In this paper, an adaptive control scheme is offered to synchronize two different uncertain chaotic systems. It is assumed that the whole dynamics of both master and slave chaotic systems and their bounds are unknown and different. The error system stabilization is achieved in two cases: with input nonlinearities and without input nonlinearities. We design an adaptive control scheme based on the state boundedness property of the chaotic systems. The proposed method does not need any information about nonlinear/ linear terms of the chaotic systems. It only uses an adaptive feedback control strategy. The stability of the proposed controllers is proved by using the Lyapunov stability theory. Finally, the designed adaptive controllers are applied to synchronize two different pairs of the chaotic systems (Lorenz-Chen and electromechanical device-electrostatic transducer).

This article proposes an adaptive neural output tracking control scheme for a class of nonlinear fractional order (FO) systems in the presence of unknown actuator faults. By means of backstepping terminal sliding mode (SM) control technique, an adaptive fractional state-feedback control law is extracted to achieve finite time stability along with output tracking for an uncertain faulty FO system. The unknown nonlinear terms are approximated by radial-basis function neural network (RBFNN) with unknown approximation error upper bound. Using convergence in finite time and fractional Lyapunov stability theorems, the finite time stability and tracking achievement are proved. Finally, the proposed fault tolerant control (FTC) approach is validated with numerical simulations on two fractional models including fractional Genesio–Tesi and fractional Duffing's oscillator systems.

This article presents a new design of robust finite-time controller which replaces the traditional automatic voltage regulator for excitation control of the third-order model synchronous generator connected to an infinite bus. The effects of system uncertainties and external noises are fully taken into account. Then a single input robust controller is proposed to regulate the system states to reach the origin in a given finite time. The designed robust finite-time excitation controller can refine the system behaviors in convergence and robustness against model uncertainties and external disturbances. The robustness and finite-time stability of the closed-loop system are analytically proved using the finite-time control idea and Lyapunov stability theorem. The suitability and robustness of the designed controller are shown in contrast with two other strong nonlinear control strategies. The main advantages of the proposed controller are as follows: a) robustness against system uncertainties and external noises; b) convergence to the equilibrium point in a given finite time; and c) the use of a single control input. V C 2015 Wiley Periodicals, Inc. Complexity 21: 203-213, 2016

This article is concerned with designing of a robust adaptive observer for a class of nonautonomous chaotic system with unknown parameters having unknown bounds. The proposed observer is established from the offered output measurement and robust against model uncertainties and external disturbances. Convergence analysis of the observation error dynamics is realized and proved by Lyapunov stabilization theory. Finally, for verification and demonstration, the proposed method is applied to the Chen as an autonomous chaotic system and the electrostatic transducer as a nonautonomous chaotic system. The numerical simulations illustrate the excellent performance of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 145–153, 2015

In this paper, adaptive fractional control design is established for uncertain nonlinear fractional order strict feedback form systems with unknown actuator failures. The fractional actuator failure compensation problem is considered in the sense of two actuation shapes, and output matching conditions for these shapes are employed. By means of a fractional backstepping control method, two fractional adaptive state feedback control laws are designed to accomplish output tracking and to guarantee closed-loop stability in the presence of unknown actuator failures and unknown system parameters. A fractional order filter is proposed to avoid the problem of computational explosion of the backstepping design. The stability is proved via fractional order analysis method for the whole closed-loop system. Finally, simulation results for the control of fractional Chua’s circuit and fractional Genesio–Tesi systems demonstrate the effectiveness of the proposed actuator failure compensation method and output tracking property along with fast convergence of unknown parameters estimations.