High-order Multi-agent Systems Research Articles

Event-triggered design for optimal output consensus of high-order multi-agent systems

In this paper, we study the optimal output consensus problem for networked linear multi-agent systems. Existing distributed algorithms usually rely on continuous communication among neighbouring agents or continuous update of each agent's local controller. To save communication and computation resources, we apply event-triggered technique to this optimal output consensus problem. We first constructively develop an event-triggered algorithm with a set of applicable parameters relying on event-triggered communication and control and show its effectiveness in solving the problem by rigorous proofs. Then we extend it to the case where the triggering conditions only have to be checked in some sampling time instants. Two simulation examples are given to illustrate the efficacy of our designs.

Distributed Output-Feedback Asymptotic Consensus Tracking for High-Order Multiagent Systems With Quantized Input.

This article is devoted to distributed adaptive asymptotic consensus tracking control based on output feedback for the uncertain high-order multiagent systems with input quantization. Compared with the output-feedback canonical form, the system takes unmeasured states-dependent nonlinearities into account and also includes unknown parameters and quantized input. The improved K -filters with one dynamic gain are constructed to dispose the unmeasured states-dependent nonlinearities and estimate the unknown states. Then, the novel recursive control strategy with the aid of new first-order dynamic parameter filters is proposed, which is able to effectively counteract the filter errors and steer the consensus tracking errors to zero asymptotically with low design complexity. Moreover, the new funnel variable combined with prespecified time performance function is first introduced, which can predefine practical transition time and maximum overshoot of consensus error. Finally, simulation results are presented to illustrate the validity and superiority of the proposed scheme.

Distributed fixed-time control for high-order multi-agent systems with FTESO and feasibility constraints

In this study, a fixed-time distributed anti-disturbance control strategy is designed for a class of higher-order multi-agent systems in an undirected static topology. Inspired by the existing literature, the strategy introduces a unique way of defining neighborhood errors during the design process to deal with the connectivity maintenance and collision avoidance problems among the neighbor agents in the system. The control strategy not only solves the full state constraint and transient steady state performance constraint control problems simultaneously, but also considers the effects of internal uncertainties and external disturbances of the system, which enhances the difficulty of controller design. To address these challenges, a fixed-time extended state observer is introduced to obtain the estimation of uncertainty and disturbance . Subsequently, an integrated backstepping control scheme is designed to feed-forward compensate for uncertainties and disturbances, while constraining the transient steady-state performance of the system to remain within a predefined performance boundaries. This is achieved by combining the fixed-time prescribed performance and the barrier Lyapunov function. Finally, a simulation case is presented to verify the effectiveness of the designed control strategy.

Iterative learning resilient consensus of uncertain nonlinear multi-agent systems vulnerable to false data injection attacks

This work investigates the iterative learning resilient consensus of uncertain nonlinear high-order multi-agent systems (MASs) against false data injection (FDI) attacks. First, in order to reduce the impact of FDI attacks on the nonlinear MASs, a novel coordinate transformation technique is proposed, which is composed of the states after being attacked, and the Nussbaum gain technique is adopted to address the problem of unknown attack gains resulting from FDI attacks. Then, by employing compromised state variables, a fuzzy adaptive iterative learning resilient control method is presented based on the composite energy function, where unknown nonlinear functions are handled using fuzzy logic systems. The presented approach can guarantee that the outputs of all followers precisely track the leader in a limited time interval while ensuring that all closed-loop signals are bounded. Finally, a numerical simulation is provided to demonstrate the efficacy of the designed control strategy.

Distributed adaptive event-triggered consensus control for high-order multi-agent systems

In this paper, a distributed adaptive event-triggered control approach is proposed for the consensus problem of high-order multi-agent systems (MASs) with unknown dynamics and external disturbances. First, to save communication resources, the event-triggered control is proposed to ensure the consensus of MASs, where the trigger condition is established based on the neighbors’ information. The approximation properties of neural networks are used to address the unknown dynamics and external disturbances. Second, rigorous theoretical analysis proves that the MASs can achieve the leader-following consensus, as long as the communication graph of MASs contains a spanning tree with the leader as the root node. The filtered tracking errors and adaptive parameters estimated errors are proved to be uniformly ultimately bounded without Zeno behavior. Finally, the simulations and experiments illustrate the feasibility and effectiveness of the theoretical results.

