Adaptive Sliding Mode Consensus Tracking for Second-Order Nonlinear Multiagent Systems With Actuator Faults

Approximate optimal and safe coordination of nonlinear second-order multirobot systems with model uncertainties

This paper investigates the approximate optimal coordination for nonlinear uncertain second-order multi-robot systems with guaranteed safety (collision avoidance) Through constructing novel local error signals, the collision-free control objective is formulated into an coordination optimization problem for nominal multi-robot systems. Based on approximate dynamic programming technique, the optimal value functions and control policies are learned by simplified critic-only neural networks (NNs). Then, the approximated optimal controllers are redesigned using adaptive law to handle the effects of robots' uncertain dynamics. It is shown that the NN weights estimation errors are uniformly ultimately bounded under proper conditions, and safe coordination of multiple robots can be achieved regardless of model uncertainties. Numerical simulations finally illustrate the effectiveness of the proposed controller.

PD and PI Control for the Lag Consensus of Nonlinear Multiagent Systems With and Without External Disturbances

In this article, we investigate the lag consensus and lag H∞ consensus problems for second-order nonlinear multiagent systems (MASs) by utilizing the proportional-derivative (PD) and proportional-integral (PI) control methods. On the one hand, a criterion is developed for ensuring the lag consensus of the MAS by choosing an appropriate PD control protocol. Moreover, a PI controller is also provided to guarantee that the MAS can achieve lag consensus. On the other hand, several lag H∞ consensus criteria are also given for the case in which external disturbances appear in the MAS; these criteria are developed by exploiting the PD and PI control strategies. Finally, the devised control schemes and the developed criteria are verified by employing two numerical examples.

Robust Cooperative Fault-Tolerant Control for Uncertain Multi-Agent Systems Subject to Actuator Faults

This article investigates the robust cooperative fault-tolerant control problem of multi-agent systems subject to mismatched uncertainties and actuator faults. During the design process of the intermediate variable estimator, there is no need to satisfy fault estimation matching conditions, and this overcomes a crucial constraint of traditional observers and estimators. The feedback term of the designed estimator contains the centralized estimation errors and the distributed estimation errors of the agent, and this further improves the design freedom of the proposed estimator. A novel fault-tolerant control protocol is designed based on the fault estimation information. In this work, the bounds of the fault and its derivatives are unknown, and the considered method is applicable to both directed and undirected multi-agent systems. Furthermore, the parameters of the estimator are determined through the resolution of a linear matrix inequality (LMI), which is decoupled by employing coordinate transformation and Schur decomposition. Lastly, a numerical simulation result is used to demonstrate the effectiveness of the proposed method.

Distributed Discrete-time Exponential Sliding Mode Consensus Protocol for Discrete Multi-Agent System Comprise of Multiple Robotic Arms

In this paper, a Distributed Discrete-time Exponential Sliding Mode Consensus (DDESMC) protocol is proposed for the leader-follower consensus of a Discrete Multi-Agent System (DMAS). The proposed protocol ensures not only the minimal consensus effort and reaching time for the consensus among the agents but also the minimum consensus deviation in the order of O(T3). The consensus stability of DMAS with the proposed protocol is analyzed using Lyapunov theory and the maximum number of reaching steps required for achieving the consensus among all agents is calculated. The proposed protocol is validated in a simulation and experimental setup comprised of multiple 2-Degree of Freedom (DOF) robotic arms where one of the robotic arms is real, and others are virtual. Further, the consensus performance compared with the existing protocol in the literature, and it is inferred that the proposed protocol outperforms it in terms of time and effort required to achieve the consensus and the deviation from the consensus.

Bipartite consensus for multi-agent networks of fractional diffusion PDEs via aperiodically intermittent boundary control

In this paper, the exponential bipartite consensus issue is investigated for multi-agent networks, whose dynamic is characterized by fractional diffusion partial differential equations (PDEs). The main contribution is that a novel exponential convergence principle is proposed for networks of fractional PDEs via aperiodically intermittent control scheme. First, under the aperiodically intermittent control strategy, an exponential convergence principle is developed for continuously differentiable function. Second, on the basis of the proposed convergence principle and the designed intermittent boundary control protocol, the exponential bipartite consensus condition is addressed in the form of linear matrix inequalities (LMIs). Compared with the existing works, the result of the exponential intermittent consensus presented in this paper is applied to the networks of PDEs. Finally, the high-speed aerospace vehicle model is applied to verify the effectiveness of the control protocol.

