Inverse optimal control with polynomial optimization

In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very broad as a reliable solution to the problem would provide a powerful modeling tool in many areas of experimental science. We propose to the Hamilton-Jacobi-Bellman sufficient optimality conditions as a tool for analyzing the inverse problem and propose a general method that attempts at numerically solving it, with techniques of polynomial optimization and linear matrix inequalities. The relevance of the method is illustrated based on academic examples.