Quadruped robots have exhibited highly adaptive locomotion capabilities, yet reliable navigation on complex mixed unstructured terrain remains a major challenge. A key difficulty is that existing navigation frameworks typically rely on geometric costmaps, which fail to capture the fact that terrain traversability is inherently policy-dependent, as different locomotion controllers exhibit distinct contact strategies, dynamic limits, and behavioral capabilities. To address this issue, we present a unified framework that learns and exploits policy-dependent traversability for large-scale autonomous navigation with quadrupedal robots. We first develop a data-driven traversability estimator that predicts the traversability of each terrain region under a given locomotion policy, trained from a kernel-based traversability sample map aggregated from simulated policy rollouts. This estimator is used to construct a terrain-aware costmap with policy-dependent feasibility constraints. Then, a two-stage planning pipeline with grid-based search and trajectory optimization is proposed to generate smooth, policy-feasible global trajectories for execution by the corresponding locomotion policy. Finally, we extend the framework to multiple locomotion policies, enabling automatic policy switching based on predicted traversability and enhancing adaptability to diverse terrain conditions. Experiments across large and challenging environments demonstrate that our approach significantly improves navigation reliability, terrain adaptability, and long-horizon autonomy for quadrupedal robots.

Existing multirobot task allocation (MRTA) research primarily assumes an environment with known geometric and semantic information. However, in most real-world scenarios, semantic information, such as the locations and classifications of landmarks, is often uncertain. This uncertainty is exacerbated by dynamic requirements, like the sudden addition or removal of tasks, making it challenging for robots to respond reactively. Moreover, tasks in MRTA typically involve multiple constraints, including temporal requirements, diverse capabilities, varying resource needs, and inter-task dependencies. To address these challenges, we propose a reactive task allocation framework for heterogeneous multirobot systems that accounts for temporal requirements and multiple task constraints described by $\mathrm {LTL^{\mathcal {R}}}$ . Our approach assumes an environment with known geometry but unknown semantic landmarks. To efficiently solve task allocations, we encode $\mathrm {LTL^{\mathcal {R}}}$ along with the system's states into a proposed planning decision tree for exploration. Upon detecting a relevant semantic landmark, the reactive multiconstraint planning decision tree (RMC-PDT) is triggered for re-planning. Extensive experiments validate three key features of our method: 1) efficient reactive planning; 2) multiconstraint task solving; and 3) scalability.

This article is concerned with the output feedback security tracking control of a class of disturbed second-order nonlinear systems against denial-of-service (DoS) attacks. Novel radial basis function neural network (RBFNN)-based finite-time state observers are developed to estimate the system’s unavailable states. Adaptive filters are proposed to suppress the influences of disturbances and RBFNN approximation errors. Then, an RBFNN-based security controller is designed to alleviate the effects of nonlinear dynamics and DoS attacks based on the signals of observers and filters. It is established that the uniformly ultimately bounded output tracking results of the system can be obtained by utilizing an RBFNN-based finite-time observation and filtering compensation control designs through Lyapunov stability analysis. Comparative simulations are employed to display the feasibility and superiority of the designed RBFNN-based observation and filtering compensation control schemes of a nonlinear autonomous marine system (AMS).

This paper proposes a novel distributed coverage controller for a multi-agent system with constant-speed unicycle robots (CSUR). The work is motivated by the limitation of the conventional method that does not ensure the satisfaction of hard state-and input-dependent constraints and leads to feasibility issues for multi-CSUR systems. In this paper, we solve these problems by designing a novel coverage cost function and a saturated gradient-search-based control law. Theoretical proofs are provided to guarantee that the CSURs ultimately move to the optimal coverage configuration without moving out of the covered domain. The controller is implemented in a distributed manner based on a novel communication standard among the agents. A series of simulation studies are conducted to validate the correctness of our theory by showing the efficacy of the proposed coverage controller in different initial conditions and with various control parameters. A comparison study in simulation reveals the advantage of the proposed method over the conventional method in terms of avoiding infeasibility. The experimental study verifies the applicability of the method to real robots. The development procedure of the method from theoretical analysis to experimental validation provides a novel framework for multi-agent system coordinate control with complex dynamics.Note to Practitioners—This paper gives a novel method to effectively cover a polygonal area using multiple constant-speed unicycle robots (CSUR) like wheeled robots and fixed-wing unmanned aerial vehicles (fUAV). Compared to the conventional approaches, our method allows these robots to cover a target region using circular orbits without departing the covered region. Also, the method satisfies common control saturation constraints in practice and can be implemented in a reliable distributed scheme. While the efficacy and correctness of the proposed method are rigorously proved using control theory, we also provide necessary interpretive elucidations to explain its underlying mechanism and selection rationale. The method is validated to be effective for wheeled robots in experimental studies, although it can also be applied to fUAVs in theory.

This article investigates the issue of observer-based fixed-time-synchronized tracking control for Euler-Lagrange (EL) systems with uncertain dynamics, bias-actuator faults and external disturbances. A novel fixed-time observer is proposed to reconstruct the actuator faults and system uncertainties, so that the observation error can reduce to zero within a fixed time. A fixed-time stable system with fast convergence rate is developed by using switching terms to design a newly sliding mode variable with the norm-normalized sign function. Then, on the basis of the reconstructed information from the fixed-time observer and the sliding mode variable, a robust control law is developed to realize fixed-time-synchronized stability of the EL system. It is concluded by Lyapunov stability theorem that the proposed method not only can guarantee that the boundary of convergence time is irrelevant of initial values of the system states, but also make all elements of the system tracking errors reach the origin simultaneously under the influence of actuator faults, external disturbances and uncertain dynamics. Finally, several comparative simulations are carried out to validate the developed observation and control schemes as well as their effectiveness.

Solder paste position offset is a critical stencil printing quality indicator, the prediction of which using available data is important for printing quality improvement. However, existing data-driven works on solder paste position offset prediction often suffer from their poor adaptation to changing printing stages and small training samples. To address the above problems, we propose a novel multi-scale convolutional attention network based on meta-transfer strategy for solder paste position offset prediction in surface mount technology assembly lines. First, to better capture the fluctuating trends of printing sequence in different cleaning cycles, we propose a multi-scale convolutional attention network, in which a multi-head attention with position encoding is designed at each level to adaptively capture the changing trend of solder paste position offset at different stages. Then, to improve the precision of prediction model under insufficient samples, we introduce a meta-transfer strategy. Specifically, the parameters of the model are updated in the meta-training process through the bi-level optimization and the parameter fine-tuning method is used in the meta-testing process to improve the prediction performance of proposed model under complex working conditions. The proposed method is verified over practical dataset and compared with other advanced methods. The results show that the proposed method can accurately and robustly achieve solder paste position offset prediction, especially in small sample dataset.

