Abstract
This disclosure presents a novel nonlinear phase-based control architecture, termed MOTION, designed for energy-efficient actuation on compact manifolds $S^1$ and $T^N$. Unlike traditional PID controllers that rely on artificial clamping, MOTION utilizes a sinusoidal control law $u = -K \sin(\Delta\varphi)$ to achieve intrinsic effort bounding. The closed-loop system is formally derived as a dissipative port-Hamiltonian system, enabling rigorous verification of almost-global asymptotic stability (AGAS), input-to-state practical stability (ISpS), and incremental stability via contraction analysis. A key technical contribution is the FPU-free, 16-bit integer implementation optimized for embedded microcontrollers, demonstrating a 30.8% reduction in control effort ($\int U^2 dt$) compared to saturated linear feedback. This architecture is particularly applicable to drone signal stabilization, neuromorphic computing, and high-frequency robotic actuation where energy constraints and deterministic execution are critical.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Lozovyi, Olexandr, "MOTION: A Bounded Nonlinear Phase Controller Formulated as a Port-Hamiltonian System on Compact Manifolds", Technical Disclosure Commons, (April 06, 2026)
https://www.tdcommons.org/dpubs_series/9713
motion_logic.h (1 kB)
killer_benchmark.py (6 kB)
motion_angle_sweep_ieee.png (37 kB)