Discrete Inverse Problem Approach to Path Tracking in State Space Form

摘要

This paper presents a new method for determining the ideal control signal to a state-space system such that one or more of its states track specified paths. The method is based on the concept of an inverse problem, whereby we determine the ideal input which is required to track the specified output. One of the key observations is that regularization must be applied to the solution of the inverse problem to obtain a unique solution, e.g., second order regularization is used to impose smoothness on the solution for the control. The method is verified on a synthetic example of a second order system whose position is specified and tracked according to the proposed algorithm. The results can be combined with a simple controller for path tracking as a form of model predictive control for real-world systems.