This paper addresses the path planning and bipartite formation tracking (BFT) problem for multiple Euler-Lagrange agents (MELAs) subject to actuator faults and input saturation. A fully distributed three-layer framework is proposed. In the decision layer, a safe path-velocity Q-learning (SPV-Q-learning) algorithm is proposed, which ensures the rapid generation of reliable paths by introducing a decay mechanism and safety constraints. In the estimated layer, a time-base generator (TBG)-based observer is introduced to reconstruct the leader’s state using only local interactions, then, all followers acquire the leaders state under the fully distributed estimator. In the local layer, an anti-saturation fault-tolerant law is designed to handle model uncertainties, actuator degradation, and bounded inputs, thereby ensuring high-precision trajectory tracking for all agents. Simulation results demonstrate that the proposed method achieves both efficient path planning and robust BFT performance, significantly improving resilience under actuator faults and input constraints.

Power systems are vulnerable not only to physical faults but also to cyberattacks, which can prevent the communication network from receiving measurement information from bus sensors during such incidents. Therefore, the rapid detection of power line outages (LOs) is crucial for maintaining the stability of the power system in the presence of denial-of-service (DoS) attacks. This paper introduces a real-time multiple LOs (Multi-LOs) detection algorithm based on a novel distributed finite-time observer. Unlike existing observers designed for Multi-LOs detection that depend on secure communication services, the proposed observer can detect Multi-LOs within a finite time, even in the presence of DoS attacks and voltage uncertainties. A comprehensive mathematical analysis establishes the upper bound for the settling time of estimation errors and demonstrates that the proposed distributed observer converges within a finite time during DoS attacks, thereby enabling timely detection of Multi-LOs. Simulation results further validate the effectiveness and robustness of the proposed Multi-LOs detection algorithm.

This paper investigates the robust complete synchronization of coupled Boolean networks (BNs) subject to stuck-at fault. When stuck-at fault occurs, certain nodes become permanently fixed and the original synchronization conditions may no longer be applicable. To address this issue, we propose a new concept of fault-preserving subset to characterize the admissible invariant state evolution induced by stuck-at fault. Based on this concept, necessary and sufficient conditions are derived to determine whether complete synchronization remains valid without reconstructing the faulty network model. Furthermore, for coupled Boolean control networks (BCNs), a robust feedback complete synchronization scheme is developed by designing state feedback controllers based on maximal control fault-preserving subset. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed results.

This paper addresses the distributed execution of signal temporal logic (STL) tasks in second-order open networked robotic systems (ONRSs), where robots can dynamically join or leave during task execution. A novel control framework is developed that integrates a predefined-time state estimator, a distributed control barrier function-based optimization strategy, and a task decomposition and reconstruction mechanism. This approach enables each robot to accomplish temporally and logically constrained tasks using only local information from its neighbors, without relying on global communication. Theoretical analysis rigorously establishes predefined-time convergence of the estimator and optimality of the distributed control strategy, even under dynamic team compositions. Simulation and experimental results validate the proposed method’s effectiveness and robustness in executing complex temporal tasks in realistic multi-robot scenarios.

In this article, we investigate the task optimization for fixed-time control of intermittent human-robot interaction, where a human operator assists the robot intermittently in selecting the most appropriate Pareto solution. First, as for the Lyapunov fixed-time stability criterion inequality with and without the constant term, we all derive the Lyapunov stability conditions with time-varying exponents and coefficients, providing us with more flexibility and freedom to shape the contour of the convergence near the Lyapunov stable equilibrium. We then use them to propose a hierarchical fixed-time event-triggered optimization (HFTEO) algorithm based on human-oriented scheme, where the so-called human-oriented scheme means that the components constituting task information are known only to the human operator, but not to the robot, which is beneficial to ensure the confidentiality and security of the task. Simulation results are given to show the effectiveness of the proposed Lyapunov stability conditions and algorithm.

This article investigates the fast consensus problem in open multiagent systems (OMASs), where agents can randomly join or leave the network. Such dynamic behaviors significantly impact system consensus and its convergence rates. To address these challenges, we analyze both the frequency of agent switching and the duration during which the network remains nonconnected. A consensus condition for OMAS with time-varying network topology is derived, and explicit upper bounds on switching frequency and dwell time are established to guarantee consensus. To further achieve fast consensus, a convergence rate optimization scheme is proposed, along with a distributed implementation based on the alternating direction method of multiplier. Extensive simulations demonstrate the effectiveness and superiority of the proposed control strategy compared to existing OMAS consensus approaches.

This article investigates the deception-eliminating design (DED) against false information attacks by deceptive agents in asynchronous optimal consensus control. We model the asynchronous interactions among agents as multistage games and establish a Tit-for-Tat rule to compel deceptive agents to turn to transmitting true state information. Furthermore, we design a false information counterattack rule under asynchronous updates by leveraging the invariance of the rank of equivalent matrices and the convexity of positive semidefinite quadratic forms. This design effectively intimidates deceptive agents that have transitioned to cooperation, ensuring they do not revert to transmitting false information. Subsequently, by utilizing the properties of Riccati differential equations, the integrating factor methods, the Minkowski inequality, and proof by contradiction, we theoretically analyze the impact of false information on consensus and provide an explicit upper bound for the strategy update periods of agents with different performance matrices. Theoretical proof shows that as long as the strategy update periods of all agents remain below this upper bound and the above two DEDs are implemented, the asynchronous consensus is guaranteed.

