Takagi-Sugeno Fuzzy Representation Research Articles

Autonomous Vehicle State Estimation and Mapping Using Takagi-Sugeno Modeling Approach.

This paper proposes an optimal approach for state estimation based on the Takagi–Sugeno (TS) Kalman filter using measurement sensors and rough pose obtained from LIDAR scan end-points matching. To obtain stable and optimal TS Kalman gain for estimator design, a linear matrix inequality (LMI) is optimized which is constructed from Lyapunov stability criteria and dual linear quadratic regulator (LQR). The technique utilizes a Takagi–Sugeno (TS) representation of the system, which allows modeling the complex nonlinear dynamics in such a way that linearization is not required for the estimator or controller design. In addition, the TS fuzzy representation is exploited to obtain a real-time Kalman gain, avoiding the expensive optimization of LMIs at every step. The estimation schema is integrated with a nonlinear model-predictive control (NMPC) that is in charge of controlling the vehicle. For the demonstration, the approach is tested in the simulation, and for practical validity, a small-scale autonomous car is used.

TS fuzzy prediction-based SVC compensation of wind farms flicker: A dual-UKF approach

Fast fluctuations in wind farm power produce voltage flicker in the network. One way to mitigate the flicker is to place a static VAr compensator (SVC). Due to the operating delay of SVCs, it is essential to predict the wind farm reactive power. Here, a novel fuzzy nonlinear modeling approach is suggested and used in the one-step-ahead prediction of the power characteristics. The base of the developed fuzzy modeling is the Takagi-Sugeno fuzzy representation and a dual-unscented Kalman filter (D-UKF). In other words, a nonlinear TS fuzzy system is trained online via the D-UKF. The forecasted value is used as the SVC's reference signal. A large number of the actual data gathered from a wind farm are used for the performance evaluation. These data are collected in winter and summer for different climate situations. Using the actual data a current source with changing amplitude and phase which are updated every half-cycle is used to model the wind farm. Numerical results, including the flicker indices, confirm the improvement in the SVC's performance.

TS Fuzzy Observer-Based Controller Design for a Class of Discrete-Time Nonlinear Systems

This article presents an observer-based control design approach for a class of nonlinear discrete-time systems. The model nonlinearities are handled in two ways: 1) A Takagi–Sugeno fuzzy representation is used for nonlinearities that depend on measured states, and 2) nonlinearities that depend on unmeasured states are kept in their original form and handled using a slope-bound condition. The observer-based controller design conditions are given as linear matrix inequalities. The approach we propose significantly improves results in the literature by providing less restrictive design conditions. These improvements are illustrated in a detailed analytical and numerical comparison on a synthetic example; while a pendulum-on-a-cart example shows that the approach works both in simulation and in real-time experiments.

Robust stabilization and tracking control schemes for disturbed multi-input multi-output Hammerstein model in presence of approximate polynomial nonlinearities

This article presents robust stabilization and tracking control problems for multi-input multi-output Hammerstein model with external disturbances. This model is characterized by static nonlinear elements followed by a linear dynamic block. Moreover, the unknown parameters of the identified mathematical model are estimated using the multivariable output error state space subspace algorithm. Unlike the general control strategy that used the nonlinearity inversion method, the nonlinearities are supposed not bijective. In this context, inverse nonlinear functions of polynomial structure are suggested in this article. Furthermore, the composition of the static nonlinear elements and their approximate inverses in series with the linear dynamic block are then decomposed into a set of linear parts using the Takagi–Sugeno fuzzy representation. Consequently, new sufficient stability conditions with decay rate and disturbance attenuation using the [Formula: see text] criterion and linear matrix inequality tools are discussed. Finally, simulation studies are provided to illustrate the merit of our purpose.

Adaptive sliding mode fault tolerant control design for uncertain nonlinear systems with multiplicative faults: Takagi–Sugeno fuzzy approach

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 [Formula: see text] 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.

Unknown inputs observer design for fuzzy systems with application to chaotic system reconstruction

This paper deals with the observer design for nonlinear systems in Takagi–Sugeno fuzzy representation. Based on the Lyapunov method and Linear Matrix Inequalities (LMI) formulation, sufficient conditions have been derived for observers design. Unknown inputs can result either from model uncertainty, faults or due to the presence of unknown external excitation. These different results have been widely applied in the field of fault diagnosis and fault tolerance. Based on unknown inputs observer design, secure communication and chaotic system reconstruction problems have been also studied. Examples are given to illustrate a chaotic cryptosystem procedure where the plaintext (message) is encrypted using chaotic signals at the drive system side and the plaintext is retrieved via the designed unknown input observer.

Fuzzy methodology for frequency response estimation of uncertain dynamic systems

SUMMARYFuzzy frequency response: definition and analysis for uncertain dynamic systems is proposed in this paper. In terms of transfer function, the uncertain dynamic system is partitioned into several linear sub‐models and organized according to Takagi–Sugeno fuzzy representation. The main contribution of this paper is to demonstrate through the proposal of a Theorem that fuzzy frequency response is a boundary in the magnitude and phase Bode plots. Low‐ and high‐frequency analysis of fuzzy dynamic model is obtained by varying the frequency ω from zero to infinity. Copyright © 2011 John Wiley & Sons, Ltd.

Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation

Takagi-Sugeno (TS) fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input-output submodels. In this paper, the TS fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation. The TS fuzzy representation of a nonlinear system subject to actuator saturation is presented. In our TS fuzzy representation, the modeling error is also captured by norm-bounded uncertainties. A set invariance condition for the system in the TS fuzzy representation is first established. Based on this set invariance condition, the problem of estimating the domain of attraction of a TS fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality (LMI) optimization problem. By viewing the state feedback gain as an extra free parameter in the LMI optimization problem, we arrive at a method for designing state feedback gain that maximizes the domain of attraction. A fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction. An inverted pendulum is used to show the effectiveness of the proposed fuzzy controller.

Stability analysis of uncertain nonlinear systems with delay using Takagi-Sugeno fuzzy representation

This paper outlines sufficient asymptotic stability conditions in terms of LMIs (Linear Matrix Inequality), for a large class of nonlinear uncertain delay systems with a single unknown delay. Both delay-dependent and delay-independent stabilities are investigated. The proposed approach is based on a transformation of the delay-differential equation: the resulting system is similar to Takagi-Sugeno’s model, mainly used in multimodel approaches. The stability analysis is performed using Liapunov-Krasovskii functionals.