Time-varying Multi-agent Systems Research Articles

Fault-tolerant formation consensus control for time-varying multi-agent systems with stochastic communication protocol

Article Fault-tolerant formation consensus control for time-varying multi-agent systems with stochastic communication protocol Chunyu Li, Yifan Liu, Ming Gao, and Li Sheng * 1 College of Control Science and Engineering, China University of Petroleum (East China), Qingdao 266580, China * Correspondence: E-mail: shengli@upc.edu.cn Received: 4 September 2023 Accepted: 8 November 2023 Published: 26 March 2024 Abstract: This paper is concerned with the problem of fault-tolerant formation consensus control for linear time-varying (LTV) multi-agent systems (MASs) with stochastic communication protocol (SCP). The SCP is introduced to schedule the signal transmission, and only one neighbouring agent is allowed to transmit data at one instant. The purpose of this work is to design a fault-tolerant controller for each agent, so that, for all probabilistic scheduling behaviors, MASs can achieve the formation consensus performance. The state and fault are augmented into a new vector, meanwhile, each agent system is written as a singular one and a state observer is designed. By utilizing the estimated information of states and faults, the designed time-varying compensation term can reduce the impacts of unknown external disturbances and faults. Then, a sufficient condition is obtained to guarantee the performance constraint over the finite horizon for closed-loop systems. The parameters of observers and controllers are derived by solving coupled backward recursive Riccati difference equations. Finally, a numerical example is given to validate the effectiveness of the proposed fault-tolerant control scheme.

Quasi-Consensus Control for Stochastic Multiagent Systems: When Energy Harvesting Constraints Meet Multimodal FDI Attacks.

In this article, the quasi-consensus control problem is investigated for a class of stochastic nonlinear time-varying multiagent systems (MASs). The innovation points of this research can be highlighted as follows: first of all, the dynamics of the plant are stochastic, nonlinear, and time varying, which resembles the natural systems in practice closely. Meanwhile, an energy harvesting protocol is put forward to collect adequate energy from the external environment. Second, as a generalization of the existing result, the ultimate control objective is quasi-consensus in a probabilistic sense, that is, designing a distributed control protocol in order that the probability of centering the allowable region for the states of each agent is larger than some predetermined values. Third, the MASs are subject to false data-injection (FDI) attacks, and a more general multimodal FDI model is proposed. On the basis of the probabilistic-constrained analysis technique and the recursive linear matrix inequalities (RLMIs), sufficient conditions are provided to guarantee the probabilistic quasi-consensus property. To derive the controller gains, an optimal probabilistic-constrained algorithm is designed by solving a convex optimization problem. Finally, two examples are provided to substantiate the validity of the proposed framework.

Adaptive Event-triggered Cooperative Tracking Control Under Full-state Constraints Based on Nonlinear Time-varying Multi-agent Systems

Adaptive Event-triggered Cooperative Tracking Control Under Full-state Constraints Based on Nonlinear Time-varying Multi-agent Systems

Consensus control of time-varying multi-agent systems via event-triggered strategy and its application

Consensus control of time-varying multi-agent systems via event-triggered strategy and its application

Quantised data-driven iterative learning bipartite consensus control for unknown heterogeneous linear MASs with varying trial lengths

This paper aims to realise the robust output bipartite consensus for unknown heterogeneous linear time-varying multiagent systems (MASs) subject to varying trial lengths, unknown measurement disturbances and data quantisation. To this end, inspired by the idea of quantised control, a quantised data-driven adaptive iterative learning bipartite consensus (AILBC) method is proposed. Specifically, to address the problem of varying trial lengths, a distributed auxiliary output prediction system is constructed based on the agents' input-output (I/O) dynamic relationship. An adaptive update protocol is developed to estimate the measurement disturbances and unknown parameters of I/O dynamic relationship. Subsequently, a quantised distributed data-driven iterative learning control (ILC) approach based on the quantised output information is proposed for MASs to achieve robust bipartite consensus tracking, with an attempt to relax the need of explicit model information. The bipartite consensus tracking errors are ultimately bounded through rigorous analysis, and this result is further extended to switching topologies. Finally, numerical simulations are conducted to verify the validity of the AILBC method.

