An algorithm for trajectory tracking in sampled data nonlinear systems

In this work we study the trajectory tracking problem in sampled-data nonli near systems. We assume the following restrictions on the synthesis of the controller: a) we know the values of the states only at the sampling instan ts, b) the control law to be applied must be constant between sampling inst ants. If we have a control law that solves the problem without verifying a) and b ), we can attemp to implement it via the Sampling and Zero Order Hold (SZH) in order to force it to satisfy the restrictions. But there exists cases i n which the resulting tracking error is not acceptable, even if we choose a sampling period arbitrarily small. In this work, inspired by some techniques developed in the context of Posit ional Games, we present a control algorithm that, based on a solution of th e tracking problem, produces a control law that assures a bounded final tra cking error as small as wished. We also present simulations to compare this algorithm with the SZH.