Lipschitz Nonlinear Multi-agent Systems Research Articles

Observer-based adaptive time-varying formation tracking of one-sided Lipschitz nonlinear multi-agent systems

In this article, the problem of time-varying formation (TVF) tracking for nonlinear multi-agent systems (MASs) is investigated. The agent dynamics are described by one-sided Lipschitz (OSL) and quadratic inner-boundedness (QIB) function. Adaptive continuous TVF tracking protocols for nonlinear MASs are proposed. Compared to prior nonlinear system, this approach is more general and less conservative than nonlinear system with large Lipschitz constant. In addition, the continuous protocols are proposed to avoid undesirable chattering from non-zero inputs of the leader. Finally, the expected theoretical results are achieved through effective numerical simulations.

Observer-based leader-centric time-varying formation tracking control for nonlinear multi-agent systems with collision avoidance

The article introduces a novel control design methodology to achieve leader-centric time-varying formation tracking (leader-centric TVFT) with collision avoidance for Lipschitz nonlinear multi-agent systems (MASs) equipped with a leader-driven formation system. This methodology addresses key challenges, including actuator bias faults and leader maneuvering. It employs two novel control schemes: a collision avoidance scheme and a formation observer-based TVFT (FO-based TVFT) control scheme. The collision avoidance scheme ensures safe operation by preventing inter-agent collisions, while the FO-based TVFT control scheme enables followers to achieve TVFT for leader-driven formations while tracking the leader. To implement this FO-based TVFT control scheme, each follower employs a formation observer (FO) to continuously estimate the leader’s dynamically driven formations in real-time, facilitating responsive formation tracking. Notably, this FO-based TVFT control scheme establishes a novel framework for leader-centric TVFT (i.e., TVFT for leader-driven formations resulting from leader-driven formation switching) in MASs. Furthermore, this control methodology is specifically designed for Lipschitz nonlinear MASs operating under potential actuator bias faults and unpredictable leader maneuvering. It guarantees that the collective formation tracking error of followers is uniformly ultimately bounded (UUB), based on Lyapunov’s stability theory. Finally, an illustrative example validates the effectiveness of the proposed approach.

Dissipativity-based consensus for P-one-sided Lipschitz multi-agent systems via ILC

Abstract Based on dissipativity theory, the consensus via iterative learning control (ILC) is investigated for P-one-sided Lipschitz (P-OSL) nonlinear multi-agent systems (MASs). This paper only considers the P-OSL condition without using the quadratically inner-bounded constraint. Firstly, the ILC protocol is designed for such nonlinear MASs. Then, the convergence conditions of the consensus algorithm under a connected communication graph are presented from the viewpoint of dissipativity. It is shown that, on a fixed finite-time interval, the proposed algorithm can achieve perfect consensus tracking. Finally, two examples are constructed to show the effectiveness of the proposed method.

Impulsive consensus algorithms for vector second-order Lipschitz nonlinear multi-agent systems using only velocity regulation

The existing impulsive consensus algorithms for second-order Lipschitz nonlinear multi-agent systems require to apply the impulsive control to both position and velocity vectors at the same time. Such a requirement cannot be met in most of the real-world applications. To overcome the limitations of these impulsive algorithms, two kinds of new second-order impulsive consensus algorithms using only velocity regulation are proposed. Through developing a weighted discontinuous Lyapunov function-based approach that is able to leverage the spectral property of Laplacian matrix, impulse-dwell-time-dependent sufficient conditions for solving second-order impulsive consensus are derived in the form of linear matrix inequalities. Further, it is shown that if the impulsively controlled velocity subsystems are globally exponentially stable, the impulsive static consensus algorithm is able to ensure that all agents tend to an agreed position. Based on the consensus conditions, two convex optimization problems are formulated, by which the impulsive gain matrices for ensuring a prescribed exponential convergence rate can be designed. Finally, the effectiveness of the proposed distributed impulsive consensus algorithms is certified through numerical simulations.

