Fractional-order Systems Research Articles

Formula omitted] fault detection observer design for nonlinear conformable fractional-order systems

This study is concerned with the design of fault detection observers for nonlinear conformable fractional-order systems. An H∞/H− fault detection scheme is applied to maximize the sensitivity of faults and minimize the effect of disturbances. Based on basic fractional calculus lemmas and fractional-order Lyapunov stability theory, sufficient conditions are obtained to design a fault detection observer. Finally, the advantages and effectiveness of the proposed fault detection method are illustrated through a numerical example.

Avoidence Strategies for Fractional Order Systems with Caputo Derivative

Abstract A control strategy is derived for fractional-order dynamic systems with Caputo derivative to guarantee collision-free trajectories for two agents. To guarantee that one agent keeps the state of the system out of a given set regardless of the other agent’s actions a Lyapunov-based approach is adopted. As a special case showing that the given approach to choosing proposed strategy is constructive for a fractional-order system with the Caputo derivative, a linear system as an example is discussed. Obtained results extend to the fractional order case the avoidance problem Leitman’s and Skowronski’s approach.

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.

A Fractional-Order Wireless Power Transfer System With Misalignment and Detuning Tolerance

A Fractional-Order Wireless Power Transfer System With Misalignment and Detuning Tolerance

An Adaptive Approach for Battery State of Charge and State of Power Co-Estimation With a Fractional-Order Multi-Model System Considering Temperatures

An Adaptive Approach for Battery State of Charge and State of Power Co-Estimation With a Fractional-Order Multi-Model System Considering Temperatures

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.

Robust model predictive control for fractional-order descriptor systems with uncertainty

Robust model predictive control for fractional-order descriptor systems with uncertainty

Neural Network-Based Adaptive Sliding Mode Control for T-S Fuzzy Fractional Order Systems

Neural Network-Based Adaptive Sliding Mode Control for T-S Fuzzy Fractional Order Systems

On Linear-Quadratic Differential Games for Fractional-Order Systems

On Linear-Quadratic Differential Games for Fractional-Order Systems

Active control and electronic simulation of a novel fractional order chaotic jerk system

The chaotic jerk system represents a class of nonlinear systems with unique, varied, and interesting characteristics and behavior. In this study, we proposed a modified fractional-order chaotic Jerk system by the introduction of two novel nonlinear terms and two constant terms. The nonlinear terms introduced are the exponential and tangential functions while the two parameters are a and b. Stability analysis of the fractional-order Jerk system was used to establish the parameter ranges for chaotic behavior in the system. Chaos in the system was confirmed via the Lyapunov exponents. The bifurcation diagram with respect to the parameters, a and b, as well as the fractional order, α were examined. The synchronization of the system was implemented using the active control method. Finally, the studied novel circuit was realized using MultiSIM electronic software for experimental validation.

Finite-time Guaranteed Cost Control of Positive Switched Fractional-Order Systems Based on $$\Phi $$-Dependent ADT Switching

Finite-time Guaranteed Cost Control of Positive Switched Fractional-Order Systems Based on $$\Phi $$-Dependent ADT Switching

A negative imaginary lemma and state-feedback negative imaginary synthesis for commensurate fractional-order systems

This article focuses on negative imaginariness of commensurate fractional-order linear time-invariant systems. Enlightened by the generalized Kalman–Yakubovic–Popov lemma, minimal state-space realization based necessary and sufficient conditions are developed to characterize negative imaginariness of commensurate fractional-order systems for both 0<α<1 and 1<α<2 cases. Meanwhile, the problem of negative-imaginary state-feedback controller synthesis for fractional-order systems is addressed. A fractional-order viscoelastic system, a fractional-order RLC circuit network and a numerical example are used as illustrative examples to demonstrate the main developed theory.

