Fractional-order Nonlinear Systems Research Articles

Event-Triggered Adaptive Finite-Time Containment Control for Fractional-Order Nonlinear Multiagent Systems.

This article investigates the finite-time containment control problem for fractional-order nonlinear multiagent systems (FOMASs) with event-triggered inputs. First, a new Lyapunov stability lemma is developed, which provides a basic approach for the completely unknown nonlinear fractional-order system to realize finite-time convergence. Considering the containment control for FOMASs, the restricted assumption that the derivatives of leaders' trajectories are known to the followers is removed, and only the boundedness of derivatives is required in this article, whose upper bound need not be known. To reduce the burden of communication, an event-triggered condition consisting of the control input and a decreasing function related to the containment errors is devised, which can provide more design freedom to balance the system performance and communication resources. According to the proposed fractional-order finite-time convergence lemma, a distributed adaptive containment control scheme is developed, such that each follower can be steered to the convex hull spanned by the leaders in finite time. Simulation examples further demonstrate the effectiveness of our proposed method.

Adaptive Fuzzy Echo State Network Control of Fractional-Order Large-Scale Nonlinear Systems With Time-Varying Deferred Constraints

Adaptive Fuzzy Echo State Network Control of Fractional-Order Large-Scale Nonlinear Systems With Time-Varying Deferred Constraints

Evaluation of various controllers in fractional order non-linear systems with actuator fault

Evaluation of various controllers in fractional order non-linear systems with actuator fault

Observer-Based Adaptive Fuzzy Quantized Control for Fractional-Order Nonlinear Time-Delay Systems with Unknown Control Gains

This paper investigates the observer-based adaptive fuzzy quantized control problem for a class of fractional-order nonlinear time-delay systems with unknown control gains based on a modified fractional-order dynamic surface control (FODSC) technique and an indirect Lyapunov method. First, a fractional-order, high-gain state observer is constructed to estimate unavailable state information. Furthermore, the Nussbaum gain technique and a fractional-order filter are adopted to cope with the problem of unknown control gains and to reduce the computational complexity of the conventional recursive procedure, respectively. Moreover, through integration with the compensation mechanism and estimation model, the adaptive fuzzy quantized controllers and adaptive laws are designed to ensure that all the signals of the closed-loop system are bounded. In the end, the proposed controller is applied to a numerical example and a single-machine-infinite bus (SMIB) power system; the simulation results show the validity, superiority, and application potential of the developed control strategy.

Adaptive iterative learning control for a class of parameterized fractional-order systems subjected to backlash-like hysteresis

In this article, a fractional-order adaptive iterative learning control scheme is proposed for a class of parameterized fractional-order systems with unknown control gain and backlash-like hysteresis nonlinearity under disturbance. Based on the sufficient condition for the stability of linear fractional-order systems, a sliding mode surface of tracking errors is constructed to facilitate the controller design and stability analysis. A new boundary layer function is designed by using Mittag-Leffler function to relax the restriction of the identical initial condition of iterative learning control design. The fractional-order differential-type adaptive laws and difference-type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. To deal with the influence of backlash-like hysteresis nonlinearity reminder term and unknown bounded external disturbance, a robust control term is designed by employing the hyperbolic tangent function with a convergent series sequence which can guarantee the learning convergence along iteration axis. By constructing Lyapunov-like composite energy function, the stability analysis is presented to prove the convergence of the system output to a small neighborhood of the desired trajectory and the boundedness of all the closed-loop signals. Finally, a simulation example of second-order nonlinear fractional-order system is presented, which demonstrates the effectiveness of the proposed fractional-order adaptive iterative learning control scheme.

Fault-Tolerant Control and Diagnosis for Trajectory Tracking in a Class of Nonlinear Fractional Order Systems

This article deals with the Fault Tolerant Control (FTC) and Fault Diagnosis (FD) for trajectory tracking in a class of nonlinear Fractional Order (FO) systems. The proposed control scheme consists of a set of FO differential equations describing a FO dynamic controller, the estimation of the unknown pseudo-states of the system and faults, the estimators that are designed have different structures, therefore, this scheme can be considered as a hybrid type. In addition, the existence and uniqueness of the solution for the controller is proved using the Banach fixed point theorem. On the other hand, it is shown that the dynamic controller, estimators and the tracking error are globally Mittag-Leffler bounded ensuring the desired trajectory tracking, in consequence a separation principle for nonlinear FO systems is presented. This FO control scheme is illustrated by considering a FO chaotic system as an example.

