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Safe Greenhouse Climate Control Using Lagrangian-Constrained PPO with Kolmogorov-Arnold Networks

Hangzun Liu, Yuling Fan, Fang Tian, Zhilong Bie, Zaiwen Feng, Yongliang Qiao

arXiv:2609.34966v1cs.AI

TL;DR

Fixed-penalty reinforcement learning for greenhouse control cannot explicitly constrain cumulative climate violations, leaving a trade-off between crop conditions and economic return. The paper formulates control as a CMDP and combines Lagrangian safe RL with KANs and cyclic time features; simulations report fewer violations and higher profit than penalty-based PPO.

  • Problem

    Fixed reward penalties in greenhouse RL do not explicitly control long-horizon climate violations, while poorly tuned weights can yield conservative or unsafe policies.

    Source: §1 · p. 1

  • Method

    The paper formulates greenhouse control as a CMDP and uses adaptive Lagrangian safe RL with KAN policy representation and cyclic time features.

    Source: §1 · p. 2, §2.2.3 · p. 4

  • Results

    18.65% fewer cumulative climate violations and 2.91% higher economic profit than a penalty-based PPO baseline.

    Source: §6 · p. 10

  • Takeaways & Limitations

    The CMDP formulation explicitly imposes cumulative climate constraints while balancing economic performance and long-term climate-regulation safety.

    Source: §6 · pp. 9–10

    The approach is evaluated in simulation; future work calls for testing more crops, seasons, and real-world greenhouse environments.

    Source: §6 · p. 10

Abstract

from arXiv · show

Greenhouse climate control balances economic return with maintaining temperature, humidity and CO2 within crop-adapted growth ranges. Conventional reinforcement learning (RL) greenhouse controllers use fixed reward penalties to limit climate constraint violations, yet such heuristic penalties cannot explicitly constrain long-term cumulative violations. Poorly tuned weights either lead to overly conservative policies and lower yields, or fail to suppress persistent climate deviations that harm photosynthesis and induce crop diseases. To address this issue, we formulate greenhouse climate regulation as a Constrained Markov Decision Process (CMDP) and use a Lagrangian safe RL framework RCPO-PPO to separate economic optimization and cumulative safety constraints, enabling adaptive penalty adjustment without manual tuning. To handle strong nonlinear, time-varying coupling between greenhouse microclimate and crop growth, Kolmogorov-Arnold Networks (KANs) replace Multi-Layer Perceptrons (MLPs) as policy and value approximators for improved nonlinear representation. Sinusoidal cyclic time features are embedded in observations to capture diurnal environmental periodicity. Simulations use a classic winter lettuce greenhouse model driven by 40-day real weather disturbances. Compared with vanilla penalty-based PPO, our method cuts cumulative climate violations by 18.65% and raises lettuce economic profit by 2.91%, keeping violations stable near the safety threshold. This decoupled CMDP optimization with KAN-based policy representation mitigates long-term climate risks and boosts planting profits, offering a constraint-aware control strategy for precision greenhouse cultivation.

1. Introduction

Greenhouse control must balance economic returns against climate conditions that support growth and disease prevention, while fixed-penalty RL offers no explicit control of long-horizon violations. The proposed approach separates economic objectives from cumulative climate constraints and combines adaptive safe RL with KANs and cyclic time features.

1. Introduction

  • Greenhouse control must maintain growth- and disease-prevention climate ranges while reducing heating, ventilation, and CO2 enrichment costs.These goals create a trade-off between profit and climate-regulation reliability.Source: §1 · p. 1
  • Fixed reward penalties do not explicitly control the long-horizon magnitude or duration of climate violations, and poorly tuned weights can produce conservative or unsafe policies.Prolonged temperature, humidity, or CO2 deviations can suppress photosynthesis, promote disease, and reduce biomass accumulation.Source: §1 · pp. 1–2
  • The study formulates greenhouse control as a CMDP that optimizes economic profit subject to explicit cumulative climate-violation constraints.This replaces reliance on heuristic fixed penalties with explicit long-horizon constraint regulation during policy learning.Source: §1 · p. 2
  • The proposed controller combines adaptive Lagrangian constraint handling, KAN-based policy representation, and cyclic time encoding, and validates their combined value on a lettuce greenhouse model.The cyclic features capture diurnal dynamics, while KANs improve nonlinear representation.Source: §1 · p. 2
  • The integrated controller reduces cumulative climate violations and improves economic profit compared with penalty-based PPO.The introduction reports these directions of change without specifying the magnitude.Source: §1 · p. 2

2. Background

The background frames greenhouse control as a long-horizon trade-off between economic performance and climate safety. It introduces a winter lettuce model, CMDP-based constraint handling, adaptive RCPO updates, and KAN function approximators for control.

