Suboptimal control by primal-dual gradient dynamics

This note generalizes the port-Hamiltonian formulation of the continuous time primal-dual gradient algorithm for static constrained convex optimization to the convex optimal control problem.The resulting dynamics is shown to be a port-Hamiltonian system of partial differential equations, involving ordinary physical time as well ‘algorithmic’ time. Convergence to the optimal control solution is indicated, and it is argued that sub-optimal control strategies could be derived starting from the partial differential equation formulation.