Adaptive Fuzzy Output-Feedback Consensus Tracking Control of Nonlinear Multiagent Systems in Prescribed Performance.

This paper focuses on fixed-time event-triggered consensus tracking of high-order MAS over digraph and under DOS attack. The considered DOS attack is divided into connectivity-maintained attack and connectivity-broken attack. To detect connectivity-broken attack under event-triggered environment, a new cyberattack detection algorithm is presented. Next, using cyberattack detection results, a fixed-time event-triggered distributed observer is developed to estimate the leader’s states in the presence of DOS attack, which conducts event-triggered update in the normal condition and under connectivity-maintained attack and stops updating in the presence of connectivity-broken attack. Then, an adaptive event-triggered prescribed-time dynamic surface consensus tracking control protocol is proposed to eliminate mismatched disturbances caused by estimation error and achieve prescribed-time convergence of the tracking error. Stability analysis proves fixed-time convergence of the developed consensus tracking strategy and non-zeno analysis shows the developed distributed observer and consensus tracking control strategy exclude zeno behavior. This paper contributes to proposing a fixed-time leader-follower consensus control strategy for MAS under DOS attack via event-triggered approach, which eliminates the effect of DOS attack, achieves consensus tracking within a fixed time and reduces resources consumption. Finally, simulation results show the effectiveness and superiority of the developed consensus tracking approach.

This study considers the finite-time prescribed performance <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking consensus control problem in nonlinear multi-agent systems with time-varying disturbance and designs a distributed event-triggered control strategy. First, a class of time-dependent error performance constraint functions is introduced to effectively address the negative impact of disturbances on the transient and steady-state performance of a system. Second, a dynamic event-triggered protocol defined using periodic sampling data is proposed to reduce the information transmission between agents and decrease the controller’s update frequency. Third, the designed dynamic event-triggered mechanism is combined with the finite-time <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control theory, and sufficient conditions for the system to achieve tracking consensus in a finite time are obtained by employing the Lyapunov stability theory and linear matrix inequality. Finally, the feasibility of the proposed distributed control strategy is verified through numerical simulations and practical examples.

In practice, disturbances, including model uncertainties and unknown external disturbances, are always widely present and have a significant impact on the cooperative control performance of a networked multi-agent system. In this work, the distributed consensus tracking control problem for a class of multi-agent systems subject to matched and mismatched uncertainties is addressed. In particular, the dynamics of the leader agent are modeled with uncertain terms, i.e., the leader’s higher-order information, such as velocity and acceleration, is unknown to all followers. To solve this problem, a robust consensus tracking control scheme that combines a neural network-based distributed observer, a barrier function-based disturbance observer, and a tracking controller based on the back-stepping method was developed in this study. Firstly, a neural network-based distributed observer is designed, which is able to achieve effective estimation of leader information by all followers. Secondly, a tracking controller was designed utilizing the back-stepping technique, and the boundedness of the closed-loop error system was proved using the Lyapunov-like theorem, which enables the followers to effectively track the leader’s trajectory. Meanwhile, a barrier function-based disturbance observer is proposed, which achieves the effective estimation of matched and mismatched uncertainties of followers. Finally, the effectiveness of the robust consensus tracking control method designed in this study was verified through numerical simulations.

In this article, we focus on the problems of consensus control for nonlinear uncertain multiagent systems (MASs) with both unknown state delays and unknown external disturbances. First, a nonlinear function approximator is proposed for the system uncertainties deriving from unknown nonlinearity for each agent according to adaptive radial basis function neural networks (RBFNNs). By taking advantage of the Lyapunov-Krasovskii functionals (LKFs) approach, we develop a compensation control strategy to eliminate the effects of state delays. Considering the combination of adaptive RBFNNs, LKFs, and backstepping techniques, an adaptive output-feedback approach is raised to construct consensus tracking control protocols and adaptive laws. Then, the proposed consensus tracking scheme can steer the nonlinear MAS synchronizing to the predefined reference signal on account of the Lyapunov stability theory and inequality properties. Finally, simulation results are carried out to verify the validity of the presented theoretical approach.