Back-stepping projective synchronization of fractional-order unified systems based on the lower triangular structure

The synchronization of fractional-order chaotic systems (FOCSs) plays an important role in modern control theory, the projective synchronization (PS) as a class of synchronization problems, also has huge applications and has attracted much attention. It is, however, shown in the obtained literature that the results on the PS of FOCSs either loss the rigorous theoretical demonstration or verify from the viewpoint of numerical simulations. How to derive a necessary and sufficient condition to guarantee the PS of complex FOCSs by a simple controller is still open. To this end, this article is concerned with the PS of fractional-order unified systems (FO-USs) that are important in FOCSs covering fractional-order Lorenz, Chen and Lü systems, where the controller is presented based on the lower triangular structure by use of the back-stepping technique. The necessary and sufficient criterion for the PS of FO-USs is proposed by solving an algebraic equation, and the controller for the PS of FO-USs is derived based on the lower triangular structure combined with back-stepping approach. Finally, the simulation results are reported to verify the correctness and efficiency of the obtained results.

Uncertainty Observer-Based Control for a Class of Fractional- Order Non-Linear Systems with Non-Linear Control Inputs

This paper presents a novel control strategy based on an uncertainty estimator for a class of fractional-order nonlinear systems characterized by a polynomial input. The proposed strategy allows the system to be controlled without resorting to transformations or approximate linearization. This is accomplished by using a fractional-order sliding-mode observer, whose task is to estimate certain portions of the state of the nonlinear system of a non-integer order, thus allowing the control law to counteract these elements to steer the system towards a desired behavior. To validate the performance of the proposed strategy, it was implemented, both in simulation and experimentally, to regulate the temperature of the cold side of a thermoelectric module fed by a DC/DC electronic power converter of the step-down type, a system that is known to have a nonlinear polynomial-type control input.

Caputo-fabrizio fractional-order systems: periodic solution and stabilization of non-periodic solution with application to gunn diode oscillator

Fractional-order autonomous systems do not possess any non-constant periodic solutions, and to the best of our knowledge, there are no existing results regarding the existence of the periodic solution for fractional-order non-autonomous systems. The main objective of this work is to fill the above gap by studying the existence of a periodic solution of the Caputo-Fabrizio fractional-order system and also to find ways to stabilize a non-periodic solution. First, by using the concepts of an equilibrium point, it is proved that an autonomous Caputo-Fabrizio system cannot admit a non-constant periodic solution. Under a similar assumption as the one for an integer-order differential system, and by using the properties of the Caputo-Fabrizio derivative, the existence of a periodic solution of a non-autonomous Caputo-Fabrizio fractional-order differential system is established. The main result is utilized in constructing and finding the periodic solution of the linear non-homogeneous Caputo-Fabrizio system. By using the result on linear systems, we derive a periodic solution of a fractional-order Gunn diode oscillator under a periodic input voltage, and observe that the diameter of the periodic orbit keeps reducing as the fractional-order continuously increases. In the end, by using the result on a linear non-homogeneous system, and by constructing a suitable linear feedback control, the solution of the linear non-homogeneous fractional-order system is stabilized to a periodic solution. An example is presented to support the obtained result. The main advantage of the proposed method over others is the simple considerations like the concept of equilibrium point and the utilization of the property of the Caputo-Fabrizio derivatives instead of other types of fractional derivatives.

A new fractional-order 5D memristive chaotic system with special extreme multistability and its application to image encryption

Introducing memristor into the chaotic system can enrich the dynamic behaviors of the chaotic system. We propose a symbolic function memristor model and introduce it into a chaotic system to construct a fractional-order 5D memristor chaotic system. Through dynamic analysis of equilibrium point, Lyapunov exponents, phase diagram and bifurcation diagram, it is found that the system has abundant dynamic behaviors, for example, the change of equilibrium point type with parameters, transient chaos, offset-boosting and a special kind of extreme multistability. And with the change of parameters, the attractor state and shape will appear rich changes. Then the correctness of the system is verified by circuit simulation. The chaotic system is introduced into the process of image encryption, and an encryption system is constructed, which is composed of Zigzag scrambling, Hilbert curve scrambling, DNA encryption and GF257 diffusion algorithm. Finally, through a variety of security verification, the results show that the encryption system has good security and can resist many kinds of attacks effectively.

Dynamic Analysis and FPGA Implementation of a New Fractional-Order Hopfield Neural Network System under Electromagnetic Radiation.

