Nonlinear control theory and chaotic dynamical systems

Abstract

The author treats the role of multiparameters in the existence of solutions of highly coupled nonlinear dynamical systems and numerical computation of solutions. An attempt is made to develop methods applicable to control of highly coupled nonlinear dynamical systems containing multiparameters which may have a chaotic behavior. Due to the loss of components of a nonlinear dynamical system it may have a chaotic solution instead of a stable controllable observable solution. The basic mathematics involved in such nonlinear multiparameter systems is treated so as to make sufficient changes in the system without losing the system completely as far as applications are concerned. This requires the development of time-dependent multiple objective numerical algorithms involving time to acomplish various desired maneuvers results obtained can be used to establish feedback control laws for nonlinear dynamical systems of a specified form. >