Finite-Horizon $H_{\infty }$ Consensus Control of Discrete Time-Varying Multiagent Systems: A Dynamic Event-Based Learning Approach

This paper addresses the finite-horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus problem for general discrete time-varying multi-agent systems with energy-bounded external disturbances and limited network bandwidth resource. A dynamic event-based learning approach is proposed to produce a dynamic discrete-time event-triggered scheme and a dynamic distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus protocol. Based on the local state information, the dynamic distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus protocol is developed to guarantee the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus of the general discrete time-varying multi-agent systems with external disturbances. Besides, a novel criterion is established by employing the Lyapunov theory and considering the special dynamic triggering constraint, and the corresponding recursive learning algorithm is developed. In contrast with the previous works, the proposed dynamic event-based approach results in less network bandwidth utilization, and the novel recursive algorithm brings less conservatism of the designed controller. Finally, the effectiveness of the corresponding algorithm and the advantages of the proposed dynamic event-based approach are testified by a numerical simulation.

Stability Analysis for Impulsive Stochastic Time-Varying Systems

The average impulsive interval is widely used to describe the frequency of impulsive occurrence (FIO), where the occurrence number of impulses is bounded by a linear function of time interval length. However, the linear relationship may insufficiently or excessively characterize the occurrence number of impulses to stabilize impulsive time-varying systems. In this article, the impulsive density is introduced to describe a time-varying FIO, such that the occurrence number of impulses can be characterized more explicitly. Under the impulsive density, the asymptotical stability is considered for impulsive stochastic time-varying systems, where the continuous dynamics of systems, impulsive strengths, and instants are all assumed to be time-varying. In addition, the exponential stability is also investigated for impulsive stochastic time-varying systems with time-delay, which can extend some existing results. Two examples, including one example of the consensus for impulsive time-varying multiagent systems with time-delay, are presented to demonstrate the effectiveness of the proposed results.

Robust Performance Analysis for Time-Varying Multi-Agent Systems with Stochastic Packet Loss

Recently, a scalable approach to system analysis and controller synthesis for homogeneous multi-agent systems with Bernoulli distributed packet loss has been proposed. As a key result of that line of work, it was shown how to obtain upper bounds on the H2-norm that are robust with respect to uncertain interconnection topologies. The main contribution of the current paper is to show that the same upper bounds hold not only for uncertain but also time-varying topologies that are superimposed on the stochastic packet loss. Because the results are formulated in terms of linear matrix inequalities that are independent of the number of agents, multi-agent systems of any size can be analysed efficiently. The applicability of the approach is demonstrated on a numerical first-order consensus example, on which the obtained upper bounds are compared to estimates from Monte-Carlo simulations.

A Lyapunov Approach to Consensus of Linear Multi-Agent Systems with Infinite Distributed Communication Delays

This paper considers the leaderless consensus problem of linear time-invariant multi-agent systems with infinite distributed communication delays. A novel distributed low gain controller is proposed based on the solution to a parametric algebraic Riccati equation. It is shown via the newly developed Lyapunov-like method that not only the consensus of linear time-invariant multi-agent systems can be achieved exponentially under some mild assumptions but also an estimate of the exponential convergence rate of consensus is given in this work. The Lyapunov-like method is also extended to handle a special case of linear time-varying multi-agent systems. In addition, the obtained results include the results on the leaderless consensus of linear multi-agent systems with bounded distributed communication delays as special cases. To the best of our knowledge, this is the first work that develops the Lyapunov-like method for the leaderless consensus problems of both time-invariant and time-varying linear multi-agent systems with infinite distributed communication delays. Finally, a numerical example is presented to illustrate the effectiveness of the proposed controller.

Secure Finite-Horizon Consensus Control of Multiagent Systems Against Cyber Attacks.

The problem of secure finite-horizon consensus control for discrete time-varying multiagent systems (MASs) with actuator saturation and cyber attacks is addressed in this article. A random attack model is first proposed to account for randomly occurring false data injection attacks and denial-of-service attacks, whose dynamics are governed by the random Markov process. The hybrid secure control scheme is developed to mitigate the influence of arbitrary cyber attacks on system performance. Specifically, this article proposes a hybrid control law containing multiple controllers, each of which is designed to counter different types of cyber attacks. By using the stochastic analysis approach, two sufficient criteria are provided to guarantee that the time-varying MASs satisfy the finite horizon H∞ consensus performance. Then, the controller parameters are obtained by solving the recursive linear matrix inequality. The usefulness of the theoretic results presented is demonstrated via a numerical example that contains a performance comparison of different secure control schemes.