Fractional calculus research indicates that, within the field of neural networks, fractional-order systems more accurately simulate the temporal memory effects present in the human brain. Therefore, it is worthwhile to conduct an in-depth investigation into the complex dynamics of fractional-order neural networks compared to integer-order models. In this paper, we propose a magnetically controlled, memristor-based, fractional-order chaotic system under electromagnetic radiation, utilizing the Hopfield neural network (HNN) model with four neurons as the foundation. The proposed system is solved by using the Adomain decomposition method (ADM). Then, through dynamic simulations of the internal parameters of the system, rich dynamic behaviors are found, such as chaos, quasiperiodicity, direction-controllable multi-scroll, and the emergence of analogous symmetric dynamic behaviors in the system as the radiation parameters are altered, with the order remaining constant. Finally, we implement the proposed new fractional-order HNN system on a field-programmable gate array (FPGA). The experimental results show the feasibility of the theoretical analysis.

Dynamical Analysis of a 3D Fractional-Order Chaotic System for High-Security Communication and its Electronic Circuit Implementation

This article, a 3D fractional-order chaotic system (FOCS) is designed; system holds Equilibria can take on various shapes and forms by introducing a nonlinear function and the value of its parameters. To comprehend the system’s behavior under diverse conditions and parameter values, a dynamical analysis is conducted through analytical and numerical means. This analysis employs techniques like phase portraits, Lyapunov exponents (LEs), bifurcation analysis, and Lyapunov spectra. The system demonstrates attractors that are more intricate compared to a regular chaotic system with an integer value, specifically if we set the fractional order q to 0.97. This characteristic makes it highly appropriate for developing secure communication systems. Moreover, a practical implementation has been developed using an electronic circuit to showcase its feasibility of the system. A secure communication system was built using two levels of encryption techniques. The propose sound encryption algorithm is verified through tests like histogram, correlation, and spectrogram investigation. The encryption correlation coefficient between the original signal and the encrypted one is 0.0010, this result shows a strong defences against pirate attacks.

Design and implementation of a sliding mode controller and adaptive sliding mode controller for a novel fractional chaotic class of equations

In this article, we investigate the dynamics of a three-dimensional class of systems using Caputo fractional derivative. To regulate the chaos of this fractional order system, we propose a novel approach involving a sliding mode controller and an adaptive sliding mode controller. The study includes the existence and Ulam–Hyers stability results, the derivation of conditions ensuring global stability for the controlled system, even in the presence of novel uncertainties and outer interruptions. Our main contribution lies in introducing the adaptive law combined with sliding mode control, which effectively illustrates the chaotic behavior and dissipative nature of the chaotic system. This innovation has promising implications for various real-world applications where the control of chaotic dynamics is critical, such as in secure communication systems or ecological modeling Fitting the Nose–Hoover chaotic system to the defined class of equations, we have analyzed the impact of fractional order derivatives in the system and differentiate between chaotic and hyper chaotic behaviors by employing Lyapunov exponents. This differentiation has significant implications for understanding the underlying dynamics of complex systems in science and engineering. Furthermore, we have performed the bifurcation analysis to depict the chaotic behavior in the novel Nose–Hoover class, shedding light on the rich and intricate behaviors that fractional order dynamics can exhibit. To validate the proposed control scheme, we conduct numerical simulations and demonstrate its efficiency through the imposition of exponential and logarithmic uncertainties and disturbances. The model simulation results are provided.

Distributed adaptive neural network consensus control of fractional-order multi-agent systems with unknown control directions

In this work, adaptive consensus control of leader-following fractional-order multi-agent systems whose each subsystem includes functional uncertainties, external disturbances, and unknown control directions is investigated utilizing neural networks and the Nussbaum function. The controller is synthesized within the framework of the backstepping algorithm, where the “explosion of complexity” problem is mitigated through the use of a command filter, and the adverse impact of filtered errors is decreased using compensation signals. The function uncertainties of each follower are approximated by neural networks, and a disturbance update law is developed to identify the boundary of the disturbance. Importantly, a general conclusion is provided to affirm the applicability of the Nussbaum function in addressing controller design for fractional-order systems with unknown control directions. Finally, the validity of the proposed approach is verified via two numerical examples.