Well-Posedness of Singularly Perturbed Nash Games.

摘要

This thesis applies singular perturbation techniques to linear-quadratic infinite-time zero- and nonzero-sum closed-loop Nash games for systems with fast and slow modes. For the nonzero-sum game, it is shown via example that the problem is ill-posed with respect to the usual singular perturbation reduction techniques. A physically justified modification of the performance indices consistent with inadequate modeling of fast dynamics is presented which results in a well-posed problem when the natural perturbation method is applied. In the case of adequate modeling of fast dynamics, a hierarchical reduction procedure is presented which transfers fast game information to a modified slow game which leads to a well-posed problem with respect to a modified reduction procedure. For the zero-sum game, it is shown that it does not matter whether the fast modes are due to inadequate or accurate modeling and the usual reduction procedure of singular perturbation leads to a well-posed problem. (Author)