Event-triggered based security consensus control for multi-agent systems with DoS attacks

This work devotes to the security consensus problems for time-varying multi-agent systems (MASs) based on event-triggered control method with denial-of-service (DoS) attacks and parameter uncertainties. During information transmission, DoS attacks exist in both control and measurement channels, regarded as a dwell-time switching scheme, and hence the augmented system can be transformed into a class of discrete-time switched system subject to dwell-time property which contains an unstable and a stable subsystem. To increase the utilization of communication resources, the control input signal can be updated by adopting a novel event-driven mechanism with state-dependent threshold over a given finite horizon. By utilizing multiple Lyapunov functions analysis strategy, two sufficient conditions are obtained to achieve the desired H∞ consensus performance. The cone complementary linearization algorithm is employed to cope with the nonlinear terms, and the desired controller gain matrices are calculated via resolving the corresponding linear matrix inequalities. Finally, the effectiveness of this proposed method is verified by providing a simulation example and the multi-automobile system.

Strong targeted controllability of multi-agent systems with time-varying topologies over finite fields

In this paper, we study the strong targeted controllability of multi-agent systems with time-varying topologies over finite fields from a graph theoretic perspective. We consider leader–follower networks, where only some of the agents are governed by external control inputs, namely the leaders. We develop a graph-theoretic characterization for strong targeted controllability of multi-agent systems with time-varying topologies over finite fields. Specifically, we show that a time-varying multi-agent system is strongly targeted controllable over any finite field if the graphs of the system satisfy certain properties. Our main results are applicable to time-varying topologies with arbitrary fields and coupling weights. We also present a necessary and sufficient condition for the strong structural controllability of the time-invariant multi-agent systems.

Consensus of piecewise time-varying multi-agent systems with switching topologies

In this paper, a consensus problem is first investigated for piecewise time-varying multi-agent systems with switching topologies. Due to the piecewise time-varying characteristics of system matrix, it is challenging to design an appropriate controller to stabilize the error state within each piecewise time period. To overcome this difficulty, a piecewise time-varying Lyapunov function (PTVLF) approach is proposed to analyze the piecewise time-varying systems. Then, a useful lemma guaranteeing the negative definiteness of matrix polynomials is first derived, which is utilized to prove the negative definiteness of the derivative for the PTVLF. Based on this, a novel controller with time-varying gain is presented to stabilize the error state within each piecewise time period. Then, by selecting the dwell time of each topology larger than a positive threshold, the overall consensus of such systems is guaranteed. Finally, a numerical simulation is shown to illustrate the theoretical results.

Quasi-Consensus of Time-Varying Multi-Agent Systems with External Inputs under Deception Attacks.

The quasi-consensus of a class of nonlinear time-varying multi-agent systems suffering from both external inputs and deception attacks is studied in this paper. This is different from a time-varying matrix, which is assumed to be bounded; further reasonable assumptions are supposed. In addition, impulsive deception attacks modeled with Bernoulli variables are considered. Sufficient conditions to achieve quasi-consensus are given, and the upper bounds of the error state related to the deception attacks is derived. Finally, a numerical simulation example is provided to show the validity of the obtained results.

Cooperative Fault Diagnosis of Fuzzy Fractional Order Time-Varying Multi-Agent System With Directed Networks

This brief focuses on the cooperative fault diagnosis of fuzzy time-delay fractional order multi-agent system (FOMAS) over directed networks, whose fractional order belongs to (0, 1). Due to the interconnections, for each agent’s estimator, when estimating the local state and error parameters, whose purpose is to further consider faulty effects on others. Firstly, by the interconnection relationships between each agent, a new formulation scheme is proposed so that the shared signals are achieved by correctly constructing auxiliary graphs of a directed network. Then, unlike the existed papers dealing with normal fuzzy multi-agent systems, new admissible criteria of fuzzy FOMASs are proposed with time-varying. Finally, to illustrate the method proposed above is available, a practical application example of unmanned aerial vehicles is given.

