Nonlinear Fractional-order Multi-agent Systems Research Articles

Robust adaptive fault-tolerant consensus control for uncertain nonlinear fractional-order multi-agent systems with directed topologies

This paper investigates the problem of fault-tolerant consensus control (FTCC) for heterogeneous nonlinear fractional-order multi-agent systems with general directed topology, where the systems are subject to heterogeneous unknown and time-varying inertias, coupling nonlinearities, external disturbances, and actuator failures. A continuous robust adaptive FTCC protocol is designed by using a boundary layer technique to compensate for the time-varying unknown inertias, uncertain coupling dynamics/disturbances, and unpredictable actuation failures simultaneously. By artfully choosing a Lyapunov function and by generalizing an important fractional-order inequality, it is shown that the consensus configuration error converges to an adjustable small residual set in finite time. The proposed robust adaptive FTCC protocol is completely distributed in the sense that there is no need for any global information, and also is less demanding without requiring any detailed dynamic/parameters information or complicated/costly fault detection and diagnosis. The effectiveness of the proposed FTCC scheme is illustrated by numerical simulation.

Finite-Time Consensus Tracking for Incommensurate Fractional-Order Nonlinear Multiagent Systems With Directed Switching Topologies.

This article investigates the problem of finite-time consensus tracking for incommensurate fractional-order nonlinear multiagent systems (MASs) with general directed switching topology. For the leader with bounded but arbitrary dynamics, a neighborhood-based saturated observer is first designed to guarantee that the observer's state converges to the leader's state in finite time. By utilizing a fuzzy-logic system to approximate the heterogeneous and unmodeled nonlinear dynamics, an observer-based adaptive parameter control protocol is designed to solve the problem of finite-time consensus tracking of incommensurate fractional-order nonlinear MASs on directed switching topology with a restricted dwell time. Then, the derived result is further extended to the case of directed switching topology without a restricted dwell time by designing an observer-based adaptive gain control protocol. By artfully choosing a piecewise Lyapunov function, it is shown that the consensus tracking error converges to a small adjustable residual set in finite time for both the cases with and without a restricted dwell time. It should be noted that the proposed adaptive gain consensus tracking protocol is completely distributed in the sense that there is no need for any global information. The effectiveness of the proposed consensus tracking scheme is illustrated by numerical simulations.

Bipartite consensus control for fractional-order nonlinear multi-agent systems: An output constraint approach

Bipartite consensus of multiple fractional-order nonlinear systems with output constraints is assessed under signed graph. The agents’ model is completely unknown with high-order heterogeneous strict-feedback dynamics and external disturbances, which cover single- and double-integrator integer-order systems as special forms. To ensure the bipartite consensus task, a novel fully distributed controller is developed based on backstepping technique and neuro-adaptive update mechanism. A barrier Lyapunov function is introduced to limit the followers’ outputs within the preset bounds. Algebraic graph theory and Lyapunov fractional-order stability theorem are employed to deal with the analysis difficulties caused by the network of fractional-order dynamics. Sufficient conditions on bipartite consensus is established, and it is also shown that all the closed-loop error signals are uniformly ultimately bounded. The simulation results are carried out to demonstrate the effectiveness of the proposed approach.

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

In this paper robust cluster consensus is investigated for general fractional-order multi agent systems with nonlinear dynamics with dynamic uncertainty and external disturbances via adaptive sliding mode controller. First, robust cluster consensus for general fractional-order nonlinear multi agent systems is investigated with dynamic uncertainty and external disturbances in which multi agent systems are weakly heterogeneous because they have identical nominal dynamics with different norm-bounded parameter uncertainties. Then, robust cluster consensus for the fractional-order nonlinear multi agent systems with general form dynamics is investigated by using adaptive sliding mode controller. Robust cluster consensus for general fractional-order nonlinear multi agent systems is achieved asymptotically without disturbance. It is shown that the errors between agents can converge to a small region in the presence of disturbances based on the linear matrix inequality (LMI) and Mittag-Leffler stability theory. Finally, simulation examples are presented for general form multi agent systems, i.e. a single-link flexible joint manipulator which demonstrates the efficiency of the proposed adaptive controller.

Distributed adaptive cooperative tracking of uncertain nonlinear fractional-order multi-agent systems

In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws, we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.

