Adaptive output feedback control for fractional-order multi-agent systems

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.

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.

Time-varying Lyapunov functions for nonautonomous nabla fractional order systems

The classical Leibniz rule for the integer difference cannot be easily applicable for the fractional counterpart. It further leads to a great difficulty in the calculation of the Lyapunov functions with product form. To overcome such a challenge, several fractional difference inequalities are developed for Lyapunov functions which are the product of a time sequence and a function regarding to system state. To further enrich the design of time-varying Lyapunov function, the differentiable convex condition is introduced and then three elegant inequalities are derived. Those inequalities hold for the Caputo/Riemann-Liouville/Grünwald-Letnikov definitions which bring the possibility of the Lyapunov stability analysis for nonautonomous nabla fractional order systems. Finally, illustrative examples serve to illustrate the applicability and practicability of the theoretical results.

Adaptive Neural Control for a Class of Nonlinear Multiagent Systems

This article studies the adaptive neural controller design for a class of uncertain multiagent systems described by ordinary differential equations (ODEs) and beams. Three kinds of agent models are considered in this study, i.e., beams, nonlinear ODEs, and coupled ODE and beams. Both beams and ODEs contain completely unknown nonlinearities. Moreover, the control signals are assumed to suffer from a class of generalized backlash nonlinearities. First, neural networks (NNs) are adopted to approximate the completely unknown nonlinearities. New barrier Lyapunov functions are constructed to guarantee the compact set conditions of the NNs. Second, new adaptive neural proportional integral (PI)-type controllers are proposed for the networked ODEs and beams. The parameters of the PI controllers are adaptively tuned by NNs, which can make the system output remain in a prescribed time-varying constraint. Two illustrative examples are presented to demonstrate the advantages of the obtained results.