发表机构
Federal Research Center “Computer Science and Control” of Russian Academy of Sciences; Research Center for Systems and Technologies (SYSTEC), ARISE, Faculdade de Engenharia, Universidade do Porto（俄罗斯科学院计算机科学与控制联邦研究中心; 波尔图大学工程学院ARISE系统与技术研究中心（SYSTEC））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高阶状态约束的时间最优电梯问题，提出基于庞特里亚金最大值原理的间接求解框架，将问题转化为有限维方程组，并分析边界接触几何，在四阶模型上验证。
AI 中文摘要
本文研究了存在高阶状态约束的经典时间最优电梯问题。主要贡献是基于专门针对高阶约束系统制定的庞特里亚金最大值原理，构建了一个构造性的间接求解框架。首先，我们推导了专门的优化条件，并分析了由此产生的极值轨迹结构。其次，我们证明了无限维最优控制问题可以转化为一个包含切换时间、边界接触时间和乘子参数的有限维非线性代数方程组。这为使用标准非线性方程求解器计算候选最优轨迹提供了一种计算高效的方法。第三，我们刻画了边界接触的几何特性，并解释了高阶约束系统中接触颤振现象的产生机制。特别地，我们证明了正常极值轨迹不能沿约束边界持续正时间，尽管边界接触序列可能无限累积。所提出的方法在四阶电梯模型上进行了验证，计算结果通过基于IPOPT的直接优化方法独立验证。
英文摘要
In this paper, we consider the classical time-optimal elevator problem in the presence of higher-order state constraints. The main contribution is a constructive indirect solution framework based on a Pontryagin Maximum Principle specifically formulated for higher-order constrained systems. First, we derive specialized optimality conditions and analyze the resulting structure of extremal trajectories. Second, we show that the infinite-dimensional optimal control problem can be transformed into a finite-dimensional system of nonlinear algebraic equations involving switching times, boundary-contact times, and multiplier parameters. This provides a computationally efficient procedure for calculating candidate optimal trajectories using standard nonlinear equation solvers. Third, we characterize the geometry of boundary contacts and explain the emergence of contact-chattering phenomena in higher-order constrained systems. In particular, we show that normal extremals cannot evolve along the constraint boundary for a positive amount of time, although sequences of boundary contacts may accumulate indefinitely. The proposed approach is demonstrated on a fourth-order elevator model, and the computed solutions are independently verified using a direct IPOPT-based optimization method.
