Class Of Fractional-order Multi-agent Systems Research Articles

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.

Robust Consensus in a Class of Fractional-Order Multi-Agent Systems with Interval Uncertainties Using the Existence Condition of Hermitian Matrices

This study outlines the necessary and sufficient criteria for swarm stability asymptotically, meaning consensus in a class of fractional-order multi-agent systems (FOMAS) with interval uncertainties for both fractional orders 0 < α < 1 and 1 < α < 2. The constraints are determined by the graph topology, agent dynamics, and neighbor interactions. It is demonstrated that the fractional-order interval multi-agent system achieves consensus if and only if there are some Hermitian matrices that satisfy a particular kind of complex Lyapunov inequality for all of the system vertex matrices. This is done by using the existence condition of the Hermitian matrices in a Lyapunov inequality. To do this, at first it is shown under which conditions a multi-agent system with unstable agents can still achieve consensus. Then, using a lemma and a theory, the Lyapunov inequality regarding the negativity of the maximum eigenvalue of an augmented matrix of a FOMAS is used to find some Hermitian matrices by checking only a limited number of system vertex matrices. As a result, the necessary and sufficient conditions to reach consensus in a FOMAS in the presence of internal uncertainties are obtained according to the Lyapunov inequalities. Using the main theory of the current paper, instead of countless matrices, only a limited number of vertex matrices need to be used in Lyapunov inequalities to find some Hermitian matrices. As a confirmation of the notion, some instances from numerical simulation are also provided at the end of the paper.

Adaptive Containment Control for Fractional-Order Nonlinear Multi-Agent Systems With Time-Varying Parameters

This paper investigates adaptive containment control for a class of fractional-order multi-agent systems (FOMASs) with time-varying parameters and disturbances. By using the bounded estimation method, the difficulty generated by the time-varying parameters and disturbances is overcome. The command filter is introduced to solve the complexity problem inherent in adaptive backstepping control. Meanwhile, in order to eliminate the effect of filter errors, a novel distributed error compensating scheme is constructed, in which only the local information from the neighbor agents is utilized. Then, a distributed adaptive containment control scheme for FOMASs is developed based on backstepping to guarantee that the outputs of all the followers are steered to the convex hull spanned by the leaders. Based on the extension of Barbalat's lemma to fractional-order integrals, it can be proven that the containment errors and the compensating signals have asymptotic convergence. Finally, three simulation examples are given to show the feasibility and effectiveness of the proposed control method.

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.

Event-triggered adaptive neural network backstepping sliding mode control of fractional-order multi-agent systems with input delay

This article investigates the consensus problem for a class of fractional-order multi-agent systems with input delay. Each follower is modeled as a system with input delay and nonlinear dynamics. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, dynamic surface control technology is introduced into an adaptive neural network backstepping controller. A dynamic event-triggered scheme without Zeno behavior is considered, which can reduce the utilization of communication resources. The sliding mode control technology is introduced to enhance robustness. The Pade delay approximation method is extended to fractional-order systems, which converts the original systems into systems without input delay. The stability of systems is ensured by the constructed Lyapunov functions. Examples and simulation results show that the consensus tracking errors can quickly converge and all the followers can synchronize to the leader by the proposed method.

Adaptive Fuzzy Consensus Tracking Control for Uncertain Fractional-Order Multiagent Systems With Event-Triggered Input

This article focuses on the problem of adaptive fuzzy consensus tracking control with event-triggered input for a class of fractional-order multiagent systems, where systems are considered to be with unmeasurable states, mismatched uncertain external disturbances, and unknown nonlinearities. An event-triggered mechanism with a decreasing threshold function is proposed in this article, which mitigates communication burden and avoids large control impulse. To achieve better tracking performance in distributed control strategy, a compensating fractional-order adaptation law associated with consensus tracking error is introduced when agents cannot obtain the information of reference trajectory directly. Under the fractional-order stability theory, a novel distributed adaptive event-triggered controller with fuzzy observers is constructed, which ensures the boundedness of tracking errors. A simulation example demonstrates the correctness of the presented scheme.

A novel general type-2 fuzzy controller for fractional-order multi-agent systems under unknown time-varying topology

In this paper, a robust adaptive control scheme is proposed for the leader following control of a class of fractional-order multi-agent systems (FMAS). The asymptotic stability is shown by a linear matrix inequality (LMI) approach. The nonlinear dynamics of the agents are assumed to be unknown. Moreover, the communication topology among the agents is assumed to be unknown and time-varying. A deep general type-2 fuzzy system (DGT2FS) using restricted Boltzmann machine (RMB) and contrastive divergence (CD) learning algorithm is proposed to estimate uncertainties. The simulation studies presented indicate that the proposed control method results in good performance under time-varying topology, unknown dynamics and external disturbances. The effectiveness of the proposed DGT2FS is verified also on modeling problems with high dimensional real-world data sets.

Stability of fractional‐order switched non‐linear systems

This study addresses the stability issue of a class of fractional-order switched non-linear systems. A general stability condition is established based on which two new concepts named Mittag-Leffler increment and average Mittag-Leffler increment are proposed and two alternative stability conditions are obtained. These conditions fully reveal the trade-off between each subsystem's dynamics, and the value of the fractional order. The new results are further applied to a class of fractional-order multi-agent systems with switching cooperative control laws.