Distributed fault detection and isolation for uncertain linear discrete time-varying heterogeneous multi-agent systems

The distributed fault detection and isolation of linear discrete time-varying multi-agent systems subject to heterogeneous dynamics and norm bounded model uncertainties is investigated. By combining the model uncertainties and external disturbances into a new generalized disturbance, a distributed closed-loop residual generator is constructed based on the estimate of the generalized disturbance. Then, the concerned fault detection is transformed into an indefinite quadratic minimum problem by using the finite-horizon robust H∞ filtering method, for which necessary and sufficient minimum conditions are provided by the Krein-space theory. Afterwards, a computationally efficient recursive algorithm is further developed to determine the residual for individual agent. Based on the resulting residuals, the fault occurrence can be alerted by devising a novel distributed fault detection scheme, which is then applied for the fault isolation by some appropriate transformation of the output measurements. Finally, both numerical and practical simulations are proposed to verify the effectiveness of the proposed algorithm.

Distributed consensus control of periodically time-varying multi-agent systems using neural networks and fourier series expansion

This paper studies the consensus of nonlinear multi-agent systems with periodic disturbances and uncertain dynamics based on matrix theory, adaptive control, neural networks and fourier series expansion. Firstly, fourier series expansion and neural networks are used to describe the unknown periodic time-varying parameter and uncertain nonlinear dynamic, respectively. Secondly, based on adaptive control technology and reparameterization method, two new fully distributed control protocols are designed based on symbolic function and smooth hyperbolic tangent function, respectively, so that all agents can reach asymptotic consensus. Thirdly, a new positive integral bounded function is introduced to compensate for the approximation error caused by the smooth hyperbolic tangent function instead of the symbolic function, so that all network nodes achieve the same consensus effect. Finally, a simulation example is given to verify the effectiveness of the two algorithms and to illustrate their advantages and disadvantages.

Distributed Fault Detection for Linear Time-Varying Multi-Agent Systems With Relative Output Information

This paper investigates the distributed fault detection problem for linear discrete time-varying heterogeneous multi-agent systems under relative output information. Due to the lack of absolute outputs, an augmented model is built by stacking all local relative output information. Then, the fault detection problem consisting of residual-generation and residual-evaluation is handled using the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering framework. The residual-generation problem is actually a minimization problem of an indefinite quadratic form, and the Krein space-Kalman filtering theory is applied, which results in a low computational burden despite the time-varying characteristic. Using the Krein space theory, a necessary and sufficient condition for the minimum is derived, and a residual-generation algorithm is developed. Further, a residual-evaluation mechanism is designed by constructing an evaluation function and detecting faults by comparing it with a threshold. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed fault detection approach.

Bipartite output synchronization of heterogeneous time-varying multi-agent systems via edge-based adaptive protocols

This paper considers a bipartite output synchronization problem for heterogeneous linear multi-agent systems with time-varying communication networks using an adaptive distributed observer-based control strategy. Based on the relative output information from neighboring agents, a reduced-dimensional distributed observer is proposed to estimate the unavailable state information of each agent. Meanwhile, an edge-based adaptive law is designed for each agent to assign the time-varying interaction weight such that the connectivity of the communication network is preserved. Theoretical analysis is presented for the convergence of the output tracking errors under the proposed output feedback control strategy. Some numerical results are also presented to validate the proposed control strategy.

Distributed Model Predictive Consensus of Heterogeneous Time-Varying Multi-Agent Systems: With and Without Self-Triggered Mechanism

This paper provides a framework of designing distributed model predictive controller to reach consensus of a heterogeneous time-varying multi-agent system, and the dynamics of heterogeneous agents are modeled by double integrators and Euler-Lagrange (EL) equations. Firstly, a DMPC-based consensus algorithm is proposed, where the constraints in the algorithm depend on the heterogeneous dynamics. We prove that the resultant DMPC optimization problem is feasible with the designed controllers, which is stable when the system reaches consensus. To further reduce communication cost and solve the problem with asynchronous discrete-time information exchange, self-triggered mechanism is introduced into the framework. Trigger intervals are alternatively optimized with the control inputs, and the influence on the system performance is analyzed. Numerical examples are provided to verify the effectiveness and advantages of the proposed algorithms.