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

The problem of stabilization of unknown nonlinear dynamical systems is considered. An adaptive feedback law is constructed; this feedback law is based on the switching adaptive strategy proposed by the author (1996) and uses linear-in-the-weights neural networks accompanied with appropriate robust adaptive laws in order to estimate the time-derivative of the control Lyapunov function (CLF) of the system. The closed-loop system is shown to be stable; moreover, the state vector of the controlled system converges to a ball centered at the origin and having radius that can be made arbitrarily small by increasing the high gain K and the number of neural network regressor terms. No growth conditions on the nonlinearities of the system are imposed with the exception that such nonlinearities are sufficiently smooth