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arXiv · 2609.11348

Time-optimal elevator control with higher-order state constraints: analysis and computation of boundary contacts

Dmitry Karamzin·Aleksandra Zhukova·Roman Chertovskih·Pedro A. Aguiar
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Abstract

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.

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Dmitry Karamzin, Aleksandra Zhukova, Roman Chertovskih, Pedro A. Aguiar. 2026-09-10. Time-optimal elevator control with higher-order state constraints: analysis and computation of boundary contacts. https://arxiv.org/abs/2609.11348

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