Adaptive Event-Triggered Sliding-Mode Control for Consensus Tracking of Nonlinear Multiagent Systems With Unknown Perturbations

The adaptive tracking control problem of leader-following nonlinear multiagent systems (MASs) subject to unknown perturbations and limited network bandwidth is investigated by the robust adaptive event-triggered sliding-mode control method. A distributed integral sliding mode is established to realize the finite-time reachability of the states of the leader-following nonlinear MAS. An adaptive triggering control mechanism is then put forward to dynamically adjust the triggering interval, thus reducing the actuator wear and unnecessary network resource consumption. The positions and velocities of the leader-following nonlinear MAS subject to unknown external disturbances are, respectively, driven to the equilibrium point by constructing a distributed event-based robust adaptive sliding-mode protocol. Via the Lyapunov stability theory and Barbalat lemma, sufficient conditions to ensure the adaptive tracking performance are derived for leader-following nonlinear MASs. Three simulation examples to verify the efficacy of the proposed event-based robust adaptive sliding-mode controller design are presented.

Event-Triggered Sliding Mode Neural Network Controller Design for Heterogeneous Multi-Agent Systems

A class of heterogeneous second-order multi-agent consensus problems is studied, in which an event-triggered method is used to improve the feasibility of the control protocol. The sliding mode control method is used to achieve the robustness of the system. A special type of general radial basis function neural network is applied to estimate the uncertainties. The event-triggered mechanism is introduced to reduce the update frequency of the controller and the communication frequency among the agents. Zeno behavior is avoided by ensuring a lower bound between two adjacent trigger instants. Finally, the simulation results are provided to demonstrate that the time evolution of consensus errors eventually approaches zero. The consensus of multi-agent systems is achieved.

Consensus Tracking of Nonlinear Agents Using Distributed Nonlinear Dynamic Inversion with Switching Leader-Follower Connection

In this paper, a consensus tracking protocol for nonlinear agents is presented, which is based on the Nonlinear Dynamic Inversion (NDI) technique. Implementation of such a technique is new in the context of the consensus tracking problem. The tracking capability of nonlinear dynamic inversion (NDI) is exploited for a leader-follower multi-agent scenario. We have provided all the mathematical details to establish its theoretical foundation. Additionally, a convergence study is provided to show the efficiency of the proposed controller. The performance of the proposed controller is evaluated in the presence of both (a) random switching topology among the agents and (b) random switching of leader-follower connections, which is realistic and not reported in the literature. The follower agents track various trajectories generated by a dynamic leader, which describes the tracking capability of the proposed controller. The results obtained from the simulation study show how efficiently this controller can handle the switching topology and switching leader-follower connections.

Stable Spinning Deployment Control of a Triangle Tethered Formation System

The tethered formation system has been widely studied due to its extensive use in aerospace engineering, such as Earth observation, orbital location, and deep space exploration. The deployment of such a multitethered system is a problem because of the oscillations and complex formation maintenance caused by the space tether's elasticity and flexibility. In this article, a triangle tethered formation system is modeled, and an exact stable condition for the system's maintaining is carefully analyzed, which is given as the desired trajectories; then, a new control scheme is designed for its spinning deployment and stable maintenance. In the proposed scheme, a novel second-order sliding mode controller is given with a designed nonsingular sliding-variable. Based on the theoretical proof, the addressed sliding variable from the arbitrary initial condition can converge to the manifold in finite time, and then sliding to the equilibrium in finite time as well. The simulation results show that compared with classic second sliding-mode control, the proposed scheme can speed up the convergence of the states and sliding variables.

Integral Non-Singular Terminal Sliding Mode Consensus Control for Multi-Agent Systems with Disturbance and Actuator Faults Based on Finite-Time Observer

This paper studies the consensus fault-tolerant control problem of a class of second-order leader–follower multi-agent systems with unknown disturbance and actuator faults, and proposes an integral non-singular terminal sliding mode control algorithm based on a finite-time observer. First, a finite-time disturbance observer was designed based on a combination of high-order sliding mode and dual layers adaptive rules to realize fast estimation and compensation of disturbance and faults. Then, a sliding surface with additional integral links was designed based on the conventional sliding surface, and an integral non-singular terminal sliding mode controller is proposed to realize the robust consensus in finite time and accurately diminish the chattering phenomena. Finally, a numerical example and simulation verify the effectiveness.

