This paper proposes a resilient output feedback tube-based model predictive control (MPC) approach for constrained cyber-physical systems (CPSs) to handle the impact of stochastic hybrid attacks, where the hybrid attacks include false data injection (FDI) attacks and denial-of-service (DoS) attacks that occur in the sensor-controller (S-C) and controller-actuator (C-A) channels, respectively. The anomalous behavior of the attacker is revealed by the designed attack detector and comparator, which provide alert signals that guide the primary and auxiliary controllers to collaboratively generate control inputs as well as a nominal trajectory. The tolerable attack duration is determined by using the concept of$\mu $-step robust positive invariant ($\mu $-RPI) set, which limits the size of the deviation between the observer and the nominal trajectory under the hybrid attacks. Robust constraint satisfaction and robust asymptotic stability are ensured by restricting the state of the system to a tube centered on a nominal trajectory that converges gradually to the origin, and theoretical guarantees are provided. Finally, the effectiveness of the designed algorithm is validated through a supply chain model, which includes comparisons with an inelastic scheme.

This article addresses the challenge of amplitude-unbounded false data injection (FDI) attacks targeting the sensor-to-controller (S–C) channel in cyber-physical systems (CPSs). We introduce a resilient tube-based model predictive control (MPC) scheme. This scheme incorporates a threshold-based attack detector and a control sequence buffer to enhance system security. We mathematically model the common FDI attacks and derive the maximum duration of such attacks based on the hypothesis testing principle. Following this, the minimum feasible sequence length of the control sequence buffer is obtained. The system is proven to remain input-to-state stability (ISS) under bounded external disturbances and amplitude-unbounded FDI attacks. Moreover, the feasible region under this scenario is provided in this article. Finally, the proposed algorithm is validated by numerical simulations and shows superior control performance compared to the existing methods.

Leveraging cloud computing for solving nonlinear Model Predictive Control (NMPC) can address issues with slow computational efficiency and effectively handle the complexity of large-scale complex systems (LSS), characterized by numerous variables, nonlinearities, and constraints. However, current studies often overlook critical aspects such as reliability, feasibility, stability, and resource efficiency in cloud-based NMPC, potentially limiting its application in LSS. To address these challenges, this paper explores a cloud-edge cooperative MPC architecture with an event-triggered strategy. The proposed architecture comprises high-fidelity Cloud NMPC, tube-based Edge LMPC, and a Switch Module with an event-triggered strategy, seamlessly combining abundant cloud computing resources with reliable edge computing. In case of Cloud NMPC failure, the tube-based LMPC at the edge layer promptly takes over control, ensuring both the reliability of Cloud NMPC and recursive feasibility under arbitrary switching sequences. By leveraging Lyapunov functions, the minimum stability modedependent dwell time (MDT) is pre-determined offline to guarantee exponential asymptotic stability. To strike a balance between control performance and resource efficiency, an eventtriggered strategy for Cloud NMPC is devised to prevent wastage of resources due to unnecessary communication and computation. Simulations on plug-in hybrid electric vehicles (PHEVs) validate the effectiveness of the theoretical results. The superiority of the proposed scheme is underscored through a comparison with four other MPC schemes.

With the rapid advancement of autonomous driving technology, the increasing computational demands of intelligent vehicles have driven the adoption of cloud and edge computing to augment limited onboard resources. However, this cloud–edge integration presents new challenges for efficient task offloading. In addition, the high mobility of vehicles further complicates the design of reliable offloading strategies. To address these challenges, this paper proposes a Cloud-Edge-Vehicle (CEV) framework that leverages predictable vehicle trajectories for optimized task offloading. A spatio-temporal multi-head self-attention long short-term memory (ST-MHSA LSTM) model is designed to accurately predict vehicle trajectories by capturing motion trends and interactions with neighboring vehicles. Building upon the trajectory prediction information, a deep reinforcement learning (DRL)-based task offloading algorithm is proposed. This algorithm incorporates a dynamic priority assignment strategy to prioritize delay-sensitive tasks according to their urgency, thereby improving offloading performance and reducing system costs associated with task transmission and execution. To mitigate the adverse effects of inevitable trajectory prediction errors, a prediction consistency-based deviation correction strategy is further introduced, enhancing decision robustness in dynamic scenarios. Simulation results show that as task numbers increase, the proposed framework outperforms traditional methods (i.e., local, edge, cloud, and random computing) in task success ratio, processing delay, and energy consumption. Task success ratio improves by 115.79%, 114.44%, 27.09%, and 135.19% over local, edge, cloud, and random computing, respectively. Average processing delay is reduced by 70.47%, 62.23%, 38.69%, and 79.85%, while average energy consumption decreases by 65.33%, 66.59%, 59.12%, and 74.66%. These results highlight the framework’s superior performance for computation-intensive and delay-sensitive vehicular applications.

