Nonlinear Fractional-order Multi-agent Systems Research Articles

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.

Adaptive output consensus of nonlinear fractional-order multi-agent systems: a fractional-order backstepping approach

This paper presents the distributed control design for a class of fractional-order strict-feedback nonlinear multi-agent systems in the presence of unknown dynamics by employing backstepping strategy. Considering that the information of followers’ states are not fully measurable for feedback design, the fractional-order infinite-dimension neural-network state observer is introduced to estimate the unavailable states. The infinite-dimension neuroadaptive laws are also proposed to eliminate the undesirable effects of the unknown nonlinear functions. Besides, based on the Lyapunov fractional-order stability approach and graph theory, unlike the existing results, a distributed neural adaptive observer-based control architecture is designed to ensure that all the closed-loop network signals are ultimately bounded. Finally, a simulation example is given to demonstrate the validity of the proposed control method.

Quantized-observer based consensus for fractional order multi-agent systems under distributed event-triggered mechanism

This paper investigates the consensus problem of general nonlinear fractional order multi-agent systems in a directed network under event-triggered mechanism. First, observers are designed for every agent based on the outputs of them. Second, taking the constrains of communication bandwidth and storage space into consideration, the uniform quantizers are used for each channel. Then, the consensus criteria related with the general algebraic connectivity of communication topology under event-triggered mechanism are derived, furthermore, the Zeno behavior is excluded. Finally, an example is given to shown the effectiveness of the proposed methods.

Event-Based Distributed Adaptive Fuzzy Consensus for Nonlinear Fractional-Order Multiagent Systems

This article studies the problem of distributed event-triggered adaptive fuzzy consensus tracking control for a class of nonlinear fractional-order multiagent systems (FOMASs). Two new event triggering mechanisms are designed for communication and control, respectively, where triggering conditions do not depend on the global information and a positive lower bound of transmission interval can be ensured. Meanwhile, a modified event-based consensus protocol combining a continuous function is presented, which overcomes the difficulty of control design caused by discontinuous information transmission. By introducing a compensating state estimator, it is shown that the bounded consensus of higher-order FOMASs can be still achieved under a directed graph even though the derivative of the leader signal is unknown to all agents. Stability analysis based on the fractional-order Lyapunov direct method and simulation examples verify the correctness of the presented method.

Switched Fractional Order Multiagent Systems Containment Control with Event-Triggered Mechanism and Input Quantization

This paper studies the containment control problem for a class of fractional order nonlinear multiagent systems in the presence of arbitrary switchings, unmeasured states, and quantized input signals by a hysteresis quantizer. Under the framework of the Lyapunov function theory, this paper proposes an event-triggered adaptive neural network dynamic surface quantized controller, in which dynamic surface control technology can avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously. Radial basis function neural networks (RBFNNs) are used to approximate the unknown nonlinear functions, and an observer is designed to obtain the unmeasured states. The proposed distributed protocol can ensure all the signals remain semi-global uniformly ultimately bounded in the closed-loop system, and all followers can converge to the convex hull spanned by the leaders’ trajectory. Utilizing the combination of an event-triggered scheme and quantized control technology, the controller is updated aperiodically only at the event-sampled instants such that transmitting and computational costs are greatly reduced. Simulations compare the event-triggered scheme without quantization control technology with the control method proposed in this paper, and the results show that the event-triggered scheme combined with the quantization mechanism reduces the number of control inputs by 7% to 20%.

Adaptive bipartite output consensus of nonlinear fractional-order multi-agent systems

A distributed control approach is proposed for a class of fractional-order multi-agent systems with unknown nonlinearities under signed bipartite digraphs. Unlike the existing results, the follower's dynamics are studied with strict-feedback fractional-order form as well as a general class of actuator faults with unknown magnitude, pattern and occurrence time is studied. To provide a simple and efficient control strategy, first a novel command fractional-order filter based on the backstepping design is proposed such that the difficulty of calculation of the fractional derivative order of the virtual control laws is removed, as well as improving the bipartite output consensus accuracy. Then, to cope with dynamic's uncertainties, the proposed method is integrated with adaptive neural approximator and minimal learning parameter scheme which reduces communication loads. Besides, a distributed fault compensation protocol based upon the proposed command fractional-order filter and relative output information of neighbours' agents is extended to ensure bipartite output consensus, without relying on any global information of the singed digraph as well as any explicit fault detection mechanism. Finally, it is guaranteed that all the error signals within the closed-loop network system are converged into adjustable compact sets around the origin. The simulation results verify the validity of the presented control approach.

Adaptive Event-Triggered Consensus of Fractional-Order Nonlinear Multi-Agent Systems

The leader-following consensus of fractional-order nonlinear multi-agent systems is studied in this paper. An adaptive event-triggered control protocol is proposed to achieve the leader-following consensus scheme. By applying Lyapunov stability theory of fractional-order systems and some effective inequality techniques, some sufficient conditions for ensuring the consensus are derived intensively, and the proposed control method can reduce the communication between the agents greatly. Moreover, the Zeno behavior of event-triggered algorithm for multi-agent systems is excluded. Finally, a simulation example is presented to validate the effectiveness of the proposed consensus protocol.