Fully Distributed Hierarchical ET Intrusion- and Fault-Tolerant Group Control for MASs With Application to Robotic Manipulators

This paper studies group synchronization tracking problem for a class of high-order multi-agent systems (MASs) with nonidentical and unknown direction faults (NUDFs) under multiple cyber attacks (i.e., denial-of-service (DoS) attacks and false data injection attacks (FDIAs)). Be motivated by this, a fully distributed hierarchical (cyber layer and physical layer) Zeno-free event-triggered (ET) intrusion-and fault-tolerant controller is presented based on Nussbaum-type gain technique, where a positive inter-event time exists in the state-dependent asynchronous ET mechanism (ETM). The constructed virtual cyber layer realizes the interaction among different agents so as to avoid the interaction in physical processes and thus reduce the error propagation. This two layer controller greatly increase the flexibility of the controller design compared with single-layer control strategies. In addition, a novel Nussbaum function stability lemma (Lemma lem4lem4) is developed for the first time. Based on this lemma, the fully distributed adaptive controller can adjust the direction of the input to match the fault direction with the help of Nussbaum function. Finally, a robotic manipulator example demonstrates the effectiveness and merit of the proposed control scheme. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In industrial processes, NUDFs and cyber attacks often occur in many different systems, which usually lead to performance degradation or even serious accidents. Typically, NUDFs affect the performance of chemical and industrial processes, circuits, and sensors. Meanwhile, in driverless vehicle platoon, attackers change the control signal through the wireless network, and then issue emergency braking commands, etc. Therefore, this paper designs a fully distributed hierarchical ET intrusion-and fault-tolerant scheme for high-order MASs that are usually used to model ship dynamics, robotic manipulators, and quarter-car active suspension. The control scheme gives solutions to the problem of NUDFs, multiple cyber attacks, and network bandwidth limitations at different layers, and effectively integrates the physical and cyber layers to achieve group synchronization. Meanwhile, a new event-triggered mechanism under the framework of group synchronization is developed to save communication resources. Robotic manipulator simulation studies verify the validity of the proposed scheme.

Robust distributed Nash equilibrium seeking for high-order systems with disturbances and coupling constraints

The objective of this article is to tackle the problem of distributed searching for generalized Nash equilibrium (GNE) for high-order multi-agent systems (MASs) that are subject to external disturbances and coupling constraints. To address disturbances and linear equality constraints while ensuring that high-order agents achieve the task of seeking a GNE, a novel approach has been developed that utilizes gradient descent algorithms, extended state observers, and state feedback control. By utilizing the proposed algorithm, the agents' behavior will ultimately converge to a small range around the GNE points. The proposed algorithm's effectiveness is validated through two numerical simulations.

Scaled Position Consensus of High-Order Uncertain Multiagent Systems Over Switching Directed Graphs.

We investigate the scaled position consensus of high-order multiagent systems with parametric uncertainties over switching directed graphs, where the agents' position states reach a consensus value with different scales. The intricacy arises from the asymmetry inherent in information interaction. Achieving scaled position consensus in high-order multiagent systems over directed graphs remains a significant challenge, particularly when confronted with the following complex features: 1) uniformly jointly connected switching directed graphs; 2) complex agent dynamics with unknown inertias, unknown control directions, parametric uncertainties, and external disturbances; 3) interacting with each other via only relative scaled position information (without high-order derivatives of relative position); and 4) fully distributed in terms of no shared gains and no global gain dependency. To address these challenges, we propose a distributed adaptive algorithm based on a acrlong MRACon scheme, where a linear high-order reference model is designed for every individual agent employing relative scaled position information as input. A new transformation is proposed which converts the scaled position consensus of high-order linear reference models to that of first-order ones. Theoretical analysis is presented where agents' positions achieve the scaled consensus over switching directed graphs. Numerical simulations are performed to validate the efficacy of our algorithm and some collective behaviors on traditional consensus, bipartite consensus, and cluster consensus are shown by precisely choosing the scales of the agents.

