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

Adaptive hybrid function projective synchronization of chaotic systems with fully unknown periodical time-varying parameters

In this paper, an adaptive learning control approach is presented for the hybrid functional projective synchronization (HFPS) of different chaotic systems with fully unknown periodical time-varying parameters. Differential-difference hybrid parametric learning laws and an adaptive learning control law are constructed via the Lyapunov–Krasovskii functional stability theory, which make the states of two different chaotic systems asymptotically synchronized in the sense of mean square norm. Moreover, the boundedness of the parameter estimates are also obtained. The Lorenz system and Chen system are illustrated to show the effectiveness of the hybrid functional projective synchronization scheme

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

Development of new learning control approaches

Ph.DDOCTOR OF PHILOSOPH

Projective synchronization analysis for BAM neural networks with time-varying delay via novel control

In this paper, the projective synchronization of BAM neural networks with time-varying delays is studied. Firstly, a type of novel adaptive controller is introduced for the considered neural networks, which can achieve projective synchronization. Then, based on the adaptive controller, some novel and useful conditions are obtained to ensure the projective synchronization of considered neural networks. To our knowledge, different from other forms of synchronization, projective synchronization is more suitable to clearly represent the nonlinear systems’ fragile nature. Besides, we solve the projective synchronization problem between two different chaotic BAM neural networks, while most of the existing works only concerned with the projective synchronization chaotic systems with the same topologies. Compared with the controllers in previous papers, the designed controllers in this paper do not require any activation functions during the application process. Finally, an example is provided to show the effectiveness of the theoretical results

A Novel Disturbance Rejection Zeroing Neurodynamic Approach for Robust Synchronization of Chaotic Systems

Robust synchronization of chaotic systems becomes a hot topic in scientific and engineering fields because of the ubiquitous existence of time-variant external disturbances in complex application scenarios. In contrast with existing studies that the resultant synchronization error has a supremum or even diverges under the influence of time-variant external disturbances, this paper proposes a disturbance rejection zeroing neurodynamic (DRZN) approach and its related controller for the robust synchronization of chaotic systems against time-variant external disturbances. The controller designed by the proposed DRZN approach distinctively features the rejection of external disturbances with the generated synchronization error being convergence toward zero. Theoretical analyses guarantee that the DRZN approach and its related controller inherently possess robustness. Moreover, numerical studies including three examples substantiate the effectiveness of the proposed DRZN approach and its related controller for the synchronization of chaotic systems against the time-variant external disturbances. Comparisons with existing approaches, e.g., the conventional zeroing neurodynamic (CZN) approach and the linear-active control (LAC) approach, show the superiority of the proposed DRZN approach. Extensive tests further verify that the proposed DRZN approach possesses the outstanding anti-disturbance performance, and thus is suitable for the practical applications with time-variant external disturbances

LMI-based H∞ synchronization of second-order neutral master-slave systems using delayed output feedback control

Submitted version of an article published in the journal: International Journal of Control, Automation and Systems. The original publication is available at www.springerlink.com: http://dx.doi.org/10.1007/s12555-009-0306-5The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method. The simulation results illustrate the effectiveness of the proposed methodology. © ICROS, KIEE and Springer 2009