Adaptive NN-Based Consensus for a Class of Nonlinear Multiagent Systems With Actuator Faults and Faulty Networks

This article addresses the problem of fault-tolerant consensus control of a general nonlinear multiagent system subject to actuator faults and disturbed and faulty networks. By using neural network (NN) and adaptive control techniques, estimations of unknown state-dependent boundaries of nonlinear dynamics and actuator faults, which can reflect the worst impacts on the system, are first developed. A novel NN-based adaptive observer is designed for the observation of faulty transformation signals in networks. On the basis of the NN-based observer and adaptive control strategies, fault-tolerant consensus control schemes are designed to guarantee the bounded consensus of the closed-loop multiagent system with disturbed and faulty networks and actuator faults. The validity of the proposed adaptively distributed consensus control schemes is demonstrated by a multiagent system composed of five nonlinear forced pendulums.

Fault-Tolerant Cooperative Control for Multiple Vehicle Systems Based on Topology Reconfiguration

In this article, the fault-tolerant synchronization and time-varying tracking control problem is investigated for nonlinear multivehicle systems (MVSs) in the presence of partial loss-of-control-effectiveness (LoCE) faults. Based on the graph theory, a two-level fault-tolerant cooperative control framework is proposed, namely, the low-level distributed nominal control scheme and the high-level topology reconfiguration protocols. The low-level scheme is developed to guarantee system performances in the fault-free scenario. With the low-level scheme, the high-level topology reconfiguration protocols, each of which corresponds to one partial LoCE fault scenario, are then proposed to mitigate the fault impact by adjusting the underlying topology. Accordingly, without modifying the structure or the design parameter of the low-level control scheme, the proposed framework can guarantee the synchronization and tracking errors of the MVS asymptotically convergent to zero in both fault-free and fault scenarios. Finally, the effectiveness of the proposed control method is verified via a simulation study of three degree-of-freedom helicopters.

Cooperative Global Robust Practical Output Regulation of Nonlinear Lower Triangular Multiagent Systems via Event-Triggered Control

In this article, the problem of cooperative global robust practical output regulation is examined for uncertain nonlinear multiagent systems in a lower triangular form via event-triggered control. The problem is dealt with in three steps. At the first step, a decentralized internal model is constructed based on the lower triangular form such that the regulation issue is translated to a stabilization one. Next, a nonlinear decentralized state-feedback controller is designed to achieve input-to-state stabilization with the sampling error as the input. In the third step, a simple event-triggering mechanism is embedded in the controller to achieve an event-based controller redesign. An illustrative example is presented to verify the theoretical results.

Fully Distributed Adaptive Fault-Tolerant Sliding-Mode Control for Nonlinear Leader-Following Multiagent Systems With ANASs and IQCs

In this article, by combining the skills of the pseudo-PID sliding-mode control (SMC) method with adaptive control techniques, two novel fully distributed adaptive fault-tolerant control strategies are proposed to handle the leader-following consensus problem of nonlinear multiagent systems with integral quadratic constraints (IQCs) and actuator faults, with and without asymmetric nonlinear actuator saturations (ANASs). For the no-saturation case, the designed controller has a simple structure and low computation but requires the crude information of the system model. To overcome this weakness, for the saturation case, the controller is redesigned by introducing a novel anti-windup compensator and fuzzy-logic systems (FLSs), where the problem of reducing computational complexity is also considered. The controllers only need local neighbor information instead of global topology information and ensure the practical consensus of the leader-following systems in finite time. Finally, simulation results demonstrate the effectiveness of the proposed approaches.

Model-Based Event-Triggered Sliding-Mode Control for Multi-Input Systems: Performance Analysis and Optimization

This article is concerned with the model-based event-triggered sliding-mode control (SMC) issue for multi-input systems, which is motivated by some existing results in a single-input case. A model-based event-triggered SMC scheme is first designed. In particular, a triggered condition is co-designed with SMC to achieve the reachability condition of a specified sliding surface. Thus, it can effectively mitigate the burden of data communication, and also eliminate the effect of the matched external disturbance and the model uncertainties in both system and input. For ensuring the stability of the model dynamics and the resulting sliding-mode dynamics simultaneously, an auxiliary disturbance input is introduced to the nominal model by compensating the switching term of the designed SMC law. Furthermore, the positive lower bound for the minimum interevent time is analyzed to ensure the feasibility of the proposed approach. To illustrate the proposed model-based event-triggered SMC approach from a practical viewpoint, two design problems to maximize the system robustness and performance are proposed, respectively. The nontrivial optimization problems are then solved by a genetic algorithm (GA). Finally, jet transport aircraft is utilized to demonstrate the effectiveness of the proposed results and algorithm.