This paper considers the consensus problem of two class of multi-agent systems with communication disturbance by using iterative learning control(ILC) method and both of them has a fixed information topology with a spanning tree. Firstly, a distributed iterative learning-based control protocol is designed for a time-varying linear multi-agent system, a sufficient condition is obtained such that the consensus problem is solved. By the same way, a sufficient condition is also given for a class of nonlinear time-varying multi-agent systems to solve consensus problem. The main contribution of the proposed results is that they can restrain any type of repetitive disturbance. The validity of them is verified by the simulation results.

In this article, the adaptive consensus tracking control is developed for uncertain multiagent systems with time-varying state delay in the case that leader's state is accessible at sampling instants. By proposing a distributed sampled observer with hybrid form, adaptive tracking controller with the complementary term is designed for first-order multiagent systems, and then is extended to high-order multiagent systems with the aid of dynamic surface control. Through the complementary term, the effects of parameter estimation error as well as dynamical terms with time-varying delays are eliminated and thus less conservative condition on time delays is required. It is proved that, under criteria in terms of linear matrix inequalities (LMIs), tracking error and estimation error exponentially converge to zero for first-order systems, and to a sufficiently small neighborhood of zero for high-order systems.

Consensus tracking and vibration control for multiple single-link flexible manipulators with input signal quantization

Observer-based adaptive fuzzy containment control for state-constrained nonlinear MASs based on quantization communication

This article studies the problem of event-triggered adaptive fault-tolerant fuzzy output feedback consensus tracking control for nonlinear fractional-order multiagent systems with actuator failures under a directed graph. Considering the fact that the actual system works near the equilibrium point most of the time, a novel dynamic event-triggering strategy with the reset mechanism is proposed, where the dynamic threshold can be actively adjusted according to the preset conditions, so that the resource utilization can be further reduced. Based on an improved event-based consensus error, the state estimator about the derivative of reference trajectory and the adaptive law about the information of graph are constructed, which makes distributed consensus tracking control achieved without obtaining global information. Then, by introducing two adaptive compensating terms to deal with actuator failures and event-triggered measurement errors, it is shown in the sense of fractional-order stability criterion that tracking errors can converge to a compact set even if the fault parameters and modes are completely unknown. Finally, the correctness of the presented method is verified by a simulation example.

In this paper, the consensus tracking problem for nonlinear multi-agent systems subjected to the output constraint, data loss and switching topologies is considered. Firstly, a consensus term is defined based on the communication information in present of the nonlinear output saturation and time-varying switching topologies. Since the random data loss is taken into consideration, the consensus term is redesigned by an introducing stochastic variable, which obeys the Bernoulli sequence with known probability. Then, a novel distributed ILC algorithm is designed by using the incomplete communication data of agents, which is more universal than the results without considered nonlinear constraint and random factors simultaneously. Through the contraction mapping method, an obtained convergence condition can also guarantee the asymptotic convergence of the agent along the iteration axis under nonlinear saturation factor and random factors. It is verified that the proposed algorithm can handle more complex situations in the consensus control of multi-agent systems. Simulation examples are further provided to verify the effectiveness of the proposed algorithm.

This paper investigates the optimal synchronisation problem for unknown nonlinear heterogeneous multi-agent systems (MASs) with an active leader and disturbances. Due to the external input signal of the active leader, the resulted uncooperative behaviours and unpredictability increase difficulty to derive the analytical solution of the coupled Bellman equation. To this end, we develop a distributed model reference adaptive critic learning algorithm with a hierarchical and distributed synchronisation control framework, which transforms the synchronisation problem of unknown nonlinear MASs into that of defined reference ones. Moreover, the algorithm extends our previous work to the distributed MASs, so that it is guaranteed that all the agents reach an agreement with the minimised transient errors and robustness against the disturbances and the neural network (NN) approximation errors. It is proved that the local neighbour tracking errors and the NN weight estimation errors are uniformly ultimately bounded via Lyapunov stability theory. A simulation example for multi-manipulator systems demonstrates the effectiveness of the algorithm.