The coordination of electric vehicle battery charging stations (BCSs), battery swapping stations (BSSs), and residential buildings (RBs) within a community microgrid (CM) presents a significant opportunity to enhance system flexibility and reduce operational costs. However, the randomness of user behaviors and the intermittency of renewable energy pose threats to the stability of the CMs. This article investigates the robust cooperative operation of CMs with BCSs and BSSs, allowing for energy sharing. First, a robust energy management framework utilizing cooperative game theory is developed among a BCS, a BSS, and a set of RBs within a CM, achieving proactive energy sharing and fair distribution of benefits. Then, an alternating direction method of multipliers algorithm combined with robust optimization is designed to address the energy management problem in a distributed manner, ensuring the protection of private data and enhancing system robustness. Finally, numerical examples verify the effectiveness and superiority of the proposed method. In comparison with the noncooperative benchmark, the proposed method achieves a reduction in operational costs of 5.69%, 9.1%, and 8.48% for the BCS, BSS, and RBs, respectively.

The battery swapping mode, due to its high energy replenishment efficiency for electric vehicles (EVs), has progressively seen widespread application. However, uncertainties inherent in battery swapping stations (BSSs) pose challenges to ensuring profitability and service quality in actual operations. To overcome these challenges, the chance constraint is firstly introduced in this paper to guarantee quality of service (QoS). A BSS multi-stage stochastic optimization model with risk consideration is then proposed by adopting the conditional value at risk (CVaR) model, aiming to reduce costs under acceptable QoS levels. The stochastic dual dynamic integer programming (SDDiP) algorithm is utilized for developing a real-time multi-stage BSS stochastic planning algorithm. Simulation results demonstrate that the proposed optimization method can effectively increase revenue while ensuring service quality, providing feasible decision-making strategies for real-time BSS operations.

Safe reinforcement learning (RL) has shown great potential for building safe general-purpose robotic systems. While many existing works have focused on post-training policy safety, it remains an open problem to ensure safety during training as well as to improve exploration efficiency. Motivated to address these challenges, this work develops shielded planning guided policy optimization (SPPO), a new model-based safe RL method that augments policy optimization algorithms with path planning and shielding mechanism. In particular, SPPO is equipped with shielded planning for guided exploration and efficient data collection via model predictive path integral (MPPI), along with an advantage-based shielding rule to keep the above processes safe. Based on the collected safe data, a task-oriented parameter optimization (TOPO) method is used for policy improvement, as well as the observation-independent latent dynamics enhancement. In addition, SPPO provides explicit theoretical guarantees, i.e., clear theoretical bounds for training safety, deployment safety, and the learned policy performance. Experiments demonstrate that SPPO outperforms baselines in terms of policy performance, learning efficiency, and safety performance during training.

Addressing safe and efficient navigation in dynamic, realistic, and complex environments stands as a pivotal inquiry within the realm of robotics. Recently, numerous learning-based methods are introduced into the field of navigation, yielding notable outcomes. In this letter, we propose a hierarchical safe reinforcement learning navigation approach (HSRLN) for mapless navigation. It trains mapless navigation policies for non-homogeneous complex scenarios in a hierarchical manner through a kind of three-stage learning, global planning reinforcement learning (RL) + expert imitation learning (IL) + transfer RL (TRL). The innovations of this work are fourfold: a) It effectively reduces the difficulty of training for complex navigation by effectively narrowing the task horizon of RL through a hierarchical framework. b) We designed an imitation learning method based on Relative Driving Safety Index (RDSI) [1] to focus on learning critical expert actions. c) It employs a TRL approach to improve generalization under non-homogeneity assumptions by fine-tuning the policy. d) HSRLN extracts significant features important for navigation decisions from raw observations via velocity obstacle modeling. Experiments indicate that it has performs better than existing hierarchical RL navigation methods (HDRL [2], SRL-ORCA [3]). Relative to SRL-ORCA, it improves navigation success by 12.1% under the non-homogeneity assumption. Videos are available at https://youtu.be/24h9JmcIfMw.

Integrating Large Language Models (LLMs) into robotics significantly enhances autonomous task planning. However, ensuring that multi-step task plans (action sequence) generated by LLMs comply with pre-defined safety constraints during planning and execution remains a challenge, limiting their adaptability in complex environments. To address this issue, a mechanism that can monitor and adjust the plan generated by the LLM-driven task planner and guide the motion planner to avoid potential risks during action execution is required. Therefore, this paper proposes a cross-layer sequence supervision mechanism. Specifically, we employ linear temporal logic syntax to express safety constraints and convert them into a set of nondeterministic Büchi automatons to build a cross-layer safety supervisor. For the task planning layer, the safety supervisor provides a closed-loop correction mechanism that can identify violations in the task plan in real time and guide LLM-driven planners to correct this plan to ensure compliance. For the motion planning layer, the safety supervisor introduces virtual "obstacle" information into the task plan to form the task plan tuple. Based on this plan tuple, the motion planner can proactively prevent unsafe behaviors during action execution. Extensive experimentation demonstrates significant improvements in safety with this cross-layer supervision mechanism, highlighting its potential to enhance LLM-driven robotic technology. Experiment details can be found in https://youtu.be/BDdSSEP6HJw.

Safety as a fundamental requirement for human-swarm interaction has attracted a lot of attention in recent years. Most existing approaches solve a constrained optimization problem at each time step, which has a high real-time requirement. To deal with this challenge, this article formulates the safe human-swarm interaction problem as a Stackerberg-Nash game, in which the optimization is performed over the entire time domain. The leader robot is supposed to be in a dominant position, interacting directly with the human operator to realize trajectory tracking and responsible for guiding the swarm to avoid obstacles. The follower robots always take their best responses to leader's behavior with the purpose of achieving the desired formation. Following the bottom-up principle, we first design the best-response controllers, that is, Nash equilibrium strategies, for the followers. Then, a Lyapunov-like control barrier function-based safety controller and a learning-based formation tracking controller for the leader are designed to realize safe and robust cooperation. We show that the designed controllers can make the robotic swarms move in a desired geometric formation following the human command and modify their motion trajectories autonomously when the human command is unsafe. The effectiveness of the proposed approach is verified through simulation and experiments. The experiment results further show that safety can still be guaranteed even when there exists a dynamic obstacle.

