AI 中文总结
本文提出一种基于耗散性的MPC方案，利用端口-哈密顿结构建立转折集，无需稳态或周期轨道假设，并证明闭环实际稳定性，通过数值示例验证。
AI 中文摘要
我们研究了一种基于耗散性的模型预测控制（MPC）方案，用于离散时间非线性单输入单输出（SISO）端口-哈密顿系统的能量最优约束输出镇定，该系统由差分和微分表示描述。对于每个MPC步骤中需要求解的最优控制问题，我们建立了测度转折（turnpike）行为。在我们的工作中，转折集是从底层端口-哈密顿结构获得的，而不假设存在稳态或周期轨道。特别是，与通常针对受控前向不变集（如最优稳态或最优周期轨道）建立转折性质（turnpike property）的现有结果不同，我们不要求转折集是前向控制不变的。对于MPC，我们建立了递归可行性，并利用耗散性和端口-哈密顿结构，证明了相对于MPC闭环对转折集的实际稳定性。最后，我们通过两个数值示例展示了我们的结果。
英文摘要
We study a dissipativity-based model predictive control (MPC) scheme for energy-optimal constrained output stabilization of a discrete-time nonlinear SISO port-Hamiltonian system described by difference and differential representation. For the optimal control problem to be solved in each MPC step, we establish a measure turnpike behavior. The turnpike set in our work is obtained from the underlying port-Hamiltonian structure without assuming existence of steady-states or periodic orbits. In particular, unlike existing results which typically establish the turnpike property w.r.t. a controlled forward invariant set such as optimal steady-states or optimal periodic orbits, we do not require the turnpike set to be forward control invariant. For MPC, we establish recursive feasibility and show practical stability to the turnpike set w.r.t. the MPC closed loop leveraging both dissipativity and the port-Hamiltonian structure. Finally, we demonstrate our results using two numerical examples.
Comments20 pages and 4 figures, submitted to journal