Formation control based on path planning is an important and critical research topic in robotics, which focuses on generating collision-free paths for multiagent systems (MASs) from an initial position to a target position while maintaining the desired formation. This article realizes adaptive path planning and formation control for MASs with the presence of lumped uncertainties and saturation input. To achieve this goal, a hierarchical adaptive formation planning and control (HAFPC) framework, including a formation path planning layer and an adaptive formation control layer, is constructed. In the formation path planning layer, the signed-distance-field-based formation path planning (SDF-FPP) algorithm is proposed to find a collision-free continuous trajectory in an unknown environment from the initial position to the target position. Based on this collision-free trajectory, a nonanalytic function that evaluates the shortest distance between this collision-free trajectory and obstacles is computed via the signed distance field (SDF) method. Then, this nonanalytic function will be further processed in the next layer for obstacle avoidance of all agents. In the adaptive formation control layer, the proposed adaptive-offset formation control (AOFC) algorithm converts the nonanalytic function into the adaptive offset functions for all agents and manipulates MASs to achieve adaptive formation control for obstacle avoidance with the presence of lumped uncertainties as well as saturation input. Simulations are presented to validate the proposed architecture.

Targeting to improve the time synchronization accuracy of multi-hop Time-Sensitive Wireless Sensor Networks (TS-WSNs) for mission-critical industrial automation applications, a Minimum Variance Time Synchronization (MVTS) algorithm utilizing the concept of Packet-Coupled Oscillators (PkCOs) is proposed. This MVTS algorithm utlizes an output feedback approach to mitigate the impact of communication noise on the accumulation of synchronization errors. In addition, a Time-Division Multiple Access (TDMA) packet-exchange superframe is introduced to achieve efficient and low-overhead time synchronization. The optimal gain matrix of the MVTS algorithm is obtained by the Linear Matrix Inequality (LMI) optimization with theoretic analysis. The proposed MVTS algorithm is evaluated by both simulation and experiments on an IEEE 802.15.4 hardware testbed. The experimental results show that the proposed algorithm can effectively reduce the growth rate of clock offset along multi-hop nodes and improve the time synchronization accuracy of the TS-WSNs. Note to Practitioners—This paper explores a method to achieve precise time synchronization in TS-WSNs. The primary challenge being addressed is the accumulation of synchronization errors that occur in multi-hop TS-WSNs, which can compromise the accuracy of time synchronization. To mitigate this challenge while taking communication overhead into account, we propose a solution that combines a TDMA-based packet-exchange superframe structure with the MVTS algorithm. This approach introduces an output feedback consensus control scheme to minimize synchronization error variance. The optimal gain matrix for this consensus control scheme is derived through LMI optimization. The algorithm is implemented on an IEEE 802.15.4-compatable wireless node SAM R21 by Microchip and the experimental results of a 10-hop netowrk shows that the maximum synchronization error is$8.32\mu s$, reduced by 56% and 32%, repsectivly, compared to the baseline method FTSP and the recent PISync.

This paper presents the hierarchical Q-learning path planning (HQPP) architecture for solving the cooperative tracking control problem of multi-agent systems (MASs) with lumped uncertainties in an unknown environment. The presented architecture consists of three layers, namely, the decision layer, the distributed estimated layer, and the local control layer. Specifically, in the decision layer, we propose the dynamic parameter and trajectory fitting Q-learning (DPTF-Q-learning) algorithm to find a feasible continuous trajectory to the target in an unknown environment. In addition, two dynamic parameters are proposed and introduced into the DPTF-Q-learning algorithm to shorten the required minimum number of steps in the training process. Then, the distributed estimated layer is designed to broadcast the continuous trajectory generated from the decision layer based on the directed communication topology containing a spanning tree. In the local control layer, the cooperative tracking control (CTC) algorithm is proposed to achieve cooperative tracking for MASs in the presence of uncertain dynamics and external disturbances. The sufficient conditions for achieving cooperative tracking control are rigorously derived by employing Lyapunov argument. Finally, numerical simulations are presented to verify the effectiveness of the proposed architecture.Note to Practitioners—This paper is motivated by the need of developing an integrated path planning and control method for cooperative tracking of multi-agent systems in a no-signal environment and without the presence of users. Most related works are limited to separate fields: 1) most existing path planning techniques are only applicable to a single agent and discrete environments, and 2) most existing cooperative tracking algorithms focus on guaranteeing control stability and error convergence without decision-making capabilities. To address the above issues, this work proposes a hierarchical control architecture based on reinforcement learning for multi-agent systems to achieve path planning and cooperative tracking tasks. In addition, multi-agent systems exhibit strong robustness and fault tolerance due to their inherent characteristics, so the above mentioned research can be well applied to post-disaster rescue, intelligent logistics, future war, and so on. Numerical simulations based on Matlab and Python verify the effectiveness of the proposed architecture.

