An optimization approach to estimating stability regions using genetic algorithms

The problem of estimating regions of asymptotic stability for nonlinear dynamic systems is considered as an optimization problem. Genetic algorithms are then proposed to solve the resulting optimization problems. Three test systems are used to evaluate the performance of the proposed genetic algorithms. The test systems are 6th, 8th, and 17th order nonlinear power electronics systems. The performance of the genetic algorithms are also compared with that of the classical Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm and the simplex method of Nelder and Mead. Time domain simulations of the test systems are performed to validate the results of the optimization algorithms. Issues involved with the successful implementation of genetic algorithms to estimate regions of attraction are discussed. It is observed that genetic algorithms outperform the classical optimization algorithms in estimating regions of asymptotic stability.