Finite-time formation control of nonaffine nonlinear systems under directed communication interactions

This paper studies the problem of finite-time formation tracking control for networked nonaffine nonlinear systems with unmeasured dynamics and unknown uncertainties/disturbances under directed topology. A unified distributed control framework is proposed by integrating adaptive backstepping control, dynamic gain control and dynamic surface control based on finite-time theory and consensus theory. Auxiliary dynamics are designed to construct control gains with non-Lipschitz dynamics so as to guarantee finite-time convergence of formation errors. Adaptive control is used to compensate for uncertain control efforts of the transformed systems derived from original nonaffine systems. It is shown that formation tracking is achieved during a finite-time period via the proposed controller, where fractional power terms are only associated with auxiliary dynamics instead of interacted information among the networked nonlinear systems in comparison with most existing finite-time cooperative controllers. Moreover, the continuity of the proposed controller is guaranteed by setting the exponents of fractional powers to an appropriate interval. It is also shown that the improved dynamic surface control method could guarantee finite-time convergence of formation errors, which could not be accomplished by conventional dynamic surface control. Finally, simulation results show the effectiveness of the proposed control scheme.     

Collision-avoiding formation for multiple Euler–Lagrange systems against external disturbances and actuator faults

In this paper, for multiple Euler–Lagrange systems embodying external disturbances and unknown uncertainties, the problems of collision-avoiding formation (CAF) are investigated. With regard to Euler–Lagrange systems under healthy actuator condition and under actuator failures, two distributed collision-avoiding formation (DCAF) control laws are proposed. In one case, which the systems are under healthy actuator condition, firstly, a robust continuous term with adaptive variable gain is utilized to reduce the influence of external disturbances under unknown range. In addition, in order to handle the uncertainties of dynamical systems and collision avoidance, both the estimations for uncertain terms and repulsive potential functions are established in design of algorithms. For the other case, the systems under actuator failures, by utilizing the Lyapunov function and relevant adaptive updating laws, the effects subjected to partial loss of actuator effectiveness can be eliminated. Eventually, two distributed algorithms are proposed to achieve the expected formation configuration with no collision occurred. Numerical simulations are conducted to illustrate the validities of the presented control methodologies.     

Adaptive synchronization of unknown heterogeneous agents: An adaptive virtual model reference approach

This work deals with state synchronization of heterogeneous linear agents with unknown dynamics. The problem is solved by formulating the synchronization problem as a special model reference adaptive control where each agent tries to converge to the model defined by its neighbors. For those agents that do not know the reference signal that drives the flock, a fictitious reference is estimated in place of the actual one: the estimation of such reference is distributed and requires measurements from neighbors. By using a matching condition assumption, which is imposed so that the agents can converge to the same behavior, the fictitious reference estimation leads to adaptive laws for the feedback and the coupling gains arising from distributed matching conditions. In addition, the coupling connection is not scalar as in most literature, but possibly vector-valued. The proposed approach is applicable to heterogeneous agents with arbitrarily large matched uncertainties. A Lyapunov-based approach is derived to show analytically asymptotic convergence of the synchronization error: robustification in the presence of bounded errors or unknown (constant) leader input is also discussed. Finally, a motivational example is presented in the context of Cooperative Adaptive Cruise Control and numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Adaptive iterative learning protocol design for nonlinear multi-agent systems with unknown control direction

This paper investigates a new adaptive iterative learning control protocol design for uncertain nonlinear multi-agent systems with unknown gain signs. Based on Nussbaum gain, adaptive iterative learning control protocols are designed for each follower agent and the adaptive laws depend on the information available from the agents in the neighbourhood. The proper protocols guarantee each follower agent track the leader perfectly on the finite time interval and the Nussbaum-type item can seek control direction adaptively. Furthermore, the formation problem is studied as an extension. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method in this article.     

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.     

Two-layer distributed hybrid affine formation control of networked Euler–Lagrange systems

This paper tackles a distributed hybrid affine formation control (HAFC) problem for Euler–Lagrange multi-agent systems with modelling uncertainties using full-state feedback in both time-varying and constant formation cases. First, a novel two-layer framework is adopted to define the HAFC problem. Using the property of the affine transformation, we present the sufficient and necessary conditions of achieving the affine localizability. Because only parts of the leaders and followers can access to the desired formation information and states of the dynamic leaders, respectively, we design a distributed finite-time sliding-mode estimator to acquire the desired position, velocity, and acceleration of each agent. In the sequel, combined with the integral barrier Lyapunov functions, we propose a distributed formation control law for each leader in the first layer and a distributed affine formation control protocol for each follower in the second layer respectively with bounded velocities for all agents, meanwhile the adaptive neural networks are applied to compensate the model uncertainties. The uniform ultimate boundedness of all the tracking errors can be guaranteed by Lyapunov stability theory. Finally, corresponding simulations are carried out to verify the theoretical results and demonstrate that with the proposed control approach the agents can accurately and continuously track the given references.     

