The design of feedback laws for systems characterized by complicated nonlinear dynamical behavior is a challenging research task which has attracted an increasing interest in recent years. Advances in nonlinear control theory will substantially improve the design of control systems for light-weighted robot arms, for autopilots and guidance systems of highly maneuverable aircrafts, increase the flexibility and energy efficiency in the regulation of chemical plants, facilitate the real-time reconfiguration of a control system after the occurrence of a failure. Among the many problems which must be confronted, a most important one is the desing of feedback laws achieving tracking of prescribed exogenous commands and rejection of exogenous disturbances. The approaches to the problem of tracking/rejection of exogenous inputs in a control system depend upon the model chosen to describe the family of exogenous inputs which are expected to affect the system. If no model is available, an appealing strategy -which revealed itself very powerful and attractive in the case of linear systems- is to base the design on the worst possible situation. For instance, in the frequency domain, the feedback laws are designed so as to minimize the maximal amplitude of the frequency response to the exogenous inputs. This research project would contribute to the extension of these design methodologies to systems described by nonlinear mathematical models. Using methods and results from the geometric theory of control systems, the theory of differential games and the qualitative theory of dynamical system, the purpose of the research is to establish sufficiently general results about existence and actual design of feedback control laws achieving attenuation of unmodeled external disturbances.
