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

For a class of nonlinear continuous time systems xdot = 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 ultimately bounded and the control law is continuous.