Since the teleoperation process of networked mobile robotic systems (NMRSs) is generally affected by the coupling of the human force, complex dynamical model, external environment and nonholonomic constraints, designing an effectiveness control to guarantee the desired performance for the teleoperation task is a challenging work. Besides, due to the limitation of the communication and control technology, the controller for the teleoperation system is usually required to have low computation load and low monitoring sampling frequency. To address these challenges, a novel self-triggered model predictive control (STMPC) framework, being consisted of the local STMPC, high-order estimation and M/R fixed-time controller, is constructed. Compared to traditional MPC methods, our proposed local STMPC offers lower computational load and requires fewer monitoring resources while retaining the ability to optimize control performance and handle multiple constraints. Using the presented STMPC framework in a hierarchical manner and newly designed high-order estimation, we successfully and simultaneously solve the teleoperation task while accounting for the self-triggering mechanism, decentralized control implementation, disturbance rejection, and complex nonholonomic model. Additionally, we derive sufficient conditions for ensuring the stability of the closed-loop system. Finally, the simulation and experiment results are provided to demonstrate the effectiveness of the proposed STMPC framework. Note to Practitioners—Our research introduces a groundbreaking framework, self-triggered model predictive control (STMPC), specifically designed to elevate control efficiency, quality, and reliability in the context of remote operation of networked mobile robotic systems (NMRSs). This innovation holds immense promise, particularly in domains requiring the utilization of autonomous vehicle fleets, such as large-scale exploration, search and rescue missions, and escort operations in hazardous or hard-to-reach areas (e.g., forest firefighting, warzone patrolling, saturation attacks, and space escort). These environments are often characterized by extreme external conditions and unpredictable external influences, such as meteorite impacts, flames, obstacles, and explosions, posing significant challenges for the control and task execution of unmanned vehicle fleets. Moreover, these missions demand high precision and control responsiveness from the robotic clusters to swiftly accomplish urgent tasks. Consequently, the need arises for autonomous vehicle fleets that not only possess the capacity to adapt to various constraints and external disturbances but also execute mission tasks swiftly and precisely. STMPC, as presented in this paper, demonstrates its capability to address these issues and requirements effectively, making it a versatile and powerful tool for enhancing control and system performance in various scenarios.

Hydropower dominated systems often experience negative damping and severe power flow oscillations due to improperly tuned governor parameters, even with power system stabilizers. Conventional methods optimize these parameters in a single-machine infinite bus model, neglecting interactions between generations during primary frequency control. This article proposes a deep reinforcement learning based cooperative primary frequency controller using a goal representation heuristic dynamic programming model to address this challenge. The controller minimizes power flow oscillations and frequency deviation through cooperative action among hydrogenerations. Case studies on an IEEE 9 bus system demonstrate that the proposed method achieves superior damping of power oscillations and achieves a much shorter regulation time in the primary frequency control compared to the traditional PID controllers.

Voltage regulation in distribution grids often suffers uncertainties such as model mismatches and parameter changes due to the installation of renewable energy sources. This article proposes a model-free robust online feedback optimization (OFO) framework that addresses these challenges. By reformulating the classical optimization problem into an incremental input form under box constraints, an OFO method that solely relies on measurement data is developed. To handle unknown input–output constraint relationships, an adaptive forgetting factor least-squares algorithm for gradient estimation is adopted, which can swiftly track the gradient information. Sound theoretical proof is laid out to show the convergence property of the proposed method. Simulations using a modified IEEE 22-bus system and real distribution grid data validate the proposed method’s effectiveness and robustness.

Industrial manufacturing processes present unique challenges in implementing demand response due to their complex equipment interactions, diverse operation modes, and safety constraints. Conventional model-based optimization methods often struggle in this context, requiring complete mathematical models and accurate uncertainty distributions. In this article, we propose a model-free safe deep reinforcement learning approach for real-time scheduling of industrial manufacturing systems, ensuring constraint adherence and accommodating diverse equipment operation modes. Specifically, the approach formulates the industrial demand response problem as a constrained Markov decision process with hybrid action space, capturing the intricate interplay between variable-speed equipment and discrete actuators, while considering safety constraints. To enhance exploration and robustness, the proposed method combines Lagrange multipliers based on soft actor–critic to satisfy the constraints. The cross-attention mechanism is utilized to find the association rules between hybrid actions to solve the challenges posed by the spatial gradient of hybrid actions. The proposed approach is trained and tested on a real-world dataset, demonstrating its superior performance in achieving significant cost reductions for manufacturing while satisfying operational constraints. Furthermore, sensitivity analysis underpins robustness against the variable real-time prices, showcasing its industrial applicability.

Open multiagent systems (OMASs) feature a dynamic structure with agents continuously joining or leaving, resulting in shifting Nash equilibria and frequent disruptions of equality constraints. This inherent instability poses a significant challenge to traditional incremental-consensus-based distributed optimization or game methods, which rely on a stable and consistent agent population to compute and maintain equilibrium solutions effectively. The necessity for these methods to continuously enforce constraints and the time-intensive process of recalculating equilibria in response to agent dynamics present a substantial bottleneck in the optimization of OMASs. To address this challenge, we develop an innovative incremental consensus-based distributed (ICBD) algorithm to achieve the dynamic Nash equilibrium (NE) for constrained noncooperative game of OMASs. The ICBD algorithm leverages predefined-time stability and integral sliding-mode control to enable rapid recalibration to new equilibria and maintain constraints without the need for prolonged recalculations. Finally, several numerical simulations validate our approach to demonstrating its effectiveness.

This paper considers the distributed nonconvex optimization problem, where the goal is to minimize the average of local nonconvex cost functions through local information exchange. Firstly, we propose a distributed optimization algorithm that integrates the gradient tracking method with a dynamic event-triggered communication scheme, thereby reducing communication overhead. Secondly, we demonstrate that the algorithm linearly converges to the global optimum under the Polyak-Łojasiewicz condition, which indicates that every stationary point is a global minimizer. The numerical experiment is presented to validate the theoretical results and confirm the algorithm's effectiveness.

