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This article considers the H∞ sampled-data fuzzy observer (SDFO) design problem for nonlinear parabolic partial differential equation (PDE) systems under spatially local averaged measurements (SLAMs). Initially, the nonlinear PDE system is accurately represented by the Takagi–Sugeno (T–S) fuzzy PDE model. Then, based on the T–S fuzzy PDE model, an SDFO under SLAMs is constructed for the state estimation. To attenuate the effect of the exogenous disturbance and the design disturbance, an H∞ SDFO design under SLAMs is developed in terms of linear matrix inequalities by utilizing Lyapunov functional and inequality techniques, which can guarantee the exponential stability and satisfy an H∞ performance for the estimation error fuzzy PDE system. Finally, simulation results on the state estimation of the FitzHugh–Nagumo equation are given to support the presented H∞ SDFO design method. [ABSTRACT FROM AUTHOR]

In this paper, we present a new scheme for designing a H∞ stabilizing controller for discrete‐time Takagi‐Sugeno fuzzy systems with actuator saturation and external disturbances. The weighting‐dependent Lyapunov functions approach is used to design a robust static output‐feedback controller. To address the input saturation problem, both constrained and saturated control input cases are considered. In both cases, stabilization conditions of the fuzzy system are formulated as a convex optimization problem in terms of linear matrix inequalities. Two simulation examples are included to illustrate the effectiveness of the proposed design methods. A comparison with the results given in recent literature on the subject is also presented. [ABSTRACT FROM AUTHOR]

Byline: Mohammed Oudghiri, Mohammed Chadli, Ahmed El Hajjaji This paper presents online sensor Fault Detection and Isolation (FDI) and the associated Fault-Tolerant Control (FTC) algorithm for a vehicle lateral dynamics represented by the uncertain Takagi-Sugeno (T-S) fuzzy model. The fault-detection scheme is based on a bank of observers method. Using the LMI formulation, the T-S fuzzy model of the vehicle non-linear dynamics is used to design an observer-based output feedback controller. To demonstrate the effectiveness of the proposed strategy, simulation results are given.

Byline: Mohammed Chadli, Abdelkader Akhenak, Jose Ragot, Dider Maquin In this paper, we consider the design of an fuzzy observer for a non-linear system with unknown inputs described by a fuzzy model. The main objective is to estimate state variables of the fuzzy model subject to unknown inputs which influence states and outputs of the system simultaneously. Using the Lyapunov method and Linear Matrix Inequalities (LMI), sufficient conditions are proposed to design the proposed unknown input fuzzy observer. The pole placement in an LMI region is also considered. The validity of the proposed methodology is illustrated by an academic example.

Byline: Mohammed Chadli, Ahmed Elhajjaji, Mohammed Oudghiri This paper deals with the robust control for Four Wheels Steering (4WS) vehicle dynamics when the road adhesion conditions change and the sideslip angle is unavailable for measurement. The non-linear model of the vehicle is first represented by an uncertain Takagi-Sugeno model. Next, the robust output stabilisation of the vehicle is considered. The controller and the observer are designed in terms of Bilinear Matrix Inequalities (BMI) problem. A method is then proposed to get the LMI formulation resolved sequentially. The obtained simulation results indicate that considerable improvements in the vehicle handling can be achieved when the vehicle is governed by the proposed fuzzy observer-based controller.

Byline: Mohammed Chadli, Abdelkader Akhenak, Didier Maquin, Jose Ragot This paper addresses the design of a fuzzy observer for unknown input Takagi-Sugeno (T-S) fuzzy model. The main contribution of this paper is the development of a robust fuzzy observer in the presence of disturbances. Based on Lyapunov function, it is shown how to determine the observers gains in Linear Matrix Inequalities (LMI) terms. The proposed observer structure allows to estimate simultaneously and systematically the unknown inputs and state variables. The designed T-S observer is used for detection and reconstruction of faults which can affect a non-linear model and can be applied directly for fault detection and isolation of actuator faults. The validity of the proposed methodology is illustrated by estimating the state and faults of an automatic steering vehicle.