Observer-Based Event-Triggered Iterative Learning Consensus for Locally Lipschitz Nonlinear MASs

This paper aims to realize the robust tracking for nonidentical locally Lipschitz nonlinear multiagent systems (MASs) with unmeasurable states, for which an observer-based distributed event-triggered iterative learning control (ILC) framework is proposed. With this framework, distributed state observers provide the indispensable state information for agents to learn to complete the task. An initial state learning strategy is implemented to relax consistent initial conditions, which can improve the learning accuracy. An event-triggering mechanism is designed to reduce the occupation of communication and computing resources during the iterative learning process of MASs. With locally Lipschitz nonlinearities and iteration-varying uncertainties caused by nonrepetitive initial states, the double-dynamics analysis (DDA) method is adopted to illustrate the convergence of the ILC process. By setting appropriate learning gains and constructing a quasi-globally Lipschitz condition via the DDA method, the robust convergence can be achieved for MASs in the presence of switching topologies. A numerical simulation is used to show the validity of the proposed framework.

Observer-Based Adaptive Consensus for Lipschitz Nonlinear Multiagent Systems via Asynchronous Event-Triggered Strategy

Observer-Based Adaptive Consensus for Lipschitz Nonlinear Multiagent Systems via Asynchronous Event-Triggered Strategy

Leader–follower tracking in lipschitz nonlinear multi agent systems under undirected graph with noisy sinusoidal motion of the leader

Leader–follower tracking in lipschitz nonlinear multi agent systems under undirected graph with noisy sinusoidal motion of the leader

Observer-based consensus of multi-agent systems under odd distributed impulsive control protocol

In this paper, for leader-follower Lipschitz nonlinear multi-agent systems (MASs) affected by external disturbances, observer-based distributed controller design problems are discussed in order to realize the MASs consensus. Firstly, to deal with unmeasured system states and the unknown disturbances, for each follower, a joint unknown input observer is proposed. To do so, through an interval observer, a mathematical relationship between the state and the disturbance is set up in advance. Secondarily, by using the estimations of the state and the disturbance, a local feedback controller is designed aiming at stabilizing the linear part of each follower. Thirdly, an odd distributed impulsive control method is proposed which is utilized to deal with the nonlinearity. Then the MASs consensus goal is realized by combining the local feedback controller and the distributed impulsive controller. At last, a simulation is discussed so as to display the effectivity of the raised scheme.

Edge-event-triggered encryption-decryption observer-based control of multiagent systems for privacy protection under multiple cyber attacks

This study investigates the secure and privacy-preserving consensus problem for a class of Lipschitz nonlinear multiagent systems (MASs) under undirected topology and multiple cyber attacks. An observer-based dynamic cryptography-based encryption-decryption (CED) pairing algorithm is proposed to achieve privacy preservation and defend against replay attacks simultaneously. To reduce the computation and communication resources and facilitate paired password design, a Zeno-free edge-event-triggered mechanism (EETM) based on edge (rather than neighbor) information is developed in a completely distributed manner, using only local observation information without any knowledge about the global topology. The designed EETM can accommodate multiple event-triggered functions, which simplifies the EETM design procedure. Interestingly, the CED pairing algorithm makes the effect of replay attacks equivalent to that of denial-of-service (DoS) attacks. Thus, DoS and replay attacks can be handled as the same types of attacks. In addition, a resilient EETM-based control strategy against DoS and replay attacks is proposed to make the MAS reach consensus faster, within the attack sleep time. Furthermore, sufficient conditions for the frequency and duration of replay and DoS attacks are established to achieve secure consensus of the MAS. Finally, a numerical example is provided to demonstrate the validity and superiority of the proposed method.

