Optimal control of ODEs via smoothed Hamiltonians: adaptive Pontryagin solvers and costate optimization with value error bounds

Deterministic optimal control problems for ODEs can be attacked through Pontryagin's maximum principle, which leads to a boundary-value problem for state and costate, or through the Hamilton–Jacobi–Bellman equation, a first-order nonlinear PDE. Both routes suffer when the Hamiltonian is nonsmooth, as in bang-bang regimes. We present a research line that regularises the Hamiltonian by log-sum-exp smoothing of piecewise-affine surrogates and builds on it two solver families: an adaptive Pontryagin shooting method with a posteriori error control (arXiv:2606.25731), and an unconstrained costate-optimization method with exact value equivalence and certified primal–dual bounds derived from HJB subsolutions. Benchmarks include nonsmooth, singular, hypersensitive, and high-dimensional problems.

Joint work with S. Ksous, S. Lalvay Segovia, M. Sandberg, E. von Schwerin, and A. Szepessy.