Differential game is an effective technique to describe the negotiation between the humans and robots, which is widely used to realize the trajectory tracking tasks in the human-robot interaction (HRI). However, most existing works consider the control-affine HRI systems and assume the desired trajectory is available to both the human and the robot, which limit the scope of applications. To overcome these difficulties, this work focuses on the nonaffine HRI system and supposes that the desired trajectory is not available to the robot. A novel differential game framework encoding the desired trajectory estimator is proposed, where the desired trajectory is estimated via the Gaussian process regression (GPR) technique. To address the challenge arising from the nonlinearity of the HRI system, we equivalently transform the original problem into the one in a differentially flat space, and seek the equilibrium strategies for the transformed problem substitutionally. We further prove that the trajectory tracking error satisfies a probabilistic bound, whose confidence interval tightens as the decrease of noise variance during the interaction. Comparative simulation results show that our method outperforms the learning-based method in terms of robustness, parameters setting, and time consumption. Experiment results further show that the tracking error under the proposed human-robot cooperative algorithm is reduced by 55% compared to the human direct control.

The optimization of printed circuit board assembly (PCBA) for a beam head placement machine is a multivariable and multiconstraint combinatorial problem. Current techniques falter in solving a variety of PCBA problems since heuristic algorithms lack theoretical guarantees of optimality, and mathematical modeling methods have high computational complexity for the whole problem. This article proposes a novel two-phase optimization for PCBA, integrating the advantages of mathematical modeling with heuristic algorithms. We divide the problem into the head task assignment and the placement route schedule. For the former, an effective integer linear programming model with component partition is proposed, encompassing key efficiency-influencing factors. A recursive heuristic-based initial solution speeds up the solving convergence, while the reduction strategies enhance model solvability. For the placement route schedule, a tailored greedy algorithm yields high-quality solutions, leveraging the results of the model, and an aggregated route relink heuristic does further optimization. In addition, we propose a selection criterion for the solution pool of the model to pre-evaluate the placement movement, which builds the connection between the two phases. Finally, we validate the performance of the two-phase optimization, which provides an average efficiency improvement of 8.66%–21.83% compared to other mainstream research.

This article is centered on the cybersecurity research of dynamic state estimation for power systems with measurement delays. Relying on mixed measurements from phasor measurement units (PMUs) and remote terminal units (RTUs), a delayed measurement model is constructed. A modified state estimator based on the Kalman filter (KF) is designed, which can obtain the optimal estimated states under measurement delays. Moreover, the measurement data transmitted from the sensor to the estimator are vulnerable to cyberattacks. Especially, false data-injection (FDI) attacks are frequently encountered in the power system state estimation (PSSE) process. In the case of measurement delays, an FDI attack strategy is designed to interfere with the state estimator and evade detection by the chi-square detector. By utilizing the attacked estimated information and the uncorrupted measurement information, two measurement residual vectors are designed. According to these two residual vectors, a chi-square-based attack detection method is proposed, which has the ability to detect the attack without being affected by the delayed measurements. The proposed KF algorithm and attack detection method are implemented on an IEEE 14-bus system and they are confirmed to be effective and feasible.

This article is concerned with the output feedback security control of a class of high-order nonlinear-interconnected systems with denial-of-service (DoS) attacks, nonlinear dynamics, and exogenous disturbances. First, extreme learning machine (ELM) and adaptive techniques are adopted to approximate the unknown nonlinearities. Then, novel adaptive ELM-based nonlinear state observers with adaptive compensation functions are developed to estimate the unmeasurable states during DoS attacks under the influence of the disturbances. Further, by combining with the backstepping control and filtering techniques, adaptive ELM-based controllers are proposed to achieve uniformly ultimately bounded results based on the observation and adaption control signals under the influence of DoS attacks, nonlinear dynamics, and exogenous disturbances. Comparative studies are carried out to validate the effectiveness of the developed ELM-based adaptive observation and control strategies for two interconnected power systems.

In this article, two novel distributed variational Bayesian (VB) algorithms for a general class of conjugate-exponential models are proposed over synchronous and asynchronous sensor networks. First, we design a penalty-based distributed VB (PB-DVB) algorithm for synchronous networks, where a penalty function based on the Kullback-Leibler (KL) divergence is introduced to penalize the difference of posterior distributions between nodes. Then, a token-passing-based distributed VB (TPB-DVB) algorithm is developed for asynchronous networks by borrowing the token-passing approach and the stochastic variational inference. Finally, applications of the proposed algorithm on the Gaussian mixture model (GMM) are exhibited. Simulation results show that the PB-DVB algorithm has good performance in the aspects of estimation/inference ability, robustness against initialization, and convergence speed, and the TPB-DVB algorithm is superior to existing token-passing-based distributed clustering algorithms.

It is of great significance to develop a coordinated battery swapping station (BSS) recommendation method to reduce the cost of electric vehicles (EVs) and optimize the operation of BSS system. In this paper, the BSS recommendation problem is studied by comprehensively considering the battery swapping cost, diversity of BSS capacities, and differentiated demands of EVs, so as to be as close to the actual situation as possible. To describe the interactions among EVs, we propose a game theory-based approach to recommend appropriate BSSs for EVs to minimize the total cost (namely the sum of travel cost and battery swapping cost) of each EV. Under the game framework, a price function is designed to regulate the swapping price of each BSS, which acts as a coordination signal to induce EVs to join the game and also to alleviate congestion of BSSs. Then, an iterative algorithm is devised to seek the Nash equilibrium, through which a suitable BSS is determined for each EV. Compared to the shortest distance approach, the case studies indicate that the proposed approach can effectively reduce the average cost of EVs, improve the success rate of battery swapping, and balance the utilization ratio of BSSs.