Output feedback consensus control for fractional-order nonlinear multi-agent systems with directed topologies

This paper is devoted to the output feedback consensus control problem for a class of nonlinear fractional-order multi-agent systems (MASs) with general directed topologies. It is worth noting that the considered fractional-order MASs including the second-order MASs as special cases. By introducing a distributed filter for each agent, a control algorithm uses only relative position measurements is proposed to guarantee the global leaderless consensus can be achieved. Also the derived results are further extended to consensus tracking problem with a leader whose input is unknown and bounded. Finally, two simulation examples are provided to verify the performance of the control design.

Parameters estimation using mABC algorithm applied to distributed tracking control of unknown nonlinear fractional-order multi-agent systems

This paper addresses the parameters estimation and distributed tracking control of unknown nonlinear fractional-order multi-agent systems (FOMASs) with external disturbances from the viewpoint of optimization. Firstly, a modified artificial bee colony (mABC) algorithm is put forward to enhance the exploration and exploitation abilities of the original ABC algorithm. Secondly, a parameters estimation approach based on the above mABC algorithm is proposed to estimate the unknown fractional orders and system parameters, where the parameters estimation is converted into a multi-dimensional functional optimization problem. Thirdly, the obtained parameters estimation values are further utilized to construct a distributed control algorithm for solving the tracking control problem. Finally, the experimental results illustrate that the proposed approaches can accurately estimate and robustly control such unknown nonlinear FOMASs.

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

ABSTRACTThis paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.

Iterative learning control for fractional-order multi-agent systems

In this paper, we apply iterative learning control to both linear and nonlinear fractional-order multi-agent systems to solve consensus tacking problem. Both fixed and iteration-varying communicating graphs are addressed in this paper. For linear systems, a PDα-type update law with initial state learning mechanism is introduced by virtue of the memory property of fractional-order derivative. For nonlinear systems, a Dα-type update law with forgetting factor and initial state learning is designed. Sufficient conditions for both linear and nonlinear systems are established to guarantee all agents achieving the asymptotic output consensus. Simulation examples are provided to verify the proposed schemes.

On leaderless consensus of fractional-order nonlinear multi-agent systems via event-triggered control

The consensus problem of fractional-order multi-agent systems is investigated by eventtriggered control in this paper. Based on the graph theory and the Lyapunov functional approach, the conditions for guaranteeing the consensus are derived. Then, according to some basic theories of fractional-order differential equation and some properties of Mittag–Leffler function, the Zeno behavior could be excluded. Finally, a simulation example is given to check the effectiveness of the theoretical result.

Generalised exponential consensus of the fractional-order nonlinear multi-agent systems via event-triggered control

ABSTRACTIn this paper, the leader-following consensus problem of the fractional-order nonlinear multi-agent systems via event-triggered control is considered. An effective event-triggered controller is designed and then generalised exponential consensus of the controlled multi-agent systems is studied in the sense of Mittag-Leffler stability of fractional-order systems. The event-triggering function design is dependent on the parameter of the system structure and the minimum inter-event interval can be flexibly adjusted with different fractional-order α. With the event-triggered control scheme, the consensus condition is obtained and the convergence rate of the system is estimated. Numerical simulation indicates the effectiveness of the theoretical results.

Leader-following consensus of nonlinear fractional-order multi-agent systems over directed networks

This paper investigates the leader-following consensus of nonlinear fractional-order multi-agent systems where the linear part is depicted by the general linear dynamics on directed networks with the order p belonging to $$p \in (0,1]$$ and $$p \in (1,2)$$ , respectively. By utilizing the Mittag-Leffler function, the Laplace transform, and the inequality technique, some algebraic-type consensus tracking criteria relying on the coupling strength, the coupling gain matrix and the network structure are obtained. It is interesting to find that the leader-following consensus can be attained by only using the position information among the agent and its neighbors for $$p \in (0,1]$$ and $$p \in (1,2)$$ . The theoretical results are illustrated by several numerical simulation examples.