This paper delves into a class of distributed nonconvex optimization control (DNOC) problems for multiagent systems (MASs), aiming to attain consensus among agents while minimizing the collective sum of local cost functions, referred to as the global cost function, through local information exchange. To accomplish this objective, it is introduced a novel distributed predefined-time optimal (DPTO) control algorithm. We prove that the proposed DPTO control algorithm guides the system states towards convergence to the global optimal solution within a user-defined time frame, provided that the global cost function satisfies the Polyak-Lojasiewicz condition, which is less stringent than the standard strong convexity condition. Finally, theoretical findings are substantiated through simulation studies.

Planning trajectories and trajectory tracking are significant and fundamental tasks for Lagrange-based autonomous ground vehicles. In this paper, a novel unified framework integrating path planning and trajectory tracking is proposed based on deep reinforcement learning for Lagrange-based autonomous ground vehicles considering motion limitation and energy consumption, namely, hierarchical piecewise-trajectory planning (HPP) framework. The framework consists of three layers, namely the path planning layer, the trajectory planning layer, and the local control layer. Firstly, the path planning layer enables the vehicle to find a discrete path from its initial position to its target position. Afterward, the trajectory planning layer ensures that discrete trajectory points are transformed into continuous trajectory functions based on the polynomial curve interpolation method. The adaptive asymptotic acceleration planning algorithm is proposed to satisfy the limitations of maximum velocity and acceleration for vehicles. Finally, the trajectory tracking control algorithm and poweroff trigger mechanism are developed to achieve the following two goals in the local control layer: 1) regulating the vehicle to follow its continuous trajectory curve, 2) switching off the power to save energy when its instantaneous kinetic energy is adequate to supply the energy consumption. Numerous simulation results show that our framework enables autonomous ground vehicles to accomplish integrated path planning and trajectory tracking tasks with the presence of motion limitation. Two extra examples are presented to demonstrate that our method is generalizable in terms of energy savings compared to existing optimization-based methods.

This article studies the secure surrounding formation (SSF) problem of networked marine surface vehicles subject to denial of service (DoS) attacks. A hierarchical control framework is developed for designing the predefined-time fuzzy reinforcement learning controller, which consists of two layers. The distributed resilient estimator is proposed to accurately estimate the trajectory of the leader center in the predefined-time under DoS attacks over digraphs. The fuzzy reinforcement learning local controller is designed to achieve the SSF within the predefined-time. The sufficient conditions for system convergence and stability are derived based on the Lyapunov stability theory. Finally, simulation experiments are conducted to verify the effectiveness of the theoretical results.

This article investigates the problem of predefined-time distributed formation tracking for networked marine surface vehicles in the presence of external disturbances. To address this problem, we propose a novel hierarchical predefined-time formation control (HPTFC) framework that integrates a novel sliding mode surface with the vector control Lyapunov functions-based (VCLFs) method. Specifically, the local control layer based on VCLFs is established, which circumvents the usual requirement for positive-definite Lyapunov functions and only necessitates semidefinite positive components. This enables us to search for more appropriate control algorithms in a broader solution space generated by more suitable Lyapunov functions with more general conditions. Through comprehensive theoretical analysis, we demonstrate that the proposed HPTFC framework achieves predefined-time convergence successfully. Eventually, numerical simulations are exhibited to illustrate the effectiveness and superiority of the proposed HPTFC scheme.

The high penetration of renewable energy in grid-connected microgrids creates the tie-line power fluctuations, which can increase operating costs and even pose security and stability risks. Yet, we continue to lack efficient tools to smooth the tie-line power fluctuations within the context of microgrids. In this article, a hierarchical regulation strategy is proposed for smoothing the fluctuations of tie-line power flow in grid-connected microgrids equipped with battery storage units (BSUs), where the BSUs are aggregated into several battery storage aggregators (BSAs) to facilitate the management. This strategy comprises two layers: an upper layer employs a multiple-horizon predictive optimization-based approach to compute the required power allocation for each BSA, ensuring smoothed power trajectories while adhering to system constraints. Subsequently, a lower layer employs a distributed fast tracking-based technique to distribute the allocated power among BSUs within each BSA using predefined-time control theory. Case studies validate the effectiveness of our approach.

This paper presents a novel distributed predefined-time optimization scheme consisting of the distributed optimization estimator and the local controller for the networked marine surface vehicles. Concretely, the distributed optimization estimator is developed to estimate the optimal solution on to the set constraints. In the local control layer, a sliding mode scheme is built to guarantee that the sailing states of networked marine surface vehicles can track the optimal signals obtained by the distributed optimization estimator. Besides, the regulating time of both the estimation and the local tracking process is independent of the initial system states and can be artificially determined by directly adjusting the sum of serval control parameters. Later, a singularity avoidance scheme is further designed to avoid the possible singularity problems of the local control layer. Finally, a simulation example is given to show the efficacy of the proposed distributed predefined-time optimization algorithm.

Fast detection of power line outages is critical for maintaining the stable operation of the power system. The aim of this article is to address the real time detection problem of multiple line outages in power systems. To effectively tackle the high-computational complexity issues associated with traditional approaches, we propose a multiple line outages detection algorithm that utilizes a distributed finite-time observer. The proposed method utilizes only local measurements and information from neighboring buses to update local observer for each bus. The proposed observer is mathematically proven to converge in a finite time, ensuring rapid detection of multiple line outages. Finally, simulation results demonstrate the effectiveness and rapidity of the proposed detection algorithm.

