Control engineering plays a pivotal role in understanding and designing systems ranging from biological feedback loops to complex engineered infrastructures. Traditionally, the foundations of control theory have been built on abstract mathematical axioms, driving advances in both linear and nonlinear systems. While mathematical rigor has ensured the reliable performance of linear control systems, challenges remain in mapping such rigor onto nonlinear and adaptive systems due to their inherent complexity and the limitations arising from idealized assumptions. Current debates emphasize the misalignment between abstract proofs and practical predictability, especially as dynamic systems become more data-driven and as computational hardware, measurement noise, disturbances, and uncertainty become defining factors in system behavior.
Recent studies have highlighted the limitations of relying on nonphysical premises and ideal axioms in control engineering which for example assume infinite precision of quantities processed by physical systems. Although some progress has been made in developing proofs for nonlinear and hybrid systems, their practical adoption is impeded by prohibitively high verification and validation costs, and by performance inconsistencies stemming from real-world complexities not captured by classical models. Notably, the increasing influx of data and prevalence of digital computation demand a foundational overhaul to ensure that new control strategies remain robust, verifiable, and accessible. This is important also for the accountability of human decision making in critical systems. As fields like physics and engineering increasingly intermingle with data-centric approaches, there is a clear imperative to bridge the gap between theoretical rigor and practical applicability.

This Research Topic aims to develop a new, data-driven foundation for control engineering that aligns more closely with physical realities and leverages the advances in digital computation. The objective is to move beyond axiomatic rigor towards practical guarantees of stability, performance, and robustness in real-world dynamic systems. Key questions include how to construct floating point mathematical frameworks for modeling and analysis without nonphysical assumptions, and how to make these approaches accessible from primary education upwards. Additionally, the goal is to inspire novel methodologies for deriving fundamental physics equations and to establish new standards for reducing the cost and complexity of system verification and validation.

The scope of this Research Topic encompasses a wide spectrum of theoretical and practical research on the integration of data-driven approaches into control engineering, while excluding purely abstract or axiomatic studies that do not address physical implementation. We welcome contributions that explore, but are not limited to, the following themes:

- Development of dynamical system models that accurately represent and correspond to empirical data, including alternatives to classical differential or difference equations.

- Innovative educational strategies for teaching foundational floating point mathematics and computation from early learning stages.

- Revisiting and rederiving core physics equations (from mechanics to quantum mechanics) rooted in engineering data and reality-based premises.

- Novel frameworks and practices for system design that minimize verification and validation costs while ensuring reliability.

- Analysis of robustness, stability, and performance guarantees for control systems in noisy and resource-constrained environments.

- Discussions on bridging control engineering theory and real-world implementation in the age of pervasive data and computation.

Appendix: We accept original research articles, perspective papers, methods, and reviews that align with these themes.

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Towards practical rigor in control engineering for the modern age