PERSISTENCE OF EXCITATION CONDITIONS IN PASSIVE LEARNING CONTROL

摘要

This article proves exponential convergence of both the system state and parameter estimates in passive learning control applications. The analysis is valid for any linear in parameter approximator. In addition, the article presents a specific analysis pertinent to approximators that are composed of basis elements with local support. This class of approximators includes many of those commonly used: radial basis functions, splines, wavelets, certain fuzzy systems, and CMAC networks. In particular, the analysis shows that as long as a reduced dimension subvector of the regressor vector is persistently exciting, then a specialized form of exponential convergence will be achieved.