Takagi-Sugeno Form Research Articles

Sampled-data [formula omitted] fault detection and isolation for nonlinear systems in T–S form: An approximate model approach

A direct discrete-time design methodology for the sampled-data fault detection and isolation (FDI) problem is proposed for a nonlinear system in Takagi–Sugeno form. The generalized observer scheme is adopted, accompanied by a bank of the sensors' number of observers. A sufficient condition to find observer and residual gains, based on an accessible approximate—rather than unavailable exact—discrete-time model is proposed in terms of matrix inequalities so that it exhibits H−/H∞ performance and asymptotic stability. An algorithm involving a convex optimization is presented using the cone complementary linearization technique. We show that the FDI observer ensures (modified) H−/H∞ performance and Lagrange stability, when it is connected to the actual nonlinear system.

Performance recovery of intelligent digital redesign for observer‐based output feedback under immeasurable premise variables

This study discusses an intelligent digital redesign (IDR) for observer-based output-feedback controllers in Takagi–Sugeno form under immeasurable premise variables. A delta operator that asymptotically connects an analogue control system with its discrete-time model is adopted. The condition for the IDR problem with stability is proposed in terms of matrix inequality. The authors show that the proposed IDRed sampled-data controller recovers the analogue control performance from the perspective of the closed-loop trajectory under the fast sampling limit.

Nonquadratic ${{\cal H}}_\infty$ Stabilization Conditions for Observer-Based T–S Fuzzy Control Systems

This paper investigates the nonquadratic output-feedback stabilization problem for nonlinear systems in Takagi-Sugeno's (T-S) form. To achieve improved performance in the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sense, this paper provides two kinds of relaxation techniques: one for the case where all premise variables are measurable and one for the case where the premise variables are immeasurable. In particular, the emphasis of the second technique is the use of estimated premise variables for nonquadratic Lyapunov functions.

Decoupled Nested LMI conditions for Takagi-Sugeno Observer Design

This work extends recent investigations on control design of continuous-time nonlinear models to non-quadratic observer design. The models under consideration are exactly rewritten in the Takagi-Sugeno form. By means of the Finsler's Lemma or a Tustin-like transformation, the progressively complex observer gains and the Lyapunov function are decoupled, thus providing the flexibility of using a quadratic Lyapunov functions while preserving the non-quadratic nature of the observer. Conditions obtained are expressed as linear matrix inequalities which are efficiently solved by convex optimization techniques. Examples are provided to show the effectiveness of the proposed approach.

Robust Sensor Fault-Tolerant Control Scheme for Wind Turbines with Hydrostatic Transmission

In this paper, an observer bank design for sensor fault diagnosis and fault-tolerant control schemes for wind turbines with hydrostatic transmissions are presented. The sensor faults are detected and isolated by several observers using different sensor signals. Starting from a detailed problem formulation that takes into account structured model uncertainties and external inputs, the sufficient conditions for robust observer and controller design are obtained by using multiple Lyapunov functions. Thereafter, the drive train is modeled and the resulting nonlinear continuous-time system is transformed into a discrete-time Takagi-Sugeno form. Within the latter model, a fault-tolerant control scheme is set up by means of a switched observer-based parallel distributed controller (PDC) structure, where only the observed state vector, which is not affected by sensor faults, is fed back. Finally, the obtained results are applied to a fault tolerant speed control for wind turbines with hydrostatic transmission in the presence of permanent pressure or displacement sensor faults.

Asymptotically necessary and sufficient stability conditions for discrete-time Takagi–Sugeno model: Extended applications of Polya's theorem and homogeneous polynomials

The stability and stabilization conditions of the nonlinear system in Takagi–Sugeno's form are considered. The homogeneously polynomially nonquadratic (HPNQ) Lyapunov functions and homogeneously polynomially parameterized (HPP) state feedback laws are adopted. By generalizing the procedure based on the Polya's theorem, the asymptotically necessary and sufficient (ANS) stability and stabilization conditions in the case of HPNQ Lyapunov functions and HPP control laws are reformulated. The major contribution of this paper is to give the parallel results using the multiple indices, so that the slack matrices can be extensively utilized to improve the numerical efficiency. The effectiveness of the results is illustrated by the numerical examples.