In this article, the consensus problem of linear systems is revisited from a novel geometric perspective. The interaction network of these systems is assumed to be piecewise fixed. Moreover, it is allowed to be disconnected at any time but holds a quite mild joint connectivity property. The system matrix is marginally stable and the input matrix is not of full-row rank. By directly examining the subspace determined by the network, we first establish convergence by resorting to an observability condition. Then, according to joint connectivity, we are able to extend this convergence uniformly to the entire orthogonal complement of the consensus manifold. In this way, we work out the necessary and sufficient condition for exponential consensus. It turns out that, with a suitably designed feedback matrix, exponential consensus can be realized globally and uniformly if and only if a jointly (δ,T) -connected condition and an observability condition relying only on the system and input matrices are satisfied. We also characterize the lower bound of the convergence rate. Simple yet effective examples are presented to illustrate the findings.

This article studies the containment control problem for a group of linear systems, consisting of more than one leader, over switching topologies. The input matrices of these linear systems are not required to have full-row rank and the switching can be arbitrary, making the problem quite general and challenging. We propose a novel analysis framework from the viewpoint of a state transition matrix. Specifically, according to the inherent linearity, we successfully establish a connection between state transition matrices of the above multileader system and a virtual leader-following system obtained by combining those leaders. This enlightening result relates the containment problem to a consensus one. Then, by analyzing the property of the state transition matrix, we uncover that each component of any follower's state converges to the convex hull spanned by the corresponding components of the leaders', provided some mild conditions are satisfied. These conditions are derived in terms of the concept of a positive linear system. A special case of the second-order linear system is further discussed to illustrate these conditions. Moreover, two different design methods of the feedback gain matrix are provided, which additionally require that the network topology contains a united spanning tree all the time.

Optimal energy management of smart grids requires the information exchange between devices, which may disclose private information to the adversaries and further lead to great losses. To this end, this article considers the privacy-preserving optimal energy management problem for smart grids, which integrates both the power allocation of distributed energy resources on the supply side and the demand response of distributed load demands on the demand side. We first propose a cloud-edge computing structure of the smart grid and model the optimal energy management problem as the maximization problem of social welfare including the supply-side net benefit and the demand-side net utility, while maintaining the supply–demand balance and satisfying the operating constraints. A privacy-preserving average consensus algorithm is then developed, where each node sends the projected states to their neighbors to protect the privacy of the initial state. By applying the privacy-preserving average consensus algorithm, we propose a distributed privacy-preserving optimal energy management algorithm based on the generalized alternating direction method of multipliers. Finally, simulation examples are provided to validate the effectiveness of the proposed algorithms.

The development of electric vehicle (EV) industry is facing a series of issues, among which the efficient charging of multiple EVs needs solving desperately. This paper investigates the coordinated charging of multiple EVs with the aim of reducing the charging cost, ensuring a high battery state of charge (SoC), and avoiding the transformer overload. To this end, we first formulate the EV coordinated charging problem with the above multiple objectives as a Markov Decision Process (MDP) and then propose a multi-agent deep reinforcement learning (DRL)-based algorithm. In the proposed algorithm, a novel interaction model, i.e., communication neural network (CommNet) model, is adopted to realize the distributed computation of global information (namely the electricity price, the transformer load, and the total charging cost of multiple EVs). Moreover, different from the most existing works which make specific constraints on the size, the location, or the topology of the distribution network, what we need in the proposed method is only the transformer load. Besides, due to the use of long and short-term memory (LSTM) for price prediction, the proposed algorithm can flexibly deal with various uncertain price mechanisms. Finally, simulations are presented to verify the effectiveness and practicability of the proposed algorithm in a residential charging area.

In this article, we study a multiplayer Stackelberg-Nash game (SNG) pertaining to a nonlinear dynamical system, including one leader and multiple followers. At the higher level, the leader makes its decision preferentially with consideration of the reaction functions of all followers, while, at the lower level, each of the followers reacts optimally to the leader's strategy simultaneously by playing a Nash game. First, the optimal strategies for the leader and the followers are derived from down to the top, and these strategies are further shown to constitute the Stackelberg-Nash equilibrium points. Subsequently, to overcome the difficulty in calculating the equilibrium points analytically, we develop a novel two-level value iteration-based integral reinforcement learning (VI-IRL) algorithm that relies only upon partial information of system dynamics. We establish that the proposed method converges asymptotically to the equilibrium strategies under the weak coupling conditions. Moreover, we introduce effective termination criteria to guarantee the admissibility of the policy (strategy) profile obtained from a finite number of iterations of the proposed algorithm. In the implementation of our scheme, we employ neural networks (NNs) to approximate the value functions and invoke the least-squares methods to update the involved weights. Finally, the effectiveness of the developed algorithm is verified by two simulation examples.

Inspired by the collective decision making in biological systems, such as honeybee swarm searching for a new colony, we study a dynamic collective choice problem for large-population systems with the purpose of realizing certain advantageous features observed in biology. This problem focuses on the situation where a large number of heterogeneous agents subject to adversarial disturbances move from initial positions toward one of the destinations in a finite time while trying to remain close to the average trajectory of all agents. To overcome the complexity of this problem resulting from the large population and the heterogeneity of agents, and also to enforce some specific choices by individuals, we formulate the problem under consideration as a robust mean-field game with non-convex and non-smooth cost functions. Through Nash equivalence principle, we first deal with a single-player$H_{\infty }$tracking problem by taking the population behavior as a fixed trajectory, and then establish a mean-field system to estimate the population behavior. Optimal control strategies and worst disturbances, independent of the population size, are designed, which give a way to realize the collective decision-making behavior emerged in biological systems. We further prove that the designed strategies constitute$\epsilon _{N}$-Nash equilibrium, where$\epsilon _{N}$goes toward zero as the number of agents increases to infinity. The effectiveness of the proposed results are illustrated through two simulation examples.

This article is concerned with the robust adaptive control circuit design for pulse wide modulation (PWM)-based dc–dc buck converters with load variations and exogenous disturbances. A robust adaptive perturbation rejection control strategy is first developed to suppress time-varying and state-dependent perturbations, which are composed of load variations and disturbances. Then, equivalent analog control circuits of the adaptive control strategy are implemented on the basis of the circuit theory. Bounded tracking of the closed-loop converter system in the presence of perturbations is achieved based on the Lyapunov stability theorem. Simulations and experimental results are provided to validate the efficiency of the proposed adaptive perturbation rejection control strategy in a dc–dc buck converter system.

