Fractional-order Multi-agent Systems Research Articles

Adaptive Neural Control for a Class of Random Fractional-Order Multi-Agent Systems with Markov Jump Parameters and Full State Constraints

Based on an adaptive neural control scheme, this paper investigates the consensus problem of random Markov jump multi-agent systems with full state constraints. Each agent is described by the fractional-order random nonlinear uncertain system driven by random differential equations, where the random noise is the second-order stationary stochastic process. First, in order to deal with the unknown functions with Markov jump parameters, a radial basis function neural network (RBFNN) structure is introduced to achieve approximation. Second, for the purpose of keeping the agents’ states from violating the constraint boundary, the tan-type barrier Lyapunov function is employed. By using the stochastic stability theory and adopting the backstepping technique, a novel adaptive neural control design method is presented. Furthermore, to cope with the differential explosion problem in the design course, the extended state observer (ESO) is developed instead of neural network (NN) approximation or command filtering techniques. Finally, the exponentially noise-to-state stability in the mean square is analyzed rigorously by the Lyapunov method, which guarantees the consensus of the considered multi-agent systems and all the agents’ outputs are bounded in probability. Two simulation examples are provided to verify the effectiveness of the suggested control strategy.

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.

Comments on “Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth”

Despite the proposed results on the non-existing of finite time stable equilibria for fractional order systems (Shen and Lam, 2014), the commented paper (Wang et al., 2020) has shown finite time convergence of fractional order control systems via a couple of theorems. This comment demonstrates that the proofs of the given theorems in Wang et al. (2020) are incorrect.

Adaptive Control for group consensus of fuzzy singular fractional order multi-agent systems under non-fragile controller

Adaptive Control for group consensus of fuzzy singular fractional order multi-agent systems under non-fragile controller

Boundary Control Strategies for Consensus of Fractional-Order Multi-Agent Systems Based on Coupling PDE-ODEs

Boundary Control Strategies for Consensus of Fractional-Order Multi-Agent Systems Based on Coupling PDE-ODEs

Fuzzy control of singular fractional order multi-agent systems with actuator saturation

In this paper, a T-S fuzzy model is established to describe nonlinear fuzzy singular fractional order multi-agent systems (SFOMASs) exhibiting actuator saturation when the order is between 0 and 2. We focus on the case where the system state is difficult to measure or cannot be directly measured, so it needs to be estimated based on other measurable signals. To this end, a fuzzy observer is designed, which can process fuzzy or imprecise input and output signals through fuzzy processing. Then the observer-based leader-following consensus problem of fuzzy SFOMASs with actuator saturation is addressed. To address input saturation, we use some mathematical tools to represent the saturated linear feedback on the convex hull, which is then transformed into seeking the optimal solution of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed approach is verified through the adoption of a numerical example.

Quantization-Based Event-Triggered H∞ Consensus for Discrete-Time Markov Jump Fractional-Order Multiagent Systems with DoS Attacks

This paper investigates the H∞ consensus problem of discrete-time Markov jump fractional-order multiagent systems (DTMJFOMASs) under denial-of-service (DoS) attacks. By applying the short-memory principle, we can obtain discrete-time Markov jump multiagent systems with partially unknown probabilities. A novel quantized event-triggering mechanism (QETM), based on a mode-dependent logarithmic quantizer, is proposed to enhance transmission efficiency among multiagents. A distributed controller with quantized output is developed. Sufficient conditions are provided to ensure the system achieves H∞ consensus through Lyapunov stability theory. Finally, two examples are given to verify the effectiveness of the proposed model.

Composite adaptive fuzzy bipartite consensus of fractional-order multiagent systems with a switched event-triggered mechanism

This paper focuses on online recorded-data-based composite adaptive fuzzy bipartite consensus control for uncertain fractional-order multiagent systems with interconnected terms and external disturbances by employing a switched-threshold-based event-triggered mechanism (ETM) under the backstepping structure. Fuzzy logic system is used as an universal function approximation to deal with function uncertainties that are not prone to model in the system. A new composite learning adaptive parameter design scheme that synthesizes both prediction error and tracking error is developed to enhance the tracking performance, where the prediction error is raised from the utilization of online recorded data and instantaneous data. A unique switched-threshold-based ETM is introduced, in which the information transmission between the sensor and the controller is imposed on one of the individuals. One merit of this work consists in that it can automatically and rapidly switch and adjust between the fixed threshold and relative threshold ETM according to the amplitude of input signals to balance the network resources and impede the occurrence of pulse phenomenon. In addition, it is theoretically proven that the proposed scheme can ensure that all internal signals of the closed-loop system are bounded and achieve local bipartite consistent errors through the fractional Lyapunov stability criterion. Finally, a numerical example is provided to confirm the feasibility of the proposed approach.

