Adaptive Backstepping Control for Fractional-Order Nonlinear Systems with External Disturbance and Uncertain Parameters Using Smooth Control

In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller is proposed with adaptive laws that are used to estimate the unknown system parameters and the bound of unknown disturbance. Instead of using discontinuous functions such as the $\mathrm{sign}$ function, an auxiliary function is employed to obtain a smooth control input that is still able to achieve perfect tracking in the presence of bounded disturbances. Indeed, global boundedness of all closed-loop signals and asymptotic perfect tracking of fractional-order system output to a given reference trajectory are proved by using fractional directed Lyapunov method. To verify the effectiveness of the proposed control method, simulation examples are presented.Comment: Accepted by the IEEE Transactions on Systems, Man and Cybernetics: Systems with Minor Revision

Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

This paper presents an adaptive nonlinear delayed feedback control scheme for stabilizing the UPO of unknown fractional-order chaotic systems. The proposed control scheme uses the Lyapunov approach and sliding mode control technique to ensure that the closed-loop control system is asymptotically stable on a periodic trajectory sufficiently close to the UPO of the fractional-order chaotic system. It is guaranteed that the closed-loop system will be robust to external disturbances with unknowable bounds. Finally, the proposed method is used to stabilize the UPO of the fractional-order Duffing and Gyro systems, and extensive simulation results are used to evaluate its performance

Rikitake dynamo system, its circuit simulation and chaotic synchronization via quasi-sliding mode control

Rikitake dynamo system (1958) is a famous two-disk dynamo model that is capable of executing nonlinear chaotic oscillations similar to the chaotic oscillations as revealed by palaeomagnetic study. First, we detail the Rikitake dynamo system, its signal plots and important dynamic properties. Then a circuit design using Multisim is carried out for the Rikitake dynamo system. New synchronous quasi-sliding mode control (QSMC) for Rikitake chaotic system is studied in this paper. Furthermore, the selection on switching surface and the existence of QSMC scheme is also designed in this paper. The efficiency of the QSMC scheme is illustrated with MATLAB plots

The global sliding mode tracking control for a class of variable order fractional differential systems

In this paper, a novel variable order fractional control approach is proposed for tracking control of both of variable order fractional and constant order fractional order system with uncertain and external disturbance terms. In term of the global sliding mode control theory and terminal sliding mode control method, the system states are guaranteed to stay on the switching surface from the initial time, and then converge to the origin by the designed controllers which are continuous input signals. Such controllers avoid the undesirable chattering and remove the effects of uncertain and external disturbance completely. Finally, the comparison between the variable order fraction controller and the constant order fractional controller is given by numerical simulation, furthermore, numerical results on the effects of the tracking control are provided.This paper has been supported by National Natural Science Foundation of China (No.12002194; No.12072178; No.11732005), Natural Science Foundation of Shandong Province (No.ZR2020QA037; No.ZR2020MA054), Ministerio de Ciencia, Innovación y Universidades (No. PGC2018-097198-B-I00) and Fundación Séneca de la Región de Murcia (No.20783/PI/18)

Adaptive fuzzy tracking control for a class of uncertain MIMO nonlinear systems using disturbance observer

In this paper, the adaptive fuzzy tracking control is proposed for a class of multi-input and multioutput (MIMO) nonlinear systems in the presence of system uncertainties, unknown non-symmetric input saturation and external disturbances. Fuzzy logic systems (FLS) are used to approximate the system uncertainty of MIMO nonlinear systems. Then, the compound disturbance containing the approximation error and the time-varying external disturbance that cannot be directly measured are estimated via a disturbance observer. By appropriately choosing the gain matrix, the disturbance observer can approximate the compound disturbance well and the estimate error converges to a compact set. This control strategy is further extended to develop adaptive fuzzy tracking control for MIMO nonlinear systems by coping with practical issues in engineering applications, in particular unknown non-symmetric input saturation and control singularity. Within this setting, the disturbance observer technique is combined with the FLS approximation technique to compensate for the effects of unknown input saturation and control singularity. Lyapunov approach based analysis shows that semi-global uniform boundedness of the closed-loop signals is guaranteed under the proposed tracking control techniques. Numerical simulation results are presented to illustrate the effectiveness of the proposed tracking control schemes

Adaptive neural complementary sliding-mode control via functional-linked wavelet neural network

[[abstract]]Chaos control can be applied in the vast areas of physics and engineering systems, but the parameters of chaotic system are inevitably perturbed by external inartificial factors and cannot be exactly known. This paper proposes an adaptive neural complementary sliding-mode control (ANCSC) system, which is composed of a neural controller and a robust compensator, for a chaotic system. The neural controller uses a functional-linked wavelet neural network (FWNN) to approximate an ideal complementary sliding-mode controller. Since the output weights of FWNN are equipped with a functional-linked type form, the FWNN offers good learning accuracy. The robust compensator is designed to eliminate the effect of the approximation error introduced by the neural controller upon the system stability in the Lyapunov sense. Without requiring preliminary offline learning, the parameter learning algorithm can online tune the controller parameters of the proposed ANCSC system to ensure system stable. Finally, it shows by the simulation results that favorable control performance can be achieved for a chaotic system by the proposed ANCSC scheme.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子

Output Feedback Fractional-Order Nonsingular Terminal Sliding Mode Control of Underwater Remotely Operated Vehicles

For the 4-DOF (degrees of freedom) trajectory tracking control problem of underwater remotely operated vehicles (ROVs) in the presence of model uncertainties and external disturbances, a novel output feedback fractional-order nonsingular terminal sliding mode control (FO-NTSMC) technique is introduced in light of the equivalent output injection sliding mode observer (SMO) and TSMC principle and fractional calculus technology. The equivalent output injection SMO is applied to reconstruct the full states in finite time. Meanwhile, the FO-NTSMC algorithm, based on a new proposed fractional-order switching manifold, is designed to stabilize the tracking error to equilibrium points in finite time. The corresponding stability analysis of the closed-loop system is presented using the fractional-order version of the Lyapunov stability theory. Comparative numerical simulation results are presented and analyzed to demonstrate the effectiveness of the proposed method. Finally, it is noteworthy that the proposed output feedback FO-NTSMC technique can be used to control a broad range of nonlinear second-order dynamical systems in finite time

Fractional Order Fault Tolerant Control - A Survey

In this paper, a comprehensive review of recent advances and trends regarding Fractional Order Fault Tolerant Control (FOFTC) design is presented. This novel robust control approach has been emerging in the last decade and is still gathering great research efforts mainly because of its promising results and outcomes. The purpose of this study is to provide a useful overview for researchers interested in developing this interesting solution for plants that are subject to faults and disturbances with an obligation for a maintained performance level. Throughout the paper, the various works related to FOFTC in literature are categorized first by considering their research objective between fault detection with diagnosis and fault tolerance with accommodation, and second by considering the nature of the studied plants depending on whether they are modelized by integer order or fractional order models. One of the main drawbacks of these approaches lies in the increase in complexity associated with introducing the fractional operators, their approximation and especially during the stability analysis. A discussion on the main disadvantages and challenges that face this novel fractional order robust control research field is given in conjunction with motivations for its future development. This study provides a simulation example for the application of a FOFTC against actuator faults in a Boeing 747 civil transport aircraft is provided to illustrate the efficiency of such robust control strategies