We formulate open-loop optimal control problems for general port-Hamiltonian systems with possibly state-dependent system matrices and prove their well-posedness. The optimal controls are characterized by the first-order optimality system, which is the starting point for the derivation of an adjoint-based gradient descent algorithm. Moreover, we discuss the relationship of port-Hamiltonian dynamics and minimum cost network flow problems. Our analysis is underpinned by a proof of concept, where we apply the proposed algorithm to static minimum cost flow problems and dynamic minimum cost flow problems with a simple directed acyclic graph. The numerical results validate the approach.

翻译：针对具有可能状态依赖系统矩阵的广义端口-哈密顿系统，我们建立了开环最优控制问题的数学形式并证明了其适定性。最优控制由一阶最优性系统刻画，这为推导基于伴随的梯度下降算法奠定了基础。进一步，我们探讨了端口-哈密顿动力学与最小成本网络流问题之间的内在联系。通过概念验证实验，将所提算法应用于简单有向无环图上的静态和动态最小成本流问题，数值结果验证了该方法的有效性。