Consensus Conditions for a Class of Fractional-Order Nonlinear Multiagent Systems with Constant and Time-Varying Time Delays

The consensus problem for a class of fractional-order nonlinear multiagent systems with a distributed protocol containing input time delay is investigated in this paper. Consider both cases of constant time delay and time-varying delay, the delay-independent consensus conditions are obtained to achieve the consensus of the systems, respectively, by adopting the linear matrix inequality (LMI) methods and stability theory of fractional-order systems. As illustrated by the numerical examples, the proposed theoretical results work well and accurately.

Consensus of a class of nonlinear fractional-order multi-agent systems via dynamic output feedback controller

This paper addresses the consensus of a class of nonlinear fractional-order multi-agent systems (FOMASs) with positive real uncertainty. First, a fractional non-fragile dynamic output feedback controller is put forward via the output measurements of neighboring agents, then appropriate state transformation reduced the consensus problem to a stability one. A sufficient condition based on direct Lyapunov approach, for the robust asymptotic stability of the transformed system and subsequently for the consensus of the main system is presented. In addition, utilizing S-procedure and Schur complement, the systematic stabilization design algorithm is proposed for fractional-order system with and without nonlinear terms. The results are formulated as an optimization problem with linear matrix inequality constraints. Simulation results are given to verify the effectiveness of the theoretical results.

Leader-follower non-fragile consensus of delayed fractional-order nonlinear multi-agent systems

This paper addresses the leader-follower non-fragile consensus of nonlinear fractional-order (FO) multi-agent systems (FOMAS) with state time delay. The structured uncertainties occurring in both the plant and the controller are considered for the first time. Using the linear matrix inequality approach and the FO Razumikhin theorem, a delay- and order-dependent protocol is obtained to guarantee the leader-follower non-fragile consensus of the FOMAS with uncertain parameters. New sufficient conditions for the leader-follower non-fragile consensus of FO linear multi-agent systems are presented. The feasibility and effectiveness of the protocol proposed is verified with three numerical examples. Compared with the existing schemes, the approach reveals good robustness and can be extended to different kinds of consensus problems.

Type-2 fuzzy consensus control of nonlinear multi-agent systems: An LMI approach

This paper considers a class of nonlinear fractional-order multi-agent systems (FOMASs) with time-varying delay and unknown dynamics, and a new robust adaptive control technique is proposed for cooperative control. The unknown nonlinearities of the systems are online approximated by the introduced recurrent general type-2 fuzzy neural network (RGT2FNN). The unknown nonlinear functions are estimated, simultaneously with the control process. In other words, at each sample time the parameters of the proposed RGT2FNNs are updated and then the control signals are generated. In addition to the unknown dynamics, the orders of the fractional systems are also supposed to be unknown. The biogeography-based optimization algorithm (BBO) is extended to estimate the unknown parameters of RGT2FNN and fractional-orders. A LMI based compensator is introduced to guarantee the robustness of the proposed control system. The excellent performance and effectiveness of the suggested method is verified by several simulation examples and it is compared with the other methods. It is confirmed that the introduced cooperative controller results in a desirable performance in the presence of time-varying delay, unknown dynamics, and unknown fractional-orders.

Exponential bipartite consensus of fractional‐order non‐linear multi‐agent systems in switching directed signed networks

This study considers the exponential bipartite consensus problem of a class of non-linear fractional-order multi-agent systems (FOMASs) in a general coopetition network with signed directed graph, where the signed directed graph is composed of both positive and negative interaction links. Without the assumption of the signed directed graph among agents is fixed and strongly connected, the exponential bipartite consensus problem of non-linear FOMASs is solved by utilising some techniques and tools from signed graph theory, matrix transformation and linear matrix inequalities. For the FOMASs in a fixed signed directed topology containing a spanning tree, the authors design a continuous distributed control protocol which can ensure the bipartite consensus error converges to zero exponentially if the parameters of the protocol are suitably selected. For the FOMASs in directed signed networks with switching topologies only frequently but not always contain a spanning tree, a distributed intermittent control protocol is further designed, where the bipartite consensus error converges to zero exponentially. Numerical simulations are given to show the effectiveness of the designed method.

Cluster consensus of fractional-order non-linear multi-agent systems with switching topology and time-delays via impulsive control

In this paper, a cluster consensus problem for fractional-order nonlinear multi-agent systems with fixed and switching topologies and time delays is considered. The problem is solved in three cases: (i) fixed topology and time delays, (ii) switching topology, and (iii) switching topology and time delays. Cluster consensus is achieved for fractional-order multi-agent systems by using the impulsive control method. Cluster consensus algorithms are studied by using Mittag–Leffler stability and the fractional Lyapunov direct method and some sufficient conditions are obtained to achieve cluster consensus of fractional-order multi-agent systems with nonlinear dynamics under switching topologies and time delays. Finally, simulation results are presented to show the validity of the proposed control strategies.

Iterative Learning Control for Locally Lipschitz Nonlinear Fractional-order Multi-agent Systems

In this paper, we design P-type and PIβ-type iterative learning control update laws to deal with the consensus tacking problem for nonlinear fractional-order multi-agent systems with both fixed and iteration-varying communicating graphs. The leader-follower model is used in the communication graph of the multi-agent system. The nonlinear function in each agent is required to be locally Lipschitz condition only. Sufficient conditions are proposed to guarantee the asymptotical output consensus. Numerical simulations are conducted to verify the theoretical analysis.

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.