This paper studies the distributed adaptive neural network (NN) predefined-time (PT) fault-tolerant consensus tracking control for unknown non-strict feedback nonlinear multi-agent systems (MASs) with time-varying full state constraints (TVFSCs), arbitrary switching behavior functions (possibly asynchronous), actuator faults and high powers. Compared with existing results, the convergence time estimation bound in this paper is less conservative due to the upper bound of convergence time presents as a tuning parameter. This paper avoids the control gain of each virtual controller to appear in the next virtual controller by using separable function technique, so it can reduce the control action complexity. Besides, this paper does not use any filters or piecewise continuous function in the controller design process, which can effectively avoid the potential singularity problem. An adaptive NN fault-tolerant consensus tracking controller is designed via backstepping technique and tangent barrier Lyapunov functions (BLF-Tans), which can ensure that all the closed-loop signals are bounded within a PT and the TVFSC bounds are not violated. Finally, numerical simulation and practical example further verify the effectiveness of the presented control algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Many practical (underactuated, weakly coupled and unstable mechanical systems) control systems can be modeled as uncertain high-order MAS with high powers. Due to the influence of environment and other factors, the values of some variables in the practical systems are limited and cannot be arbitrarily selected. In addition, the actual systems may fail due to human factors and in most of the relevant literatures, it is often assumed that the powers are equal to 1 and only achieve the controlled systems asymptotic stability as time approaches infinity. Therefore, in this paper, an adaptive PT fault-tolerant control scheme is developed for MASs with high powers, time-varying full state constraints and actuator faults. The effectiveness of the control scheme is illustrated based on simulation study.

In this article, the asymptotic tracking consensus problem of higher-order multiagent systems (MASs) with general directed communication graphs is addressed via designing event-triggered control strategies. One common assumption utilized in most existing results on such tracking consensus problem that the inherent dynamics of the leader are the same as those of the followers is removed in this article. In particular, two cases that the dynamics of the leader are subjected, respectively, to bounded input and unknown nonlinearity are considered. To do this, distributed event-triggered observers are first constructed to estimate the state information of the leader. Then, local event-triggered tracking control protocols are designed for each follower to complete the goal of tracking consensus. One distinguishing feature of the present distributed observers lies in the fact that they could avoid the continuous monitoring for the states of the neighbors' observer states. It is also worth pointing out that the present tracking consensus control strategies are fully distributed as no global information related to the directed communication graph is involved in designing the strategies. Two simulation examples are finally presented to verify the efficiency of the theoretical results.

This article studies the bipartite containment control problem for nonlinear multiagent systems (MASs) with input quantization over a signed digraph. The design objective is to provide an appropriate distributed protocol such that the followers converge to a convex hull containing each leader's trajectory as well as its opposite trajectory different in sign. Based on a nonlinear decomposition approach of input quantization, an event-triggered control scheme is developed via backstepping technique. A fuzzy observer is constructed to estimate unmeasurable states. Moreover, the bipartite containment control scheme for nonlinear MASs is designed. It is demonstrated that all signals in the closed-loop system are semiglobally uniformly ultimately bounded and Zeno behavior is excluded. Finally, a simulation example is given to verify the validity of the designed method.

In this article, we devote to solve the consensus problem for nonlinear multiagent system under energy consumption constraint. A novel control protocol which combines impulse control with event-triggered mechanism is proposed. By setting the event decision time at pulse time, it can not only reduce triggered times but also avoid the occurrence of “Zeno behavior.” In order to reduce the conservatism of control protocol, input saturation constraint and state saturation constraint are both discussed, for the limited receiving channel of the agent and limited sampling range of the sampler, respectively. Further, the dynamic model of multiagent systems with fuzzy information is proposed for the uncertain factors in actual environment. Finally, for the sake of proving the effectiveness about the control protocols, some simulation examples are presented.