In this article, considering three different working modes (including the human-supervised, human-aided, and human-manned modes), we present a novel mode-switched control architecture for solving the human-in-the-loop (HIL) teleoperation problem of multislave robots with local slave-to-slave (S2S) communication, long-distance master-to-slave (M2S) communication and transmission delays. Throughout the control process, the S2S communication is updated following the event-triggered mechanism; meanwhile, the data transmission is fully distributed, namely, no global information can be transmitted. Besides, we also deal with the concerns of enhancing “telepresence”, namely, reconstructing the interaction force between a user-determined slave robot and its task environment at the human side, and then allow the human operator to control the multislave robots in a “virtual reality” way. To this end, by making full use of the historical and current data, the data-training-based (DTB) observer is designed to obtain the interaction force at the side of the slave robot and then assist the human operator to choose a proper control mode. The presented architecture is hierarchically designed for data collection, data processing and physical regulation, involving the DTB observer and the fully distributed event-based (FDEB) estimator in a unified framework. Finally, numerical examples are conducted to demonstrate the effectiveness of the architecture.

This article investigates the control problem for networked switched systems under denial-of-service (DoS) attacks. The switching signal and the quantized system state are transmitted to the remote controller via a network, which suffers from bandwidth constraints and DoS attacks. To save communication resources in both time and space, a Zeno-free dynamic event-triggered mechanism (DETM) and a dynamic quantization mechanism are co-constructed. However, the triggering error and the quantization error are induced simultaneously. Meanwhile, the quantization saturation and the system instability issues are raised due to the asynchronous mode and the bandwidth-constrained network under DoS attacks. To tackle these problems, a quantization-dependent DETM is presented in terms of a quantization parameter. A dynamic quantizer with a mode-dependent variable quantization level (MDVQL) is proposed. The constraint conditions on the quantization level and the event-triggered parameters are obtained to ensure the unsaturation of the quantizer, and sufficient conditions are provided for the exponential stability of the switched systems. Lastly, simulation examples are carried out to verify the effectiveness of the theoretical results and show the merits of the proposed methods for saving communication bandwidth.

When realizing multiagent optimal consensus control, it may encounter the situation that malicious agents transmit false information. Besides, due to the unreliability of information interaction and the uncertainty of the system itself, the agent may not fully know its own cost function. In this article, an improved Bayesian graphical game method is proposed to solve the optimal consensus problem of linear dynamical networks in the presence of false information. The agent’s probabilistic estimate of the uncertainty is named belief, and the update of probability estimate is named belief update. An information tradeoff principle is designed to solve the belief update problem in the presence of malicious neighbors. The principle can not only reduce the loss caused by false information but also force malicious agents to switch from deception to cooperation. On this basis, a new belief update method with information tradeoff principle is established. It is proved that this new belief update method has a faster convergence rate than the Bayesian belief update method when malicious neighbors exist. As an illustrative example, the graphical game solution is applied to the formation tracking control problem of a quad-rotor unmanned aerial vehicle swarm. Theoretical proof and simulation comparisons can illustrate the proposed method’s advantages.

This article investigates the hierarchical synthesis of fuzzy fault-tolerant controllers for networked perturbed mechanical systems to solve the problem of finite-time multitarget surrounding, namely, encircling multiple moving targets in a finite time. Given the system with actuator failures, faults, and perturbations (namely, parametric uncertainties and external disturbances), we propose a hierarchical framework for synthesizing a cascade-form controller to stabilize the system state in a finite time, as well as decouple and solve the abovementioned problem. Specifically, the methods of fuzzy logic systems and finite-time adaptive laws are included within the synthesized controller to approximate the unknown perturbations, and meanwhile to compensate the negative effects of the actuator failures and faults. By employing the theories of perturbations and fault-tolerant analysis, we derive the sufficient conditions on control gains for finite-time convergence of the closed-loop system. Finally, we carry out several simulation experiments on a network of six 2-DOF robots and four moving targets to verify the performance of the synthesis method and the obtained controller.

This article studies the lag-bipartite formation tracking (LBFT) problem of the networked robotic systems (NRSs) with directed matrix-weighted signed graphs. Unlike the traditional formation tracking problems with only cooperative interactions, solving the LBFT problem implies that: 1) the robots of the NRS are divided into two complementary subgroups according to the signed graph, describing the coexistence of cooperative and antagonistic interactions; 2) the states of each subgroup form a desired geometric pattern asymptotically in the local coordinate; and 3) the geometric center of each subgroup is forced to track the same leader trajectory with different plus-minus signs and a time lag. A new hierarchical control algorithm is designed to address this challenging problem. Based on the Lyapunov stability argument and the property of the matrix-weighted Laplacian, some sufficient criteria are derived for solving the LBFT problem. Finally, simulation examples are proposed to validate the effectiveness of the main results.