Learning driving policies using an end-to-end network has been proved a promising solution for autonomous driving. Due to the lack of a benchmark driver behavior dataset that contains both the visual and the LiDAR data, existing works solely focus on learning driving from visual sensors. Besides, most works are limited to predict steering angle yet neglect the more challenging vehicle speed control problem. In this paper, we propose a novel end-to-end network, FlowDriveNet, which takes advantages of sequential visual data and LiDAR data jointly to predict steering angle and vehicle speed. The main challenges of this problem are how to efficiently extract driving-related information from images and point clouds, and how to fuse them effectively. To tackle these challenges, we propose a concept of point flow and declare that image optical flow and LiDAR point flow are significant motion cues for driving policy learning. Specifically, we first create an enhanced dataset that consists of images, point clouds and corresponding human driver behaviors. Then, in FlowDriveNet, a deep but efficient visual feature extraction module and a point feature extraction module are utilized to extract spatial features from optical flow and point flow, respectively. Additionally, a novel temporal fusion and prediction module is designed to fuse temporal information from the extracted spatial feature sequences and predict vehicle driving commands. Finally, a series of ablation experiments verify the importance of optical flow and point flow and comparison experiments show that our flow-based method outperforms the existing image-based approaches on the task of driving policy learning.

In this paper, we investigate the issue of security on the remote state estimation in cyber-physical systems (CPSs), where a wireless sensor utilizes the channel hopping scheme to transmit the data to the remote estimator over multiple channels in the presence of periodic denial-of-service attacks. Assume that the jammer can interfere with a subset of channels at each attack time in active period. For an energy-constraint jammer, the problem of how to select the number of channels at each attack time to maximally deteriorate the CPS performance is investigated. Based on the index of average estimation error, we introduce two different attack strategies, which include selecting identical number of channels and unequal number of channels at each attack time, and further show theoretically that the attack effect by selecting unequal number of channels is better than that of selecting identical number of channels. By formulating the problem of selecting the number of channels as integer programming problems, we present the corresponding algorithm to approximate the optimal attack schedule for both cases. The numerical results are presented to validate the theoretical results and the effectiveness of the proposed algorithms.

Considering the fact that in the real world, a certain agent may have some sort of advantage to act before others, a novel hierarchical optimal synchronization problem for linear systems, composed of one major agent and multiple minor agents, is formulated and studied in this article from a Stackelberg-Nash game perspective. The major agent herein makes its decision prior to others, and then, all the minor agents determine their actions simultaneously. To seek the optimal controllers, the Hamilton-Jacobi-Bellman (HJB) equations in coupled forms are established, whose solutions are further proven to be stable and constitute the Stackelberg-Nash equilibrium. Due to the introduction of the asymmetric roles for agents, the established HJB equations are more strongly coupled and more difficult to solve than that given in most existing works. Therefore, we propose a new reinforcement learning (RL) algorithm, i.e., a two-level value iteration (VI) algorithm, which does not rely on complete system matrices. Furthermore, the proposed algorithm is shown to be convergent, and the converged values are exactly the optimal ones. To implement this VI algorithm, neural networks (NNs) are employed to approximate the value functions, and the gradient descent method is used to update the weights of NNs. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.

This paper is concerned with the robust constrained control problem for a class of fault-tolerant time-varying systems against actuator faults and input amplitude saturation. An adaptive technique is proposed to compensate for the impacts of actuator bias faults and partial loss of control effectiveness, as well as to eliminate the effects of unknown time-varying parameters of the systems. An auxiliary system is developed to ensure that the actuator behaves within the limitation of the actuator amplitude. Based on the compensation strategies and auxiliary signals, a novel adaptive fault-tolerant constrained controller is constructed to guarantee the convergence of the system states into a small stability domain in the presence of actuator faults, actuator amplitude limitations, and unknown system parameters. An example of F-18 flight control systems is given to illustrate the proposed procedures and its effectiveness.

Recent works have proved that combining spatial and temporal visual cues can significantly improve the performance of various vision-based robotic systems. However, for the ultrasonic sensors used in most robotic tasks (e.g. collision avoidance, localization and navigation), there is a lack of benchmark ultrasonic datasets that consist of spatial and temporal data to verify the usability of spatial and temporal ultrasonic cues. In this paper, we are the first to propose a Spatio-Temporal Ultrasonic Dataset (STUD), which aims to develop the ability of ultrasonic sensors by mining spatial and temporal information from multiple ultrasonic measurements. In particular, we first propose a novel Spatio-Temporal (ST) ultrasonic data gathering scheme, in which an innovatory data instance is designed. Besides, part of the data in the STUD is collected in a robot simulator, in which a well-designed corridor map is utilized to increase the data diversity. Then a selection algorithm is proposed to find a proper length of data sequences to obtain the best description of the navigation environments. Finally, we present an end-to-end learning benchmark model that learns driving policies by extracting spatial and temporal ultrasonic cues from the STUD. With the help of our STUD and this benchmark model, more powerful deep neural networks can be trained for addressing the tasks of indoor navigation or motion planning of mobile robots, which is unachievable by using the existing ultrasonic datasets. Comparison experiments verified the effectiveness of spatial and temporal ultrasonic cues for the robot driving policy learning.

Economic dispatch (ED) and unit commitment (UC) problems need to be revisited in order to make a transition from a traditional power system to a smart grid. In this paper, we formulate the ED and UC problems into a unified form, which is also capable of characterizing the infinite horizon UC problem. Based on the formulation, a centralized Q -learning-based optimization algorithm is proposed. The proposed algorithm runs in an online manner and requires no prior information on the mathematical formulation of the actual cost functions, thus being capable of dealing with situations for which such cost functions are too difficult to obtain. Then, the distributed counterpart of the centralized algorithm is developed by relaxing the demand for global information and balancing exploration and exploitation cooperatively in a distributed way. Theoretical analysis of the proposed algorithms is also provided. Finally, several case studies are presented to demonstrate the effectiveness of the proposed algorithms.

This article considers the resilient consensus problems of discrete-time complex cyber-physical networks under F-local deception attacks. A resilient consensus algorithm, where extreme values received are removed by each node, is first introduced. By utilizing the presented algorithm, a necessary and sufficient condition to ensure resilient consensus in the absence of trusted edges is then provided by means of network robustness. We further generalize the notion of network robustness and present the necessary and sufficient condition for the achievement of resilient consensus in the presence of trusted edges. In addition, we show that through appropriately assigning the trusted edges, the resilient consensus can be reached under arbitrary communication network. Finally, the validity of the theoretical findings is demonstrated by simulation examples.

