Robust multi-tracking of heterogeneous multi-agent systems with uncertain nonlinearities and disturbances

A robust multi-tracking problem is solved for heterogeneous multi-agent systems with uncertain nonlinearities and disturbances. The nonlinear function satisfies a Lipschitz condition with a time-varying gain, the integral of which is bounded by a linear function. A distributed impulsive protocol is proposed, where the position data and velocity data of desired trajectories are needed only at sampling instants. Based on the system decomposition technique, the error dynamic system of achieving multi-tracking is decomposed into two impulsive dynamic systems with vanishing perturbation and nonvanishing perturbation, respectively. Constructing a nominal model, then the multi-tracking problem is converted into the stability of impulsive dynamic system with nonvanishing perturbation under some conditions. It is proved that the proposed impulsive protocol is robust enough to solve the multi-tracking problem. Numerical examples are presented to illustrate the effectiveness of our theoretical results.     

Prescribed-time containment control with prescribed performance for uncertain nonlinear multi-agent systems

The existing studies on prescribed-time control cannot directly deal with nonlinear functions which don’t satisfy Lipschitz growth conditions. No results are available for prescribed-time containment control of pure-feedback UNMASs with prescribed performance. Therefore, completely unknown nonlinear function, prescribed-time tracking of system states and prescribed performance of containment errors are simultaneously considered in this paper. Fuzzy logic systems are utilized to approximate completely unknown nonlinear function. Prescribed-performance function is introduced and further incorporated into a novel speed function. Combining the proposed speed function and barrier Lyapunov function, this article presents a novel adaptive fuzzy prescribed-time containment control method which can guarantee, under prescribed performance, all followers converge to a convex formed by dynamic leaders in a prescribed time. Moreover, all tracking errors converge to predefined regions in a prescribed time. The effectiveness of the proposed prescribed-time containment control method are confirmed by strict proof and simulation.     

Event-triggered time-varying formation control for general linear multi-agent systems

This paper investigates event-triggered formation control problems for general linear multi-agent systems. The time-varying formation this paper studied can be described by a bounded piecewise differentiable vector-valued function. Firstly, a time-varying formation control protocol based on event-triggered scheme is constructed by the states of the neighboring agents. Each agent broadcasts its state information to neighbor nodes if the triggering condition is satisfied, and the communication load is decreased significantly. Then, an algorithm consisting of three steps is proposed to design the event-triggered formation control protocol. Moreover, it is proven that under the designed event-triggered formation protocol, the multi-agent systems can achieve the desired time-varying formation which belongs to the feasible formation set with the bounded formation error and the closed systems do not exhibit Zeno behavior. Finally, simulation results are given to demonstrate the effectiveness of the theoretical analysis.     

Robust cooperative output regulation of heterogeneous uncertain linear multi-agent systems by intermittent communication

In this paper, we study the robust cooperative output regulation problem of heterogeneous linear multi-agent systems with system uncertainties and directed communication topology. A robust distributed event-triggered control scheme is proposed based on the internal model principle. To avoid continuous monitoring of measurement errors for the event-triggering condition, a novel self-triggered control scheme is further proposed. Moreover, by introducing a fixed timer in the triggering mechanisms, Zeno behavior can be excluded for each agent. An example is finally provided to demonstrate the effectiveness of the proposed self-triggered control scheme.     

Affine formation control for multi-agent systems with prescribed convergence time

In this paper, the affine formation control problem for multi-agent systems with prescribed convergence time is investigated. Firstly, on the basis of a time-varying scaling function, a distributed continuous control algorithm is designed, under which a stationary affine formation of the nominal configuration is able to be achieved within a prescribed time. Secondly, to track a time-varying formation within the prescribed time, a distributed control protocol is proposed by employing a leader–follower control strategy. Furthermore, the boundary layer technique is adopted to avoid chattering effect. Finally, simulation examples are provided to demonstrated the effectiveness of the proposed design.     

Time-varying formation control for nonlinear multi-agent systems against actuator attacks

The formation control problem with time-varying characteristics is investigated for the time-delayed nonlinear multi-agent systems against actuator attacks. A neural-network-based adaptive control method is constructed to achieve the desired control objective, which is outputs of the followers can complete the desired transformation of formation configuration. To eliminate the influence of malicious attacks on the actuators, an actuator attacks defense strategy is proposed to resist false data injection attacks occurred in the actuator. The uncertainty of the dynamics caused by nonlinear functions is resolved by the neural-network approximate method. The problem of the time delay is handled by an improved Lyapunov-Krasovskii functional approach, which can also avoid the singularity problem that may occur during the construction of the control method. Based on the Lyapunov stability theory, it is proved that all signals of closed-loop systems are semi-globally stable and the formation error can converge to a small neighborhood of the origin. Finally, the results of simulations are provided to verify the feasibility of the theoretical analysis and the effectiveness of the proposed control method.     