This article investigates the synchronization problem of interconnected linear two-time-scale systems (TTSSs) with switching topology. By utilizing the Chang transformation, a distributed synchronization protocol is proposed with event-triggered communication. Static and dynamic event-triggered mechanisms are proposed successively, which both contain two separated event-triggering conditions corresponding to the slow and the fast subsystems. The existence of a strictly positive time period between any two successive transmissions is ensured regardless of the initial states. The main difficulty of this study lies in that the state jump and parametric uncertainty appear because of the system transformation. To overcome the difficulty, the system is first modeled as an uncertain hybrid system. Then, the control gain is properly designed by solving Riccati-like equations dependent on the rough bounds of the eigenvalues of communication graph Laplacians, and a piecewise quadratic Lyapunov function is proposed with which the jump caused by the switching topology is subtly evaluated. Sufficient conditions are thus established to achieve the event-triggered synchronization. Furthermore, the results are also extended to solve the synchronization problem of the interconnected impulsive linear TTSSs. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Impulsive control is widely applied to achieve the consensus of multiagent networks (MANs). It is noticed that malicious agents may have adverse effects on the global behaviors, which, however, are not taken into account in the literature. In this study, a novel delayed impulsive control strategy based on sampled data is proposed to achieve the resilient consensus of MANs subject to malicious agents. It is worth pointing out that the proposed control strategy does not require any information on the number of malicious agents, which is usually required in the existing works on resilient consensus. Under appropriate control gains and sampling period, a necessary and sufficient graphic condition is derived to achieve the resilient consensus of the considered MAN. Finally, the effectiveness of the resilient delayed impulsive control is well demonstrated via simulation studies.

This article investigates the predefined-time stabilization problems of Takagi–Sugeno (T–S) fuzzy systems. For addressing the considered problems, a class of novel integral sliding mode surface is first designed based on the time-regulator function, on which the system states are forced to converge to the origin in a predefined time after the sliding mode surface is reached. Further, the proposed sliding surface is employed to construct predefined-time integral sliding mode controller for the time delayed and disturbed T–S fuzzy system. The settling time appears as the sum of two predefined-time parameters in the controller design, which, respectively, adjusts the convergence time for reaching the sliding mode surface and the convergence time for arriving the origin from the sliding mode surface. The sufficient conditions for maintaining the predefined-time stability of the T–S fuzzy systems are obtained through systematic Lyapunov stability analysis. Finally, a numerical simulation example on delayed and disturbed Chua circuit is presented to verify the effectiveness of the proposed predefined-time integral sliding mode controller.

This article investigates the multitarget tracking problem for multiple Lagrangian plants (MLPs) in the presence of sampled-data interactions, uncertain dynamic terms, and input-to-output redundancy. Two classes of impulsive estimator-based control (IEC) algorithms, including the first- and higher-order IEC algorithms, are newly designed to observe the dynamic uncertain terms, estimate the states of the multiple targets, and finally solve the above-mentioned problem. Based on the properties of the small-value norms, Lyapunov stability theory, Schur stability theory, and Hurwitz criterion, some sufficient conditions and the convergence radius are derived for guaranteeing the convergence of these IEC algorithms. Finally, numerical simulations are performed on networked heterogeneous manipulators to verify the effectiveness of the proposed algorithms.

Designing an efficient distributed economic dispatch (DED) strategy for the smart grid (SG) in the presence of multiple generators plays a paramount role in obtaining various benefits of a new generation power system, such as easy implementation, low maintenance cost, high energy efficiency, and strong robustness against uncertainties. It has drawn a lot of interest from a wide variety of scientific disciplines, including power engineering, control theory, and applied mathematics. We present a state-of-the-art review of some theoretical advances toward DED in the SG, with a focus on the literature published since 2015. We systematically review the recent results on this topic and subsequently categorize them into distributed discrete- and continuous-time economic dispatches of the SG in the presence of multiple generators. After reviewing the literature, we briefly present some future research directions in DED for the SG, including the distributed security economic dispatch of the SG, distributed fast economic dispatch in the SG with practical constraints, efficient initialization-free DED in the SG, DED in the SG in the presence of smart energy storage batteries and flexible loads, and DED in the SG with artificial intelligence technologies.

Disturbances, uncertainties, noises and device faults commonly exist in microgrids and often undermine the system stability. To meet these challenges, robust control methods have been recently employed in microgrids systems. In this paper, an active fault-tolerant control scheme is proposed for DC islanded microgrids subjected to sensor fault and external disturbance. Firstly, a distributed H∞observer is designed to estimate the uncorrupted voltage and current with high accuracy. Then, an observer based state feedback controller is proposed to ensure stability of voltage regulation for the system. A consensus based control layer in the secondary level is provided to realize current sharing. For the plug-and-play operation of DC microgrids, decentralized parameters design approaches for the observer and controller are both discussed. Finally, simulation studies and experiments are carried out on a DC microgrid system to evaluate the effectiveness of the proposed fault-tolerant control scheme. The simulation and experiment results show that compared with previous works, the proposed observer based control strategy can significantly improve the reliability and resilience of DC microgrid systems.

This article investigates the finite-time output multiformation tracking (OMFT) problem of networked heterogeneous robotic systems (NHRSs), where each robot model involves external disturbances, parametric uncertainties, and possible kinematic redundancy. Besides, the interactions among robotic systems are described as a directed graph with an acyclic partition. Then, several novel practical finite-time hierarchical control (FTHC) algorithms are designed. The convergence analysis of the closed-loop dynamics is extremely difficult due to the lack of effective analysis methods. Based on the mathematics induction and reductio ad absurdum, a new nonsmooth Lyapunov function is proposed to derive the sufficient conditions and settling time functions. Finally, numerical simulations are performed on the NHRS to verify the main results.