Leaderless Consensus Control of Fractional-Order Nonlinear Multi-Agent Systems With Measurement Sensitivity and Actuator Attacks

Leaderless Consensus Control of Fractional-Order Nonlinear Multi-Agent Systems With Measurement Sensitivity and Actuator Attacks

Global Stability of Fractional Nonlinear Differential Systems With State-Dependent Delayed Impulses.

The fractional-order (FO) nonlinear differential system with state-dependent (SD) delayed impulses (DI) is considered in this brief. The considered impulses are related to the delayed state of the system and the delays are SD. A novel lemma for the monotonicity of the solution of Caputo's FO derivative equation is given. By means of linear matrix inequality (LMI) and several comparative arguments, criteria of uniform stability, uniform asymptotical stability, and Mittag-Leffler stability are obtained. Compared with other works on integer-order (IO) impulsive delayed systems with SD delays or fixed delays, how to impose constraints on parameters and impulses is explored, without imposing the boundedness on the state delays. Two examples are implemented to examine the practicality and sharpness of our theoretical analysis.

Consensus Control of Nonlinear Fractional-order Multi-agent Systems with Input Saturation: A T-S Fuzzy Method

Consensus Control of Nonlinear Fractional-order Multi-agent Systems with Input Saturation: A T-S Fuzzy Method

Approximate Optimized Backstepping Control of Uncertain Fractional-Order Nonlinear Systems Based on Reinforcement Learning

Approximate Optimized Backstepping Control of Uncertain Fractional-Order Nonlinear Systems Based on Reinforcement Learning

Fuzzy Weight-Based Reinforcement Learning for Event-Triggered Optimal Backstepping Control of Fractional-Order Nonlinear Systems

Fuzzy Weight-Based Reinforcement Learning for Event-Triggered Optimal Backstepping Control of Fractional-Order Nonlinear Systems

Stabilization for a Class of Partially Observable Uncertain Fractional-Order Nonlinear Systems With Time-Varying Delays and Disturbance

Stabilization for a Class of Partially Observable Uncertain Fractional-Order Nonlinear Systems With Time-Varying Delays and Disturbance

NOVEL UNIFIED STABILITY CRITERION FOR FRACTIONAL-ORDER TIME DELAY SYSTEMS WITH STRONG RESISTANCE TO FRACTIONAL ORDERS

In this study, a novel unified stability criterion is first proposed for general fractional-order systems with time delay when the fractional order is from 0 to 1. Such a new unified criterion has the advantage of having an initiative link with the fractional orders. A further advantage is that the corresponding asymptotic stability theorem, derived from the proposed criterion used to analyze the asymptotic stability, is only slightly affected by the change of the fractional order. In addition, the unified stability criterion is applied to general multi-dimensional nonlinear fractional-order systems with time delays, the corresponding asymptotic stability criterion is applied by combining the vector Lyapunov function with the M-matrix method. Compared with the traditional stability criterion, the unified stability criterion is slightly influenced by the changing fractional order and large time delays. The reliability and effectiveness of the novel uniform stability criterion were verified through three representative examples.

Robust tracking control for nonlinear fractional order delayed systems: Modified repetitive control approach

AbstractThis study focuses on the problem of perturbation suppression and tracking control of nonlinear fractional order systems with time‐varying delay. To simplify the control process for such systems, the Takagi–Sugeno fuzzy model is used to describe the nonlinear fractional order delayed systems. Additionally, a modified repetitive controller is applied to develop an output feedback technique for the proposed systems. To ensure system stability, the study establishes new delay‐dependent stabilization conditions using a novel Lyapunov–Krasovskii functional (LKF). These stability conditions are expressed in formation of linear matrix inequalities (LMIs) by adopting a frequency‐distributed model transformation and some slack matrices. The proposed method demonstrates that the system output can track the desired input with ignorable error, while effectively rejecting disturbances. Finally, the efficacy of the proposed method is evaluated through simulations of the modified Chua circuit and the hydraulic turbine governing system (HTGS).