Distributed Adaptive Forwarding Finite-Time Output Consensus of High-Order Multiagent Systems via Immersion and Invariance-Based Approximator.

A finite-time output consensus control problem is investigated in this article for an uncertain nonlinear high-order multiagent systems (MASs). For this class of MASs, the order of individual follower is reduced gradually by implementing the immersion and invariance (I&I) control theory repeatedly, and a requirement of solving partial differential equations (PDEs) in I&I control theory is obviated. Furthermore, an I&I-based radial basis function neural network (RBFNN) approximator is developed, where an extra cross term is added in the approximation mechanism, and the form of an update law for weights is transformed into a proportional and integral one. This I&I-based RBFNN approximator does not rely on a cancellation of the perturbation term, and these uncertainties are reconstructed by the I&I manifold adaptively, which is for improvement of approximation behaviors of traditional RBFNNs. On this basis, a distributed adaptive forwarding finite-time output consensus control strategy is proposed by combining a sign function, and the convergence time of the MAS can be adjusted with appropriate finite-time parameters. Finally, two illustrative examples verify the effectiveness of the theoretical claims.

Resilient Time-Varying Formation Tracking for Heterogeneous High-Order Multiagent Systems With Multiple Dynamic Leaders

This paper investigates time-varying output formation tracking problems for heterogeneous multiagent systems in an adversarial environment, where both leaders and followers are vulnerable to cyber-attacks. Despite the presence of adversarial agents, the normal followers not suffering from cyber-attacks seek to achieve a desired for-mation configuration and track a safe trajectory generated by normal leaders' outputs simultaneously. To this end, a resilient time-varying output formation (RTVOF) tracking scheme is presented in this work. Firstly, to counteract the effect of adversarial agents, a safety strategy is proposed for general linear heterogeneous systems, which is a syn-thesis of the mean-subsequence-reduced family algorithms and an attack detection procedure. Secondly, using the neighboring interaction, a resilient distributed observer and a local formation controller are designed for each normal follower to estimate the state and track the output of the safe formation reference. Then, it is proved that the hetero-geneous multiagent system with multiple dynamic leaders and time-varying topologies can accomplish the RTVOF tracking if specific graph-theoretic properties and forma-tion feasibility conditions are satisfied. Finally, simulation examples are given to demonstrate the effectiveness of obtained results.

Distributed Optimal Resource Allocation With Local Feasibility Constraints for High-Order Multiagent Systems

Distributed Optimal Resource Allocation With Local Feasibility Constraints for High-Order Multiagent Systems

Non-singular fixed-time consensus tracking of high-order multi-agent systems with unmatched uncertainties and practical state constraints

In this study, a fixed-time consensus-tracking problem of an uncertain nonlinear multi-agent system with practical state constraints that can be fully or partially constrained is considered. A novel unified transformation is proposed to address practical state constraints. Based on the proposed transformation function, a distributed fixed-time observer is designed for the followers to approximate the transformation of a leader's output. Furthermore, we apply an adaptive neural network technique and add a power integrator technique to design a nonsingular fixed-time controller that ensures practical fixed-time consensus tracking and satisfies state constraints. Finally, simulations are performed to verify the theoretical results.

Neuro-adaptive non-singular terminal sliding mode control for distributed fixed-time synchronization of higher-order uncertain multi-agent nonlinear systems

This paper presents a novel design for a distributed fixed-time synchronization controller based on neuro-adaptive non-singular terminal sliding mode control for higher-order multi-agent nonlinear systems. In this study, a distributed control strategy is employed in which networked nonlinear systems, referred to as nodes, communicate through a predefined network topology. Within this framework, a leader-follower configuration is adopted, designating one node as the leader and the others as follower agents. Notably, the dynamics of the agents are assumed to be unknown, leading to the development of a generalized uncertain higher-order nonlinear dynamical system model that accounts for the disturbed dynamics of all agents, including the matched bounded uncertainty with an upper algebraic bound. The control design leverages radial basis function neural networks for approximation, effectively addressing unknown nonlinear terms, such as drift terms and input channels. Importantly, the proposed technique successfully mitigated matched-type uncertainty, resulting in rapid sliding-mode enforcement with reduced chattering and stress. This innovative approach establishes fixed-time synchronization by creating a sliding mode with respect to the sliding surface of networked synchronization mismatches. To underscore the effectiveness of this approach, a simulation example that vividly illustrates its captivating properties and contributions is presented.