This paper investigates a distributed model predictive control (DMPC) for linear heterogeneous systems tracking arbitrary periodic references. The control objective consists of two parts: (i) driving the output of each subsystem consensus; (ii) steering the outputs as close as possible to an exogenous periodic reference. The artificial state reference and control input are considered as decision variables to track unreachable references. The optimal control problem (OCP) is then solved in a distributed manner using Alternating Direction Multiplier Method (ADMM). The proposed method does not need ADMM convergence at each time step, which greatly reduces the computation time. Under several mild assumptions, the feasibility of the OCP and the closed-loop asymptotic stability with respect to an optimal reachable cooperative trajectory are presented. The performance of the approach is demonstrated with some simulation results.Note to Practitioners—The paper is motivated by the problem of cooperative tracking unreachable references for heterogeneous systems. The generation of the reference signal often ignores the dynamics feature of systems, leading to such reference may not be fully tracked (unreachable reference). However, existing methods either lack optimality or cannot achieve cooperative tracking of unreachable references. Therefore, this study develops a novel DMPC approach to make up for the above lack. In addition, the proposed method greatly reduces the computation time while ensuring optimality, and has a wider initial feasibility. The proposed controller can be extended to cooperative track unreachable constant signal. The proposed method can be used for highly collaborative tasks, such as formation missions, collaborative transportation and spacecraft collaboration. In future research, we will address the problem of cooperative tracking unreachable references for nonlinear heterogeneous systems.

This paper addresses the challenges of energy consumption, driving safety, and robustness in tracking control for autonomous vehicles under stochastic disturbances by proposing a robust economic model predictive control (REMPC) algorithm without terminal constraints. The disturbances considered include high-probability small disturbances as well as low-probability large disturbances in tracking control. A tightening constraint is introduced to ensure robustness against small disturbances, leveraging constraint tightening theory. Additionally, a maximum probability interval is derived to account for the large disturbances that the vehicle can withstand. To further enhance driving safety and energy efficiency, a variable space constraint is adaptively designed based on road slope information. The paper demonstrates recursive feasibility and robust asymptotic performance of the optimization problem with variable space constraints. Robust asymptotic stability in probability of the system is ensured by deriving a probability condition and a lower bound on the prediction horizon, with an exhaustive principle for selecting the prediction horizon. The efficiency and superiority of the proposed REMPC algorithm are verified by a comprehensive case study under various operating conditions.

Nonlinear model predictive control (NMPC) is a promising approach for controlling large-scale complex systems (LSS) that exhibit nonlinearity and constraints. However, its computational and real-time limitations hinder its widespread adoption. To address this challenge, we propose a cloud-edge cooperative model predictive control (MPC) scheme that overcomes these limitations while ensuring the desired control performance. Specifically, our proposed approach involves designing a cloud-based NMPC with a high-fidelity nonlinear model for the cloud layer. Meanwhile, the edge layer is equipped with a simplified backup linear model predictive control (LMPC) that uses a linearized model based on constraint tightening to mitigate model mismatch errors. Additionally, we develop an automatic strategy that employs a sliding weighted average method to switch between the cloud and edge controllers, enhancing the system’s reliability under non-ideal networking conditions. We provide a thorough analysis of the recursive feasibility and asymptotic average performance of the control scheme with different prediction models in the cloud and edge layers. To validate our approach, we apply it to a charging system for plug-in hybrid electric vehicles (PHEVs). Furthermore, we compare the performance and computation efficiency of our proposed cloud-edge cooperative MPC scheme with four other MPC schemes.Note to Practitioners—This work aims to overcome the challenge of reducing the computational burden and increasing the applicability of nonlinear model predictive control (NMPC) in large-scale complex systems (LSS) with input nonlinearity. To address these issues, we propose a cloud-edge cooperative MPC scheme that involves deploying the cloud layer on a remote cloud server and the edge layer locally onboard the system. The proposed scheme not only provides a practical solution for LSS with input nonlinearity but is also applicable to general nonlinear systems. Further research will focus on exploring the relevant theory and practical aspects of the scheme.