The risk of transmission lines overload in the power grid is increasing with the large-scale integration of fluctuating distributed renewable energies. Meanwhile, the requirement for accommodating more distributed resources in the future smart grids promotes the transition from the current highly centralized control structure toward a distributed one. In this article, we propose a distributed corrective control approach to mitigate line overloads in a real-time and close-loop manner. Unlike the conventional centralized approach, only simple computation and local information exchange are required to update the local corrective control action. This makes it possible to mitigate line overloads timely and adapt to the topology changes of grids. Furthermore, the introduction of system measurements and security constraints in the proposed algorithm ensures an effective and secure corrective control without new line overloads. The performance of the proposed distributed approach is demonstrated in the IEEE 14-Bus and 118-Bus systems.

Online experimentation systems that support remote and/or virtual experiments in an Internet-based environment play an important role in skill-enhanced online learning, especially in the field of engineering. This article explores a human-centered online system with a unified architecture that covers the entire process of control engineering experimentation. The control and security-oriented design are presented and the human-centered design including the HTML5-based web application and the configurable graphical user interface is also introduced. Interactive features such as tuning parameters and 3-D animations and interactions are integrated into the system. Enhanced 3-D effects such as anaglyph 3-D and parallax 3-D are also provided. Thus, users can experience different types of 3-D effects on experiment equipment or in a 3-D virtual world while conducting experiments. Details of an application example with a dual tank system are also explored to verify the performance of the proposed system.

This paper proposes several hierarchical controller-estimator algorithms (HCEAs) to solve the coordination problem of networked Euler-Lagrange systems (NELSs) with sampled-data interactions and switching interaction topologies, where the cases with both discontinuous and continuous signals are successfully addressed in a unified framework. The HCEAs comprise two main layers (i.e., a control layer and an estimator layer) and one optional layer (i.e., a filter layer), in which the coordination problem is tackled in the main layers and the transient response can be optionally smoothed in the filter layer. For stabilizing the corresponding cascade closed-loop systems, several sufficient conditions on the upper bound of the aperiodic sampling intervals and the lower bound of the control parameters are established. In addition, the HCEAs are extended to address the task-space coordination problem of networked heterogeneous robotic systems, which shows the versatility of the HCEAs. Finally, comparison studies and simulation results are provided to demonstrate the effectiveness, significance, and advantages of the presented algorithms.

We consider the quasi-synchronization problem of a continuous time generalized Markovian switching heterogeneous network with time-varying connectivity, using pinned nodes that are event-triggered to reduce the frequency of controller updates and internode communications. We propose a pinning strategy algorithm to determine how many and which nodes should be pinned in the network. Based on the assumption that a network has limited control efficiency, we derive a criterion for stability, which relates the pinning feedback gains, the coupling strength, and the inner coupling matrix. By utilizing the stochastic Lyapunov stability analysis, we obtain sufficient conditions for exponential quasi-synchronization under our stochastic event-triggering mechanism, and a bound for the quasi-synchronization error. Numerical simulations are conducted to verify the effectiveness of the proposed control strategy.

Delayed impulsive controllers are proposed in this paper to enable the agents in a class of second-order multiagent systems (MASs) to achieve state consensus, based, respectively, on the relative full-state and partial-state sampled-data measurements among neighboring agents. It is a challenging task to analyze the consensus behaviors of the considered MASs as the dynamics of such MASs will be subjected to joint effects from delay-dependent impulses, aperiodic sampling, and switchings among different communication graphs. A novel analytical approach, based upon the discretization method, state augmentation, and linear state transformation, is developed to establish the sufficient consensus criteria on the range of the impulsive intervals and the control parameters. Remarkably, it is found that consensus in the closed-loop MASs can be always ensured by skillfully selecting the control parameters as long as the nonuniform delays and the impulsive intervals are bounded. A numerical example is finally performed to validate the effectiveness of the proposed delayed impulsive controllers.

Cooperative consensus tracking and its -gain performance is investigated in this paper for a class of multiple agent systems (MASs) in the presence of a single high-dimensional leader. Compared with the traditional models for MASs, the inherent dynamics of the leader are allowed to be different with those of the followers in the present framework, which is thus much more favorable in various practical applications. A new kind of distributed controllers associated with a reduced-order state observer are designed for each follower to track the high-dimensional leader under directed switching topology. With the help of -matrix theory and stability analysis methods of switched systems, some efficient criteria are derived for cooperative consensus tracking of MASs without any external disturbance under directed switching topology. Theoretical analysis is further extended to the case of consensus tracking for MASs subject to unknown external disturbances by showing that, a finite -gain performance for tracking errors against external disturbances can be ensured if some suitable conditions are satisfied. At last, the synthesis issue of designing an observer-based controller to achieve a prescribed -gain performance for consensus tracking is studied by using tools from control theory, where the underlying topology is assumed to be undirected and fixed. The effectiveness of theoretical results is verified by performing numerical simulations.

This paper introduces the schemes of remote wiring interactions in an online control laboratory using an HTML5-based virtual 3-D interface. Although virtual laboratories have drawn increasing research attention in the last decade, wiring practice, which is a crucial part of experimentation, is normally neglected. In this paper, a practice including 3-D modeling, HTML5-based rendering, and control algorithm design is implemented for the interactive virtual wiring based on the Networked Control System Laboratory (NCSLab) framework. The wiring practice is combined with control algorithm design, which is already realized in NCSLab, where users are allowed to customize algorithms using MATLAB/Simulink real-time workshop. Apart from remotely implementing the control algorithm, the 3-D virtual wiring process must be completed correctly before the online experiments can proceed properly. The proposed wiring laboratory is evaluated in practical teaching, with both students' performance and perception considered. The conclusions derived from the report show that the 3-D virtual wiring interactions make virtual experimentation complete for simulating a real case, as well as providing an opportunity for a clearer comprehension of control systems.