Double event-triggered leader-following consensus and fault detection for Lipschitz nonlinear multi-agent systems via periodic sampling strategy

Double event-triggered leader-following consensus and fault detection for Lipschitz nonlinear multi-agent systems via periodic sampling strategy

Fault Estimation and Fault-Tolerant Tracking Control for Multi-Agent Systems With Lipschitz Nonlinearities Using Double Periodic Event-Triggered Mechanism

This paper is concerned with the problem of fault estimation and fault-tolerant consensus tracking control for Lipschitz nonlinear multi-agent systems subject to external disturbance. In order to improve the communication efficiency of main network channels, two periodic event-triggered mechanisms are developed between sensor to observer and observer to controller, respectively. An event-triggered fault observer is developed to estimate existing faults and the estimated result is used for the design of a fault-tolerant controller to ensure system security. According to Lyapunov-Krasovskii theorem and the free-weighting matrix technique, the model gains of the observer and the controller can be obtained by solving a series of bilinear matrix inequalities (BMIs). To address the difficulty associated with BMIs, two iterative algorithms based on linear matrix inequalities (LMIs) are developed. Finally, a simulation example of satellite vehicles is given to illustrate the effectiveness of the obtained theoretical results.

Guaranteed performance impulsive tracking control of multi-agents systems under discrete-time deception attacks

This paper is concerned with the impulsive consensus tracking problem of Lipschitz nonlinear multi-agent systems subject to deception attacks. The proposed distributed impulsive tracking algorithm allows only partial state variables of every agent to be governed by consensus impulses. The considered deception attacks are supposed to take place in the controller–actuator channel, and can be modelled by a set of Bernoulli processes. By considering the discrete-time deception signal as bounded external disturbance, the consensus tracking problem reduces to the exponential input-to-state stable (EISS) problem of the tracking error system. The EISS-gain is used as an assessment index in measuring the capacity of consensus control laws for attenuating attacks. Specifically, a novel EISS analysis method combined with the use of a weighted discontinuous Lyapunov function is proposed to establish the consensus tracking criterion. A convex optimization problem with linear matrix inequalities-based constraints is formulated to design the guaranteed performance distributed impulsive controller, which makes the EISS-gain as small as possible. Two illustrated examples quantify the effectiveness of the proposed analysis and design approach.

Distributed Integral-Type Edge Event- and Self-Triggered Synchronization for Nonlinear Multiagent Systems

This article presents integral-type edge event- and self-triggered policies for Lipschitz nonlinear multiagent systems, in which only edge states are employed by all controllers. An integral-type triggering function is designed to determine event instants, and the considered system can achieve Zeno-free triggering. An integral-type edge self-triggered policy is then designed to avoid sensors’ continuous measurements. Compared to traditional event-triggered schemes, the proposed strategies have relaxed triggering conditions and lowered the event frequencies. Also, the proposed edge self-triggered algorithm can avoid the requirement for continuous measurement error monitoring. Numerical simulations are given to demonstrate the effectiveness of the theoretical conclusions.

Event-based consensus control of Lipschitz nonlinear multi-agent systems with unknown input delay and quantization constraints

Event-based consensus control of Lipschitz nonlinear multi-agent systems with unknown input delay and quantization constraints

Consensus in discrete-time one-sided Lipschitz nonlinear multi-agent systems with time-varying communication delay

This paper discusses consensus in discrete-time nonlinear multi-agent systems with time-varying delay in a directed communication topology. Since each agent can obtain information only from its neighbouring agents, for the purpose of analysis, a consensus protocol is proposed that considers the relative position information between the leader and followers and between neighbouring followers under time-varying communication delay. This nonlinear problem is solved by employing nonlinear behaviour based on the one-sided Lipschitz method. By constructing an appropriate Lyapunov-Krasovskii function, the consensus criterion for the leader-following problem is established in terms of the linear matrix inequality (LMI) framework. Furthermore, the solution of gain matrix is addressed by utilizing the cone complementarity linearization (CCL) algorithm. The results of a numerical simulation indicate that this method can be used to effectively solve this problem.