This paper proposes a resilient model predictive control (MPC) strategy for constrained cyber-physical systems (CPSs) subject to disturbances and cyber attacks. The feedback sensor-controller (S-C) channel suffers from replay attack and the forward controller-actuator (C-A) channel suffers from false data injection (FDI) attack, and the defender has no prior information about the intruder. Considering that the abnormal behavior of intruder cannot be predicted, an expected one-step controllable set, and a series of minimally conservative constraints are developed to build attack detector. Two controllers are designed jointly based on infinite-horizon MPC to mitigate the negative effects caused by attack. Compared with the existing resilient control strategies, the attack model considered in this paper is less conservative, the resilient control structure is simpler, and it can avoid continuous channel refreshing caused by close-range attack. Robust constraint satisfaction, recursive feasibility and uniformly ultimate boundedness (UUB) are ensured for any admissible attack scenario and disturbance realization. Finally, simulations on a supply chain model show the efficacy of the algorithm.Note to Practitioners—With the wide application of wireless networks, vulnerabilities in the communication process can be easily exploited by intruders to launch malicious attacks. Resilient control can provide acceptable robustness and improve system safety. Additionally, many practical systems are constrained and disturbed, and MPC is one of the most effective methods for dealing with control problems in such systems. Its rolling optimization characteristics make it robust to disturbances. On the one hand, both the C-A channel and the S-C channel of the networked control system are vulnerable to attack. On the other hand, in a complex environment, the defender may not have prior information about the attacker, such as attack probability. Therefore, it is not practical to assume that only a single channel is attacked or that the algorithm relies on the attacker’s prior information. In this paper, a resilient MPC control structure is proposed to counter two types of attacks: replay attack and false data injection attack. One of its characteristics is that the attack model’s conservativeness is relatively low, and the structure is relatively simple, making the algorithm more applicable to actual needs. Another feature of the proposed approach is that it can be adapted directly to different types of attacks without modifying the overall resilient MPC architecture.

Inner convex approximation is a compelling method that enables the real-time implementation of suboptimal nonlinear model predictive controls (MPCs). However, it suffers from a slow convergence rate, which prevents suboptimal MPC from achieving better performance within a specific sample time. To address this issue, we first reformulate the conventional inner convex approximation procedure as a root-finding problem for a nonlinear equation. Then, under mild assumptions, a comprehensive functional analysis is performed on the derived nonlinear equation, focusing on its continuity, differentiability, and the invertibility of the Jacobian matrix. Building on this analysis, we propose an improved algorithm that applies Broyden's method to accelerate the root-finding procedure of this derived nonlinear equation, thereby enhancing the convergence rate of the conventional inner convex approximation method. We also provide a detailed analysis of the proposed algorithm's convergence properties and computational complexity, showing that it achieves a locally superlinear convergence rate without devoting much additional computational effort. Simulation experiments are performed in an obstacle avoidance scenario, and the results are compared to the conventional inner convex approximation method to assess the effectiveness and advantages of the proposed approach.

