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

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

Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview

Disturbance Observer has been one of the most widely used robust control tools since it was proposed in 1983. This paper introduces the origins of Disturbance Observer and presents a survey of the major results on Disturbance Observer-based robust control in the last thirty-five years. Furthermore, it explains the analysis and synthesis techniques of Disturbance Observer-based robust control for linear and nonlinear systems by using a unified framework. In the last section, this paper presents concluding remarks on Disturbance Observer-based robust control and its engineering applications.Comment: 12 pages, 4 figure

Advanced Mathematics and Computational Applications in Control Systems Engineering

Control system engineering is a multidisciplinary discipline that applies automatic control theory to design systems with desired behaviors in control environments. Automatic control theory has played a vital role in the advancement of engineering and science. It has become an essential and integral part of modern industrial and manufacturing processes. Today, the requirements for control precision have increased, and real systems have become more complex. In control engineering and all other engineering disciplines, the impact of advanced mathematical and computational methods is rapidly increasing. Advanced mathematical methods are needed because real-world control systems need to comply with several conditions related to product quality and safety constraints that have to be taken into account in the problem formulation. Conversely, the increment in mathematical complexity has an impact on the computational aspects related to numerical simulation and practical implementation of the algorithms, where a balance must also be maintained between implementation costs and the performance of the control system. This book is a comprehensive set of articles reflecting recent advances in developing and applying advanced mathematics and computational applications in control system engineering

Synchronization of two fractional-order chaotic systems via nonsingular terminal Fuzzy Sliding Mode Control

La sincronización de dos sistemas caóticos complejos de orden fraccional se discute en este documento. El parámetro incertidumbre y la perturbación externa se incluyen en el modelo del sistema, y la sincronización de los sistemas considerados caóticos se implementa en base al concepto de tiempo finito. Primero, se propone una nueva superficie deslizante terminal no singular de orden fraccional que es adecuada para los sistemas de orden fraccional considerados. Se ha demostrado que una vez que las trayectorias del estado del sistema alcancen la superficie de deslizamiento propuesta, convergerán al origen dentro de un tiempo finito dado. En segundo lugar, en términos de la superficie deslizante terminal no singular establecida, que combina el control difuso y los esquemas de control de modo deslizante, se introduce una ley de control de modo deslizante difusa única novedosa y robusta que puede forzar las trayectorias del sistema de error dinámico de circuito cerrado para alcanzar el deslizamiento superficie durante un tiempo finito. Finalmente, utilizando el teorema de estabilidad fraccional de Lyapunov, se demuestra la estabilidad del método propuesto. El método propuesto se implementa para la sincronización de dos sistemas caóticos Genesio-Tesi de orden fraccional con parámetros inciertos y perturbaciones externas para verificar la efectividad del controlador de modo de deslizamiento difuso terminal no-singular de orden fraccional propuesto.The synchronization of two fractional-order complex chaotic systems is discussed in this paper. The parameter uncertainty and external disturbance are included in the system model, and the synchronization of the considered chaotic systems is implemented based on the finite-time concept. First, a novel fractional-order nonsingular terminal sliding surface which is suitable for the considered fractional-order systems is proposed. It is proven that once the state trajectories of the system reach the proposed sliding surface they will converge to the origin within a given finite time. Second, in terms of the established nonsingular terminal sliding surface, combining the fuzzy control and the sliding mode control schemes, a novel robust single fuzzy sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface over a finite time. Finally, using the fractional Lyapunov stability theorem, the stability of the proposed method is proven. The proposed method is implemented for synchronization of two fractional-order Genesio-Tesi chaotic systems with uncertain parameters and external disturbances to verify the effectiveness of the proposed fractional-order nonsingular terminal fuzzy sliding mode controller.• National Natural Science Foundation of China. Becas U1604146, U1404610, 61473115, 61203047 • Science and Technology Research Project in Henan Province. 152102210273, 162102410024 • Foundation for the University Technological Innovative Talents of Henan Province. Beca 18HASTIT019peerReviewe

Recurrent Interval Type-2 Fuzzy Wavelet Neural Network with Stable Learning Algorithm: Application to Model-Based Predictive Control

Fuzzy neural networks, with suitable learning strategy, have been demonstrated as an effective tool for online data modeling. However, it is a challenging task to construct a model to ensure its quality and stability for non-stationary dynamic systems with some uncertainties. To solve this problem, this paper presents a novel identification model based on recurrent interval type-2 fuzzy wavelet neural network (RIT2FWNN) with new learning algorithm. The model benefits from both advantages of recurrent and wavelet neural networks such as use of temporal data and fast convergence properties. The proposed antecedent and consequent parameters update rules are derived using sliding-mode-control-theory. To evaluate the proposed fuzzy model, it is utilized to design a nonlinear model-based predictive controller and is applied for the synchronization of fractional-order time-delay chaotic systems. Using Lyapunov stability analysis, it is shown that all update rules of the parameters are uniformly ultimately bounded. The adaptation laws obtained in this method are very simple and have closed forms. Some stability conditions are derived to prove learning dynamics and asymptotic stability of the network by using an appropriate Lyapunov function. The efficacy and performance of the proposed method is verified by simulation examples

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

Finite-time disturbance reconstruction and robust fractional-order controller design for hybrid port-Hamiltonian dynamics of biped robots

In this paper, disturbance reconstruction and robust trajectory tracking control of biped robots with hybrid dynamics in the port-Hamiltonian form is investigated. A new type of Hamiltonian function is introduced, which ensures the finite-time stability of the closed-loop system. The proposed control system consists of two loops: an inner and an outer loop. A fractional proportional-integral-derivative filter is used to achieve finite-time convergence for position tracking errors at the outer loop. A fractional-order sliding mode controller acts as a centralized controller at the inner-loop, ensuring the finite-time stability of the velocity tracking error. In this loop, the undesired effects of unknown external disturbance and parameter uncertainties are compensated using estimators. Two disturbance estimators are envisioned. The former is designed using fractional calculus. The latter is an adaptive estimator, and it is constructed using the general dynamic of biped robots. Stability analysis shows that the closed-loop system is finite-time stable in both contact-less and impact phases. Simulation studies on two types of biped robots (i.e., two-link walker and RABBIT biped robot) demonstrate the proposed controller's tracking performance and disturbance rejection capability