Observer-based output consensus of leader-following fractional-order heterogeneous nonlinear multi-agent systems

ABSTRACT In this paper, the observer-based output consensus of leader-following fractional-order heterogeneous nonlinear multi-agent systems with potentially different state dimensions and different dynamics are investigated. Considering the agents' states may be not available in practice, the distributed state observer is designed for each agent. Then corresponding distributed control protocols based a proposed virtual exosystem are proposed to convert the output consensus problem into the stabilisation problem. By employing matrix theory, algebraic graph theory and the stability theory of fractional system, the state consensus of the virtual exosystem and the output consensus of heterogenous fractional nonlinear MAS is achieved. Moreover, the sufficient conditions are also obtained. Simulation examples are presented to verify the effectiveness of the main results.

Research on complex dynamic behavior control of supply chain finance nonlinear system based on fractional differential operators.

Supply chain management is a kind of behavior for enterprises to create core competitiveness in a complex competitive environment, especially for supply chain finance, which is a typical complex system with dynamic, open, and emergent non-linear characteristics in structure, environment, and behavior. For fractional order non-linear multi-agent systems, the event trigger control protocol is studied, and an event based on the threshold function of decreasing time is designed. According to the properties of the fractional linear differential equations, the consistency criterion is obtained, and the Zeno phenomenon is effectively avoided. Chaos exists in fractional-order electronic oscillators with order lower than 4th order, and the lowest order of chaos in the fractional-order system is only 2.3 orders. The research shows that under the appropriate parameter adjustment, chaos exists in the fractional-order vanderPol oscillator with order less than 4th order, and the lowest order of chaos in the fractional-order system is 2.7.

Neural Networks Based Adaptive Consensus for a Class of Fractional-Order Uncertain Nonlinear Multiagent Systems

Due to the excellent approximation ability, the neural networks based control method is used to achieve adaptive consensus of the fractional-order uncertain nonlinear multiagent systems with external disturbance. The unknown nonlinear term and the external disturbance term in the systems are compensated by using the radial basis function neural networks method, a corresponding fractional-order adaption law is designed to approach the ideal neural network weight matrix of the unknown nonlinear terms, and a control law is designed eventually. According to the designed Lyapunov candidate function and the fractional theory, the systems stability is proved, and the adaptive consensus can be guaranteed by using the designed control law. Finally, two simulations are shown to illustrate the validity of the obtained results.

Consensus analysis of fractional-order nonlinear multi-agent systems with distributed and input delays

Fractional-order nonlinear multi-agent systems with distributed and input delays are considered, in which the topology of multi-agent system corresponds to a directed weighted graph or an undirected weighted graph. Several algebraic conditions on leader-following consensus are presented by using fractional-order Razumikhin approach and algebraic graph theory. Finally, we present two numerical examples to illustrate those conditions proposed are feasible and convenient to evaluate consensus.

Adaptive robust tracking control for uncertain nonlinear fractional-order multi-agent systems with directed topologies

This paper addresses the robust consensus tracking problem for a class of uncertain nonlinear fractional-order multi-agent systems (FOMASs) under general directed topologies. More specifically, FOMASs in the presence of heterogeneous unknown nonlinearities and external disturbances are considered in this paper, which include the second-order MASs as its special cases. First, we design two distributed saturated observers to overcome the deficiency of the traditional tracking control strategies. Second, when there exists a dynamics leader with unknown and bounded state trajectory, a discontinuous observer-based distributed controller with σ-modification adaptive schemes is presented to guarantee the tracking error converges to zero asymptotically. Next, a continuous observer-based distributed controller is further proposed, under which the consensus tracking error is uniformly ultimately bounded (UUB) and can be reduced as small as desired. A neural network (NN), whose weights are tuned online, is used in the designed controllers to approximate the unknown nonlinearities. Motivated by the σ-modification adaptive method, all the proposed adaptation algorithms require only local information and allow for robust even in the presence of heterogeneous unknown disturbances and fractional-order dynamics. Finally, the simulation results validate the efficacy of our proposed method.

Leaderless consensus for the fractional-order nonlinear multi-agent systems under directed interaction topology

ABSTRACTLeaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems’ convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems’ stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results.

Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control

ABSTRACTThe coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, two novel sufficient conditions for achieving the cooperative control of a class of fractional-order nonlinear multi-agent systems are derived. Finally, two numerical simulations are verified to illustrate the effectiveness and feasibility of the proposed method.

Containment control of fractional-order nonlinear multi-agent systems under fixed topologies

Containment control of fractional-order nonlinear multi-agent systems under fixed topologies