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Circular Microalgae-Based Carbon Control for Net Zero

Federico Zocco, Joan García, Wassim M. Haddad

TL;DR

This work treats net-zero CO₂ as a network-control problem by coupling an affine carbon emitter (anaerobic digester) with a nonaffine carbon sink (microalgae) within a thermodynamical material network (TMN). It develops a finite-time, initial-condition-dependent stabilizing controller for the emitter and investigates reinforcement-learning controllers to maximize microalgal CO₂ uptake via light, tested across eight algorithms with Stable-Baselines3; ARS emerges as the fastest to train and competitive in final performance. A key finding is that a microalgae volume of 625 times the digester volume can offset emissions at steady state, improving circularity toward net-zero, and RL can further enhance uptake though without rigorous finite-time guarantees yet. The study highlights a promising integration of classical control and learning-based methods for carbon circularity and provides public code to advance TMN modeling and control for circular economy applications.

Abstract

The alteration of the climate in various areas of the world is of increasing concern since climate stability is a necessary condition for human survival as well as every living organism. The main reason of climate change is the greenhouse effect caused by the accumulation of carbon dioxide in the atmosphere. In this paper, we design a networked system underpinned by compartmental dynamical thermodynamics to circulate the atmospheric carbon dioxide. Specifically, in the carbon dioxide emitter compartment, we develop an initial-condition-dependent finite-time stabilizing controller that guarantees stability within a desired time leveraging the system property of affinity in the control. Then, to compensate for carbon emissions we show that a cultivation of microalgae with a volume 625 times bigger than the one of the carbon emitter is required. To increase the carbon uptake of the microalgae, we implement the nonaffine-in-the-control microalgae dynamical equations as an environment of a state-of-the-art library for reinforcement learning (RL), namely, Stable-Baselines3, and then, through the library, we test the performance of eight RL algorithms for training a controller that maximizes the microalgae absorption of carbon through the light intensity. All the eight controllers increased the carbon absorption of the cultivation during a training of 200,000 time steps with a maximum episode length of 200 time steps and with no termination conditions. This work is a first step towards approaching net zero as a classical and learning-based network control problem. The source code is publicly available.

Circular Microalgae-Based Carbon Control for Net Zero

TL;DR

This work treats net-zero CO₂ as a network-control problem by coupling an affine carbon emitter (anaerobic digester) with a nonaffine carbon sink (microalgae) within a thermodynamical material network (TMN). It develops a finite-time, initial-condition-dependent stabilizing controller for the emitter and investigates reinforcement-learning controllers to maximize microalgal CO₂ uptake via light, tested across eight algorithms with Stable-Baselines3; ARS emerges as the fastest to train and competitive in final performance. A key finding is that a microalgae volume of 625 times the digester volume can offset emissions at steady state, improving circularity toward net-zero, and RL can further enhance uptake though without rigorous finite-time guarantees yet. The study highlights a promising integration of classical control and learning-based methods for carbon circularity and provides public code to advance TMN modeling and control for circular economy applications.

Abstract

The alteration of the climate in various areas of the world is of increasing concern since climate stability is a necessary condition for human survival as well as every living organism. The main reason of climate change is the greenhouse effect caused by the accumulation of carbon dioxide in the atmosphere. In this paper, we design a networked system underpinned by compartmental dynamical thermodynamics to circulate the atmospheric carbon dioxide. Specifically, in the carbon dioxide emitter compartment, we develop an initial-condition-dependent finite-time stabilizing controller that guarantees stability within a desired time leveraging the system property of affinity in the control. Then, to compensate for carbon emissions we show that a cultivation of microalgae with a volume 625 times bigger than the one of the carbon emitter is required. To increase the carbon uptake of the microalgae, we implement the nonaffine-in-the-control microalgae dynamical equations as an environment of a state-of-the-art library for reinforcement learning (RL), namely, Stable-Baselines3, and then, through the library, we test the performance of eight RL algorithms for training a controller that maximizes the microalgae absorption of carbon through the light intensity. All the eight controllers increased the carbon absorption of the cultivation during a training of 200,000 time steps with a maximum episode length of 200 time steps and with no termination conditions. This work is a first step towards approaching net zero as a classical and learning-based network control problem. The source code is publicly available.

Paper Structure

This paper contains 18 sections, 3 theorems, 48 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Plants for Greenhouse Effect Mitigation
  4. Thermodynamical Material Networks for a Circular Economy
  5. Finite-Time Stabilizing Control
  6. Reinforcement Learning for Continuous-Time Control
  7. Network Design
  8. Step 1
  9. Step 2
  10. Step 3
  11. Anaerobic digester (i.e., $c^1_{1,1}$)
  12. Microalgae (i.e., $c^3_{3,3}$)
  13. Virtual ducts (i.e., $c^4_{1,2}$ and $c^5_{2,3}$)
  14. Atmosphere (i.e., $c^2_{2,2}$)
  15. Digester controller
  16. ...and 3 more sections

Key Result

Theorem 1

Consider the affine nonlinear dynamical system (eq:affineForm). Assume that there exist a continuously differentiable, radially unbounded function $V : \mathbb{R}^{n} \rightarrow \mathbb{R}$ and real numbers $c > 0$ and $\beta \in (0, 1)$ such that the following conditions hold: where $\bm{L}_2 : \mathbb{R}^{n} \rightarrow \mathbb{R}^{1 \times l}$ is continuous on $\mathbb{R}^{n}$ and $\bm{R}_2(\

Figures (3)

  • Figure 1: Proposed carbon dioxide network design: Physical representation with geometry in (a) and its compartmental digraph in (b). The red arrows indicate the flow of carbon dioxide.
  • Figure 2: Components of the state of $c^1_{1,1}$ vs. time with the initial-condition-dependent controller (Theorem \ref{['th:inCoDepCon']}).
  • Figure 3: Dynamics of compartments $c^2_{2,2}$, $c^3_{3,3}$, $c^4_{1,2}$, and $c^5_{2,3}$ using the values in Table \ref{['tab:valuesOfParam']}.

Theorems & Definitions (8)

  • Remark 1
  • Theorem 1: haddad2015finite
  • Theorem 2: Initial-condition-dependent control
  • proof
  • Remark 2
  • Corollary 1
  • proof
  • Remark 3