Ahmed Toumi

Non-fragile H∞ output feedback control design for continuous-time fuzzy systems

In this paper, we investigate the problem of non-fragile H∞ fuzzy control design for continuous Takagi Sugeno (T-S) fuzzy systems with uncertainties, external disturbance and unmeasurable state variables. For the case of controller and observer gain additive variations, we propose a new solution of the fragility problem by developing the non-fragile design schemes ensuring the asymptotic stability and H∞ performance for the resulting closed loop systems. By considering a fuzzy Lyapunov function and by introducing slack variables, we propose the new sufficient stabilization conditions formulated in LMI constraints which can be easily solved using the convex optimization tools. The effectiveness the proposed results are illustrated through three numerical examples.

A new approach to non-fragile H ∞ observer-based control for discrete-time fuzzy systems

In this article, a new approach regarding H ∞ and non-fragile stability analysis and observer-based controller synthesis problem for a class of discrete-time fuzzy systems is investigated. The multiplicative gain variations under consideration are contained in both the controller gain and observer gain. By defining a basis-dependent Lyapunov function and introducing some additional matrix variables, new sufficient conditions are derived to guarantee the stability of the non-fragile H ∞ observer-based control system. Seeking computational convenience, the developed results are cast in the format of linear matrix inequalities and two numerical examples are presented to illustrate the feasibility of theoretical developments.

DELAY-DEPENDENT H∞ RESILIENT OUTPUT FUZZY CONTROL FOR NONLINEAR DISCRETE-TIME SYSTEMS WITH TIME-DELAY

This paper is concerned with the problem of non-fragile (resilient) H∞ control for a class of state-delay nonlinear discrete-time systems described by (TS) fuzzy models where both the state feedback and static output feedback are investigated. Based on basis-dependent Lyapunov-krasovskii function, sufficient conditions are derived to achieve the system stability and the H∞ performance. The linear matrix inequality (LMI) approach is proposed to obtain the state-feedback gains, and a homotopy-based iterative LMI algorithm is developed to get the static output feedback gains. An illustrative example shows the effectiveness and the feasibility of the theoretical developments.

Robust reliable guaranteed cost piecewise fuzzy control for discrete-time nonlinear systems with time-varying delay and actuator failures

In this paper, we investigate the delay-dependent robust reliable guaranteed cost (RRGC) fuzzy control problem for discrete-time nonlinear systems with time-varying delays. The delays may simultaneously appear in the state and in the control input. Also, both parametric uncertainties and control component failure may exist. Through Takagi–Sugeno fuzzy modelling of nonlinear delayed-systems and based on an appropriate piecewise Lyapunov-Krasovskii functional, a piecewise fuzzy controller is designed. Sufficient conditions for the existence of a RRGC controller are derived in terms of linear matrix inequalities (LMIs). Furthermore, a suboptimal RRGC fuzzy controller is given by means of a convex optimization procedure with LMI constraints which can not only guarantee the stability of the closed-loop fuzzy system, but also provides an optimized upper bound of the given cost performance despite possible actuator faults. Two numerical examples are presented in this paper to illustrate the feasibility of the theoretical developments.

Adaptive fuzzy sliding mode controller for a class of SISO nonlinear time-delay systems

In this paper, we propose an adaptive fuzzy controller for a class of nonlinear SISO time-delay systems. The plant model structure is represented by a Takagi–Sugeno (T–S) type fuzzy system. The T–S fuzzy model parameters are adjusted online. The proposed algorithm utilizes the sliding surface to adjust online the parameters of T–S fuzzy model. The controller is based on adjustable T–S fuzzy parameters model and sliding mode theory. The stability analysis of the closed-loop system is based on the Lyapunov approach. The plant state follows asymptotically any bounded reference signal. Two examples have been used to check performances of the proposed fuzzy adaptive control scheme.

An indirect adaptive fuzzy sliding mode controller for a class of SISO non-linear systems

In this paper, we propose an indirect adaptive fuzzy controller for a class of SISO non-linear systems. The plant model structure is represented by a Takagi-Sugeno (T-S) type fuzzy system. The parameters of the T-S fuzzy model are adjusted online; the proposed algorithms are based on sliding manifold. The indirect adaptive fuzzy controller is based on a adjustable T-S fuzzy parameters model and sliding mode theory. The analysis of the stability of the adaptive algorithms is based on the Lyapunov approach. The plant state tracks asymptotically any bounded reference input signal. Inverted pendulum and mass spring damper are two examples used to check performances of the proposed fuzzy adaptive control scheme.

Direct fuzzy adaptive control based on sliding surface for a class of SISO non-linear systems

In this work we are interested in direct fuzzy adaptive control. The continuous SISO non-linear system is presented by the Takgi-Sugeno type fuzzy state model. The strategy of reference model direct adaptive control theory is presented then the adaptive fuzzy adjustment algorithm is presented. The control law includes two terms. The first is responsible to stabilise the plant is computed based on PDC method. The second constitutes the feed forward gain. All the parameters of the controller are adjusted online. The adjustment algorithm of the controller parameters exploits the sliding surface to profit of robustness of sliding mode control. The stability analysis of the closed-loop system has been proven using the Lyapunov approach. The single synchronous generator coupled to the infinite-bus power system is used to check the performances of the proposed control scheme.

T–S Fuzzy Algorithm for Photovoltaic Panel

In this paper, we propose a new Maximum Power Point Tracking algorithm for a photovoltaic conversion chain. The system energy conversion, which includes photovoltaic array panel, DC/DC converter, and load, is described by some nonlinear equations. The operating point depends mainly on climatic parameters and load. For each temperature and irradiation pair, there exists only one operating point for maximum energy. The Takagi–Sugeno fuzzy system has been used to model energy conversion system. The proposed algorithm which constitutes the controller is based on modified parallel distributed compensation. The controller has two terms, the first includes the errors and the second includes the integrators of the errors. The controller parameters have been computed based on linear matrices inequalities. Some simulations have been done to check the performance of the proposed algorithm.

MPPT Algorithm for Photovoltaic Panel Based on Augmented Takagi-Sugeno Fuzzy Model

This paper deals with the Maximum Power Point Tracking (MPPT) for photovoltaic energy system. It includes photovoltaic array panel, DC/DC converter, and load. The operating point for photovoltaic energy system depends on climatic parameters and load. For each temperature and irradiation pair, there exists only one optimal operating point which corresponds to the maximum power transmitted to the load. The photovoltaic energy system is described by nonlinear equations. It is transformed into an augmented system which is described with a Takagi-Sugeno (T-S) fuzzy model. The proposed MPPT algorithm which permits transfering the maximum power from the panel to the load is based on Parallel Distributed Compensation method (PDC). The control parameters have been computed based on Linear Matrix Inequalities tools (LMI). The Lyapunov approach has been used to prove the stability of the system. Some reliable simulation results are provided to check the efficiency of the proposed algorithm.

Robust sensor faults estimation with H∞ performance for Lipschitz uncertain nonlinear systems

This paper treats with the issue of disturbances, noises, uncertainties and sensor faults estimation for uncertain nonlinear systems whose nonlinearity satisfies the Lipschitz condition. The general idea of this approach is to establish an augmented model by supposing the sensor faults as an auxiliary state. In order to ensure the robustness of the proposed observer and guaranteed the convergence conditions, we have used the Lyapunov theory and the H∞ criterion. So as to illustrate the design approach a control system of satellite attitude is presented.