2.1. Greenhouse Climate Model

  • The winter lettuce greenhouse model captures coupled microclimate and crop growth, and is discretized using fourth-order Runge–Kutta with a 30-minute sampling time.Its definitions cover system states, manipulable controls, weather disturbances, and measurable outputs.Source: §2.1 · p. 2

2.2.1. Constrained Markov Decision Process

  • A CMDP extends MDPs with cost functions and thresholds, separating return optimization from constraint satisfaction; d_i quantify acceptable long-term risk.Source: §2.2.1 · pp. 2–3

2.2.2. Safe Reinforcement Learning

  • Lagrange multipliers support primal–dual optimization of reward and constraint satisfaction; unlike CBFs or shielding, this model-free approach avoids requiring highly precise analytical dynamics.Source: §2.2.2 · pp. 3–4

2.2.3. Reward Constrained Policy Optimization

  • RCPO maximizes the Lagrangian while adaptively updating multipliers to penalize violations, helping keep cumulative constraint costs near predefined thresholds.The multiplier update projects onto the nonnegative orthant.Source: §2.2.3 · p. 4

2.3. Kolmogorov–Arnold Networks

  • KANs place learnable spline-based nonlinear transformations on network edges and replace MLP policy and value approximators in the reinforcement learning framework.Source: §2.3 · p. 4

3. Method

The method separates greenhouse profit optimization from cumulative climate-safety constraints in a CMDP, then combines RCPO with PPO, KAN actor–critic networks, and cyclic time features.

3.1. CMDP formulation for greenhouse climate control

  • The observation combines greenhouse outputs, prior controls, weather look-ahead, growing-period progress, and cyclic time features; the six-hour weather forecast is perfect.At a 30-minute sampling interval, the look-ahead uses the current weather and twelve forecast steps, with forecast-error effects not modeled.Source: §3.1 · p. 5
  • The CMDP maximizes cumulative reward while limiting cumulative climate violations to a user-defined budget, with violation cost aggregating magnitude and duration.The control objective balances economic return against keeping climate variables in crop-suitable ranges over the growing horizon.Source: §3.1 · pp. 5–6

3.2. RCPO-based controller implementation

  • RCPO-PPO optimizes a Lagrangian objective and updates its nonnegative multiplier every four episodes, adapting penalties to regulate cumulative violations without manually tuned fixed coefficients.The policy is optimized using PPO on the modified reward, while the multiplier is adjusted to enforce the cumulative constraint.Source: §3.2 · p. 6

3.3.1. KAN-based policy and value networks

  • KANs replace MLPs in the actor and critic, modeling nonlinear transformations with learnable edge functions while preserving PPO’s actor–critic interfaces and training procedure.The KAN network architecture and implementation settings are summarized in Table 2.Source: §3.3.1 · p. 6, Table 2 · p. 6

3.3.2. Time feature encoding

  • Sinusoidal cyclic time features are appended to observations to represent time of day and capture periodic greenhouse dynamics without raw-time discontinuities.The motivation is the diurnal variation in solar radiation, outdoor temperature, and operating schedules.Source: §3.3.2 · p. 7

4. Experimental Setup

The experiments evaluate controllers in simulation using a nonlinear winter-lettuce greenhouse–crop model, measured weather disturbances, and PPO-based training with RCPO for cumulative climate constraints.

