Nonlinear Fractional-order Multi-agent Systems Research Articles

Securing Bipartite Nonlinear Fractional-Order Multi-Agent Systems against False Data Injection Attacks (FDIAs) Considering Hostile Environment

This study investigated the stability of bipartite nonlinear fractional-order multi-agent systems (FOMASs) in the presence of false data injection attacks (FDIAs) in a hostile environment. To tackle this problem we used signed graph theory, the Razumikhin methodology, and the Lyapunov function method. The main focus of our proposed work is to provide a method of stability for FOMASs against FDIAs. The technique of Razumikhin improves the Lyapunov-based stability analysis by supporting the handling of the intricacies of fractional-order dynamics. Moreover, utilizing signed graph theory, we analyzed both hostile and cooperative interactions between agents within the MASs. We determined the system stability requirements to ensure robustness against erroneous data injections through comprehensive theoretical investigation. We present numerical examples to illustrate the robustness and efficiency of our proposed technique.

Observer-based bipartite consensus tracking of nonlinear fractional-order multi-agent systems with pull-based dynamic event-triggered mechanism

This paper investigates the observer-based bipartite consensus tracking of nonlinear fractional-order multi-agent systems (FOMASs) by employing a pull-based dynamic event-triggered mechanism (DETM). First, considering that the relevant state information of each agent is not always measurable, a class of distributed observers is considered for each agent to estimate its state information. Then, a pull-based DETM for FOMASs is proposed to avoid continuous controller updates, in which the dynamic threshold is modulated according to the preset conditions. The pull-based DETM constructed in this paper enables each agent to update the controller only based on its own trigger instants. Furthermore, an observer-based dynamic event-triggered control protocol is designed to guarantee the bipartite consensus tracking of FOMASs. Correspondingly, sufficient conditions are obtained by using graph theory and choosing suitable Lyapunov candidate functions. Moreover, the Zeno behavior is precluded. Finally, two simulation examples are presented to illustrate the theoretical results efficiently.

Hybrid finite‐time fault‐tolerant consensus control of non‐linear fractional order multi‐agent systems based on fault detection and estimation

AbstractThis paper addresses the problem of achieving finite‐time fault‐tolerant consensus control for a class of non‐linear fractional‐order multi‐agent systems (NFO‐MAS) using finite‐time fault detection and estimation, as well as a finite‐time state observer. To achieve this, a specific lemma is utilized to rewrite the high‐order model of NFO‐MAS as a lower‐order NFO unique system. By employing new identification rules and introducing a fault estimation method, both the state variables and faults of the agents are estimated within a finite time. Subsequently, a finite‐time sliding mode control law is designed based on the estimated fault and the state variables obtained from the proposed finite‐time observer to achieve consensus within a finite time for the fractional‐order non‐linear MAS. The stability of the fault estimation, state observer, and consensus controller is proven using the finite‐time Lyapunov theory. The effectiveness of the proposed approach is demonstrated through numerical simulations.

Event-Triggered Adaptive Finite-Time Containment Control for Fractional-Order Nonlinear Multiagent Systems.

This article investigates the finite-time containment control problem for fractional-order nonlinear multiagent systems (FOMASs) with event-triggered inputs. First, a new Lyapunov stability lemma is developed, which provides a basic approach for the completely unknown nonlinear fractional-order system to realize finite-time convergence. Considering the containment control for FOMASs, the restricted assumption that the derivatives of leaders' trajectories are known to the followers is removed, and only the boundedness of derivatives is required in this article, whose upper bound need not be known. To reduce the burden of communication, an event-triggered condition consisting of the control input and a decreasing function related to the containment errors is devised, which can provide more design freedom to balance the system performance and communication resources. According to the proposed fractional-order finite-time convergence lemma, a distributed adaptive containment control scheme is developed, such that each follower can be steered to the convex hull spanned by the leaders in finite time. Simulation examples further demonstrate the effectiveness of our proposed method.

