Fault‐tolerant containment control of uncertain nonlinear systems in strict‐feedback form

This paper investigates the containment control problem of uncertain nonlinear strict‐feedback systems in the presence of actuator faults. The communication topology among the agents is directed, and there exists at least one leader that has a directed path to each follower. Based on fuzzy logic systems and the dynamic surface control technique, a fault‐tolerant containment control scheme is developed to guarantee that the outputs of all followers converge to the convex hull spanned by multiple dynamic leaders with bounded containment errors. The result is extended to a fault‐tolerant containment control with prescribed performance, such that the error surfaces are confined to predefined bounds regardless of actuator faults. Simulation results are provided to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed containment control for nonlinear multiagent systems in pure‐feedback form

In this paper, the problem of distributed containment control for pure‐feedback nonlinear multiagent systems under a directed graph topology is investigated. The dynamics of each agent are molded by high‐order nonaffine pure‐feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed‐loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.     

Containment control of multi‐agent systems by exploiting the control inputs of neighbors

This paper studies the containment control problem for multi‐agent systems consisting of multiple leaders and followers connected as a network. The objective is to design control protocols so that the leaders will converge to a certain desired formation while the followers converge to the convex hull of the leaders. A novel protocol is proposed by exploiting the control input information of neighbors. Both continuous‐time and discrete‐time systems are considered. For continuous‐time systems, it is proved that the protocol is robust to any constant delays of the neighbors' control inputs. For discrete‐time systems, a sufficient condition on the feedback gain for the containment control is given in terms of the time delay and graph information. Some numerical examples are given to demonstrate the results. Copyright © 2013 John Wiley & Sons, Ltd.     

Distributed Containment Control for Nonlinear Multi‐Agent Systems with Time‐Delayed Protocol

In this paper, the containment control problem is considered for nonlinear multi‐agent systems with directed communication topology. Under the guidance of designed distributed communication protocols with/without previous state information, the followers are expected to converge to a dynamic convex hull spanned by multiple leaders. Two multi‐step algorithms are proposed to construct the corresponding protocols, the state feedback protocol and the delay‐coupled protocol, under which the containment control can be achieved asymptotically. Furthermore, it is found that the delay‐coupled protocol is rather sensitive to time delays. That is, real‐time tracking will become impossible by only using long‐dated previous state information. Finally, a numerical example is given to demonstrate the applicability and efficiency of the proposed schemes.     

Coordinated control with multiple dynamic leaders for uncertain Lagrangian systems via self‐tuning adaptive distributed observer

This paper studies coordinated control of multiple Lagrangian systems with parametric uncertainties subject to external disturbances by proposing a fully distributed continuous control law based on the improved self‐tuning adaptive observer inspired by non‐identifier‐based high‐gain adaptive control technique. Under this distributed continuous control law, a group of Lagrangian systems are driven to the convex hull spanned by multiple heterogenous dynamic leaders, which can be any combination of step signals of arbitrary unknown magnitudes, ramp signals of arbitrary unknown slopes, and sinusoidal signals of arbitrary unknown amplitudes, initial phases, and any unknown frequencies. It is also worth to mention that this control law we propose, depending neither on any information of leader systems for uninformed followers, nor on external disturbances, even independent of neighbors' velocity, can achieve asymptotic tracking of multiple leaders without any additional condition instead of ensuring the ultimate boundedness of the containment error as in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Fault‐Tolerant Control Allocation for Overactuated Nonlinear Systems

This paper addresses the problem of fault‐tolerant control allocation for input affine nonlinear systems. The proposed scheme is divided in three main tasks: fault detection and estimation using a nonlinear observer, fault isolation through a bank of unknown input observers with a resetting policy to reduce the effects of nonlinearities and control reconfiguration based on reduced order allocation. Analytical results regarding the isolability and reconfigurability of actuator faults are derived and a simulation example is used to illustrate the the proposed fault tolerant control methodology.     

Distributed fault‐tolerant control design for spacecraft finite‐time attitude synchronization

This paper develops two distributed finite‐time fault‐tolerant control algorithms for attitude synchronization of multiple spacecraft with a dynamic virtual leader in the presence of modeling uncertainties, external disturbances, and actuator faults. The leader gives commands only to a subset of the followers, and the communication flow between followers is directed. By employing a novel distributed nonsingular fast terminal sliding mode and adaptive mechanism, a distributed finite‐time fault‐tolerant control law is proposed to guarantee all the follower spacecraft that finite‐time track a dynamic virtual leader. Then utilizing three distributed finite‐time sliding mode estimators, an estimator‐based distributed finite‐time fault‐tolerant control law is proposed using only the followers' estimates of the virtual leader. Both of them do not require online identification of the actuator faults and provide robustness, finite‐time convergence, fault‐tolerant, disturbance rejection, and high control precision. Finally, numerical simulations are presented to evaluate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Semi‐global and global containment control of multi‐agent systems with second‐order dynamics and input saturation

