Uncertain Multi-agent Systems Research Articles

Adaptive neural inverse optimal tracking control for uncertain multi-agent systems

An adaptive neural inverse optimal consensus control method is presented for a class of multi-agent systems (MASs) with uncertain dynamics and time-varying disturbance. The auxiliary system is constructed for every agent, and then, based on backstepping technique, neural networks are utilized to approximate the unknown function and develop the distributed controllers. Additionally, there is only one unknown parameter need to be learned for each agent. It is proved that the proposed control scheme can ensure that all states of MASs are bounded and each agent is Input-to-state stabilizable (ISS). In the meantime, the inverse optimal controller also minimizes a meaningful cost function given in advance, which contains system input and disturbance. That is, the control scheme also reduces the cost of input. Simulation experiments illustrate the feasibility of the proposed method.

Leaderless Consensus for Second-Order Inertia Uncertain Multi-Agent Systems Under Directed Graphs Without Relative Velocity Information

In this paper, we investigate the leaderless consensus problem for second-order multi-agent systems (MASs) with unknown inertias and parametric uncertainties. The graph that describes the interaction among the agents is generally directed. We consider both fixed and switching graphs. For a fixed directed topology, the associated graph needs to contain a spanning tree. For dynamically switching topologies, the uniform joint connectivity is required. We proposed consensus algorithms without relative velocity measurements, which are fully distributed in the sense that no common control gains are used and no global gain dependency conditions are required. The cases of agent dynamics with unknown nonidentical control directions and the asymptotic consensus in the presence of external disturbances are further investigated.

Global Adaptive Consensus Control for Multiagent Systems with Predefined Accuracy

This paper addresses a consensus problem for uncertain nonlinear multiagent systems with predefined precision under disturbance. By employing the neural networks method and backstepping technique, adaptive controllers for each agent are created. In contrast to the exiting global control methods for multiagent systems, global precision consensus control scheme is first put forward. Moreover, by using three n th-order continuous differentiable functions, adaptive tuning laws and virtual controllers and the real controller are designed. It is proved that the presented method can ensure that all signals are globally bounded and systems can be consistent with a given accuracy under disturbance. Finally, a practical simulation verifies the correctness for the devised control protocol.

Guaranteed Cost Leaderless Consensus Protocol Design for Fractional-Order Uncertain Multi-Agent Systems with State and Input Delays

This paper addresses the guaranteed cost leaderless consensus of delayed fractional-order (FO) multi-agent systems (FOMASs) with nonlinearities and uncertainties. A guaranteed cost function for FOMAS is proposed to simultaneously consider consensus performance and energy consumption. By employing the linear matrix inequality approach and the FO Razumikhin theorem, a delay-dependent and order-dependent consensus protocol is formulated for FOMASs with input delay. The proposed protocol not only guarantees the robust stability of the closed-loop system error but also ensures that the performance degradation caused by the system uncertainty is lesser than that obtained with other approaches. Two numerical examples are provided in order to verify the effectiveness and accuracy of the proposed protocol.

A Unified Optimization-Based Framework to Adjust Consensus Convergence Rate and Optimize the Network Topology in Uncertain Multi-Agent Systems

This paper deals with the consensus problem in an uncertain multi-agent system whose agents communicate with each other through a weighted undirected (primary) graph. The considered multi-agent system is described by an uncertain state-space model in which the involved matrices belong to some matrix boxes. As the main contribution of the paper, a unified optimization-based framework is proposed for simultaneously reducing the weights of the edges of the primary communication graph (optimizing the network topology) and synthesizing a controller such that the consensus in the considered uncertain multi-agent system is ensured with an adjustable convergence rate. Considering the NP-hardness nature of the optimization problem related to the aforementioned framework, this problem is relaxed such that it can be solved by regular LMI solvers. Numerical/practical-based examples are presented to verify the usefulness of the obtained results.