This article proposes a resilient distributed model predictive control (DMPC) algorithm for a class of constrained dynamically coupled multiple cyber-physical systems (CPSs) subject to bounded additive disturbances. The algorithm is designed to address severe attacks on the forward controller-actuator (C-A) channel, the feedback sensor-controller (S-C) channel, and the channels between subsystems, without any prior information about the intruder available to the defender. To mitigate the negative effects of intruders, we consider a one-step time delay strategy in the local model predictive controller design. This strategy allows the generated controller data to be checked for acceptability before use. To ensure constraint satisfaction for an infinite-horizon MPC problem while accounting for the unknown duration of attacks, we develop a set of minimally conservative constraints in the open-loop control mode using a constraint tightening technique. Moreover, we obtain an equivalent finite number of constraints for the infinite-horizon problem to ensure recursive feasibility. To prevent tampered data from affecting control performance, a detector module is designed to decide whether data is used by its receiver. It is shown that the closed-loop system is uniformly ultimate boundedness (UUB) under any admissible attack scenario and disturbance realization. Finally, the effectiveness of the proposed algorithm is validated by a case study.

This paper presents a hierarchical economic model predictive control (EMPC) framework for electric vehicles (EVs) to address traffic congestion, energy consumption, and driving safety in tracking control. The framework comprises a higher-level planner and a lower-level controller that act in tandem to achieve driving safety and economic efficiency while ensuring control performance. The higher-level planner employs an event-triggered logic by taking traffic density and economic consumption into account. The resulting optimization problem is only solved to update the reference control input of lower-level controller when the traffic density violates a pre-specified threshold. The lower-level controller ensures driving safety and control performance of EVs by designing adaptive inter-vehicle distance constraints. In addition, the robustness of the EMPC framework is ensured by adopting a robust constraint tightening policy. Recursive feasibility analyses of the optimization problems in both levels of the framework are also conducted. Rigorous proofs of asymptotic average performance and stability analysis are guaranteed for the closed-loop system. The proposed hierarchical EMPC algorithm is demonstrated to be effective and superior in a case study.

This paper addresses the longitudinal control problem of an on-ramp vehicle merging into a platoon on the main road. To tackle this challenge, a finite-time model predictive control (MPC) algorithm with a specialized feedback control law is proposed. A constraint set of the state error is designed and based on this, a decision-making scheme is established to allow the on-ramp vehicle to assess the feasibility of the merging operation at the beginning under the designed MPC strategy. If the merging is feasible, the proposed MPC strategy will be applied to drive the on-ramp vehicle towards a small neighborhood around the desired state on the basis of platoon’s velocity and position within a finite time step before joining the platoon. Furthermore, asymptotic convergence towards the desired state is achieved by a co-designed feedback control law. Otherwise, the MPC strategy will not be triggered, instead an alternative method such as slowing down the on-ramp vehicle to create space and allow the vehicles on the main road to proceed ahead. Under the proposed method, the recursive feasibility of the MPC optimization problem is achieved at all time steps and the finite time convergence to the small neighborhood of the desired state can be proved under the MPC algorithm. An upper bound on the convergence time step is also derived, which is used to prove the effectiveness of the decision-making mechanism. In addition, the closed-loop constraints satisfaction and asymptotic stability of the on-ramp vehicle are also guaranteed. The effectiveness of the proposed MPC method is demonstrated through simulation examples.

This article introduces a resilient model predictive control (MPC) approach for constrained cyber-physical systems (CPSs) in the presence of bounded disturbances and denial-of-service (DoS) attacks. An attacker aims to disrupt the communication channel between the controller and actuator (C-A) by deploying adversarial jamming signals. A resilient MPC algorithm is designed, where switching between different cost functions is considered and the control input sequences optimized are used to compensate for information loss caused by DoS attacks. We demonstrate that under certain conditions on the duration of DoS attacks and system parameters, the closed-loop system can be guaranteed to be uniformly ultimately bounded (UUB) in the attack scenario. Moreover, in the nonattack scenario, it exhibits robust asymptotic stability. By properly setting tightened constraints and cost functions, the recursive feasibility of the optimization problem can be ensured for any admissible attack scenario and disturbances realization. The maximum duration of DoS attacks that can be tolerated in the C-A channel is derived by feasibility analysis. Finally, the effectiveness of the designed algorithm is validated through a simulation example, which includes comparisons with two other algorithms.

