The application of direction basis function networks for adaptive control on nonlinear continuous time systems

For a class of nonlinear continuous time systems x = f(x) + Bu +d, when the nonlinear function f(x) is bounded or satisfies linear growth condition with unknown growth coefficient, we first prove that x falls into a compact set, then two adaptive regulators are proposed based on the approximation capability of direct basis function networks. According to the Lyapunov stability theory, the control algorithms are proved to be globally stable, the state of closed-loop system is uniformly and ultimately bounded and the control law is continuous.