Delayed output feedback based leader–follower and leaderless consensus control of uncertain multiagent systems

This paper proposes a distributed artificially delayed output feedback-based leader–follower and leaderless consensus control for the uncertain general linear multiagent systems (MASs) with an arbitrary relative degree. Based on the measured relative output and their delayed information with respect to neighbours, two distributed controllers are designed, which relaxes the requirement of all relative states information of agents. Through the Lyapunov–Krasovskii functional, linear matrix inequalities (LMIs) are formulated, and these LMIs are feasible for arbitrary small delays selected by the user. Delay-dependent sufficient conditions are provided to guarantee the asymptotic convergence of nominal error systems and ultimately uniform boundedness in the case of a perturbed error system, using the input to state stability (ISS) theory. Finally, the efficacy of the proposed method is illustrated through numerical examples.

Adaptive Fuzzy Consensus Tracking Control for Nonlinear Multiagent Systems with Time-Varying Delays and Constraints

This paper proposes an adaptive fuzzy distributed consensus tracking control scheme for a class of uncertain nonlinear dynamic multiagent systems (MASs) with state time-varying delays and state time-varying constraints. The existing controllers with Lyapunov–Krasovskii functions (LKFs) were not suitable to address time-varying delays and time-varying constraints in nonlinear MASs simultaneously. State constraints further increase the difficulty of controller design and stability analysis, especially for nonstrict feedback systems. Fuzzy logic systems (FLSs) tackle the approximation of unknown dynamics functions and parameters. Especially when the distributed consensus tracking error is infinitely close to the origin, although there is no singular value, it would lead to the rapid growth of control rate or uncontrollability. Constructing appropriate piecewise functions can effectively avoid the above occurrence and accelerate convergence. Based on Lyapunov stability theory and algebraic graph theory, the constructed tracking control can ensure states within defined time-varying constraint bounds and eliminate the influence of time delays. All signals in closed-loop systems can be guaranteed semiglobally uniformly ultimately bounded (SUUB). Finally, the validity of the theoretical method is verified by the simulation.

Cooperative neural-adaptive fault-tolerant output regulation for heterogeneous nonlinear uncertain multiagent systems with disturbance

Cooperative neural-adaptive fault-tolerant output regulation for heterogeneous nonlinear uncertain multiagent systems with disturbance

Robust Containment Control of Uncertain Multi-Agent Systems With Time-Delay and Heterogeneous Lipschitz Nonlinearity

This paper investigates the robust containment control problem of multiagent systems with heterogeneous uncertainty and nonlinearity while the nonlinear parts have to satisfy the Lipschitz condition. In this paper, both input time-delay and data transmission time-delay between the agents are considered simultaneously and communication topology of the multiagent systems may switch in the steady-state condition. Under the mentioned conditions, the objective of this paper is to make all the followers’ states converge to the convex hull shaped by the leaders’ states with an expected exponential rate. To this end, an appropriate smooth protocol is proposed. Then, a Lyapunov–Krasovskii functional composed of five terms is proposed and the stability condition is denoted by two linear matrix inequalities (LMIs). In addition to the stability assurance, solving the LMIs would obtain the suitable gains for the protocol. Finally, some numerical simulations are given to verify the theoretical analysis.

Distributed event-triggered adaptive control for second-order nonlinear uncertain multi-agent systems

In this paper, the event-triggered consensus control problem for nonlinear uncertain multi-agent systems subject to unknown parameters and external disturbances is considered. The dynamics of subsystems are second-order with similar structures, and the nodes are connected by undirected graphs. The event-triggered mechanisms are not only utilized in the transmission of information from the controllers to the actuators, and from the sensors to the controllers within each agent, but also in the communication between agents. Based on the adaptive backstepping method, extra estimators are introduced to handle the unknown parameters, and the measurement errors that occur during the event-triggered communication are well handled by designing compensating terms for the control signals. The presented distributed event-triggered adaptive control laws can guarantee the boundness of the consensus tracking errors and the Zeno behavior is avoided. Meanwhile, the update frequency of the controllers and the load of communication burden are vastly reduced. The obtained control protocol is further applied to a multi-input multi-output second-order nonlinear multi-agent system, and the simulation results show the effectiveness and advantages of our proposed method.