Output-constrained fixed-time coordinated control for multi-agent systems with event-triggered and delayed communication

In this study, we propose a fixed-time coordinated controller for high-order multi-agent systems dealing with output constraints and switching digraphs while considering event-triggered and delayed communication. To tackle the scenario where only a subset of agents have direct access to the leader, a novel event-triggered fixed-time observer is first devised. This observer effectively estimates the state of the leader, considering the influence of communication delays. Subsequently, a neural network-based fixed-time controller is formulated under output constraints, utilizing the estimated leader commands to achieve the desired control objectives. Finally, practical experiments are conducted using omni-mecanum-wheeled robots to demonstrate the practical feasibility and superior performance of the theoretical findings. This study contributes significantly by tackling the challenging problem of output-constrained fixed-time coordinated control in event-triggered and delayed communication within switching digraphs. This area has yet to be previously explored.

Resilient dynamic output feedback control for leader-following consensus of high-order uncertain multi-agent systems under sensor–actuator attacks

This paper investigates the resilient leader-following consensus problem for a class of high-order multi-agent systems subject to unmatched lower triangular uncertainty dynamics and sensor–actuator attacks. Compared with previous work, the sensor and actuator attacks are modeled to be both time-varying and state-dependent, which makes the resilient consensus control more challenging. To deal with the unmatched uncertainties and sensor–actuator attacks, a new compensator with two online tuned dynamic gains is proposed relying only on the relative output measurements of neighboring agents. Then, using only the local compensation information, a fully distributed output feedback resilient protocol is designed to guarantee the leader-following consensus. Sufficient conditions in terms of matrix inequalities are derived to determine control gains and compensator parameters and simulation studies are presented to demonstrate the proposed theoretical results.

A Backstepping-Based Approach for Distributed Output Containment Control of High Order Multi-Agent Systems with Applications in Power Systems

This paper deals with the problem of output containment control of multi-agent systems. A backstepping-based approach is used to design a novel distributed controller that allows fast output containment of high order multi-agent systems. The proposed method ensures exponential convergence of the output containment error to zero despite external disturbances. A numerical example is provided to highlight the efficiency of the proposed approach. Applications of the proposed control approach in power systems are also presented.

Dynamic Event-Triggered Byzantine-Resilient Output Regulation in Continuous-Time High-Order Multiagent Systems With Static/Dynamic Leader

Dynamic Event-Triggered Byzantine-Resilient Output Regulation in Continuous-Time High-Order Multiagent Systems With Static/Dynamic Leader

Distributed Constrained Optimization Algorithm for Higher-Order Multi-Agent Systems

Distributed Constrained Optimization Algorithm for Higher-Order Multi-Agent Systems

Predefined-time consensus tracking of high-order multiagent system with deception attack

Predefined-time consensus tracking of high-order multiagent system with deception attack

Resilient cluster consensus for discrete-time high-order multi-agent systems against malicious adversaries

This paper studies the problem of resilient cluster consensus for discrete-time high-order multi-agent systems in the presence of malicious adversaries. Based on a decomposition form of the system matrices, a high-order resilient cluster consensus algorithm is proposed. Necessary and sufficient conditions for the normal agents to reach resilient cluster consensus despite the influence of the malicious adversaries are provided. In contrast to the existing results, the proposed algorithm is suitable for general high-order multi-agent systems and can reduce the network redundancy needed to tolerate the same number of malicious adversaries. Two examples are simulated to validate the effectiveness of the theoretical results.