Bipartite consensus tracking of second-order fractional-order multi-agent systems on directed signed graphs

This paper studies the bipartite consensus tracking problems of fractional-order multi-agent systems on directed signed graphs. Each agent is modelled as a second-order fractional-order dynamics with the order belonging to ( 0 , 1 ] , and the cooperative and competitive interactions between the agents coexist in the systems. Two distributed bipartite consensus tracking protocols are proposed for the systems based on continuous information and sampled information, respectively. Under the assumption that the directed signed graph is structurally balanced, it is shown that the second-order fractional-order multi-agent systems can achieve the bipartite consensus tracking if the feedback coefficients are chosen appropriately. Finally, several simulations are provided to verify the effectiveness of the theoretical results.

Adaptive fuzzy event-triggered cooperative control for fractional-order delayed multi-agent systems with unknown control direction

In this paper, the cooperative control of fractional-order multi-agent systems with time delay and unknown control direction is studied by combining frequency distributed model and event-triggered mechanism. The Nussbaum function is employed to address the unmeasured control direction. Then, through the event-triggered mechanism, a corresponding controller is designed, which can guarantee that all signals are bounded while saving resources. The proposed theme is convenient for analyzing the stability of fractional-order systems based on a transformation of frequency distributed model. In particular, in order to enhance the universality of the proposed scheme in the fractional-order system stability analysis, a generalized fractional-order generalized lemma with respect to the Nussbaum function is given. Finally, the availability of the proposed method is confirmed by a simulation example.

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.

Admissible H$_\infty$ Control of Fuzzy Singular Fractional Order Multi-Agent Systems With External Disturbances

This brief consider the problem about admissible consensus of fuzzy singular fractional order multi agent systems (FSFOMAS). By designing a new distributed fuzzy dynamic output control strategy, the coupled system achieves admissible while satisfying <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> performance. Then, when the fuzzy models reduce to ordinary fractional order multi agent systems (FOMAS), a new sufficient condition for determining system consensus is given. The above results all depend only on the eigenvalues of the Laplace matrix and the state matrix of the system and consist of linear matrix inequalities (LMIs). Finally, a numerical example and a practical circuit example can demonstrate the feasibility and validity of the theorems. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Due to the unique memorability of fractional orders, their application to fuzzy multi-agent systems will bring system performance metrics closer to reality. This paper investigates the stabilization of singular fuzzy fractional-order multi-agent systems with the perturbation case, the pulse case. We know that in practical applications a single variable does not accurately describe the phenomenon. Therefore we have introduced the concepts of multi-agent, fuzzy, singular and fractional orders in order to describe the system model more accurately. The main objective is to bring the system into equilibrium in the closest possible approximation to reality. The performance metrics of the system are optimised to bring the system to an optimal state. Finally, two examples are used to illustrate the validity of our theorems.

Sliding Mode Control Based on Reinforcement Learning for T-S Fuzzy Fractional-Order Multiagent System With Time-Varying Delays.

This article researches the sliding mode control (SMC) for fuzzy fractional-order multiagent system (FOMAS) subject to time-varying delays over directed networks based on reinforcement learning (RL), α ∈ (0,1). First, since there is information communication between an agent and another agent, a new distributed control policy ξi(t) is introduced so that the sharing of signals is implemented through RL, whose propose is to minimize the error variables with learning. Then, different from the existed papers studying normal fuzzy MASs, a new stability basis of fuzzy FOMASs with time-varying delay terms is presented to guarantee that the states of each agent eventually converge to the smallest possible domain of 0 using Lyapunov-Krasovskii functionals, free weight matrix, and linear matrix inequality (LMI). Furthermore, in order to provide appropriate parameters for SMC, the RL algorithm is combined with SMC strategy, and the constraints on the initial conditions of the control input ui(t) are eliminated, so that the sliding motion satisfy the reachable condition within a finite time. Finally, to illustrate that the proposed protocol is valid, the results of the simulation and numerical examples are presented.

