC controllers. A simulation example with multi‐subsystem is carried out to demonstrate the effectiveness of the proposed distributed MPC algorithms. Copyright © 2016 John Wiley & Sons, Ltd.

Optimal active power control of a wind farm equipped with energy storage system based on distributed model predictive control

This study presents the distributed model predictive control (D-MPC) of a wind farm equipped with fast and short-term energy storage system (ESS) for optimal active power control using the fast gradient method via dual decomposition. The primary objective of the D-MPC control of the wind farm is power reference tracking from system operators. Besides, by optimal distribution of the power references to individual wind turbines (WTs) and the ESS unit, the WT mechanical loads are alleviated. With the fast gradient method, the convergence rate of the D-MPC is significantly improved which leads to a reduction of the iteration number. Accordingly, the communication burden is reduced. Case studies demonstrate that the additional ESS unit can lead to a larger WT load reduction, compared with the conventional wind farm control without ESS. Moreover, the efficiency of the developed D-MPC algorithm is independent from the wind farm size and is suitable for the real-time control of the wind farm with ESS.