Integral sliding mode consensus of networked control systems with bounded disturbances

This article addresses the consensus tracking problem of networked control systems with disturbances. The network topology is directed, and only partial followers can exchange information with the leader. In the light of the continuous consensus law for the nominal network control systems, a discontinuous integral sliding mode protocol is designed to ensure that networked control systems with bounded disturbances achieve the consensus in a setting time. Furthermore, this article also solve the problem that the sliding function chattering and the control gains are difficult to determine in discontinuous consistency protocol. The continuous integral sliding mode consensus protocol is proposed. It is pointed out that the advantage of adaptive control method is that it can automatically adjust the controller gain, and may ensure the control protocol execute well without prior knowledge of networked control systems. In the end, simulation results illustrate that the efficacy of this new approach is validated.

Deep Learning-Based Consensus Control of a Multi-Agents System with Unknown Time-Varying Delay

Despite the enormous progress in consensus control of a multi-agents system (MAS), amodel-based consensus control is valid only when the assumption on the system environment and on the model is valid. To overcome this limitation, several deep learning (DL) based consensus controls directly learn how to generate a control signal from the model-based control. Depending on the exploitation of knowledge from the model-based control structure, four different deep learning models were considered. Numerical simulations of MAS with unknown time-varying delays and disturbance verify that, while providing comparable performance to the model-based control for many different system configurations, the DL-based controls with explicit knowledge of the control signal structure are preferred to that with implicit knowledge of the control signal or no knowledge, which shows the promising potential of DL-based control with supervised learning.

Prescribed-time cluster lag consensus control for second-order non-linear leader-following multiagent systems

Prescribed-time Lag consensus, as a special case of prescribed-time cluster lag consensus, is first investigated. The task is to design a control protocol for each follower so that the multiagent system (MAS) achieves lag consensus in any specified time. To achieve this goal, we propose a new distributed controller, in which the control gains are designed as time-varying functions related to the pre-specified time. In addition, a state transformation is introduced to tackle the technical difficulty caused by time-varying functions of different powers in the theoretical proof process. Then, a solution for the cluster lag consensus problem of the MAS is provided, so that under the proposed control protocol, each subsystem composed of followers from the same group and the leader achieves lag consensus with a different lag time in the specified time. By using a state transformation, Graph theory and generalized Lyapunov stability theory, the validity of the designed schemes is verified theoretically and sufficient conditions for the two conclusions are given respectively. Finally, we give two simulation examples to show performances of the proposed solutions.

Decentralized Output Sliding-Mode Fault-Tolerant Control for Heterogeneous Multiagent Systems

This paper proposes a novel decentralized output sliding-mode fault-tolerant control (FTC) design for heterogeneous multiagent systems (MASs) with matched disturbances, unmatched nonlinear interactions, and actuator faults. The respective iteration and iteration-free algorithms in the sliding-mode FTC scheme are designed with adaptive upper bounding laws to automatically compensate the matched and unmatched components. Then, a continuous fault-tolerant protocol in the observer-based integral sliding-mode design is developed to guarantee the asymptotic stability of MASs and the ultimate boundedness of the estimation errors. Simulation results validate the efficiency of the proposed FTC algorithm.

Distributed Sliding-Mode Tracking Control of Second-Order Nonlinear Multiagent Systems: An Event-Triggered Approach

The event-triggered tracking control problem of second-order multiagent systems in consideration of system nonlinearities is investigated by utilizing the distributed sliding-mode control (SMC) approach. An event-triggered strategy is proposed to decrease the controller sampling frequency and save the network communication resources; the triggering condition is then established for leader-following multiagent systems. In this article, by utilizing the distributed event-based sliding-mode controller, the system state of second-order multiagent systems with system nonlinearities is capable of approaching the integral sliding-mode surface in finite time. A novel integral sliding-mode surface is constructed in this article to guarantee the consensus tracking performance in the existence of system nonlinearities as the state trajectories of second-order integrator systems move on the constructed sliding manifold. By employing the Lyapunov approach, sufficient conditions are deduced to ensure that the consensus tracking performance is obtained for the closed-loop system. Furthermore, it is presented that the triggering scheme can effectively reduce state updates and eliminate the Zeno behavior. A simulation example is provided to testify the validity of our proposed methodology.