In this paper, we investigate the output containment control problem for a network of heterogeneous linear multiagent systems. The control target is to drive the outputs of the followers into the convex hull spanned by the leaders. To this end, we first derive a necessary condition imposed on both system dynamics and network topology from the viewpoint of internal model principle. Then, based on the necessary condition, we utilize a dynamic controller to drive the outputs of the leaders and followers to track the reference trajectories to achieve containment exponentially. We consider a general network topology which only contains a united spanning tree. Both fixed and dynamic network topologies are taken into consideration. Then, the optimal control problem for containment is further studied. An optimal control law is constructed from an algebraic Riccati equation, which is proved to be a stabilizing one as well. Finally, a reinforcement learning algorithm is introduced to solve the optimal control problem on line without the knowledge the system dynamics. Simulations are given at last to validate our theoretical findings.

This paper investigates the consensus tracking problem of second-order nonlinear multiagent systems (MAS) with disturbance and actuator fault by the sliding mode control method. The communication topology of the MAS is directed and only part of the followers have access to the leader's information. First, a discontinuous sliding mode tracking protocol is studied for consensus tracking of the MAS. Second, to address the shortcoming of chattering and difficulty of setting the control gain in the discontinuous protocol, a continuous sliding mode tracking protocol with an adaptive mechanism is developed. The adaptive mechanism will adjust the gain of the control automatically and enable the tracking protocol to work well without prior knowledge of the MAS. Third, the performance of the adaptive sliding mode protocol for consensus tracking of the MAS in the presence of actuator faults of biased fault and partial loss of effectiveness fault is further investigated. Finally, numerical simulations are performed to illustrate the efficiency of the theoretical results.

An intuitionistic fuzzy cognitive map (IFCM) is an extension of a fuzzy cognitive map (FCM) that forms a graph-oriented fuzzy map describing both causal relationships between pairs of concepts and the states of concepts via intuitionistic fuzzy sets (IFSs). In contrast with an FCM, an IFCM provides much more flexibility in system modeling. However, IFCMs may lead to confusing or unreasonable results in system modeling since they do not fully consider the negative influence from conventional operations on IFSs, the activation process of concepts, and the problem of aggregating knowledge with different importance levels. To solve the challenges of IFCMs, we propose a high-order IFCM based on evidential reasoning (ER) (IFCMR) theory in this study. First, we introduce an evidential intuitionistic fuzzy aggregation (EIFA) operator and a multiplication operation on IFSs using an ER theory. Second, we establish the theory of IFCMR based on the EIFA operator and the newly introduced multiplication operation on IFSs. Third, we propose a scheme of aggregating IFCMRs with different importance levels using the EIFA operator, which can also be utilized to aggregate conflict knowledge and to determine objective connections in terms of an evidential cognitive map (ECM). Finally, several numerical and practical examples are employed to test and verify the feasibility and validity of IFCMRs in comparison with both IFCMs and ECMs.

In network systems, a group of nodes may evolve into several subgroups and coordinate with each other in the same subgroup, i.e., reach cluster synchronization, to cope with the unanticipated situations. To this end, the leader-following practical cluster synchronization problem of networks of generic linear systems is studied in this paper. An event-based control algorithm that can largely reduce the amount of communication is first proposed over directed communication topologies. In the proposed algorithm, each node decides itself when to transmit its current state to its neighbors and how to update its controller according to the estimations of the states of it and its neighbors. Then, the Lyapunov method is utilized to perform the convergence analysis. It shows that the practical cluster synchronization can be ensured by choosing appropriate parameters no matter what kind of estimation for the state is applied. Furthermore, the Zeno behavior is also excluded for each node under some mild assumptions. Besides, three kinds of common estimations for the states including zero-order hold model, first-order approximate model, and high-order model-based estimations are, respectively, analyzed from the perspective of the exclusion of Zeno behavior. Finally, the validity of the proposed algorithm is demonstrated, the effects of the concerned parameters are simply presented, and the effects of the three estimations are also compared through several simulations.

In this paper, we aim to investigate the optimal synchronization problem for a group of generic linear systems with input saturation. To seek the optimal controller, Hamilton-Jacobi-Bellman (HJB) equations involving nonquadratic input energy terms in coupled forms are established. The solutions to these coupled HJB equations are further proven to be optimal and the induced controllers constitute interactive Nash equilibrium. Due to the difficulty to analytically solve HJB equations, especially in coupled forms, and the possible lack of model information of the systems, we apply the data-based off-policy reinforcement learning algorithm to learn the optimal control policies. A byproduct of this off-policy algorithm is shown that it is insensitive to probing noise that is exerted to the system to maintain persistence of excitation condition. In order to implement this off-policy algorithm, we employ actor and critic neural networks to approximate the controllers and the cost functions. Furthermore, the estimated control policies obtained by this presented implementation are proven to converge to the optimal ones under certain conditions. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.

In this paper, the consensus problem is investigated for a class of nonaffine nonlinear multiagent systems (MASs) with actuator faults of partial loss of effectiveness fault and biased fault. To deal with the control difficulty caused by the nonaffine dynamics, a neural network (NN)-based adaptive consensus protocol is developed based on the Lyapunov analysis. The neuron input of the NN uses both the state information and the consensus error information. In addition, the negative feedback term of the NN weight update law is multiplied by an absolute value of the consensus error, which is helpful in improving the consensus accuracy. With the developed adaptive NN consensus protocol, semiglobal consensus with a bounded residual consensus error of the MAS is achieved, and the bounded NN weight matrix is guaranteed. Finally, simulation results show that the developed adaptive NN consensus protocol has advantages of fast convergence rate and good consensus accuracy and has the capability of rapid response with respect to the actuator faults.

This paper proposes three different distributed event-triggered control algorithms to achieve leader-follower consensus for a network of Euler-Lagrange agents. We first propose two model-independent algorithms for a subclass of Euler-Lagrange agents without the vector of gravitational potential forces. By model-independent, we mean that each agent can execute its algorithm with no knowledge of the agent self-dynamics. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work studying event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities, which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information, and bounds on the initial conditions. When the Euler-Lagrange agents have dynamics that include the vector of gravitational potential forces, an adaptive algorithm is proposed. This requires more information about the agent dynamics but allows for the estimation of uncertain parameters associated with the agent self-dynamics. For each algorithm, a trigger function is proposed to govern the event update times. The controller is only updated at each event, which ensures that the control input is piecewise constant and thus saves energy resources. We analyze each controller and trigger function to exclude Zeno behavior.