Hierarchical Distributed Adaptive Fault-Tolerant Control of Nonlinear Fractional-Order Multiagent Systems With Faults and Periodic Disturbances Using Event-Triggered Communication.

This article presents a distributed fault-tolerant control (FTC) scheme for nonlinear fractional-order (FO) multiagent systems (MASs) with the order lying in (0, 1, such that the proposed control architecture can be directly applied to both FO and integer-order (IO) systems without any modifications. To handle the unexpected actuator faults encountered by the FO MASs, a hierarchical FTC mechanism is developed for each system by constructing an event-triggered distributed FO estimator at the upper layer to estimate the leader system's output via conditionally triggered neighboring information, and an FTC unit at the lower layer to counteract the loss-of-effectiveness faults via Nussbaum function with FO criteria. To further address the unknown nonlinear functions involving bias faults and periodic disturbances, the Fourier series expansion technique is used to construct the input variables of fuzzy neural networks (FNNs), such that the FNNs with dynamically adjusted weight matrices, centers, and widths can be developed for each FO system to act as the learning module. It is shown by FO Lyapunov stability analysis that all follower systems can track the leader system against faults and periodic disturbances. Simulation results on FO systems and hardware-in-the-loop experiment results on IO fixed-wing unmanned aerial vehicles show the extensive feasibility of the developed scheme.

Leaderless Consensus Control of Fractional-Order Nonlinear Multi-Agent Systems With Measurement Sensitivity and Actuator Attacks

Leaderless Consensus Control of Fractional-Order Nonlinear Multi-Agent Systems With Measurement Sensitivity and Actuator Attacks

Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs

This paper investigates the problem of fixed-time distributed time-varying optimization of a nonlinear fractional-order multiagent system (FOMAS) over a weight-unbalanced directed graph (digraph), where the heterogeneous unknown nonlinear functions and disturbances are involved. The aim is to cooperatively minimize a convex time-varying global cost function produced by a sum of time-varying local cost functions within a fixed time, where each time-varying local cost function does not have to be convex. Using a three-step design procedure, a fully distributed fixed-time optimization algorithm is constructed to achieve the objective. The first step is to design a fully distributed fixed-time estimator to estimate some centralized optimization terms within a fixed time T0. The second step is to develop a novel discontinuous fixed-time sliding mode algorithm with nominal controller to derive all the agents to the sliding-mode surface within a fixed time T1, and meanwhile the dynamics of each agent is described by a single-integrator MAS with nominal controller. In the third step, a novel estimator-based fully distributed fixed-time nominal controller for the single-integrator MAS is presented to guarantee all agents reach consensus within a fixed time T2, and afterwards minimize the convex time-varying global cost function within a fixed time T3. The upper bound of each fixed time Tm(m=0,1,2,3) is given explicitly, which is independent of the initial states. Finally, a numerical example is provided to validate the results.

Adaptive Neural Consensus for Fractional-Order Multi-Agent Systems With Faults and Delays.

This article investigates the consensus control for a class of fractional-order (FO) nonlinear multi-agent systems (MASs). Severe sensor/actuator faults and time-varying delays are both considered in the FO MASs. The severe faults may cause unknown control directions in MASs. A new adaptive controller, which is composed of a distributed FO Nussbaum gain, an FO filter, and an auxiliary function, is presented to deal with the severe faults. To cope with the time-varying delays, two different methods are proposed based on barrier Lyapunov function and Lyapunov-Krasovskii function, respectively. Meanwhile, the radial basis function neural network (RBF NN) is applied to approximate the unknown nonlinear functions during the design procedures. This can result in a low-complexity controller. Finally, two simulation examples are used to verify the validity of the proposed schemes.