Robust time-varying output formation tracking for heterogeneous multi-agent systems with adaptive event-triggered mechanism

This paper investigates the time-varying output formation tracking problem of heterogeneous multi-agent systems subjected to model uncertainties and external disturbances via adaptive event-triggered mechanism. Firstly, an adaptive distributed event-triggered observer is constructed to acquire the leader’s state and a time-varying formation output tracking controller utilizing sliding mode method is proposed to deal with the model uncertainties and external disturbances can be addressed. Secondly, an algorithm is given to claim the design procedures of the event-triggered based controller and asymptotic convergence of the controller is proved based on Lyapunov theory. Thirdly, Zeno-behavior is proved to be excluded strictly. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.     

Asymptotic containment control of uncertain multi-agent systems with partially unknown non-identical control directions

This paper investigates the precise containment control problem for nonlinear multi-agent systems (MAS) subject to non-vanishing uncertainties and unknown non-identical control directions under directed communication topology. Due to the existence of the inherent non-vanishing/non-parametric uncertainties and unknown control directions, the precise (zero-error) containment control synthesis becomes nontrivial. The underlying problem becomes even complicated if the convergence rate is required to be pre-specified. This work aims at circumventing the aforementioned difficulties to derive a precise containment control solution. The salient features behind the derived algorithms are: i) the non-vanishing uncertainties are completely rejected; ii) the containment error is regulated to zero at prescribed convergence rate, in spite of the non-vanishing uncertainties and unknown non-identical control directions; and iii) the full-state containment rather than output containment is achieved. A simulation example is given to confirm the effectiveness of the proposed method.     

Signal generator based finite-time formation control for disturbed heterogeneous multi-agent systems

This paper investigates finite-time formation control problems of heterogeneous multi-agent systems subject to mismatched and matched disturbances. The studied agents are modelled with both different orders and dimensions. To achieve the desired finite-time formation control goal, a novel signal generator based finite-time formation control scheme is proposed, which is composed of two parts. In the first part, a distributed finite-time signal generator is established to produce formation references for the agents in finite time. In the second part, based on finite-time observer technique and homogeneous systems theory, a kind of composite anti-disturbance controllers are constructed for the agents to track the formation references in finite time. In this way, the studied multi-agent system completes the desired finite-time formation control task. Compared with the existing results, the proposed control scheme solves the disturbed finite-time formation control problems with both different agents’ orders and dimensions, simplifies the formation controller design by using a modular design philosophy, and makes the agents have a plug and play feature. A simulation example is shown to validate the effectiveness of the proposed control scheme.     

Adaptive sliding mode control for uncertain nonlinear multi-agent tracking systems subject to node failures

The tracking problem of high-order nonlinear multi-agent systems (MAS) with uncertainty is solved by designing adaptive sliding mode control. During the tracking process, node failures are possible to occur, a new agent replaces the failed one. Firstly, a distributed nonsingular terminal sliding mode(NTSM) control scheme is designed for the tracking agents. A novel continuous function is designed in the NTSM to eliminate the singularity and meanwhile guarantee the estimation of finite convergence time. Secondly, the unknown uncertainties in the tracking agents are compensated by proposing an adaptive mechanism in the NTSM. The adaptive mechanism adjusts the control input through estimating the derivative bound of the unknown uncertainties dynamically. Thirdly, the tracking problem with node failures and agent replacements is further investigated. Based on the constructed impulsive-dependent Lyapunov function, it is proved that the overall system will track the target in finite time even with increase of jump errors. Finally, comparison simulations are conducted to illustrate the effectiveness of proposed adaptive nonsingular terminal sliding mode control method for tracking systems suffering node failures.     

Robust distributed tracking control for linear multi-agent systems based on distributed intermediate estimator

This paper considers the distributed tracking control problem for linear multi-agent systems with disturbances and a leader whose control input is nonzero and not available to any follower. Based on the relative output measurements of neighboring agents, a novel distributed observer-based tracking protocol is proposed, where the distributed intermediate estimators are constructed to estimate the leader’s unknown control input and the states of the tracking error system simultaneously, then a distributed tracking protocol is designed based on the derived estimates. It is proved that the states of the tracking error system are uniformly ultimately bounded and an explicit tracking error bound is obtained. A simulation example of aircrafts verifies the effectiveness of the proposed method.     

Robust adaptive control for prescribed performance tracking of constrained uncertain nonlinear systems

This paper proposes a robust adaptive control strategy for a class of state-constrained uncertain nonlinear systems with prescribed transient and steady-state behavior. The prescribed tracking performance can be characterized by constraints on an output tracking error. Both state and output constraints are achieved by bounding integral barrier Lyapunov functions in the backstepping procedure. A robust adaptive term is designed to compress auxiliary system uncertainties without the knowledge of their bounds. The satisfaction of control constraints and tracking error convergence are verified by theoretical analysis and are illustrated by simulation results.     

