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In this paper, we study the existence and uniqueness of Hadamard Itô-Doob Stochastic Fractional Order Systems (HIDSFOS) using the Picard iteration method. Different from the previous works, our paper presents a new theory using the Hadamard fractional integral. We have proved the convergence of the solution of the averaged HIDSFOS to that of the standard HIDSFOS in the sense of the mean square and also in probability. Some examples are given at the end of this paper to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observer

This paper proposes fault-tolerant control design for uncertain nonlinear systems described under Takagi-Sugeno fuzzy systems with local nonlinear models that satisfy the Lipschitz condition. First, by transforming sensor faults as 'pseudo-actuator' faults, an adaptive sliding mode observer is designed in order to simultaneously estimate system states, actuator and sensor faults despite the presence of norm-bounded uncertainties. Second, an adaptive sliding mode controller is suggested to provide a solution to stabilize the closed-loop system, even in the event of simultaneous occurrence of faults in actuators and sensors. Next, the main objective of the fault-tolerant control strategy is to compensate for the effects of fault based on the feedback information. Therefore, using the LMI optimization method, sufficient conditions are developed with H-ž to calculate the gains of the observer and the controller. Then, particular attention is paid to the simultaneous maximization, by convex multi-objective optimization, of the Lipschitz nonlinear constant in Takagi-Sugeno fuzzy modelling and uncertainties attenuation level. The results of the simulation illustrate the effectiveness of our fault-tolerant control approach using a nonlinear inverted pendulum with a cart system. [ABSTRACT FROM AUTHOR]

The present article deals with adaptive sliding mode fault tolerant control design for uncertain nonlinear systems, affected by multiplicative faults, that is described under Takagi–Sugeno fuzzy representation. First, we propose to conceive robust adaptive observer in order to achieve states and multiplicative faults estimation in the presence of nonlinear system uncertainties. Under the nonlinear Lipschitz condition, the observer gains are attained by solving the multi-objective optimization problem. Second, sliding mode controller is suggested to offer a solution of the closed-loop system stability even the occurrence of real fault effects. The main objective is to compensate multiplicative fault effects based on output feedback information. Sufficient conditions are developed with H ∞ performances and expressed as a set of linear matrix inequalities subject to compute controller gains. Finally, simulation results, using the nonlinear model of a single-link flexible joint robot system, are given to illustrate the capability of the suggested fault tolerant control strategy to treat multiplicative faults. [ABSTRACT FROM AUTHOR]

The purpose of this study is to present a new robust sliding mode control design for nonlinear systems where both matched and unmatched uncertainties are considered. The proposed controller strategy is composed of two components: the integral sliding mode control and the optimal feedback control law. Moreover, an integral sliding mode surface in integral type is developed to construct the reachability of sliding mode using the Lyapunov functions method. The main advantages of the proposed approach are ensuring the robustness throughout the whole system response against the uncertainties, decrease the chattering effect and eliminate the reaching phase. Finally, the validity of the proposed design strategy is demonstrated through the simulation of a flexible joint robot. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new design for an optimal fuzzy sliding mode control based on a modified parallel distributed compensator and using a scalar sign function method. The proposed fuzzy sliding mode control uses a modified parallel distributed compensator scheme to find the optimal gains. To do this, the control gains are not considered constant through the linearized subsystem. Among these, we find state feedback gains, which are determined in offline mode using some prescribed performance criteria. Moreover, the fuzzy sliding surface of the system is designed using a stable eigenvector and the scalar sign function. The advantages of the proposed design are minimum energy control effort, faster response, and zero steady-state error. We analyze and test the performance and stability of the new optimal fuzzy sliding mode control using simulation results that show that the proposed approach is very effective. [ABSTRACT FROM AUTHOR]

This paper proposes a new robust fault reconstruction and estimation design for a class of nonlinear system described by the Takagi-Sugeno model with unmeasurable premise variables subject to faults affecting actuators, sensor faults, and unknown disturbances. The augmented Takagi-Sugeno system is introduced with a new fault vector which has two origins: the first one represents actuator faults, the second one denotes faults affecting sensors. The main contribution is focused primarily to conceive a sliding mode observer with two discontinuous terms designed to compensate for fault behavior and disturbance variation from the system states estimation. In the formalism of linear matrix inequalities, we derive sufficient conditions to guarantee the state estimation error stability and to obtain the observer gains. Meanwhile, additional effort is made to achieve simultaneous faults and disturbance reconstruction. Simulation results are given to illustrate the proposed approach performances. [ABSTRACT FROM AUTHOR]

This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observer. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for the design of robust H sliding mode observer (SMO) for a class of Lipschitz nonlinear systems where both faults and uncertainties are considered. A sufficient condition using linear matrix inequality (LMI) optimization is derived to guarantee the asymptotically stability of the estimation error dynamics and compute the observer gains. A fault estimation scheme is presented where the estimation signal can approximate the fault to some degree of accuracy. Our design approach has some advantages. The Lipschitz constant of the nonlinear term in the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. For this reason, the Lipschitz constant is suitable to a large class of uncertain nonlinear systems. Moreover, the fault estimation is much more robust against disturbances and nonlinear uncertainty and can preserve the fault signal shape effectively. Finally, a simulation study on a robotic arm system is presented to show the effectiveness of this approach. [ABSTRACT FROM AUTHOR]