Towards global optimal control via Koopman lifts

This paper introduces a framework for solving time-autonomous nonlinear infinite horizon optimal control problems, under the assumption that all minimizers satisfy Pontryagin’s necessary optimality conditions. In detail, we use methods from field of symplectic geometry to analyze eigenvalues Koopman operator lifts differential equation into suitably defined dimensional space. has advantage spectral analysis can be used characterize globally laws. A numerical method constructing feedback laws systems proceeds by computing and eigenvectors matrix is obtained projecting Pontryagin–Koopman onto finite We illustrate effectiveness this approach accurate approximations law Van der Pol system, which cannot stabilized linear law.