Distributed asynchronous impulsive consensus of one‐sided Lipschitz nonlinear multi‐agent systems

AbstractThis article investigates the consensus problem of one‐sided Lipschitz nonlinear multi‐agent systems (MASs) with distributed asynchronous impulsive control protocol. Based on the theory of discontinuous Lyapunov stability and impulsive differential equation, some new sufficient criteria about asynchronous impulsive control are derived to guarantee the consensus of one‐sided Lipschitz nonlinear MASs. Different from the existing methods of synchronous impulsive control, the asynchronous impulsive control does not need all agents are controlled simultaneously at one impulsive instant. Compared with the traditional Lipschitz condition, the one‐sided Lipschitz nonlinear function considered in this article can obtain a wider nonlinear range. Finally, some numerical simulation examples are given to verify the correctness of the theoretical analysis.

Distributed adaptive time-varying formation control for Lipschitz nonlinear multi-agent systems

In this paper, two kinds of distributed time-varying formation tracking problems for a class of Lipschitz nonlinear multi-agent systems are investigated, that is, the cases with leadless and leader-following formation. By devising a new type of edge-based adaptive algorithm, the controller of each agent can avoid the use of eigenvalues of Laplacian matrix in communication networks. The proposed algorithm only utilizes local information among neighbouring agents to form time-varying formation for nonlinear multi-agent systems with mismatched nonlinearities, and the formation tracking error is uniformly ultimately bounded. To accomplish the required time-varying formation characteristic, a predesigned formation compensation function is given. Finally, numerical simulation examples are presented to indicate the stability of the proposed algorithm, and a comparison is also given to show the superiority of the given algorithm.

Impulsive consensus of one-sided Lipschitz nonlinear multi-agent systems with Semi-Markov switching topologies

Many real systems involve not only parameter changes but also sudden variations in environmental conditions, which often causes unpredictable topologies switching. This paper investigates the impulsive consensus problem of the one-sided Lipschitz nonlinear multi-agent systems (MASs) with Semi-Markov switching topologies. Different from the existing modeling methods of the Markov chain, the Semi-Markov chain is adopted to describe this kind of randomly occurring changes reasonably. To cope with the communication and control cost constraints in the multi-agent systems, the distributed impulsive control method is applied to address the leader–follower consensus problem. Beyond that, to obtain a wider nonlinear application range, the one-sided condition is delicately developed to the controller design, and the results are different from the ones obtained in the traditional method with the Lipschitz condition (note that the existing results are usually only applicable to the case with small Lipschitz constant). Based on the characteristics of cumulative distribution functions, the theory of Lyapunov-like function and impulsive differential equation, the asymptotically mean square consensus of multi-agent systems is maintained with the proposed impulsive control protocol. Finally, an explanatory simulation is presented to validate the correctness of the proposed approach conclusively.

Leader-following consensus for multi-agent systems with nonlinear dynamics subject to additive bounded disturbances and asynchronously sampled outputs

This paper is concerned with the leader-following consensus problem for a class of Lipschitz nonlinear multi-agent systems with uncertain dynamics, where each agent only transmits its noisy output, at discrete instants and independently from its neighbors. The proposed consensus protocol is based on a continuous-discrete time observer, which provides a continuous time estimation of the state of the neighbors from their discrete-time output measurements, together with a continuous control law. The stability of the multi-agent system is analyzed with a Lyapunov approach and the exponential practical convergence is ensured provided that the tuning parameters and the maximum allowable sampling period satisfy some inequalities. The proposed protocol is simulated on a multi-agent system whose dynamics are ruled by a Chua’s oscillator.

Active fault‐tolerant consensus control of Lipschitz nonlinear multiagent systems

SummaryThis article investigates the active fault‐tolerant consensus problem for Lipschitz nonlinear multiagent systems under detailed balanced directed graph and actuator faults. First, a fault detection filter for each agent is designed, and all agents can be divided into two categories: healthy agents and possibly faulty agents. Second, fully distributed adaptive fault‐tolerant consensus protocols for healthy and possibly faulty agents are proposed to achieve state consensus. Third, based on the fault detection method and fault‐tolerant consensus protocols, active fault‐tolerant consensus algorithms are given. Simulation examples are presented to verify the effectiveness of the proposed active fault‐tolerant algorithms.