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Advocating Feedback Control for Human-Earth System Applications

Guido Cavraro

TL;DR

The paper argues that Integrated Assessment Models (IAMs) are largely open-loop and suffer from structural inaccuracies when guiding climate policy. It proposes a two-loop feedback framework where a slower outer loop computes optimal inputs $\mathbf{u}^*$ using a horizon-based optimization and a faster inner loop enforces these inputs through actuators, leveraging measurements to reject disturbances. By formulating the HES planning problem as a closed-loop Model Predictive Control (MPC) scheme, it demonstrates reduced sensitivity to model error and improved robustness in both theoretical and numerical examples. The framework is illustrated through three application domains—Stratospheric Aerosol Injection (SAI), sustainable economic pathways, and marine cloud brightening (MCB)—and a numerical AYS-model case showing superior tracking under uncertainty, highlighting the practical potential for climate policy design and geoengineering planning.

Abstract

This paper proposes a feedback control perspective for Human-Earth Systems (HESs) which essentially are complex systems that capture the interactions between humans and nature. Recent attention in HES research has been directed towards devising strategies for climate change mitigation and adaptation, aimed at achieving environmental and societal objectives. However, existing approaches heavily rely on HES models, which inherently suffer from inaccuracies due to the complexity of the system. Moreover, overly detailed models often prove impractical for optimization tasks. We propose a framework inheriting from feedback control strategies the robustness against model errors, because inaccuracies are mitigated using measurements retrieved from the field. The framework comprises two nested control loops. The outer loop computes the optimal inputs to the HES, which are then implemented by actuators controlled in the inner loop. Potential fields of applications are also identified.

Advocating Feedback Control for Human-Earth System Applications

TL;DR

The paper argues that Integrated Assessment Models (IAMs) are largely open-loop and suffer from structural inaccuracies when guiding climate policy. It proposes a two-loop feedback framework where a slower outer loop computes optimal inputs using a horizon-based optimization and a faster inner loop enforces these inputs through actuators, leveraging measurements to reject disturbances. By formulating the HES planning problem as a closed-loop Model Predictive Control (MPC) scheme, it demonstrates reduced sensitivity to model error and improved robustness in both theoretical and numerical examples. The framework is illustrated through three application domains—Stratospheric Aerosol Injection (SAI), sustainable economic pathways, and marine cloud brightening (MCB)—and a numerical AYS-model case showing superior tracking under uncertainty, highlighting the practical potential for climate policy design and geoengineering planning.

Abstract

This paper proposes a feedback control perspective for Human-Earth Systems (HESs) which essentially are complex systems that capture the interactions between humans and nature. Recent attention in HES research has been directed towards devising strategies for climate change mitigation and adaptation, aimed at achieving environmental and societal objectives. However, existing approaches heavily rely on HES models, which inherently suffer from inaccuracies due to the complexity of the system. Moreover, overly detailed models often prove impractical for optimization tasks. We propose a framework inheriting from feedback control strategies the robustness against model errors, because inaccuracies are mitigated using measurements retrieved from the field. The framework comprises two nested control loops. The outer loop computes the optimal inputs to the HES, which are then implemented by actuators controlled in the inner loop. Potential fields of applications are also identified.
Paper Structure (11 sections, 25 equations, 4 figures, 1 table)

This paper contains 11 sections, 25 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. IAMs and the current approach
  3. A feedback control framework
  4. Optimization of HES
  5. Control of Actuators
  6. Application Examples
  7. SRM via Stratospheric Aerosol Injection (SAI)
  8. Developing sustainable economic pathways.
  9. Marine cloud brightening for coral reef preservation
  10. A numerical example
  11. CONCLUSIONS

Figures (4)

  • Figure 1: Schematic representation of the HES. The Human and Earth system blocks feature internal interactions and are linked by feedback.
  • Figure 2: Block scheme representation of the proposed control framework.
  • Figure 3: a) IAMs act in an open loop fashion. b) The closed loop approach.
  • Figure 4: Left panel: the excess atmospheric carbon stock, Center panel: the GWP's growth rate. Right panel: the break-even knowledge level.