Distributed adaptive fault-tolerant formation control for heterogeneous multiagent systems under switching directed topologies

This paper studies the cooperative fault-tolerant formation control problem of tracking a dynamic leader for heterogeneous multiagent systems consisting of multipile unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults under switching directed interaction topologies. Based on local neighborhood formation information, the distributed fault-tolerant formation controllers are constructed to ensure that all follower UAVs and UGVs can accomplish the demanding formation configuration in the state space and track the dynamic leader’s trajectory. By incorporating the sliding mode control and adaptive control technique, the actuator faults and unknown parameters of follower agents can be compensated. Through the theoretical analysis, it is proved that the cooperatively semiglobally uniformly ultimately boundedness of the closed-loop system is guaranteed, and the formation tracking errors converge to a small adjustable neighborhood of the origin. A simulation example is introduced to show the validity of the proposed distributed fault-tolerant formation control algorithm.     

Novel model reference adaptive control laws for improved transient dynamics and guaranteed saturation constraints

In classical model reference adaptive control (MRAC), the adaptive rates must be tuned to meet multiple competing objectives. Large adaptive rates guarantee rapid convergence of the trajectory tracking error to zero. However, large adaptive rates may also induce saturation of the actuators and excessive overshoots of the closed-loop system’s trajectory tracking error. Conversely, low adaptive rates may produce unsatisfactory trajectory tracking performances. To overcome these limitations, in the classical MRAC framework, the adaptive rates must be tuned through an iterative process. Alternative approaches require to modify the plant’s reference model or the reference command input. This paper presents the first MRAC laws for nonlinear dynamical systems affected by matched and parametric uncertainties that constrain both the closed-loop system’s trajectory tracking error and the control input at all times within user-defined bounds, and enforce a user-defined rate of convergence on the trajectory tracking error. By applying the proposed MRAC laws, the adaptive rates can be set arbitrarily large and both the plant’s reference model and the reference command input can be chosen arbitrarily. The user-defined rate of convergence of the closed-loop plant’s trajectory is enforced by introducing a user-defined auxiliary reference model, which converges to the trajectory tracking error obtained by applying the classical MRAC laws before its transient dynamics has decayed, and steering the trajectory tracking error to the auxiliary reference model at a rate of convergence that is higher than the rate of convergence of the plant’s reference model. The ability of the proposed MRAC laws to prescribe the performance of the closed-loop system’s trajectory tracking error and control input is guaranteed by barrier Lyapunov functions. Numerical simulations illustrate both the applicability of our theoretical results and their effectiveness compared to other techniques such as prescribed performance control, which allows to constrain both the rate of convergence and the maximum overshoot on the trajectory tracking error of uncertain systems.     

Distributed fault diagnosis of networked dynamical systems with time-varying topology

In this paper, the distributed fault diagnosis (DFD) of networked dynamical systems with time-varying connected topologies, e.g., wireless sensor networks in harsh environments, is considered. Specifically, two essential problems are focused on, which are faced in extending the the decomposition-based adaptive DFD approach to such topology-varying systems. The problems introduced by the time-varying topologies are, respectively, decomposition schemes deterioration and pre-training difficulties. The causes of the two problems are detailed and addressed in our work. First, for the decomposition schemes deterioration problem, a multi-agent dynamics-based online distributed decomposition algorithm are developed, so that a decent decomposed network structure for such topology-varying network can be maintained. Second, to alleviate the pre-training difficulties in topology-varying systems, a fault detection method is proposed, which avoids the need for pre-training. The distributed decomposition algorithm is proved to converge in finite steps, and the proposed fault detection method is verified both theoretically and experimentally.     

Adaptive synchronization for a class of faulty and sampling coupled networks with its circuit implement

This paper is concerned with the asymptotic synchronization problem of a class of nonlinear complex networks with faulty and sampling couplings. A new version of the adaptive control strategy is proposed to adjust control parameters to compensate for the adverse impact of network attenuation faults, nonlinearities and sampling errors. Based on the adaptive adjustment laws, an approach that is application of knowledge of electricity is introduced to physically realize the adaptive controllers. Using Lyapunov stability theory for the synchronization error system, asymptotic synchronization of the overall networks can be established for the nonlinearly sampling and faulty couplings. Finally, the proposed adaptive control schemes are tested by simulation on Chua?s circuit network.     

