Title: Energy-optimal control of discrete-time port-Hamiltonian systems Show Chinese title

Title: 离散时间端口-哈密顿系统的能量最优控制

Abstract: In this letter, we study the energy-optimal control of nonlinear port-Hamiltonian (pH) systems in discrete time. For continuous-time pH systems, energy-optimal control problems are strictly dissipative by design. This property, stating that the system to be optimized is dissipative with the cost functional as a supply rate, implies a stable long-term behavior of optimal solutions and enables stability results in predictive control. In this work, we show that the crucial property of strict dissipativity is not straightforwardly preserved by any energy-preserving integrator such as the implicit midpoint rule. Then, we prove that discretizations via difference and differential representations lead to strictly dissipative discrete-time optimal control problems. Consequently, we rigorously show a stable long-term behavior of optimal solutions in the form of a manifold (subspace) turnpike property. Finally, we validate our findings using two numerical examples Show Chinese abstract

Abstract: 在本文中，我们研究离散时间非线性端口-哈密顿（pH）系统的能量最优控制。 对于连续时间pH系统，能量最优控制问题在设计上是严格耗散的。 这一性质表明被优化的系统以代价函数作为供应速率是耗散的，这意味着最优解具有稳定的长期行为，并在预测控制中实现了稳定性结果。 在本工作中，我们证明严格耗散性这一关键性质不会被任何保持能量的积分器如隐式中点法则直接保留。 然后，我们证明通过差分和微分表示进行离散化会导致严格耗散的离散时间最优控制问题。 因此，我们严格证明了最优解的稳定长期行为，表现为流形（子空间）遍历性。 最后，我们使用两个数值例子验证了我们的结论。