A Discrete Approximate Solution for the Asymptotic Tracking Problem in Affine Nonlinear Systems

Abstract: This paper deals with a general tracking problem for affine nonlinear systems. The approach is quite general. In fact, a Lyapunov function is chosen and a stabilizing structure of the solution to solve a general tracking problem is proposed. Nevertheless, the general final solution is a discrete one and consists of an approximation of the continuous solution. Moreover, there is an assumption which should be guaranteed in order to obtain the explicit expression of the digital final solution. Despite this assumption the solution remains valid for a wide range of applications according to practical tests. The importance of the solution consists of its generality. In fact, any kind of nonlinearity could be taken into account. Also technical nonlinearities such as hysteresis, saturations, and creep could be considered.