Distributed chattering-free containment control for multiple Euler–Lagrange systems

This paper investigates the distributed chattering-free containment control problem for multiple Euler–Lagrange systems with general disturbances under a directed topology. It is considered that only a subset of the followers could receive the information of the multiple dynamic leaders. First, by combining a linear sliding surface with a nonsingular terminal sliding manifold, a distributed chattering-free asymptotic containment control method is proposed under the assumption that the upper bounds of the general disturbances are known. Further, based on the high-order sliding mode control technique, an improved distributed chattering-free finite-time containment control algorithm is developed. Besides, adaptive laws are designed to estimate the unknown upper bounds of the general disturbances. It is demonstrated that all the followers could converge into the convex hull spanned by the leaders under both proposed control algorithms by graph theory and Lyapunov theory. Numerical simulations and comparisons are provided to show the effectiveness of both algorithms.     

Adaptive synchronization of complex networks with general distributed update laws for coupling weights

This paper discusses adaptive synchronization control for complex networks interacted in an undirected weighted graph, and aims to provide a novel and general approach for the design of distributed update laws for adaptively adjusting coupling weights. The proposed updating laws are very general in the sense that they encompass most weight update laws reported in the literature as special cases, and also provide new insights in the analysis of network system evolution and graph weight convergence. We show a rigorous proof for the synchronization stability of the overall complex network to a synchronized state, and demonstrate the convergence of adaptive weights for each edge to some bounded constants. A detailed comparison with available results is provided to elaborate the new features and advantages of the proposed adaptive strategies as compared with conventional adaptive laws. The effectiveness of the proposed approach is also validated by several typical simulations.     

Adaptive neural network dynamic surface control of uncertain strict-feedback nonlinear systems with unknown control direction and unknown actuator fault

In this paper, the tracking control problem of a class of uncertain strict-feedback nonlinear systems with unknown control direction and unknown actuator fault is studied. By using the neural network control approach and dynamic surface control technique, an adaptive neural network dynamic surface control law is designed. Based on the neural network approximator, the uncertain nonlinear dynamics are approximated. Using the dynamic surface control technique, the complexity explosion problems in the design of virtual control laws and adaptive updating laws can be overcome. Moreover, to solve the unknown control direction and unknown actuator fault problems, a type of Nussbaum gain function is incorporated into the recursive design of dynamic surface control. Based on the designed adaptive control law, it can be confirmed that all of the signals in the closed-loop system are semi-global bounded, and the convergence of the tracking error to the specified small neighborhood of the origin could be ensured by adjusting the designing parameters. Finally, two examples are provided to demonstrate the effectiveness of the proposed adaptive control law.     

Distributed cooperative learning for a group of uncertain systems via output feedback and neural networks

This paper studies the problem of adaptive neural network (NN) output-feedback control for a group of uncertain nonlinear multi-agent systems (MASs) from the viewpoint of cooperative learning. It is assumed that all MASs have identical unknown nonlinear dynamic models but carry out different periodic control tasks, i.e., each agent system has its own periodic reference trajectory. By establishing a network topology among systems, we propose a new consensus-based distributed cooperative learning (DCL) law for the unknown weights of radial basis function (RBF) neural networks appearing in output-feedback control laws. The main advantage of such a learning scheme is that all estimated weights converge to a small neighborhood of the optimal value over the union of all system estimated state orbits. Thus, the learned NN weights have better generalization ability than those obtained by traditional NN learning laws. Our control approach also guarantees the convergence of tracking errors and the stability of closed-loop system. Under the assumption that the network topology is undirected and connected, we give a strict proof by verifying the cooperative persisting excitation condition of RBF regression vectors. This condition is defined in our recent work and plays a key role in analyzing the convergence of adaptive parameters. Finally, two simulation examples are provided to verify the effectiveness and advantages of the control scheme proposed in this paper.     

Robust finite-time cooperative formation control of UGV-UAV with model uncertainties and actuator faults