Data-driven predictive control (DPC) has been studied and applied in various scenarios. However, the challenge of computational efficiency remains. With the development of cloud computing, it provides potential solutions to the computational problem. Hence, this paper proposes a workflow-based fast DPC method in cloud-edge collaborative architecture. First, a workflow construction method of DPC is designed to make full use of the distributed computing ability of cloud computing. Next, to tackle the uncertainty in the cloud workflow processing, we design a cloud-edge collaborative scheme. In this scheme, a edge data-driven disturbance observer is proposed to estimate and compensate the uncertain event with guaranteed UUB stability. Then, An autonomous cloud control experimental system based on container technology is designed and implemented to execute the workflow-based DPC controller. Evaluations demonstrate that computation times are reduced by 45.19$\%$and 74.35$\%$for two real-time control examples, and by a maximum of 85.10$\%$for a high-dimensional control example.Note to Practitioners—This work is motivated by the challenge of the further combination of cloud computing and control system such as DPC. In the existing cloud-based control system, the computation mission of native control algorithm is deployed in a single cloud server directly. However, the structure of cloud environment is distributed, and the existing computation mode could not make full use of the parallel computing of cloud computing. Thus, the computation time could not be reduced significantly, and would still have serious effects on the control quality. In this work, a novel workflow-based DPC system in cloud-edge collaborative architecture is proposed, which decompose the native control mission into distributed cloud workflow with multiple smaller computation tasks. Then, an edge disturbance observer is designed to compensate the uncertainty occurring in the cloud workflow processing. As the evaluations show, the proposed workflow-based control system in cloud-edge collaborative architecture could be applied in the control mission with real-time requirement and the high-dimension control mission with intensive data.

Heavy computational load for solving nonconvex problems for large-scale systems or systems with real-time demands at each sample step has been recognized as one of the reasons for preventing a wider application of nonlinear model predictive control (NMPC). To improve the real-time feasibility of NMPC with input nonlinearity, we devise an innovative scheme called cloud-based computational model predictive control (MPC) by using an elaborately designed parallel multiblock alternating direction method of multipliers (ADMMs) algorithm. This novel parallel multiblock ADMM algorithm is tailored to tackle the computational issue of solving a nonconvex problem with nonlinear constraints. It is ensured that the designed algorithm converges to a locally optimal solution of the optimization problem under reasonable assumptions by using the Kurdyka–Łojasiewicz property. With the help of this distributed optimization algorithm, a computational MPC scheme is developed, which can transform the NMPC optimization problem into a set of subproblems only associated with the decision variables at one prediction step. Through the parallel computing algorithm, the computational MPC can deal with large computational loads caused by high-dimensional optimization problems, and improve computational efficiency. Furthermore, to allow for a more efficient implementation of the developed computational MPC and alleviate local calculation loads, a cloud-based computational MPC architecture is devised, which makes significantly better use of computational resources provided by a cloud server. An important advantage of this architecture with Docker container to implement parallelization is that it does not lead to large increases in the solution time regardless of how long the prediction horizon is set. Finally, the developed cloud-based computational MPC architecture is trialed on a group of plug-in hybrid electric vehicles (PHEVs).

This paper presents a distributed stochastic economic model predictive control (DSEMPC) algorithm for network interconnected systems with dynamic couplings and economic considerations. Each individual subsystem is subject to stochastic disturbances and state chance constraints. Unlike many existing methods, the proposed approach relies only on the expectation information of the disturbance and real-time estimated covariance. To transform chance constraints into the deterministic form, the Cantelli and Hoeffding inequalities are employed. Moreover, a novel robust adaptive tightened term for constraints is designed based on neighbors’ reference nominal states and the estimated time-varying covariance for each subsystem. This term reduces conservativeness and decouples the dynamics, reformulating the chance constraints and ensuring recursive feasibility. The distributed control algorithm is also aimed at optimizing the economic performance whose cost function is not necessarily positive definite or quadratic in the presence of stochastic disturbance. The input-to-state stability in probability (ISSiP) of each subsystem is guaranteed through a tailored Lyapunov function in expectation form. The paper closes with a simulation of data center temperature control, highlighting the proposed results’ effectiveness and the advantage of economic performance optimization.

