Nonlinear System Design: Adaptive Feedback Linearization with Unmodeled Dynamics.

摘要

The main goal of this research has been to develop a unified geometric-asymptotic-adaptive methodology for feedback design of nonlinear control systems. Such a methodology is needed because the existing differential geometric results are restrictive and often violated by small modeling errors. Effects of these errors can be analyzed asymptotically by singular perturbation methods, which, however, are still lacking a clear geometric interpretation. Neither geometric, nor perturbational problem formulations can cope with large parametric uncertainty, for which an adaptive approach seems suitable. Conversely, both geometric and asymptotic techniques can become constructive steps in the design of an adaptive scheme and in the analysis of its robustness. In our research these three heretofore separate techniques have been to be merged into a methodology which eliminates their individual shortcomings. In a separate research direction we have initiated a study of systems with practically important nondifferentiable nonlinearities such as dead-zone, backlash and hysteresis. These systems can not be analyzed by existing methods.