Necessary and Sufficient Conditions on Consensus of General Fractional-Order Multi-Agent Systems Over Directed Networks

Necessary and Sufficient Conditions on Consensus of General Fractional-Order Multi-Agent Systems Over Directed Networks

Passivity-Based Formation Control for Fractional-Order Multiagent Systems With and Without Communication Delay

Passivity-Based Formation Control for Fractional-Order Multiagent Systems With and Without Communication Delay

Cyber secure consensus of fractional order multi-agent systems with distributed delays: Defense strategy against denial-of-service attacks

Leader-follower cyber secure consensus problem in cybersecurity is crucial as it directly addresses the need for secure and stable communication in a networked system, which is paramount in safeguarding against cyber threats like denial-of-service attacks. In this article, by utilizing control strategy with distributed delays in denial-of-service attack's presence for discrete-time multi-agent system of fractional-order, the leader-following cyber secure consensus problem is examined. Nonlinear functions have been assumed in the leader and follower equation of the system to study variations due to this function in the system. As multi-agent system is networked environment, in response to numerous threats, their security control becomes critically desirable, for example, denial of service. The consensus performance may be destabilized by resulting topologies which are caused by Denial-of-Service attacks. The connectivity between agents is destroyed, especially under connectivity-broken attacks. In order to overcome these problems, the strategy of novel defense which consists of consensus (with distributed delays) control is introduced. By using Caputo fractional difference operator sufficient criteria which includes the condition in terms LMI is derived and by using Lyapunov function approach, average dwell time and algebraic graph theory for security of addressed system's cyber secure consensus this is done for determining the obtained system of error's stability. Finally, by showing some numerical examples on the introduced systems, the effectiveness of the obtained results is determined.

Distributed adaptive neural network consensus control of fractional-order multi-agent systems with unknown control directions

In this work, adaptive consensus control of leader-following fractional-order multi-agent systems whose each subsystem includes functional uncertainties, external disturbances, and unknown control directions is investigated utilizing neural networks and the Nussbaum function. The controller is synthesized within the framework of the backstepping algorithm, where the “explosion of complexity” problem is mitigated through the use of a command filter, and the adverse impact of filtered errors is decreased using compensation signals. The function uncertainties of each follower are approximated by neural networks, and a disturbance update law is developed to identify the boundary of the disturbance. Importantly, a general conclusion is provided to affirm the applicability of the Nussbaum function in addressing controller design for fractional-order systems with unknown control directions. Finally, the validity of the proposed approach is verified via two numerical examples.

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.

A Continuous Algorithm for Finite-Time Consensus of Disturbed Fractional-Order Multiagent Systems Over Digraphs

This work studies the finite-time distributed consensus problem of fractional-order multiagent systems (FOMASs) with disturbances over directed graphs (digraphs). By utilizing the finite-time Lyapunov stability theorem and distributed estimator technique, a continuous estimator-based finite-time fully distributed algorithm with a fractional power is proposed. Under the designed algorithm, all agents’ states globally converge to a common value within a finite time in a fully distributed manner. The upper bound of the finite time is given explicitly. Finally, a numerical example is provided to validate the results.

Positive Consensus of Fractional-Order Multiagent Systems Over Directed Graphs.

This article investigates the positive consensus problem of a special kind of interconnected positive systems over directed graphs. They are composed of multiple fractional-order continuous-time positive linear systems. Unlike most existing works in the literature, we study this problem for the first time, in which the communication topology of agents is described by a directed graph containing a spanning tree. This is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains, which renders the positivity analysis fairly challenging. Based on the existing results in spectral graph theory, fractional-order systems (FOSs) theory, and positive systems theory, we derive several necessary and/or sufficient conditions on the positive consensus of fractional-order multiagent systems (PCFMAS). It is shown that the protocol, which is designed for a specific graph, can solve the positive consensus problem of agents over an additional set of directed graphs. Finally, a comprehensive comparison study of different approaches is carried out, which shows that the proposed approaches have advantages over the existing ones.