| _version_ | 1866901280663797760 |
|---|---|
| author | Pasupuleti, Ramakrishna |
| author_facet | Pasupuleti, Ramakrishna |
| contents | <p>This preprint presents a unified, domain-agnostic K–R constant–based framework for predictive system stabilization, structured uncertainty regulation, cross-domain computational deployment, and physical reservoir computing in complex dynamic systems. The framework introduces two invariant parameters: a controllable scaling constant K, representing achievable stabilization or regulation gain, and an irreducible residual constant R, representing fundamental performance limits imposed by system physics, uncertainty, or informational constraints.</p> <p>System performance and uncertainty behavior are expressed through the core relation:</p> <p><strong>P = P₀ / K + R</strong></p> <p>where P₀ denotes baseline (unregulated) system deviation or performance error, K quantifies controllable improvement achievable through stabilization or uncertainty regulation, and R represents unavoidable residual deviation arising from physical, stochastic, environmental, or computational limits. Time-varying, adaptive, nonlinear, and hybrid extensions of this formulation are developed to support discrete-time, continuous-time, and multi-scale dynamic systems.</p> <p>The framework provides a structured deterministic–stochastic balancing mechanism for regulating noise, disturbances, environmental variability, sensor and measurement uncertainty, parameter fluctuations, and non-stationary system evolution. By explicitly separating controllable improvement from irreducible limits, the formulation establishes bounded, interpretable, and scalable performance envelopes across diverse predictive and computational systems.</p> <p>Domain-level applicability is demonstrated across aerospace systems, structural and mechanical systems, environmental and earth systems, numerical simulation environments, digital twin platforms, real-time monitoring systems, and hybrid physics-based and data-driven computational infrastructures. The framework enables quantification of achievable stabilization gain and residual performance limits in each domain, replacing heuristic tuning and uncontrolled divergence with predictable and mathematically interpretable system behavior.</p> <p>The formulation is further extended to physical reservoir computing, where computation is realized through dynamical physical systems whose memory, nonlinearity, and stability are regulated using K and R constants. Mechanical, optical, electronic, fluidic, thermal, and MEMS/NEMS-based reservoirs are supported, enabling stable and interpretable computation with controlled noise utilization, echo-state stability, memory-depth regulation, and stability–memory trade-off optimization. Applications include time-series prediction, signal processing, pattern recognition, system identification, dynamic system control, and low-power edge computation.</p> <p>Analytical derivations and representative numerical interpretations demonstrate that the K–R constant formulation transforms instability-prone predictive and physical computing systems into bounded, scalable, and explainable systems with explicit performance limits. By providing a unified mathematical interpretation of stabilization and residual limits, this framework establishes a generalizable foundation for stable prediction, robust uncertainty regulation, and physically grounded computation across nonlinear, uncertain, and evolving operating environments.</p> <p>A patent application related to aspects of the K–R constant framework has been filed by the author. This Zenodo preprint presents the theoretical and methodological foundations intended for academic and research dissemination.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18491163 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A K–R Constant–Based Framework for Predictive Stabilization, Uncertainty Regulation, and Physical Reservoir Computing Pasupuleti, Ramakrishna <p>This preprint presents a unified, domain-agnostic K–R constant–based framework for predictive system stabilization, structured uncertainty regulation, cross-domain computational deployment, and physical reservoir computing in complex dynamic systems. The framework introduces two invariant parameters: a controllable scaling constant K, representing achievable stabilization or regulation gain, and an irreducible residual constant R, representing fundamental performance limits imposed by system physics, uncertainty, or informational constraints.</p> <p>System performance and uncertainty behavior are expressed through the core relation:</p> <p><strong>P = P₀ / K + R</strong></p> <p>where P₀ denotes baseline (unregulated) system deviation or performance error, K quantifies controllable improvement achievable through stabilization or uncertainty regulation, and R represents unavoidable residual deviation arising from physical, stochastic, environmental, or computational limits. Time-varying, adaptive, nonlinear, and hybrid extensions of this formulation are developed to support discrete-time, continuous-time, and multi-scale dynamic systems.</p> <p>The framework provides a structured deterministic–stochastic balancing mechanism for regulating noise, disturbances, environmental variability, sensor and measurement uncertainty, parameter fluctuations, and non-stationary system evolution. By explicitly separating controllable improvement from irreducible limits, the formulation establishes bounded, interpretable, and scalable performance envelopes across diverse predictive and computational systems.</p> <p>Domain-level applicability is demonstrated across aerospace systems, structural and mechanical systems, environmental and earth systems, numerical simulation environments, digital twin platforms, real-time monitoring systems, and hybrid physics-based and data-driven computational infrastructures. The framework enables quantification of achievable stabilization gain and residual performance limits in each domain, replacing heuristic tuning and uncontrolled divergence with predictable and mathematically interpretable system behavior.</p> <p>The formulation is further extended to physical reservoir computing, where computation is realized through dynamical physical systems whose memory, nonlinearity, and stability are regulated using K and R constants. Mechanical, optical, electronic, fluidic, thermal, and MEMS/NEMS-based reservoirs are supported, enabling stable and interpretable computation with controlled noise utilization, echo-state stability, memory-depth regulation, and stability–memory trade-off optimization. Applications include time-series prediction, signal processing, pattern recognition, system identification, dynamic system control, and low-power edge computation.</p> <p>Analytical derivations and representative numerical interpretations demonstrate that the K–R constant formulation transforms instability-prone predictive and physical computing systems into bounded, scalable, and explainable systems with explicit performance limits. By providing a unified mathematical interpretation of stabilization and residual limits, this framework establishes a generalizable foundation for stable prediction, robust uncertainty regulation, and physically grounded computation across nonlinear, uncertain, and evolving operating environments.</p> <p>A patent application related to aspects of the K–R constant framework has been filed by the author. This Zenodo preprint presents the theoretical and methodological foundations intended for academic and research dissemination.</p> |
| title | A K–R Constant–Based Framework for Predictive Stabilization, Uncertainty Regulation, and Physical Reservoir Computing |
| url | https://doi.org/10.5281/zenodo.18491163 |