This paper presents a novel indoor localization method for skid-steering mobile robot by fusing the readings from encoder, gyroscope, and magnetometer which can be read as an enhanced dead-reckoning localization method. Compared with the traditional dead-reckoning localization method implemented by encoder only, the accuracy and reliability can be improved significantly in spite of the price of slightly higher cost in digital devices. The proposed strategy consists mainly of an orientation algorithm and a localization algorithm. First, realizing that gyroscope is barely affected by magnetic field and magnetometer-based orientation has no cumulative error, a novel orientation algorithm, based on the self-tuning Kalman filter coupled with a gross error recognizer, is developed. This orientation algorithm can be applied to determine the robot heading angle in the situation with abundant ferromagnetic materials. Second, based on the orientation algorithm we have proposed, a novel localization algorithm is designed by decomposing the robot motion into uniform linear motion and uniform circular motion. The effectiveness of the proposed indoor localization method is verified via the real-world experiment using a tracked mobile robot developed in our laboratory.

The cluster synchronization problem is investigated using intermittent pinning control for the interacting clusters of nonidentical nodes that may represent either general linear systems or nonlinear oscillators. These nodes communicate over general network topology, and the nodes from different clusters are governed by different self-dynamics. A unified convergence analysis is provided to analyze the synchronization via intermittent pinning controllers. It is observed that the nodes in different clusters synchronize to the given patterns if a directed spanning tree exists in the underlying topology of every extended cluster (which consists of the original cluster of nodes as well as their pinning node) and one algebraic condition holds. Structural conditions are then derived to guarantee such an algebraic condition. That is: 1) if the intracluster couplings are with sufficiently strong strength and the pinning controller is with sufficiently long execution time in every period, then the algebraic condition for general linear systems is warranted and 2) if every cluster is with the sufficiently strong intracluster coupling strength, then the pinning controller for nonlinear oscillators can have its execution time to be arbitrarily short. The lower bounds are explicitly derived both for these coupling strengths and the execution time of the pinning controller in every period. In addition, in regard to the above-mentioned structural conditions for nonlinear systems, an adaptive law is further introduced to adapt the intracluster coupling strength, such that the cluster synchronization for nonlinear systems is achieved.

In this paper, the problem of fault tolerant tracking control for a linear time-invariant system subject to actuator faults and saturations is addressed. An auxiliary system is developed to ensure actuators behave within amplitude and rate limits under the influence of partial loss of control effectiveness. Based on the auxiliary system, a fault tolerant compensation controller is constructed to guarantee tracking errors to converge to a small region. Some relationships among tracking errors, command signals, actuator faults, amplitude and rate limits as well as controller parameters are comprehensively studied and explicitly illustrated with formulas. An example of rudder-roll damping control for a cruise keeping ship is included to illustrate the proposed procedures and their effectiveness.

The vehicle emission remote sensing system is one promising solution to monitor the emissions of on-road vehicles that contribute to the air pollution in urban areas. To implement such a system an effective location strategy to place the monitors is yet to be designed. To this purpose we formulate a novel location problem where the minimum subset of roads on which traffic emission monitors are located is to be found only using the topological structure and some other available information of the traffic network. We solve this problem by transforming it into a graph-theoretic problem and considering more characteristics such as the traffic regulations and limits. After modeling the real-world traffic network as a digraph, a two-step algorithm is developed. The first step is to find all directed circuits to establish hypergraph-based set of directed circuits using the depth first searching strategy. In the second step, an approximation algorithm is designed to find the greedy transversal which is a subset of roads to place vehicle emission monitors in order to cover all the traffic circuits. The performance of the location strategy is validated by both theoretical developments and illustrative examples.

In this paper, the non-fragile finite-time tracking control problem is addressed for a class of uncertain linear systems with controller multiplicative coefficient variations. An adaptive control strategy is constructed to ensure that the system tracks a time-varying target orbit. The relationship of the bound of tracking errors and the size of uncertainties and controller multiplicative coefficient variations is deeply investigated. On the basis of Lyapunov stability theory, it shows that the bounded tracking of resulting adaptive system can be reached within a finite time, and the tracking errors of the system can be reduced as small as desired by adjusting controller parameters. The effectiveness of the proposed design is illustrated via a decoupled longitudinal model of F-18 aircraft.

This paper is concerned with developing a distributed k-means algorithm and a distributed fuzzy c-means algorithm for wireless sensor networks (WSNs) where each node is equipped with sensors. The underlying topology of the WSN is supposed to be strongly connected. The consensus algorithm in multiagent consensus theory is utilized to exchange the measurement information of the sensors in WSN. To obtain a faster convergence speed as well as a higher possibility of having the global optimum, a distributed k-means++ algorithm is first proposed to find the initial centroids before executing the distributed k-means algorithm and the distributed fuzzy c-means algorithm. The proposed distributed k-means algorithm is capable of partitioning the data observed by the nodes into measure-dependent groups which have small in-group and large out-group distances, while the proposed distributed fuzzy c-means algorithm is capable of partitioning the data observed by the nodes into different measure-dependent groups with degrees of membership values ranging from 0 to 1. Simulation results show that the proposed distributed algorithms can achieve almost the same results as that given by the centralized clustering algorithms.

The bipartite consensus problem for a group of homogeneous generic linear agents with input saturation under directed interaction topology is examined. It is established that if each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique. The convergence analysis of the proposed control strategy is performed by means of the Lyapunov method which can also specify the convergence rate. At last, the validity of the theoretical findings is demonstrated by two simulation examples.

This paper investigates group synchronization for multiple interacting clusters of nonidentical systems that are linearly or nonlinearly coupled. By observing the structure of the coupling topology, a Lyapunov function-based approach is proposed to deal with the case of linear systems which are linearly coupled in the framework of directed topology. Such an analysis is then further extended to tackle the case of nonlinear systems in a similar framework. Moreover, the case of nonlinear systems which are nonlinearly coupled is also addressed, however, in the framework of undirected coupling topology. For all these cases, a consistent conclusion is made that group synchronization can be achieved if the coupling topology for each cluster satisfies certain connectivity condition and further, the intra-cluster coupling strengths are sufficiently strong. Both the lower bound for the intra-cluster coupling strength as well as the convergence rate are explicitly specified.