Practical fixed-time adaptive consensus control for a class of multi-agent systems with full state constraints and input delay

This paper concentrates on a fixed-time consensus issue for nonstrict nonlinear uncertain multi-agent systems (MASs) with state constraints and input delay. In comparison with previous works, the topic of full state constraints and input delay is first embodied in nonstrict MASs in a fixed time. A semi-global practical fixed-time stability (SPFTS) is employed to handle the consensus problem in this note. The radial basis function neural networks (RBFNNs) are developed to counteract unknown items in each agent. Pade approximation approach is introduced to cope with input delay. By using the backstepping technique, adaptive virtual controllers, adaption laws and the actual consensus controller are devised. And the rest followers can converge to a specified trajectory built by the leader in fixed time. Finally, a practical example is employed to test the correctness for the proposed control protocol.

Fully Distributed Dynamic Event-Triggered Semiglobal Consensus of Multi-agent Uncertain Systems with Input Saturation via Low-gain Feedback

This paper investigates the event-triggered consensus problem of multi-agent systems with uncertainties and input saturation. First, a fully distributed robust consensus low-gain feedback control strategy is proposed, in which some global information, such as the communication graph and the scale of network, is not needed. Then, by defining an internal dynamic variable to memory the past state, an adaptive dynamic event-triggering mechanism is proposed, which contributes to reducing the usage of communication resources and also does not rely on any global information. Furthermore, Lyapunov-based consensus analysis results are presented, and it is also formally shown that Zeno behavior can be excluded with the proposed consensus protocols. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Topology reconstruction based fault identification for uncertain multi-agent systems with application to multi-axis motion control system

In the industrial multi-agent systems, the effect of the faults occurring on any subsystem may diffuse to the whole system through network topology and cause the control performance degradation. This paper aims to solve the issue of fault identification for uncertain multi-agent systems with sensor faults. Firstly, a randomized cooperative fault detection system composed by a group of decoupled filters is presented, where a joint fault detection performance assessment scheme is designed. On this basis, a novel topology reconstruction-based fault isolation strategy is proposed. Finally, two case studies on the multi-axis motion control system are conducted, and the results illustrate the effectiveness of the proposed framework.

Cooperative Adaptive Containment Control With Parameter Convergence via Cooperative Finite-Time Excitation

This article addresses the problem of cooperative adaptive containment control for multiagent systems, which specifies the objective of jointly achieving containment control and accurate adaptive learning/identification of unknown system parameters. We consider a class of linear uncertain multiagent systems with multiple leaders subject to bounded unmeasurable inputs and multiple followers subject to unknown system dynamics. A novel cooperative adaptive containment control architecture is proposed, which consists of a discontinuous nonlinear state-feedback control law and a filter-based cooperative adaptation law. This new control architecture is compelling in the sense that exponential convergence of both containment tracking errors to zero and adaptation parameters to their true values can be achieved simultaneously under a mild cooperative finite-time excitation condition. This condition significantly relaxes existing ones (e.g., persistent excitation and finite-time excitation) for parameter identification in adaptive control systems. Effectiveness of the proposed approach has been demonstrated through both rigorous analysis and a case study.

Adaptive Neural Control for a Class of Nonlinear Multiagent Systems.

This article studies the adaptive neural controller design for a class of uncertain multiagent systems described by ordinary differential equations (ODEs) and beams. Three kinds of agent models are considered in this study, i.e., beams, nonlinear ODEs, and coupled ODE and beams. Both beams and ODEs contain completely unknown nonlinearities. Moreover, the control signals are assumed to suffer from a class of generalized backlash nonlinearities. First, neural networks (NNs) are adopted to approximate the completely unknown nonlinearities. New barrier Lyapunov functions are constructed to guarantee the compact set conditions of the NNs. Second, new adaptive neural proportional integral (PI)-type controllers are proposed for the networked ODEs and beams. The parameters of the PI controllers are adaptively tuned by NNs, which can make the system output remain in a prescribed time-varying constraint. Two illustrative examples are presented to demonstrate the advantages of the obtained results.