This paper investigates the finite-time cooperative formation control problem for a heterogeneous system consisting of an unmanned ground vehicle (UGV) - the leader and an unmanned aerial vehicle (UAV) - the follower. The UAV system under consideration is subject to modeling uncertainties, external disturbance as well as actuator faults simultaneously, which is associated with aerodynamic and gyroscopic effects, payload mass, and other external forces. First, a backstepping controller is developed to stabilize the leader system to track the desired trajectory. Second, a robust nonsingular fast terminal sliding mode surface is designed for UAV and finite-time position control is achieved using terminal sliding mode technique, which ensures the formation error converges to zero in finite time in the presence of actuator faults and other uncertainties. Furthermore, by combining the radial basis function neural networks (NNs) with adaptive virtual parameter technology, a novel NN-based adaptive nonsingular fast terminal sliding formation controller (NN-ANFTSMFC) is developed. By means of the proposed adaptive control strategy, both uncertainties and actuator faults can be compensated without the prior knowledges of the uncertainty bounds and fault information. By using the proposed control schemes, larger actuator faults can be tolerated while eliminating control chattering. In order to realize fast coordinated formation, the expected position trajectory of UAV is composed of the leader position information and the desired relative distance with UGV, based on local distributed theory, in the three-dimensional space. The tracking and formation controllers are proved to be stable by the Lyapunov theory and the simulation results demonstrate the effectiveness of proposed algorithms.     

Adaptive synchronization of multi-agent systems via variable impulsive control

This paper mainly focuses on the adaptive synchronization problem of multi-agent systems via distributed impulsive control method. Different from the existing investigations of impulsive synchronization with fixed time impulsive inputs, the proposed distributed variable impulsive protocol allows that the impulsive inputs are chosen within a time period (namely impulsive time window) which can be described by the distances of the left (right) endpoints or the centers between two adjacent impulsive time windows. Obviously, this kind of flexible control scheme is more effective in practical systems (especially for the complex environment with physical restrictions). Moreover, the proposed adaptive control technique is helpful to solve the problem with uncertain system parameters. By means of Lyapunov stability theory, impulsive differential equations and adaptive control technique, three sufficient impulsive consensus conditions are given to realize the synchronization of a class of multi-agent nonlinear systems. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis.     

Formation consensus for discrete-time heterogeneous multi-agent systems with link failures and actuator/sensor faults

In this paper, a distributed control protocol is presented for discrete-time heterogeneous multi-agent systems in order to achieve formation consensus against link failures and actuator/sensor faults under fixed and switching topologies. A model equivalent method is proposed to deal with the heterogeneous system consists of arbitrary order systems with different parameters. Based on graph theory and Lyapunov theory, stability conditions to solve formation consensus problem are developed for the underlying heterogeneous systems with communication link failures. In order to tolerate actuator/sensor faults, a distributed adaptive controller is proposed based on fault compensation. The desired control is designed by linear matrix inequality approach together with cone complementarity linearisation algorithm. After applying the new control scheme to heterogeneous systems under the directed topologies with link failures and faults, the resulting closed-loop heterogeneous system is validated to be stable. The effectiveness of the new formation consensus control strategy and its robustness are verified by simulations.     

Distributed average tracking for uncertain directed multiagent networks

This paper studies a distributed average tracking problem of uncertain multiagent systems over directed graphs. The basic idea is to establish an appropriate reference model by introducing an adaptive control scheme. The output of the reference model is the average of multiple time-varying reference signals. This implies that the reference model partially solves the problem of distributed average tracking of directed graphs. Moreover, an appropriate control law is designed to make the output of the multiagent system with uncertain parameters approaches the average of the reference signals from the reference model. The feasibility of the proposed scheme is theoretically proved and the effectiveness of the scheme is verified through a simulation example.     

Adaptive consensus control for output-constrained nonlinear multi-agent systems with actuator faults

This paper addresses the problem of leader-follower consensus fault-tolerant control for a class of nonlinear multi-agent systems with output constraints. Specifically, a new nonlinear state transformation function is proposed to deal with the asymmetric constraint on output. Moreover, by integrating backstepping and radial basis function neural network approaches, an adaptive consensus control framework is developed with a single parameter estimator, which mitigates the computation of control algorithm in comparison with conventional adaptive approximation based control techniques. Then an adaptive compensation method is proposed to eliminate the effect of actuator failure. Under the proposed control scheme, all the closed-loop signals of the systems are bounded and the consensus tracking error converges to an adjustable small neighborhood of zero. To evaluate the developed control algorithm, a group of four networked two-stage chemical reactors is used to illustrate the effectiveness of the theoretic results obtained.     

Adaptive fuzzy tracking control for switched uncertain strict-feedback nonlinear systems

This paper concerns an adaptive fuzzy tracking control problem for a class of switched uncertain nonlinear systems in strict-feedback form via the modified backstepping technique. The unknown nonlinear functions are approximated by the generalized fuzzy hyperbolic model (GFHM). It is shown that if the designed parameters in the controller and adaptive laws are appropriately selected, then all closed-loop signals are bounded and the stability of the system can be kept under average dwell time methods. In the end, simulation studies are presented to illustrate the effectiveness of the proposed method.