Neural Control: Adjoint Learning Through Equilibrium Constraints

• URL: http://arxiv.org/abs/2605.03288v1
• Date: Tue, 05 May 2026 02:19:37 GMT
• Title: Neural Control: Adjoint Learning Through Equilibrium Constraints
• Abstract summary: We propose a boundary-control framework that computes trajectory-dependent, memory-efficient proxy gradients.<n>We show improved performance over gradient-free baselines such as SPSA and CEM.
• Score: 7.41073008855977
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many physical AI tasks are governed by implicit equilibrium: an agent actuates a subset of degrees of freedom (boundary DoFs), while the remaining free DoFs settle by minimizing a total potential energy. Even seemingly basic tasks such as bending a deformable linear object (DLO) to a target shape can exhibit strongly nonlinear behavior due to multi-stability: the same boundary conditions may yield multiple equilibrium shapes depending on the actuation trajectory. However, learning and control in such systems is brittle because the actuation-to-configuration map is defined only implicitly, and naive backpropagation through iterative equilibrium solvers is memory- and compute-intensive. We propose Neural Control, a boundary-control framework that computes trajectory-dependent, memory-efficient proxy gradients by differentiating equilibrium conditions via an adjoint formulation, avoiding unrolling of solver iterations. To improve robustness over long horizons, we integrate these sensitivities into a receding-horizon MPC scheme that repeatedly re-anchors optimization to realized equilibria and mitigates basin-switching in multi-stable regimes. We evaluate Neural Control in simulation and on physical robots manipulating DLOs, and show improved performance over gradient-free baselines such as SPSA and CEM.

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