In this paper, the controllability property for a class of Takagi-Sugeno (T-S) fuzzy models is analyzed, while a fully nonlinear stabilizer is designed in a practical way. It is shown that global fuzzy stabilizers can be constructed in a nonconservative way by means of a relatively simple approach. The existence of such controllers depends on the fuzzy controllability conditions, which are derived in a straightforward way. The main advantage of the proposed approach is that the convergence of the closed-loop system can be imposed arbitrarily. Some examples are given in order to illustrate the validity of the method. Finally, the proposed controller is applied on an underactuated system known as “pendubot” and the results are compared with an stabilizer designed on the basis of LMIs.

An approach to design stabilizers and observers for a class of Multiple-Input Multiple-Output (MIMO) Takagi-Sugeno (TS) fuzzy models is developed on the basis of local gains and the searching for a set of interpolation functions capable of properly combining the aforementioned local gains. As expected, the existence of such interpolation functions depends on the controllability and observability properties of the overall multivariable TS fuzzy model. For that reason, practical controllability and observability tests are also proposed for MIMO TS fuzzy systems. Some numerical simulations are used in order to validate the efficacy of the method. Besides, the results are compared with an approach based on Linear matrix Inequalities (LMIs), namely Parallel Distributed Compensation (PDC).

This paper is devoted to solve the regulation problem on the basis of local regulators, which are combined using “new” membership functions. As a result, the exact tracking of references is achieved. The design of linear local regulators is suggested in this paper, but now adequate membership functions are computed in order to ensure the proper combination of the local regulators in the interpolation regions. These membership functions, which are given as mathematical expressions, solve the fuzzy regulation problem in a relative simple way. The form of the new membership functions is systematically derived for a class of Takagi-Sugeno (T-S) fuzzy systems. Some numerical examples are used to illustrate the viability of the proposed approach.

Based on the general structure of mechanical systems described by their state-space representation, the Takagi-Sugeno fuzzy modelling, and the controllability property of fuzzy systems, an algebraic and practical approach to compute the fuzzy gain capable of ensuring the stability property of the Takagi-Sugeno fuzzy model is proposed. The main idea consists of finding a continuous fuzzy gain such that, any linear behavior, defined by the adequate selection of eigenvalues, is induced in the closed-loop fuzzy system. Therefore, by continuity, if the fuzzy model is an approximation sufficiently close to the mechanical system, then such a nonlinear system is also stabilized by the fuzzy controller. A notable advantage of the proposed method, when compared with similar approaches, is the simplicity of the resulting gain. The validity of the approach is illustrated through the numerical simulation of a sufficiently complex nonlinear system.

The authors recently introduced a Kalman filter-based approach for estimating noise-contaminated unmodeled signals. However, in that work, the dimension of the Kalman filter depends on the complexity of the signals being estimated, which are not known a priori. This typically requires a trial-and-error process, often resulting in an excessively large filter dimension that complicates the method’s practical application. To overcome this problem, this paper proposes a solution for estimating complex, unmodeled, and noise-contaminated signals while simultaneously obtaining a low-dimensional dynamical model whose output approximates the actual noise-free signal. This is achieved by incorporating a fuzzy error covariance matrix into the standard linear Kalman filter algorithm. The proposed modification prevents the Kalman filter estimate from drifting away from the true signal and provides an alternative to the traditional abrupt resetting of the error covariance matrix. Notably, this modification can be seen as a soft reset of certain initial conditions and, as demonstrated, does not compromise the Kalman filter’s stability. Furthermore, the result shows that incorporating simple fuzzy logic concepts may substantially enhance the performance of some established algorithms.

The exact output regulation problem for Takagi-Sugeno (TS) fuzzy models, designed from linear local subsystems, may have a solution if input matrices are the same for every local linear subsystem. Unfortunately, such a condition is difficult to accomplish in general. Therefore, in this work, an adaptive network-based fuzzy inference system (ANFIS) is integrated into the fuzzy controller in order to obtain the optimal fuzzy membership functions yielding adequate combination of the local regulators such that the output regulation error in steady-state is reduced, avoiding in this way the aforementioned condition. In comparison with the steepest descent method employed for tuning fuzzy controllers, ANFIS approximates the mappings between local regulators with membership functions which are not necessary known functions as Gaussian bell (gbell), sigmoidal, and triangular membership functions. Due to the structure of the fuzzy controller, Levenberg-Marquardt method is employed during the training of ANFIS.