$\Theta$-Control: Memory as a Control Resource
Year: 2026
Type: preprint
Abstract: This paper introduces Θ-Control, a control framework that explicitly incorporates system memory as a resource. We propose extending the classical state-space representation from ẋ = f(x, u, t) to ẋ = f(x, u, Θ, t), where Θ = BK [ x(t) - x(t-τ) ] captures the difference between present and past states. Through numerical experiments on a second-order oscillator and the nonlinear Duffing system, we demonstrate that Θ-Control: - Outperforms optimally tuned PID: 70% lower ISE, 2.3x faster rise time, 81% less overshoot- Requires only one tuning parameter (Kθ)- Needs no plant model- Stabilizes chaotic behavior (Duffing oscillator) This work suggests that memory — traditionally treated as a source of instability — can be transformed into an active control resource, enabling superior performance with unprecedented simplicity. **Version 2.0 - Revised and Enhanced (June 2026)** This is a revised version of the preprint originally released on June 10, 2026. Key improvements include: - Corrected system parameters to ensure exact consistency with ωn = 2.00 rad/s and ζ = 0.600 - Enhanced numerical simulations with longer transients for the Duffing oscillator - Improved figures with clear visual comparisons (same-scale Poincaré maps) - New spectral analysis of the Duffing oscillator showing period-1 stabilization - Expanded discussion on memory as an energy organizer The main conclusions remain unchanged and are further strengthened by this revision. All code is available on GitHub: https://github.com/marconi-unicamp/theta-control
Author: Kolm Madrid, Marconi
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165148301
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