Approximation property of partition of unity and its applications

摘要

The linear combination of certain partition of unity,subordinate to certain open covering of a compact set,is proved to be capable of approximating to a continuous function at arbitrarily precision.By using proper open covering and partition of unity,the robust nonlinear controllers and adaptive laws are designed for a class of nonlinear systems with uncertainties.The states and parameters of the closed-loop systems can be stabilized in the meaning of UUB (uniformly ultimately bounded) via the robust nonlinear controllers and adaptive laws.Finally,an example shows the validity of method in this paper.