Tuning of a TS Fuzzy Output Regulator Using the Steepest Descent Approach and ANFIS

Abstract

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.

On the output regulation for linear fractional systems

“…From ( 13), it can be readily observed that e ss (t) tends to zero if: 1) all the eigenvalues of matrix A − BK are in the left side of the complex plane, and 2) AΠw(t)) + BΨw(t) + P w(t) = Sw(t) , which can be rewritten as (7). However, notice that ( 7) is a matrix equation involving n × ℓ + p × ℓ unknowns in n × ℓ equations.…”

“…It is important to mention that the nonlinear regulator relies on the solution of a set of nonlinear partial differential equations, which, in some cases, are very difficult of obtain. Thus, in order to overcome such a drawback, in [4][5][6][7][8][9] the linear solution has been extended to the nonlinear area by means of area of the fractional-order differential equations has been gaining interest among researchers, including those working on control topics. For example, the designing of observers of fractional order has been analyzed in [12].…”

Synchronization of Discrete-Time Chaotic Fuzzy Systems by means of Fuzzy Output Regulation Using Genetic Algorithm

“…Unfortunately these equations in many cases are too difficult to solve in a practical manner. For this reason in [20] the approach based on the weighted summation of local linear regulators is presented and in [21] the new membership functions in the regulator are approximated by soft computing techniques.…”

Polynomial Fuzzy-Model-Based Control Systems: Stability Analysis via Approximated Membership Functions Considering Sector Nonlinearity of Control Input

“…The relaxation techniques contain the concept of parallel distributed compensation (PDC) and slack matrices through S-procedure [29]. Despite of the research on stability analysis, the concept of fuzzy control was extended to other control problems such as output feedback control [30]- [32].…”