This paper considers both semi‐global and global containment control for a second‐order multi‐agent system that is composed by a network of identical harmonic oscillators or double integrators with multiple leaders and input saturation. A distributed low gain feedback algorithm is proposed to solve the semi‐global containment control problem for the network whose topology is directed and initial condition is taken from any a priori given bounded set. In particular, by using a parametric Lyapunov equation approach, M‐matrix properties and algebraic graph theory, an upper bound of the low gain parameter is estimated such that the low gain feedback matrix can be analytically determined without involving numerical computation. Furthermore, under the assumption that the induced subgraph formed by the followers is strongly connected and detail balanced, two linear feedback protocols are designed for coupled harmonic oscillators and coupled double integrators, respectively, to asymptotically achieve the global containment control of the network with any initial condition. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

In this paper, an adaptive fault‐tolerant time‐varying formation control problem for nonlinear multiagent systems with multiple leaders is studied against actuator faults and state‐dependent uncertainties. Simultaneously, the followers form a predefined formation while tracking reference signal determined by the convex combination of the multiple leaders. Based on the neighboring relative information, an adaptive fault‐tolerant formation time‐varying control protocol is constructed to compensate for the influences of actuator faults and model uncertainties. In addition, the updating laws can be adjusted online through the adaptive mechanism, and the proposed control protocol can guarantee that all the signals in the closed‐loop systems are bounded. Lyapunov‐like functions are addressed to prove the stability of multiagent systems. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.     

Distributed adaptive containment control for high-order nonlinear multi-agent systems

This paper considers the adaptive containment control of high-order nonlinear multi-agent systems with nonlinear parameterisation. Without imposing any conditions on the unknown nonlinearities and unknown parameters, the distributed controllers are constructed recursively with only neighbours’ information by using the backstepping design method. Under the assumption that the leaders set is globally reachable, it is shown that all the signals of the closed-loop systems are global uniformly ultimately bounded (UUB), and all the followers will exponentially converge to the convex hull spanned by the dynamic leaders with adjustable tracking errors. Finally, two simulation examples demonstrate the effectiveness of the control scheme.     

Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

In this paper, distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays and general disturbances is investigated under directed topology by using sliding‐mode control technique. We consider that the information of dynamic leaders can be obtained by only a portion of the followers. Firstly, a nonsingular fast terminal sliding surface is selected to achieve the finite‐time convergence for the error variables. Then, a distributed finite‐time containment control algorithm is proposed where the neural network is utilized to approximate the model uncertainties and external disturbances of the systems. Furthermore, considering that error constraint method can improve the performance of the systems, a distributed finite‐time containment control algorithm is developed by transforming the error variable into another form. It is demonstrated that the containment errors are bounded in finite time by using Lyapunov theory, graph theory, and finite‐time stability theory. Numerical simulations are provided to show the effectiveness of the proposed methods.     

Cooperative Adaptive Fuzzy Output Feedback Control for Synchronization of Nonlinear Multi‐Agent Systems in the Presence of Input Saturation

This paper considers the leader‐following synchronization problem of nonlinear multi‐agent systems with unmeasurable states in the presence of input saturation. Each follower is governed by a class of strict‐feedback systems with unknown nonlinearities and the information of the leader can be accessed by only a small fraction of followers. An auxiliary system is introduced and its states are used to design the cooperative controllers for counteracting the effect of input saturation. By using fuzzy logic systems to approximate the unknown nonlinearities, local adaptive fuzzy observers are designed to estimate the unmeasurable states. Dynamic surface control (DSC) is employed to design distributed adaptive fuzzy output feedback controllers. The developed controllers guarantee that the outputs of all followers synchronize to that of the leader under directed communication graphs. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop systems are semiglobally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood of the origin. An example is provided to show the effectiveness of the proposed control approach.     

Containment control of linear multi‐agent systems with multiple leaders of bounded inputs using distributed continuous controllers

This paper considers the containment control problem for multi‐agent systems with general linear dynamics and multiple leaders whose control inputs are possibly nonzero and time varying. Based on the relative states of neighboring agents, a distributed static continuous controller is designed, under which the containment error is uniformly ultimately bounded and the upper bound of the containment error can be made arbitrarily small, if the subgraph associated with the followers is undirected and, for each follower, there exists at least one leader that has a directed path to that follower. It is noted that the design of the static controller requires the knowledge of the eigenvalues of the Laplacian matrix and the upper bounds of the leaders’ control inputs. In order to remove these requirements, a distributed adaptive continuous controller is further proposed, which can be designed and implemented by each follower in a fully distributed fashion. Extensions to the case where only local output information is available and to the case of multi‐agent systems with matching uncertainties are also discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐Time Fault‐Tolerant Control for a Class of Non‐Affine Nonlinear System Using Sliding Mode Disturbance Observer

This study investigates a finite‐time fault‐tolerant control scheme for a class of non‐affine nonlinear system with actuator faults and unknown disturbances. A global approximation method is applied to non‐affine nonlinear system to convert it into an affine‐like expression with accuracy. An adaptive terminal sliding mode disturbance observer is proposed to estimate unknown compound disturbances in finite time, including external disturbances and system uncertainties, which enhances system robustness. Controllers based on finite‐time Lyapunov theory are designed to force tracking errors to zero in finite time. Simulation results demonstrate the effectiveness of proposed method.     