Non‐fragile H ∞ fuzzy filtering for discrete‐time non‐linear systems

This study is concerned with the problem of non-fragile H ∞ filtering for discrete-time non-linear systems in Takagi–Sugeno's form. Additive interval uncertainty that reflects imprecision in filter implementation because of finite word length effects is considered. Based on vertex theory and probabilistic robust approach, deterministic and randomised filtering algorithms are proposed, respectively. Compared with the deterministic algorithm, the randomised algorithm has acceptable computational complexity, especially for high-dimensional systems. Two examples are given to illustrate the effectiveness of the proposed algorithms.

Multi-model identification of a fractional non linear system

Takagi-Sugeno fuzzy models have proved to be a powerful tool for non-linear system identification. Due to their simplicity, linear integer sub-models are mainly used in such structure. In this paper multi-model approach, based on Takagi-Sugeno form is used to perform identification of fractional non-linear systems, applying fractional local models. In this purpose, an output error method is used, and the algorithm is extended to the fractional case. Numerical simulations are performed in order to analyze the two sub-models: integer and fractional, fitting ability to approximate the non linear system behaviour. The validation of the method is carried out on real data of the heat diffusion.

Decentralized Load-Frequency Control of Large-Scale Nonlinear Power Systems: Fuzzy Overlapping Approach

This paper develops a design methodology of a decentralized fuzzy load-frequency controller for a large-scale nonlinear power system with valve position limits on governors. The concerned system is locally exactly modeled in Takagi-Sugeno's form. Sufficient design condition for uniform ultimate boundedness of the closed-loop system is derived based on the overlapping decomposition. Convergence of all incremental frequency deviations to zero is also investigated. A simulation result is provided to visualize the effectiveness of the proposed technique.

타카기-수게노 형태의 비선형 시스템의 효율적 분산 샘플치 제어: 중복 지능형 디지털 재설계 접근법

본 논문은 대규모 비선형 시스템의 분산 샘플치 제어 문제를 논한다. 대상 시스템은 타카기-수게노 퍼지모델로 표현된다. 중복분해 기법을 이용하여 아날로그 분산 제어기를 설계하고 이것은 지능형 디지털 재설계 기법에 의하여 샘플치 제어기로 변환된다. 설계조건은 선형행렬부등식으로 표현된다. 모의실험 결과에 의하여 제안된 기법의 효용성을 입증한다. This paper discusses a decentralized sampled-data control problem for large-scale nonlinear systems. The system is represented in Takagi-Sugeno's form. Next, we design a decentralized analog controller based on the overlapping decomposition technique. The final step is to apply the intelligent digital redesign scheme for converting the analog controller into the sampled-data one. Design condition is represented in terms of linear matrix inequalities. A simulation result is provided for the effectiveness of the proposed design method.

Sampled-data observer-based output-feedback fuzzy stabilization of nonlinear systems: Exact discrete-time design approach

This paper presents a new direct discrete-time design methodology of a sampled-data observer-based output-feedback fuzzy controller for a class of nonlinear system that is exactly modeled in Takagi–Sugeno's form at least locally. A fundamental yet challenging issue in this direction is the unavailability of the exact discrete-time model of the nonlinear plant in a closed form. In contrast to the earlier works that are based on an approximate discrete-time model thus the stability obtained in the design step is not preserved in the implementation step, we employ an exact discrete-time fuzzy model in an integral form. Sufficient asymptotic stabilization conditions are investigated in the discrete-time Lyapunov sense. We then show that the resulting sampled-data controller indeed asymptotically stabilizes the nonlinear plant. An example is provided to illustrate the effectiveness of the proposed methodology.

Stabilization via extended nonquadratic boundedness for constrained nonlinear systems in Takagi–Sugeno's form

This paper studies stabilization of the Takagi–Sugeno fuzzy system with input and state constraints and bounded noise. The technique of extended nonquadratic boundedness is proposed based on the existing quadratic boundedness. Under the non-parallel distributed compensation law, the state of the closed-loop system is stabilizing to a neighborhood of the origin specified via an extended nonquadratic Lyapunov function. The existing technique for relaxing the linear matrix inequality conditions can be properly applied to obtain computationally tractable stability conditions. A simulation example is given to show the effectiveness of the controller.

Sensor fault detection observer design for nonlinear systems in Takagi–Sugeno’s form

This paper addresses sensor fault detection observer design problems for discrete- and continu- ous-time nonlinear systems in Takagi-Sugeno's (T-S) form. It is desired that the fault detection observer is as sensitive to fault and robust against disturbance as possible. To this end, sufficient conditions for stable T-S fuzzy model-based observer design with H−/H∞ performance are derived in terms of linear matrix inequalities in both cases. An example on the backing-up problem of a truck-trailer is provided to illustrate the effectiveness of the proposed methodol- ogy.