Edge-Event-Triggered Synchronization for Multi-Agent Systems with Nonlinear Controller Outputs

This paper addresses the synchronization problem of multi-agent systems with nonlinear controller outputs via event-triggered control, in which the combined edge state information is utilized, and all controller outputs are nonlinear to describe their inherent nonlinear characteristics and the effects of data transmission in digital communication networks. First, an edge-event-triggered policy is proposed to implement intermittent controller updates without Zeno behavior. Then, an edge-self-triggered solution is further investigated to achieve discontinuous monitoring of sensors. Compared with the previous event-triggered mechanisms, our policy design considers the controller output nonlinearities. Furthermore, the system’s inherent nonlinear characteristics and networked data transmission effects are combined in a unified framework. Numerical simulations demonstrate the effectiveness of our theoretical results.

Estimation of Domain of Attraction for Aperiodic Sampled-Data Switched Delayed Neural Networks Subject to Actuator Saturation

In this paper, for the case of the asynchronous switching caused by that subsystem's switching occuring during a sampling interval, the domain of attraction estimation problem is investigated for aperiodic sampled-data switched delayed neural networks (ASDSDNNs) subject to actuator saturation. A parameters-dependent time-scheduled Lyapunov functional consisting of a novel looped-functional is constructed using segmentation technology and linear interpolation. By employing this novel functional and using an average dwell time (ADT) approach, exponential stability criteria are proposed for polytopic uncertain ASDSDNNs subject to actuator saturation. And a relationship between ADT and sampling period is revealed for ASDSDNNs. As a corollary, exponential stability criteria are proposed for nominal ASDSDNNs subject to actuator saturation. Furthermore, by describing the domain of attraction as a time-varying ellipsoid determined by the time-scheduled Lyapunov matrix, the proposed theoretical conditions are transformed into a linear matrix inequality (LMI)-based multi-objective optimization problem. The dynamic estimates of the domain of attraction for ASDSDNNs are solved. Numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

Adaptive sliding mode control for disturbed multirobot systems performing target tracking under continuously time-varying topologies

This article studies coordination control of the multirobot system for target tracking problem with disturbances in time-varying communication environment. An adaptive sliding mode control is designed to complete the target tracking task with the effect of disturbances and continuously time-varying topologies. This means that the communication between the robots is not switching among constant topologies but changes continuously along with time. The continuously time-varying topology is constructed by a set of fixed Laplacian matrices and variable scheduling functions, which is known as polytopic model structure. The designed adaptive sliding mode control can effectively lower the influence of disturbance and improve tracking performance even under the continuously time-varying topology. Furthermore, numerical simulations are given to demonstrate the effectiveness of the obtained results.

Fault-Tolerant Consensus Tracking Control for Linear Multiagent Systems Under Switching Directed Network

In this paper, for linear leader-follower networks with multiple heterogeneous actuator faults, including partial loss of effectiveness fault and actuator bias fault, a cooperative fault-tolerant control (CFTC) approach is developed. Assume that the interaction network topology among all nodes is a switching directed graph. To address the difficulty of designing the distributed compensation control laws under the time-varying asymmetrical network structure, a novel distributed-reference-observer-based fault-tolerant tracking control approach is established, under which the global tracking errors are proved to be asymptotically convergent in the presence of actuator failures. First, by constructing a group of distributed reference observers based on neighborhood state information, all followers can estimate the leader's state trajectories directly. Second, a decentralized adaptive fault-tolerant tracking controller via local estimation is designed to achieve the global synchronization. Furthermore, the reliable coordination problem under switching directed topology with intermittent communications is solved by utilizing the presented CFTC approach. Finally, the effectiveness of the proposed coordination control protocol is illustrated by its applications to a networked aircraft system.

Neural Network-Based Adaptive Consensus Control for a Class of Nonaffine Nonlinear Multiagent Systems With Actuator Faults

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.