An event-triggered sliding mode control mechanism to exponential consensus of fractional-order descriptor nonlinear multi-agent systems

The problem of leader-following exponential consensus is addressed for fractional-order descriptor nonlinear multi-agent systems by designing an event-triggered sliding mode control strategy. Such an exponential consensus is achieved by defining a suitable sliding surface and a controller under the Mittag–Leffler stability of fractional-order systems. Due to the memory nature of the fractional-order calculus operator, a new condition is established to avoid Zeno behaviors happening, which is different from existing event-triggered schemes. Finally, to illustrate the effectiveness and feasibility of the proposed method, two examples are provided.

Cluster consensus of general fractional-order nonlinear multi agent systems via adaptive sliding mode controller

Cluster consensus of general fractional-order nonlinear multi agent systems via adaptive sliding mode controller

Distributed output-based bipartite consensus for nonlinear fractional-order multi-agent systems with continuous and intermittent communications

This paper studies the distributed output-based bipartite consensus problem in a nonlinear fractional-order multi-agent system (FOMAS) subjected to heterogeneous nonlinear functions and disturbances over a signed directed graph. Two types of distributed bipartite consensus algorithms are proposed to solve the bipartite consensus problem by utilizing continuous and intermittent output measurements, respectively. A novel discontinuous algorithm with a nominal controller is first developed to derive that all agents reach the sliding-mode surface in finite time, and meanwhile, each agent’s dynamics can be described by a linear FOMAS with a nominal controller. When each agent can access its neighbors’ output measurements continuously all the time, a continuous output-based nominal controller is designed for the linear FOMAS to realize bipartite consensus asymptotically. When each agent can only access its neighbors’ output measurements intermittently in some disconnected time intervals, an intermittent output-based nominal controller is further designed, where the communication rate is required to be greater than a derived threshold value. Numerical simulations are performed to validate the effectiveness of the main results.

Event-Triggered Distributed Sliding Mode Control of Fractional-Order Nonlinear Multi-Agent Systems

In this study, the state consensus problem is investigated for a class of nonlinear fractional-order multi-agent systems (FOMASs) by using a dynamics event-triggered sliding mode control approach. The main objective is to steer all agents to some bounded position based on their own information and the information of neighbor agent. Different from the existing results, both asymptotic consensus problem and Zeno-free behavior are ensured simultaneously. To reach this objective, a novel event-triggered sliding mode control approach is proposed, composed of distributed dynamic event-triggered schemes, event-triggered sliding mode controllers, and auxiliary switching functions. Moreover, to implement the distributed control scheme, the fractional-order adaptive law is also developed to tuning the coupling weight, which is addressed in distributed protocol. With the improved distributed control scheme, all signals in the fractional-order closed-loop systems are guaranteed to be consensus and bounded, and a novel approach is developed to avoid the Zeno behavior. Finally, the availability and the effectiveness of the above-mentioned approach are demonstrated by means of a numerical example.

Cluster consensus and cluster formation for nonlinear fractional-order multi-agent systems

Cluster consensus and cluster formation for nonlinear fractional-order multi-agent systems

Containment control for fractional order MASs with nonlinearity and time delay via pull-based event-triggered mechanism

The containment control for fractional order multi-agent systems with nonlinearity and time delay is investigated in this article. Firstly, a distributed control protocol with fixed time delay is proposed for the purpose of achieving containment control for nonlinear fractional order multi-agent systems. Secondly, by using the pull-based event-triggered mechanism, a distributed event-based control law with time delay is further given to accomplish containment control for fractional order multi-agent systems with nonlinearity. In this way, the controller of each agent is merely updated at its own trigger moments. Hence, it can decrease network correspondence congestion and lower computational cost. Thanks to the stability theory of fractional order calculus, matrix theory, and properties of Mittag-Leffler function, the feasibility of the designed control protocols is confirmed. Furthermore, the Zeno behavior is precluded by the strict proof. Ultimately, two simulation examples are used to illustrate the availability of above theoretical analysis respectively.

