Universal stabilization using control Lyapunov functions, adaptivederivative feedback, and neural network approximators

摘要

In this paper, the problem of stabilization of unknown nonlinearndynamical systems is considered. An adaptive feedback law is constructednthat is based on the switching adaptive strategy proposed by the authornand uses linear-in-the-weights neural networks accompanied withnappropriate robust adaptive laws in order to estimate thentime-derivative of the control Lyapunov function (CLF) of the system.nThe closed-loop system is shown to be stable; moreover, the state vectornof the controlled system converges to a ball centered at the origin andnhaving a radius that can be made arbitrarily small by increasing thenhigh gain K and the number of neural network regressor terms. No growthnconditions on the nonlinearities of the system are imposed with thenexception that such nonlinearities are sufficiently smooth. Finally, wenmention that neither the system dynamics or the CLF of the system neednto be known in order to apply the proposed methodology