Predefined Time Fuzzy Adaptive Control of Switched Fractional-Order Nonlinear Systems with Input Saturation

Article Predefined Time Fuzzy Adaptive Control of Switched Fractional-Order Nonlinear Systems with Input Saturation Lusong Ding, and Weiwei Sun * 1 Institute of Automation, Qufu Normal University, Qufu 273165, China * Correspondence: wwsun@hotmail.com Received: 31 August 2023 Accepted: 31 October 2023 Published: 21 December 2023 Abstract: This article investigates the predefined-time fuzzy adaptive tracking control problem for a class of nonlinear switched fractional-order systems with input saturation and external disturbances under a nonstrict feedback structure. By combining the backstepping technique and the common Lyapunov function method, a predefined-time switching control method is constructed based on a novel fractional-order auxiliary function. The fuzzy logic system and the adaptive method are introduced to identify unknown compounded continuous functions. Moreover, the issue of calculating explosion and the problem of singularity are tackled through the newly proposed predefined-time and filter-based dynamic surface control. Especially, the construction of a continuous term in the controller eliminates possible chattering. The developed control strategy achieves that the closed-loop system is practically predefined-time stable under arbitrary switchings, where the upper bound of the settling-time can be defined by users in advance. Finally, two simulation examples are illustrated to prove the feasibility and effectiveness of the presented scheme.

Anti-windup scheme-based control for fractional-order systems subject to actuator and sensor saturation

This paper addresses the problem of dissipative-based stabilization for fractional-order nonlinear control systems with uncertainties, time-delay, external disturbances, actuator faults, actuator and sensor saturations. Specifically, a non-fragile reliable dynamic output feedback controller is designed for the purpose of stabilization of the addressed system. Due to the effect of saturation phenomena occurring in both the actuator and sensor, the anti-windup loops framed with the help of the observer design are incorporated into the controller design. Some sufficient conditions are formulated in terms of linear matrix inequalities by choosing a suitable Lyapunov function thereby assuring the dissipative-based stabilization. The derived results are thus validated by two numerical examples including the practical model of two-stage chemical reactor.

Adaptive Fuzzy Fault-Tolerant Control of Uncertain Fractional-Order Nonlinear Systems with Sensor and Actuator Faults

In this work, an adaptive fuzzy backstepping fault-tolerant control (FTC) issue is tackled for uncertain fractional-order (FO) nonlinear systems with sensor and actuator faults. A fuzzy logic system is exploited to manage unknown nonlinearity. In addition, a novel FO nonlinear filter-based dynamic surface control (DSC) method is constructed, effectively avoiding the inherent complexity explosion problem in the backstepping recursive process, and in the light of the construction of auxiliary functions, compensating the coupling term introduced by faults. On account of certain assumptions, the stability criterion of the FO Lyapunov function is applied to guarantee the stability of the closed-loop system. Finally, the simulation example verifies the validity of the presented control strategy.

STATE ESTIMATION FOR A CLASS OF FRACTIONAL-ORDER UNCERTAIN NONLINEAR SYSTEMS

The robust state estimation problem for a class of fractional-order uncertain non- linear systems is investigated in this paper. The class of fractional-order uncertain nonlinear systems is more general than the existing one in the literature. For the first time, a method based on a new fractional-order state observer is proposed to give robust state estimation of the fractional-order uncertain nonlinear systems. A new condition for the existence of the fractional-order observer in terms of an optimization problem is proposed. The effectiveness of the proposed method is demonstrated through two examples.

Event-Triggered Fuzzy Adaptive Control of Incommensurate Fractional-Order Nonlinear Systems With Prescribed Performance

Event-Triggered Fuzzy Adaptive Control of Incommensurate Fractional-Order Nonlinear Systems With Prescribed Performance

Event-Triggered Predefined-Time Output Feedback Control for Fractional-Order Nonlinear Systems With Input Saturation

The event-triggered predefined-time output feed- back control problem is considered for fractional-order nonlinear systems (FONSs) with input saturation. The controlled plant contains unknown nonlinear dynamics and unmeasured states. The unknown nonlinear dynamics are handled by using fuzzy approximation technique, a fuzzy state observer is established to estimate unmeasured states and an event-triggered mechanism is given to improve the efficiency of communication resource utilization. The predefined-time stable criterion of fractional- order nonlinear systems is first developed. Then, an event- triggered predefined-time output feedback control is proposed by using the dynamic surface control (DSC) technique. Based on the proposed predefined-time stable criterion and Lyapunov function, it is proved that the controlled system is semi-global practically predefined-time stable (SGPPTS) and all the signals are bounded in predefined-time interval. Finally, the simulation results are given to confirm the effectiveness of the presented predefined-time control method.