Consensus tracking for a class of fractional-order non-linear multi-agent systems via an adaptive dynamic surface controller

In this paper we investigate bottlenecks in adaptive dynamic surface control (DSC) and unveil an innovative consensus tracking controller to track the desired trajectory for a class of fractional-order multi-agent systems with non-linear dynamics. The study derives an algorithm by implementing graph theory and the DSC method. The main approaches in the control of fractional-order systems are the DSC and the adaptive DSC techniques to avoid the computational complexity of fractional-order virtual control law. According to these techniques, a virtual control law is formulated and the proposed controller is passed through a fractional-order dynamic surface. By employing the DSC and adaptive DSC laws, we demonstrate that the desired consensus tracking between agents can be ensured. To verify the performance of the new approach, we simulate the desirable scenarios and evaluate the results against a popular adaptive sliding mode technique.

Fractional-Order Nonlinear Multi-Agent Systems: A Resilience-Based Approach to Consensus Analysis with Distributed and Input Delays

In this article, a resilient consensus analysis of fractional-order nonlinear leader and follower systems with input and distributed delays is assumed. To make controller design more practical, it is considered that the controller is not implemented as it is, and a disturbance term is incorporated into the controller part. A multi-agent system’s topology ahead to a weighted graph which may be directed or undirected is used. The article examines a scenario of leader–follower consensus through the application of algebraic graph theory and the fractional-order Razumikhin method. Numerical simulations are also provided to show the effectiveness of the proposed design for the leader–follower consensus.

Reset Event-Triggered Adaptive Fuzzy Consensus for Nonlinear Fractional-Order Multiagent Systems With Actuator Faults.

This article studies the problem of event-triggered adaptive fault-tolerant fuzzy output feedback consensus tracking control for nonlinear fractional-order multiagent systems with actuator failures under a directed graph. Considering the fact that the actual system works near the equilibrium point most of the time, a novel dynamic event-triggering strategy with the reset mechanism is proposed, where the dynamic threshold can be actively adjusted according to the preset conditions, so that the resource utilization can be further reduced. Based on an improved event-based consensus error, the state estimator about the derivative of reference trajectory and the adaptive law about the information of graph are constructed, which makes distributed consensus tracking control achieved without obtaining global information. Then, by introducing two adaptive compensating terms to deal with actuator failures and event-triggered measurement errors, it is shown in the sense of fractional-order stability criterion that tracking errors can converge to a compact set even if the fault parameters and modes are completely unknown. Finally, the correctness of the presented method is verified by a simulation example.

Preset-Time Consensus of Heterogeneous Fractional-Order Nonlinear Multi-Agent Systems

The preset-time consensus problem of a class of heterogeneous fractional-order nonlinear multi-agent systems was studied. A type of time-varying function-based preset-time fractional integral controllers were designed, to convert the fractional-order nonlinear multi-agent system into a 1st-order nonlinear multi-agent system. Then, by means of the integer-order Lyapunov function method combined with the preset-time control technology, the accurate bipartite consensus control of multi-agent systems with the connected undirected graph and the directed graph containing spanning trees was realized, respectively. The preset time can be preset with the time-varying function, independent of system initial values and parameters. An example verifies the effectiveness of the theoretical results.

Event-Triggered Saturated Adaptive Iterative Learning Control of Nonlinear Fractional-Order Multi-Agent Systems

Event-Triggered Saturated Adaptive Iterative Learning Control of Nonlinear Fractional-Order Multi-Agent Systems

Command-filtered adaptive containment control of fractional-order multi-agent systems via event-triggered mechanism

In this paper, the containment control problem of a class of fractional-order nonlinear multi-agent systems is studied, in which the multi-agent system contains unmeasured states and system nonlinearity. An adaptive neural network backstepping controller combined with event-triggered mechanism is proposed to ensure all followers can converge to the convex hull spanned by the leaders. The command filter is introduced into the proposed fractional-order control system to obtain fractional derivatives for virtual control functions continuously and avoid “explosion of complexity.” From the Lyapunov stability theory, all the signals can remain semi-global uniformly ultimately bounded in the closed-loop system. Numerical example and simulation results confirm the feasibility of the proposed control method.