Work

Hypersensitivity and Turnpikes in Optimal Control of Inverted Pendulum: A Dynamical Systems Perspective

Year: 2026

Type: preprint

Abstract: The hypersensitivity and turnpike phenomena in the optimal control of an inverted pendulum are investigated from a dynamical-systems perspective. We show that, for a fixed terminal time and a fixed terminal state optimal control problem, (1) the hypersensitivity originates from the fractal structure of the set of initial adjoint variables in the associated Hamiltonian dynamics, (2) the turnpike arises from slow dynamics in the vicinity of a degenerate center manifold, and (3) the escape channels are formed by normally hyperbolic invariant manifolds (NHIMs). As a consequence, small perturbations in the initial adjoint variables lead to qualitatively distinct extremal trajectories, resulting in severe numerical instability in trajectory optimization. Both the fractal structure and the invariant sets are characterized numerically and analytically.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.22801

Authors: Bando, Mai, Sato, Yuzuru

Institution: Kyushu University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Japan Society for the Promotion of Science, Moonshot Research and Development Program

Awards: Control Theory for Spacecraft Leveraging Chaotic Transport Structures, G2333688445, G3357476459, G8330765809, control theory based on reduced order representations of nonlinear dynamical systems

OpenAlex ID: W7214025958

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