Robust adaptive sliding mode control for uncertain discrete-time systems with time delay

This paper focuses on robust adaptive sliding mode control for discrete-time state-delay systems with mismatched uncertainties and external disturbances. The uncertainties and disturbances are assumed to be norm-bounded but the bound is not necessarily known. Sufficient conditions for the existence of linear sliding surfaces are derived within the linear matrix inequalities (LMIs) framework by employing the free weighting matrices proposed in He et al. (2008) [3], by which the corresponding adaptive controller is also designed to guarantee the state variables to converge into a residual set of the origin by estimating the unknown upper bound of the uncertainties and disturbances. Also, simulation results are presented to illustrate the effectiveness of the control strategy.     

Robust adaptive visual tracking control for uncertain robotic systems with unknown dead-zone inputs

This paper is concerned with the image-based visual servoing (IBVS) control for uncalibrated camera-robot system with unknown dead-zone constraint, where the uncertain kinematics and dynamics are also considered. The control implementation is achieved by constructing a smooth inverse model for dead-zone-input to eliminate the nonlinear effect resulting from the actuator constraint. A novel adaptive algorithm, which does not require a priori knowledge of the parameter intervals of dead-zone model, is proposed to update the parameter values online, and the dead-zone slopes are not required the same. Furthermore, to accommodate the uncertainties of uncalibrated camera-robot system, adaptation laws are developed to estimate the uncertain parameters, simultaneously avoiding singularity of the image Jacobian matrix. With the full consideration of unknown dead-zone constraint and system uncertainties, an adaptive robust visual tracking control scheme together with dead-zone compensation is subsequently established such that the image tracking error converges to the origin. Based on a 3-DOF manipulator, simulations are conducted to verify the tracking performance of the proposed controller.     

Robust event-driven tracking control with preassigned performance for uncertain input-quantized nonlinear pure-feedback systems

This paper presents a simplified design methodology for robust event-driven tracking control of uncertain nonlinear pure-feedback systems with input quantization. All nonlinearities and quantization parameters are assumed to be completely unknown. Different from the existing event-driven control approaches for systems with completely unknown nonlinearities, the main contribution of this paper is to design a simple event-based tracking scheme with preassigned performance, without the use of adaptive function approximators and adaptive mirror models. It is shown in the Lyapunov sense that the proposed event-driven low-complexity tracker consisting of nonlinearly transformed error surfaces and a triggering condition can achieve the preselected transient and steady-state performance of control errors in the presence of the input quantization.     

New distributed adaptive protocols for uncertain nonlinear leader-follower multi-agent systems via a repetitive learning control approach

In this paper, the distributed consensus problem of leader-follower multi-agent systems with unknown time-varying coupling gains and parameter uncertainties are investigated, and the fully distributed protocols with the adaptive updating laws of periodic time-varying parameters are designed by using a repetitive learning control approach. By virtue of algebraic graph theory, Barbalat’s lemma and an appropriate Lyapunov-Krasovskii functional, it is shown that each follower agent can asymptotically track the leader even though the dynamic of the leader is unknown to any of them, i.e., the global asymptotic consensus can be achieved. At last, a simulation example is given to illustrate the feasibility and efficiency of the proposed protocols.     

Distributed robust event-triggered adaptive control for a class of uncertain nonlinear multi-agent systems with actuator saturation

This paper studies the event-triggered consensus control problem for high-order uncertain nonlinear multi-agent systems with actuator saturation. By using a smooth Lipschitz function to approximate the saturation nonlinearity, an augment system and the Nussbaum function are adopted to deal with the residual terms of saturation nonlinearity based on adaptive backstepping method. Since excessive energy and communication resources will be consumed during the procedure to handle actuator saturation, two event-triggered mechanisms are proposed to save the communication resources and reduce the controllers’ update frequency. Whenever the triggered conditions are satisfied, the control signals transmitted to the actuators are updated and broadcasted to the neighboring area. A ’disturbance-like’ term is integrated so that the event-triggered control problem with actuator saturation can be transformed into a robust problem while the unknown disturbances are tackled by adaptive update laws. Moreover, the requirement for global communication topology known by all the agents is relaxed by introducing new estimators. All the signals in the closed-loop system are uniformly bounded and the consensus tracking errors are exponentially converged to a bounded set. Meanwhile, the Zeno behavior is excluded. Simulation results are employed to validate the advantages of our proposed methods.     

一类非线性不确定多时滞中立型系统的鲁棒自适应控制（英文）

针对一类不确定多时滞中立型非线性系统，在其非线性不确定项的范数有界，但其上界未知的情况下，论证了自适应鲁棒控制器存在的条件，并给出了能适应未知参数变化且使得最终闭环系统一致最终有界的鲁棒控制律的设计方法。最后，具体算例的仿真结果说明了此法的有效性。