Hybrid Function Approximation: A Variational Approach

In this paper we study the problem of representing trajectories through a concatenation of trajectories obtained from solving different differential equations. These trajectories are moreover allowed to undergo discontinuous jumps in order to make the approximation better. Our solution is based on a variational approach, in which both jump heights as well as switch times are taken as optimization parameters. The main application for this method is data compression, where the original trajectory is represented through mode sequences, switch times, and jump heights.