4.1. Simulation environment

  • The simulation uses a nonlinear winter-lettuce greenhouse–crop model, discretized at 30-minute intervals, with 2.5% relative uncertainty independently resampled across all 28 parameters at each control step.The model couples crop biomass and indoor climate dynamics under control actions and exogenous weather disturbances.Source: §4.1 · p. 7
  • The agent observes greenhouse measurements, previous controls, weather forecasts, and time features, and controls CO2 injection, ventilation, and heating.Climate operating ranges and control-input bounds define the target region and cumulative violation cost.Source: §4.1 · p. 7
  • Weather inputs cover 40 continuous cultivation days of real measurements from Bleiswijk, Netherlands, beginning February 9, 2014.White noise with standard deviation 0.3 produces perturbed weather profiles for training episodes and evaluation runs, identically across controllers.Source: §4.1 · p. 7

4.2. Training and hyperparameter settings

  • All reinforcement-learning controllers use PPO with identical hyperparameters, while RCPO adds a Lagrange multiplier to regulate cumulative climate-violation cost against economic performance.PPO settings and RCPO-specific settings are summarized separately in Tables 5 and 6.Source: §4.2 · p. 7

5. Results and Discussion

The proposed RCPO-PPO controller reduces cumulative climate violations while increasing profit, and its representation enhancements and resource-use results further characterize performance across the four evaluated subsections.

5.1. Main performance comparison

  • Compared with baseline PPO, RCPO-PPO reduces cumulative violation cost by approximately 18.65% and increases cumulative profit by approximately 2.91%, regulating cumulative violations near the predefined threshold.Source: §5.1 · pp. 7–8

5.2. Ablation study on policy representation enhancements

  • Cyclic time features improve training performance over baseline PPO, while KAN-based policy networks add faster early convergence and higher final average return.The ablation compares baseline PPO, PPO with cyclic time features, and PPO with both time features and KAN networks, without RCPO constraint regulation.Source: §5.2 · p. 8, Figure 3 · p. 8

5.3. Reduction in climate constraint violations by variable

  • Humidity violations fall 20.3%, CO2 violations 15.6%, and temperature violations 9.2% versus baseline PPO; disease incidence itself is not modeled.The largest reduction is in relative humidity; the figure normalizes baseline PPO to 100%.Source: §5.3 · p. 9, Figure 4 · p. 9

5.4. Reduction in heating and CO2 input usage

  • CO2 input cost falls 22.5%, heating cost 5.4%, and total operation cost 8.8% versus baseline PPO.The passage links lower heating and CO2 enrichment use to improved economic performance because they are major reward-function costs.Source: §5.4 · p. 9, Figure 5 · p. 9

6. Conclusion and Future Work

The conclusion presents a CMDP-based safe reinforcement learning controller using RCPO, KANs, and cyclic time features. Simulations report lower violations and higher profit than penalty-based PPO, while broader crop, seasonal, and real-world validation remains future work.

  • The greenhouse task is formulated as a CMDP with explicit cumulative climate-violation constraints, solved using RCPO with an adaptive Lagrange multiplier.KANs and cyclic time features enhance policy representation for nonlinear greenhouse dynamics and diurnal patterns.Source: §6 · pp. 9–10
  • In a standard lettuce greenhouse model, cumulative climate violations fall approximately 18.65% and economic profit rises about 2.91% versus penalty-based PPO.Further analyses report humidity-violation reductions and lower heating and CO2 input usage.Source: §6 · p. 10
  • Future work will extend evaluation to more crop types and seasonal conditions and validate the approach in real-world greenhouses.The conclusion also identifies advanced safe RL algorithms and uncertainty-aware decision-making as possible directions.Source: §6 · p. 10

Appendix A. Lettuce Greenhouse Model

The appendix specifies the continuous-time nonlinear lettuce greenhouse model and how it is converted into the discrete-time model used for controller training and evaluation.

  • The study uses a continuous-time nonlinear lettuce greenhouse model adapted from.It is consistent with the state, input, output, and disturbance definitions introduced in Section 2.1.Source: Appendix A · p. 10
  • The model is discretized with the fourth-order Runge–Kutta method for controller training and evaluation.Source: Appendix A · p. 10
  • The discretized model uses a sampling time of Δt = 30 min.Source: Appendix A · p. 10

State, input, output, and disturbance variables

The section defines the greenhouse state, control, weather-disturbance, and measurable-output vectors; their detailed physical meanings are given in Table 1.

Continuous-time dynamics

The continuous-time greenhouse model is introduced in this section.

Measurement equations

The section introduces definitions for the measurable outputs.

Auxiliary flux terms

This section names auxiliary greenhouse flux terms and notes the model’s parameter table and controller-design discretization.

Auxiliary flux terms

Remark on discretization

  • For controller design, the continuous-time model is discretized using fourth-order Runge–Kutta with a 30-minute sampling interval.Source: Remark on discretization · p. 11
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