Spectral Transitions in Optimal Control Order for Dissipative SystemsThis preprint presents a control-theoretic analysis of controller order selection in dissipative systems subject to environmental spectral forcing. A system tracking an external signal must maintain viability under switching costs and internal dynamical lag. Each controller class (proportional, integral, predictive, and hybrid) defines a feasible parameter region constrained by a viability threshold on terminal resource. We formalize controller selection as a feasibility geometry problem: higher-order controllers become optimal when the feasible volume of lower-order classes contracts under changes in environmental power spectrum or internal stiffness. An analytic activation boundary for integration under switching cost is derived, yielding a critical condition of the form λ_c ≈ (G_n τ)/4. Numerical Monte Carlo sweeps (1000 parameterizations per regime) confirm discrete transitions in optimal controller class as high-frequency noise and lag increase. All simulation scripts, parameter sweeps, and summary tables are included to ensure reproducibility. This release (v1.0) represents the foundational statement of the spectral feasibility framework.

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access