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.

This article develops a distributed economic model predictive control (EMPC) method which is applied in a group of interconnected linear subsystems subject to unknown bounded disturbances. Multiple subsystems are coupled through the dynamics, and the control objective is to optimize some general performance criteria of the whole system which may take economic considerations into account. First, a two operation modes EMPC optimization problem is formulated, which incorporates the constraints derived from the Lyapunov technique. In the first mode, each subsystem focuses on the optimization of the economic performance while maintaining the state in a certain region. In the second mode, the system states are steered to a neighborhood of a steady state by making use of the Lyapunov-based constraints. Furthermore, a consensus alternating direction method of multipliers (ADMM) is adopted to solve the model predictive control optimization problems with a coupled predicted model constraint in a distributed way. By introducing consensus constraints, the resulting local optimization problem does not depend on real-time optimal solutions from neighboring subsystems and allows subsystems to solve it in parallel. Moreover, the closed-loop system is ensured to be input-to-state stable (ISS) with respect to the disturbances. To demonstrate the effectiveness of the algorithm, we conduct numerical simulations on a thermal power interconnected system.

This article considers the data-driven optimal control problem for unknown linear systems subject to system constraints from a computation efficiency improvement perspective. We propose a novel Computational Data-enabled Predictive Control (CDeePC) algorithm in a cloud environment, built on a recent work DeePC[1]. First, massive input–output data samples are precollected to describe the system input/output behavior through a behavioral systems theory approach, which might result in a large-scale online optimization problem with high dimensional decision variables. To solve it, in CDeePC, a multiblock alternating direction method of multipliers (ADMMs) algorithm is then employed, in which a solution to the original large problem can be calculated by solving iteratively a set of small subproblems. Next, to further improve the robustness of the algorithm, an online feedback CDeePC (OCDeePC) algorithm is proposed by utilizing real-time data samples to better capture the system characterization. Two analytic inversion formulas are derived for fast computation of time-varying controller parameters based on the result at the previous time. After that, we discuss the computational complexity and provide the convergence proof of proposed algorithms. Finally, after designing a cloud-based control architecture and formulating the iterative scheme to compute control actions as a workflow, we construct and deploy the proposed controllers as a service in the cloud. A case study of tracking control of wheeled mobile robots is provided to illustrate the efficacy of the proposed algorithms.

In this article, we propose a novel economic model-predictive control (MPC) algorithm for a group of disturbed linear systems and implement it in a distributed manner. The system consists of multiple subsystems interacting with each other via dynamics and aims to optimize an economic objective. Each subsystem is subject to constraints both on states and inputs as well as unknown but bounded disturbances. First, we divide the computation of control inputs into several local optimization problems based on each subsystem's local information. This is done by introducing compatibility constraints to confine the difference between the actual information and the previously published reference information of each subsystem, which is the key feature of the proposed distributed algorithm. Then, to ensure the satisfaction of both state and input constraints under disturbances, constraints are tightened on the state and the input of nominal systems by considering explicitly the effect of uncertainties. Moreover, based on an overall optimal steady state, a dissipativity constraint and a terminal constraint are designed and incorporated in the local optimization problems to establish recursive feasibility and guarantee stability for the resulting closed-loop system. Finally, the efficiency of the distributed economic MPC algorithm is demonstrated in a building temperature control case study.

For taking out the adjustment process of sparse auto-encoder for broad learning system, Fenget al.proposed fuzzy broad learning system by replacing the feature nodes of broad learning system with Takagi–Sugeno fuzzy systems. In fuzzy broad learning system, artificial parameters selection of ridge regression might result in the decrease in testing accuracy. To overcome this shortcoming of fuzzy broad learning system, this article builds a novel model of fuzzy broad learning system based on accelerating amount by introducing the accelerating amount into fuzzy broad learning system. The theoretical result on the universal approximation property of fuzzy broad learning system based on accelerating amount is presented. Three experiment studies on the regression problems of UCI, fashion MNIST, and medical MNIST datasets are performed to show the improvement in testing accuracy.