Recursive Sliding-Mode Dynamic Surface Containment Control With Nonlinear Gains for Uncertain Nonlinear Multiagent Systems

Containment control is one of critical issues in multiagent systems (MASs). A recursive sliding-mode dynamic surface control (DSC) strategy with a nonlinear gain is addressed for the containment problem of uncertain MASs in strict-feedback form. Two factors, a recursive dynamic sliding-mode surface and a nonlinear gain function, are introduced to solve the contradiction between control accuracy and dynamic performance in the traditional DSC method. The function approximation technique, by radial basis function neural networks, is employed to compensate unknown dynamics. On the basis of the backstepping and graph theory, a full-state feedback containment control strategy is presented. Subsequently, we propose an output feedback containment control strategy via a state observer for individual followers. From the Lyapunov stability theorem, we construct an improvement Lyapunov function for the MAS, and it is proven that all followers converge to a convex hull formed by leaders for both full-state feedback and output feedback cases. Simulation examples are presented for verification of the effectiveness of the strategy.

Adaptive Consensus Tracking Control of Uncertain Nonlinear Multiagent Systems With Predefined Accuracy.

In this article, we consider the leader-follower consensus control problem of uncertain multiagent systems, aiming to achieve the improvement of system steady state and transient performance. To this end, a new adaptive neural control approach is proposed with a novel design of the Lyapunov function, which is generated with a class of positive functions. Guided by this idea, a series of smooth functions is incorporated into backstepping design and Lyapunov analysis to develop a performance-oriented controller. It is proved that the proposed controller achieves a perfect asymptotic consensus performance and a tunable L2 transient performance of synchronization errors, whereas most existing results can only ensure the stability. Simulation demonstrates the obtained results.

On the robustness of distributed proportional‐integral consensus protocols under channel uncertainties

AbstractThis article studies the robust consensus problem for uncertain multiagent systems under distributed proportional‐integral (PI) protocols. For both continuous‐time and discrete‐time multiagent systems, we allow additive channel uncertainties that are stable and bounded in norm. By exploiting the generalized network complementary sensitivity function (GNCSF), necessary and sufficient conditions under which the robust consensus with distributed PI protocols can be guaranteed are derived. For the continuous‐time case, it is shown that the robust consensus can be reached if and only if the uncertainty radius and the norm of the GNCSF satisfy certain constraint. For the discrete‐time case, it is shown that the robust consensus can be preserved under both the constraints on the parameters of the PI protocols and the relationship of the uncertainty radius and the norm of the GNCSF. Finally, numerical examples are provided to show the effectiveness of the theoretical results.

A distributed adaptive scheme for multiagent systems

AbstractIn traditional adaptive control, the certainty equivalence principle suggests a two‐step design scheme. A controller is first designed for the ideal situation assuming the uncertain parameter was known, and it renders a Lyapunov function. Then, the uncertain parameter in the controller is replaced by its estimation that is updated by an adaptive law along the gradient of Lyapunov function. This principle does not generally work for a multiagent system as an adaptive law based on the gradient of (centrally constructed) Lyapunov function cannot be implemented in a distributed fashion, except for limited situations. In this paper, we propose a novel distributed adaptive scheme, not relying on gradient of Lyapunov function, for general multiagent systems. In this scheme, asymptotic consensus of a second‐order uncertain multiagent system is achieved in a network of directed graph.

A Hierarchical Security Control Framework of Nonlinear CPSs Against DoS Attacks With Application to Power Sharing of AC Microgrids.

In this article, we investigate the distributed resilient observers-based decentralized adaptive control problem for cyber-physical systems (CPSs) with time-varying reference trajectory under denial-of-service (DoS) attacks. The considered CPSs are modeled as a class of nonlinear multi-input uncertain multiagent systems, which can be used to model an AC microgrid system consisting of distributed generators. When the communication to a subsystem from one of its neighbors is attacked by a DoS attack, the transmitted information is unavailable and the existing distributed adaptive methods used to estimate the bound of the n th-order derivative of the reference trajectory become nonapplicable. To overcome this difficulty, we first design a new distributed estimator for each subsystem to ensure that the magnitude of the state of the estimator is larger than the bound of the n th-order derivative of the reference trajectory after a finite time. By employing the estimator state, a distributed observer with a switching mechanism is proposed. Then, a new block backstepping-based decentralized adaptive controller is developed. Based on the DoS communication duration property, convex design conditions of observer parameters are derived with the Lebesgue integral theory and the average dwell time method. It is proved that the output tracking errors will approach a compact set with the developed method. Finally, the design method is successfully applied to show the effectiveness of the proposed method to solve the power sharing problem for AC microgrids.