Linear Function Of Input Variables Research Articles

Variable Gain Takagi–Sugeno Fuzzy Logic Controllers

Most of the Takagi-Sugeno Fuzzy (TSF) systems found in the literature have only used linear functions of input variables as rule consequent and can be called as TSF Models with Fixed Coefficient (TSFMFC). This paper presents TSF model with variable coefficient (TSFMVC) which can more closely approximate a class of nonlinear systems, nonlinear dynamic systems, and nonlinear control systems. It is also shown that TSFMFC is a special case of TSFMVC. Moreover Variable Gain TSF Controller (VGTSFC) is defined and it performs better, as shown by the simulation results, when compared with Fixed Gain TSF Controller (FGTSFC).

A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators

Universal approximation is the basis of theoretical research and practical applications of fuzzy systems. Studies on the universal approximation capability of fuzzy systems have achieved great progress in recent years. In this paper, linear Takagi-Sugeno (TS) fuzzy systems that use linear functions of input variables as rule consequent and their special case, named simplified fuzzy systems that use fuzzy singletons as rule consequent, are investigated. On condition that overlapped fuzzy sets are employed, new sufficient conditions for simplified fuzzy systems and linear TS fuzzy systems as universal approximators are given, respectively. Then, a comparative study on existing sufficient conditions is carried out with numeric examples.

Automated test data generation using an iterative relaxation method

An important problem that arises in path oriented testing is the generation of test data that causes a program to follow a given path. In this paper, we present a novel program execution based approach using an iterative relaxation method to address the above problem. In this method, test data generation is initiated with an arbitrarily chosen input from a given domain. This input is then iteratively refined to obtain an input on which all the branch predicates on the given path evaluate to the desired outcome. In each iteration the program statements relevant to the evaluation of each branch predicate on the path are executed, and a set of linear constraints is derived. The constraints are then solved to obtain the increments for the input. These increments are added to the current input to obtain the input for the next iteration. The relaxation technique used in deriving the constraints provides feedback on the amount by which each input variable should be adjusted for the branches on the path to evaluate to the desired outcome.When the branch conditions on a path are linear functions of input variables, our technique either finds a solution for such paths in one iteration or it guarantees that the path is infeasible. In contrast, existing execution based approaches may require an unacceptably large number of iterations for relatively long paths because they consider only one input variable and one branch predicate at a time and use backtracking. When the branch conditions on a path are nonlinear functions of input variables, though it may take more then one iteration to derive a desired input, the set of constraints to be solved in each iteration is linear and is solved using Gaussian elimination. This makes our technique practical and suitable for automation.