The containment control is studied for the second-order multiagent systems over a heterogeneous network where the position and velocity interactions are different. We consider three cases that multiple leaders are stationary, moving at the same constant speed, and moving at the same time-varying speed, and develop different containment control algorithms for each case. In particular, for the former two cases, we first propose the containment algorithms based on the well-established ones for the homogeneous network, for which the position interaction topology is required to be undirected. Then, we extend the results to the general setting with the directed position and velocity interaction topologies by developing a novel algorithm. For the last case with time-varying velocities, we introduce two algorithms to address the containment control problem under, respectively, the directed and undirected interaction topologies. For most cases, sufficient conditions with regard to the interaction topologies are derived for guaranteeing the containment behavior and, thus, are easy to verify. Finally, six simulation examples are presented to illustrate the validity of the theoretical findings.

Some applications of the interconnected embedded systems such as sensor networks rely on all nodes in the network to execute certain tasks simultaneously. To meet this demand for simultaneity, a multi-timer model based fully distributed task synchronization algorithm is proposed in this paper. In this multi-timer model, each node containing an embedded system is characterized by a timer. The microcontrollers (MCUs) within the interconnected embedded systems are switched to the assigned tasks by timer interrupts. Each timer decides when to trigger interrupts by only using the information from its neighbors. Task synchronization is realized by using the proposed synchronization algorithm. Some simulation examples are presented in the end to verify the effectiveness of the proposed synchronization algorithm.

In this paper, the contraction theory is used to analyze the synchronization for a collection of partial-state linearly coupled linear systems. First, the synchronization problem of the linear systems is transformed by defining proper error variables such that a stability problem of error systems is to be investigated. Then, the contraction analysis is performed with respect to the error system dynamics. It turns out that the error system dynamics is contracting, which in turn proves that the original systems reach synchronization exponentially fast. In addition, a brief comparison between Lyapunov method and contraction analysis is also provided. Finally, two examples are presented in order to illustrate the effectiveness of the theoretical result.

This paper studies the fault-tolerant consensus problem for a group of double-integrator agents with actuator faults and strongly connected topology. The proposed fault-tolerant consensus protocol is an active fault-tolerant control strategy which consists of a nominal control and an estimation of fault severity. To solve the fault-tolerant consensus problem, a Lyapuov method is employed based on the algebraic connectivity of strongly connected digraph. The results show that the consensus will be achieved if the nominal control is designed properly and the estimation of actuator fault is within a certain accuracy. Finally, a simulation example is given to demonstrate the validity of the theoretical results.

A unified approach to the analysis of synchronization for complex dynamical networks, i.e., networks of partial-state coupled linear systems and networks of full-state coupled nonlinear oscillators, is introduced. It is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks, thus making it feasible to consider the error dynamics for the whole network system. Different from the other various methods given in the existing literature, the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form, but also explicitly specifying the convergence rate.

This paper investigates the H∞ consensus control problem of nonlinear multiagent systems under an arbitrary topological structure. A novel Takagi-Sukeno (T-S) fuzzy modeling method is proposed to describe the problem of nonlinear follower agents approaching a time-varying leader, i.e., the error dynamics between the follower agents and the leader, whose dynamics is evolving according to an isolated unforced nonlinear agent model, is described as a set of T-S fuzzy models. Based on the model, a leader-following consensus algorithm is designed so that, under an arbitrary network topology, all the follower agents reach consensus with the leader subject to external disturbances, preserving a guaranteed H(∞) performance level. In addition, we obtain a sufficient condition for choosing the pinned nodes to make the entire multiagent network reach consensus. Moreover, the fuzzy modeling method is extended to solve the synchronization problem of nonlinear systems, and a fuzzy H(∞) controller is designed so that two nonlinear systems reach synchronization with a prescribed H(∞) performance level. The controller design procedure is greatly simplified by utilization of the proposed fuzzy modeling method. Finally, numerical simulations on chaotic systems and arbitrary nonlinear functions are provided to illustrate the effectiveness of the obtained theoretical results.

We consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs. Different algorithms are proposed and analyzed for different settings, including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies, as well as the case with a group velocity reference signal under switching velocity interaction. It is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions. Such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify. Rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory, matrix analysis as well as the Lyapunov stability theory.

This paper is concerned with the asynchronous consensus problem of discrete-time second-order multi-agent system under dynamically changing communication topology, in which the asynchrony means that each agent detects the neighbors' state information to update its state information by its own clock. It is not assumed that the agents' clocks are synchronized. Nor is it assumed that the time sequence over which each agent update its state information is evenly spaced. By using tools from graph theory and nonnegative matrix theory, particularly the product properties of row-stochastic matrices from an infinite set, we finally show that essentially the same result as that for the synchronous discrete-time system holds in the face of asynchronous setting. This generalizes the existing result to a very general case.

The problem of the convergence of the consensus strategies for multiple agents with double-integrator dynamics is studied in this paper. The investigation covers two kinds of different settings. In the setting with the interaction topologies for the position and velocity information flows being modeled by different graphs, some sufficient conditions on the fixed interaction topologies are derived for the agents to reach consensus. In the setting with the interaction topologies for the position and velocity information flows being modeled by the same graph, we systematically investigate the consensus algorithm for the agents under both fixed and dynamically changing directed interaction topologies. Specifically, for the fixed case, a necessary and sufficient condition on the interaction topology is established for the agents to reach (average) consensus under certain assumptions. For the dynamically changing case, some sufficient conditions are obtained for the agents to reach consensus, where the condition imposed on the dynamical topologies is shown to be more relaxed than that required in the existing literature. Finally, we demonstrate the usefulness of the theoretical findings through some numerical examples.

This paper is concerned with synchronizing complex networks with arbitrary topological structures via pinning control. The necessary and sufficient conditions are established for choosing the pinned nodes to guarantee the pinning synchronzability of the complex networks. Under the assumption of the sufficient large coupling strength, it is shown that the way to pin the nodes is a decisive factor in determining the pinning synchronizability of complex networks and the entire network can achieve an exponentially fast speed of synchronization.