Trajectory Tracking for Nonholonomic Mobile Robots based on Extended Models

AbstractThis paper offers a novel approach to circumvent some problems derived from the nonholonomic structure of a two-wheeled mobile robot. It is shown that suitably extending a well-known third-order error model, new kinematics are found that allow direct Lyapunov-based control design as well as straightforward PDC control for its Takagi-Sugeno form. In the latter case, controllability issues are overcome thanks to the proposed design which decouples the uncontrollable mode from the rest of the system. Illustrative examples are provided that show the effectiveness of this technique.

Individual Exhaust gas mass flow estimation using a periodic observer Design

AbstractIn this paper, we propose a method to estimate the individual exhaust mass flow rate for a gasoline IC engine. In order to achieve this goal a periodic observer for a class of non linear models in the discrete Takagi-Sugeno form is designed. The adopted framework to prove the stability of the observer is based on the Lyapunov theory and use linear matrix inequality (LMI) formalism. Some simulation and experimental results are provided to show the efficiency of the proposed observer.

Fuzzy Filter Design for Nonlinear Systems in Finite-Frequency Domain

This paper is concerned with the problem of fuzzy-filter design for discrete-time nonlinear systems in the Takagi-Sugeno (T-S) form. Different from existing fuzzy filters, the proposed ones are designed in finite-frequency domain. First, a so-called finite-frequency l2 gain is defined that extends the standard l2 gain. Then, a sufficient condition for the filtering-error system with a finite-frequency l2 gain is derived. Based on the obtained condition, three fuzzy filters are designed to deal with noises in the low-, middle-, and high-frequency domain, respectively. The proposed fuzzy-filtering method can get a better noise-attenuation performance when frequency ranges of noises are known beforehand. An example about a tunnel-diode circuit is given to illustrate its effectiveness.

Fuzzy Stabilization of Nonlinear Systems Under Sampled-Data Feedback: An Exact Discrete-Time Model Approach

This paper addresses stabilization problems for a nonlinear system via a sampled-data fuzzy controller. The nonlinear system is assumed to be exactly modeled in Takagi-Sugeno's form, at least locally. Unlike the conventional direct discrete-time design approach based on an approximate discrete-time model, the sampled-data fuzzy controllers are designed based on an exact discrete-time model. Sufficient design conditions are formulated in terms of linear matrix inequalities. It is shown that whenever the exact discrete-time fuzzy model is asymptotically stabilizable via the sampled-data fuzzy controller uniformly bounded in the state, then so is the original nonlinear system. A numerical example is given to illustrate the effectiveness of the proposed methodology.

Control Law Proposition for the Stabilization of Discrete Takagi–Sugeno Models

This paper deals with the stabilization of a class of discrete nonlinear models, namely those in the Takagi-Sugeno form; its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate Lyapunov functions and an enhanced control law. It is shown that the use of the aforementioned Lyapunov function leads to less-pessimistic solutions. The usefulness of the new control law is shown through several examples.

Reformulation of LMI-based stabilisation conditions for non-linear systems in Takagi–Sugeno's form

This article addresses the stabilisation of non-linear systems represented by a discrete-time Takagi–Sugeno model. Based on an extended non-quadratic Lyapunov function and a non-parallel distributed compensation (non-PDC) law, some additional slack matrices are introduced. Compared with the existing methods, which collect the interactions among the subsystems into a sequence of collection matrices, the new method re-collects the newly introduced slack matrices into another collection matrix. In this way, a stability result more relaxed than some existing ones are obtained. Further, the convexity of the fuzzy blending rules is utilised, with a further improved result obtained. The corresponding robust stability results are also proposed. The effectiveness of the new results is validated by two simulation examples.

Nonquadratic Stabilization Conditions for a Class of Uncertain Nonlinear Discrete Time TS Fuzzy Models: A New Approach

The discrete-time uncertain nonlinear models are considered in a Takagi-Sugeno form and their stabilization is studied through a non- quadratic Lyapunov function. The classical conditions consider a one- sample variation, here, the main results are obtained considering k samples variation, i.e., Delta <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> V(x(t)) = V(x(t + k)) - V(x(t)). The results are shown to always include the classical cases, and several examples illustrate the effectiveness of the approach.