This paper addresses the problem of stability for general two-dimensional (2D) discrete-time and continuous-discrete time Lyapunov systems, where the linear matrix inequalities (LMI's) approach is applied to derive a new sufficient condition for the asymptotic stability. [ABSTRACT FROM AUTHOR]

This study is concerned with the finite-time observer (FTO) design for a class of singular systems subject to unknown inputs in both the state and the output equations. First, in order to overcome the restriction of the classical FTO method, two different non-singular auxiliary dynamic systems, which are simultaneously equivalent to the original singular system, are constructed to act as the new reference systems for the sub-observers' design. Second, based on the observer matching condition and strong observability condition, it is proven that an FTO can be designed where the observer parameters are given by an algebraic method. Also, in order to present a systematical method to compute the observer parameters, an alternative linear matrix inequality method is proposed. The advantages of the FTO over the conventional asymptotic convergence observer are discussed and numerical examples are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents an H∞ static output-feedback control of electrical power steering (EPS) subject to actuator saturation. It deals with different practical problems in designing control of EPS systems, such as unavailability for measurement of the sideslip angle, friction effect, disturbances and the assist motor input current optimization. In order to guarantee good and stable driving, the nonlinear model of the EPS combined with bicycle model of electrical vehicles is used. Firstly, a new Takagi-Sugeno model is established, then using a fuzzy Lyapunov function, an H∞ static output-feedback is designed in terms of linear matrix inequalities. Finally, the proposed control schemes are applied to an EPS system. Simulation results and comparison with previous works show the effectiveness of the proposed control methods. [ABSTRACT FROM AUTHOR]

This paper aims at presenting a maximum power point tracking (MPPT) controller for photovoltaic (PV) systems subject to asymmetric input constraint. Indeed, the output voltage of the DC‐DC converter used for adjusting the photovoltaic output power can be controlled by means of variation of duty ratio limited between 1 and 0. The control design goal is to improve the efficiency of PV systems under asymmetric saturation of duty ratio. To achieve this goal, first, a Takagi‐Sugeno (T‐S) fuzzy model is used to represent the nonlinear behavior of the PV system. A T–S reference model is employed to give the ideal state direction which must be followed. To achieve a good steady state tracking, the integral of the state tracking error is used to define an extended system state vector. Second, the input characteristic is partitioned into several regions. In each region, the asymmetric saturation function can be considered as a symmetric saturation function. Furthermore, H∞ stabilization conditions for the resulting switching fuzzy control of the PV system under actuator saturation are formulated in term of linear matrix inequalities (LMI) using the Lyapunov approach. Simulation results are exhibited to demonstrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper presents a fast and accurate robust path-following control approach for a fully actuated marine surface vessel in the presence of external disturbances. The path following is realized by simultaneously converging the yaw rate and sway velocity to their respective desired values, which are generated according to the path-following demand. An improved combined control strategy using an integral terminal sliding mode (ITSM) based composite nonlinear feedback (CNF) technique considering the external disturbances, time-varying tracking reference, input saturations and transient performance improvement is proposed in this study. The proposed ITSM-CNF combines the advantages of the CNF control in improving the transient performance and of the ITSM control in guaranteeing good robustness and finite-time convergence. A continuous and smooth sliding mode controller, based on an integral nonsingular terminal sliding surface, is added to the CNF controller to eliminate chattering. The overall stability of the closed-loop system is strictly proved based on the Lyapunov method. Simulations verify the effectiveness of the ITSM-CNF controller in improving the transient path-following performance, inhibiting overshoots, eliminating steady-state errors, rejecting external disturbances and removing chattering effects, considering input saturations, varying path curvature and finite-time convergence. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fault detection filter design for discrete-time polynomial fuzzy systems with faults and unknown disturbances. The frequency ranges of the faults and the disturbances are assumed to be known beforehand and to reside in low, middle or high frequency ranges. Thus, the proposed filter is designed in the finite frequency range to overcome the conservatism generated by those designed in the full frequency domain. Being of polynomial fuzzy structure, the proposed filter combines the H − / H ∞ performances in order to ensure the best robustness to the disturbance and the best sensitivity to the fault. Design conditions are derived in Sum Of Squares formulations that can be easily solved via available software tools. Two illustrative examples are introduced to demonstrate the effectiveness of the proposed method and a comparative study with LMI method is also provided. [ABSTRACT FROM AUTHOR]

In this paper, the state estimator design problem of interval type-2 Takagi–Sugeno fuzzy systems suffering from bounded disturbances is studied. To enhance the resilience of the estimator, a non-fragile design scheme is proposed to tackle the estimator gain variations. Meanwhile, an event-triggered communication mechanism is introduced for relieving the transmission burden over networks. To settle down the non-fragile estimator design issue subject to bounded disturbances and event-induced error, we propose a new definition of quadratic boundedness via the multiple Lyapunov functions. Based on this definition, a novel co-design method of estimator and event generator for fuzzy system models in the presence of both measurable and immeasurable premise variables is presented. In virtue of quadratic boundedness framework, less conservative conditions of the existence and quadratic stability of the fuzzy estimators are obtained, and the upper bound of estimation error is given explicitly. The desired estimator gains are determined by convex optimization technique using slack matrices. Two illustrative examples are exploited to validate the availability and superiority of the addressed design approach. [ABSTRACT FROM AUTHOR]