Integrated design of robust fault estimation and fault‐tolerant control against simultaneous actuator and sensor faults

This paper investigates the problems of simultaneous actuator and sensor faults estimation, as well as the fault‐tolerant control scheme for a class of linear continuous‐time systems subject to external disturbances. First, the original system is transformed into a singular form by extending the actuator fault and sensor fault to be parts of the new state. Then, a new estimation technique named non‐fragile proportional‐derivative observer is designed for the singular system to achieve simultaneous estimations of states and faults. With the obtained estimations information, an integrated design of the non‐fragile output feedback fault‐tolerant controller is explored to compensate for the effect of faults by stabilizing the closed‐loop system. Finally, a simulation study on a two‐stage chemical reactor with recycle streams is provided to verify the effectiveness of the proposed approach.     

Adaptive decentralized fault‐tolerant tracking control for large‐scale nonlinear systems with input quantization

In this paper, an adaptive decentralized tracking control scheme is designed for large‐scale nonlinear systems with input quantization, actuator faults, and external disturbance. The nonlinearities, time‐varying actuator faults, and disturbance are assumed to exist unknown upper and lower bounds. Then, an adaptive decentralized fault‐tolerant tracking control method is designed without using backstepping technique and neural networks. In the proposed control scheme, adaptive mechanisms are used to compensate the effects of unknown nonlinearities, input quantization, actuator faults, and disturbance. The designed adaptive control strategy can guarantee that all the signals of each subsystem are bounded and the tracking errors of all subsystems converge asymptotically to zero. Finally, simulation results are provided to illustrate the effectiveness of the designed approach.     

Fault tolerant control using virtual actuator for continuous‐time Lipschitz nonlinear systems

In this brief, we extend the existing results on fault tolerant control via virtual actuator approach to a class of systems with Lipschitz nonlinearities to maintain the closed‐loop stability after actuator faults. This generalization is established by relying on the input‐to‐state stability properties of cascaded systems. The virtual actuator block, placed between faulty plant and nominal controller, generates useful input signals for faulty plant by using output signals of the nominal controller to guarantee the closed‐loop stability in the presence of actuator faults. This design problem is reduced to a matrix inequality that can be turned to an LMI by fixing a variable to a constant value and solving the resulting LMI feasibility problem. The proposed fault tolerant control method is successfully evaluated using a nonlinear system. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive fault‐tolerant control for a nonlinear flexible aircraft wing system

Fault‐tolerant control problems have been extensively studied in all kinds of control systems. However, there is little work on fault‐tolerant control for distributed parameter systems. In this paper, a novel adaptive fault‐tolerant boundary control scheme is proposed for a nonlinear flexible aircraft wing system against actuator faults. The whole system is regarded as a distributed parameter system, and the dynamic model of the flexible wing system is described by a set of partial differential equations (PDEs) and ordinary differential equations (ODEs). The proposed controller is designed by using the Lyapunov's direct method and adaptive control strategies. Based on the online estimation of actuator faults, the adaptive controller parameters can update automatically to compensate the actuator faults of the system. Besides, a fault‐tolerant controller is also developed for this system in the presence of external disturbances. Differing from existing works about adaptive fault‐tolerant control, the adaptive controller presented in this paper is designed for a distributed parameter system. Finally, numerical simulations are carried out to illustrate the effectiveness of the proposed control scheme.     

Formation‐containment control of networked collision‐free Lagrangian systems

The distributed formation‐containment (DFC) problem under a directed graph is addressed for networked Euler‐Lagrange systems. First, using a leader‐follower framework, the DFC problem is properly defined. For the leaders and the followers, respectively, a DFC control law is next proposed without using velocity information. Based on the artificial potential function, all the agents can achieve the control objective satisfactorily while avoiding collisions with others as well as the obstacles in the environment. By the Lyapunov stability theory, the boundedness of the error signals is guaranteed. Simulations are finally given to show the feasibility of this approach.     

Distributed adaptive fault‐tolerant leader‐following formation control of nonlinear uncertain second‐order multi‐agent systems

This paper presents a distributed integrated fault diagnosis and accommodation scheme for leader‐following formation control of a class of nonlinear uncertain second‐order multi‐agent systems. The fault model under consideration includes both process and actuator faults, which may evolve abruptly or incipiently. The time‐varying leader communicates with a small subset of follower agents, and each follower agent communicates to its directly connected neighbors through a bidirectional network with possibly asymmetric weights. A local fault diagnosis and accommodation component are designed for each agent in the distributed system, which consists of a fault detection and isolation module and a reconfigurable controller module comprised of a baseline controller and two adaptive fault‐tolerant controllers, activated after fault detection and after fault isolation, respectively. By using appropriately the designed Lyapunov functions, the closed‐loop stability and asymptotic convergence properties of the leader‐follower formation are rigorously established under different modes of the fault‐tolerant control system.