Year: 2026
Type: preprint
Abstract: We consider the energy-optimal control problem for double-integrator systems subject to state and control constraints, with fixed terminal time and free terminal speed. When the constraints become active, the optimal trajectory consists of a combination of bang, unconstrained, and coast arcs, whose switching instants must be computed explicitly. In this paper, we derive closed-form expressions for the switching times of all admissible profiles, including both constrained and unconstrained arcs, reducing the computation in each case to explicit algebraic equations. In contrast to prior work, we classify all possible combinations of arcs, including special cases, and provide the specific conditions under which each case arises. Furthermore, we prove that when the initial unconstrained trajectory violates both speed and control constraints, the optimal solution follows a predetermined bang-affine-coast profile, enabling direct identification of the optimal trajectory without intermediate feasibility checks.
Source: arXiv (Cornell University)
Institutions: Cornell University, Engineering Systems (United States)
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: Collaborative Research: SLES: Improving Safety by Synthesizing Interacting Model-based and Model-free Learning Approaches, NRI: Addressing Safe Interaction Between Autonomous and Human-Driven Vehicles, Collaborative Research: CPS: Medium: An Online Learning Framework for Socially Emerging Mixed Mobility
OpenAlex ID: W7154491950
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