The economic dispatch problem is investigated in this paper for a class of smart grids subject to unknown communication uncertainties. Compared with existing works related to economic dispatch where the dispatch algorithms are carried out by a centralized controller, a new kind of distributed dispatch algorithms are developed to achieve optimal dispatch of electric power by appropriately sharing the load among different generating units while guaranteeing consensus among incremental costs. An adaptive weight-adjustment technique is suggested that enables the dispatch algorithms to choose the communication weights among neighboring generating units which yield consensus of incremental costs under both cases with or without capacity limitations. The achievement of such a consensus leads to optimal dispatch of electronic power and secures the system performance against unknown communication uncertainties. Meanwhile, it is proved that the power demand and supply of the considered smart grids will be kept in a balanced state during the dispatch process. The interesting issue of how to assign the power outputs among generating units to balance the power demand and supply of the considered smart grids is also addressed. Finally, the numerical results of several case studies have been provided to verify the effectiveness of the proposed algorithms.

In this paper, an optimal retail market pricing design for demand response in day-ahead scheduling of smart distribution networks is investigated. Through the well-designed retail market electricity price, the profit of each user is maximized; while the profit of the Distribution Network Operator (DNO) is guaranteed and the risk management model based on the Information Gap Decision Theory (IGDT) method is proposed to protect the DNO from financial risk arising out of the uncertainty of wholesale market prices. Because of the convexity of the problems of users and the DNO, the demand response program is developed based on the Predictor Corrector Proximal Multiplier, which is a distributed algorithm and guaranteed to converge to a global optimal solution, i.e. the retail market electricity price. The numerical simulation is given to show the effectiveness of the proposed pricing method.

This paper studies the fully-distributed consensus problem for multi-agent systems with unknown dynamics and bounded external disturbances. The interaction topology of the multi-agent system is assumed to contain a directed spanning tree. Based on adaptive gains, we present the fully-distributed consensus protocol which can obtain consensus without using any global information. The simulation examples are given to verify the effectiveness of the main results.

The multi-tracking problem of second-order multi-agent system with communication delay is investigated in this paper. An intermittent control protocol is proposed on the basis of only relative position measurement, where the information of agent is quantized before transmission using stochastic quantization scheme. On the basis of algebraic graph theory, stochastic quantization and stability theory, some necessary and sufficient conditions are obtained. It is proved that the multi-agent systems equipped with the designed protocol can track the desired trajectory. Case study illustrates the proposed algorithm can solve the multi-tacking problem effectively.

The classical power allocation/reallocation faces difficult challenges in a future power grid with a great many distributed generators and fast power fluctuations caused by high percentage of renewable energy. To perform power reallocation fast in a future power grid with a large number of participants and disturbances, a hierarchical distributed scheme based on a partition framework is proposed. In the proposed scheme, the power grid is naturally partitioned into a certain number of regions, and the total energy demand in the power grid with disturbances is automatically estimated rather than given in advance. Besides, the centralized local optimizations in regions and the distributed global optimization among regions are coupled to solve the power reallocation problem, in which each region performs as a single agent. Thus, the agents in the proposed scheme are much fewer than the purely distributed ones, hence the communication load is greatly relieved and the reallocation process is significantly simplified. Effectiveness of the proposed scheme is verified by the cases.

This paper proposes a control framework, called pulse-modulated intermittent control, which unifies impulsive control and sampled control. Specifically, the concept of pulse function is introduced to characterize the control/rest intervals and the amplitude of the control. By choosing some specified functions as the pulse function, the proposed control scheme can be reduced to sampled control or impulsive control. The proposed control framework is applied to consensus problems of multiagent systems. Using discretization approaches and stability theory, several necessary and sufficient conditions are established to ensure the consensus of the controlled system. The results show that consensus depends not only on the network topology, the sampling period and the control gains, but also the pulse function. Moreover, a lower bound of the asymptotic convergence factor is derived as well. For a given pulse function and an undirected graph, an optimal control gain is designed to achieve the fastest convergence. In addition, impulsive control and sampled control are revisited in the proposed control framework. Finally, some numerical examples are given to verify the effectiveness of theoretical results.

To reduce information exchange requirements in smart grids, an event-triggered communication-based distributed optimization is proposed for economic dispatch. In this work, the θ-logarithmic barrier-based method is employed to reformulate the economic dispatch problem, and the consensus-based approach is considered for developing fully distributed technology-enabled algorithms. Specifically, a novel distributed algorithm utilizes the minimum connected dominating set (CDS), which efficiently allocates the task of balancing supply and demand for the entire power network at the beginning of economic dispatch. Further, an event-triggered communication-based method for the incremental cost of each generator is able to reach a consensus, coinciding with the global optimality of the objective function. In addition, a fast gradient-based distributed optimization method is also designed to accelerate the convergence rate of the event-triggered distributed optimization. Simulations based on the IEEE 57-bus test system demonstrate the effectiveness and good performance of proposed algorithms.