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

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

cs.AISep 28, 2026

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

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

Organizations: College of Informatics, Huazhong Agricultural University, Wuhan 430070, China · Yunnan Modern Agricultural Industry Research Institute Co., Ltd.,Kunming, Yunnan 650000, China · College of Biological and Agricultural Engineering, Jilin University, Changchun 130022, China · Key Laboratory of Efficient Sowing and Harvesting Equipment, Ministry of Agriculture and Rural Affairs, Jilin University, Changchun 130022, China

Abstract

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.

Figures & tables

Figure 1: Framework of the proposed KAN-based safe reinforcement learning greenhouse climate control system.

Figure 2: Greenhouse-crop system dynamic relationship diagram.

State $x(t)$		Output $y(t)$
$x_{1}(t)$	Dry-weight ( $\text{kg/m}^{2}$ )	$y_{1}(t)$	Dry-weight ( $\text{g/m}^{2}$ )
$x_{2}(t)$	Indoor $\text{CO}_{2}$ ( $\text{kg/m}^{3}$ )	$y_{2}(t)$	Indoor $\text{CO}_{2}$ (ppm)
$x_{3}(t)$	Indoor temperature ( ∘ C)	$y_{3}(t)$	Indoor temperature ( ∘ C)
$x_{4}(t)$	Indoor humidity ( $\text{kg/m}^{3}$ )	$y_{4}(t)$	Indoor humidity (%)
Control input $u(t)$		Disturbance $d(t)$
$u_{1}(t)$	$\text{CO}_{2}$ injection ( $\text{mg/m}^{2}/\text{s}$ )	$d_{1}(t)$	Radiation ( $\text{W/m}^{2}$ )

Table 1: Definitions of state, input, output, and disturbance variables

Item	Value
Observation dimension $n_{\mathrm{obs}}$	$62$
KAN layers (actor)	3: $[62,\,128,\,128,\,128]$
KAN layers (critic)	3: $[62,\,128,\,128,\,128]$
Spline order $k$	3
Grid size	3
Grid range	$[-1,\,1]$

Table 2: Network and implementation settings of the KAN-based actor and critic networks.

Variable	Value	Unit	Description
$c_{CO_{2}}$	0.1906	€/kg	CO 2 price coefficient
$c_{heat}$	0.1281	€/kWh	Heating price coefficient
$c_{DW}$	22.29	€/kg	Crop dry-weight price
$\lambda_{CO_{2}}$	$5\times 10^{-5}$	–	Weight for CO 2 violations
$\lambda_{T}^{\min}$	$3\times 10^{-3}$	–	Weight for lower temperature violations
$\lambda_{T}^{\max}$	$5\times 10^{-3}$	–	Weight for upper temperature violations

Table 3: Economic parameters and constraint cost coefficients.

Variable	Lower	Upper	Unit
Climate variables
$y_{CO_{2}}$	500	1600	ppm
$y_{T}$	10	20	∘ C
$y_{RH}$	0	80	%
Control inputs
$u_{CO_{2}}$	0	1.2	mg/m 2 /s

Table 4: Climate variable ranges and control input limits.

Hyperparameter	Value
Total training timesteps	$4\times 10^{6}$
Number of parallel environments ( $n_{\mathrm{envs}}$ )	$8$
Rollout length ( $n_{\mathrm{steps}}$ )	$1920$
Batch size	$1920$
Optimization epochs per update	$10$
Discount factor ( $\gamma$ )	$0.98$

Table 5: PPO hyperparameters used in the experiments.

Hyperparameter	Symbol	Value
Initial penalty coefficient	$\lambda_{0}$	$1.0$
Minimum penalty coefficient	$\lambda_{\min}$	$0.05$
Maximum penalty coefficient	$\lambda_{\max}$	$50.0$
Constraint threshold	$d$	$0.7$
Penalty update interval (episodes)	$K$	$4$
Penalty learning rate	$\alpha_{\lambda}$	$0.01$

Table 6: RCPO hyperparameters for constraint regulation.

Method	Cumulative profit	$\Delta$ Profit (%)	Cumulative violation	$\Delta$ Violation (%)
PPO (baseline)	$3.782$ ( $\pm 0.146$ )	– ( $\pm 3.86$ )	$0.858$ ( $\pm 0.027$ )	– ( $\pm 3.15$ )
RCPO w/o KAN & Time	$3.543$ ( $\pm 0.061$ )	$-6.32$ ( $\pm 1.72$ )	$0.695$ ( $\pm 0.026$ )	$-19.00$ ( $\pm 3.74$ )
RCPO w/o Time	$3.635$ ( $\pm 0.064$ )	$-3.89$ ( $\pm 1.76$ )	$0.712$ ( $\pm 0.039$ )	$-17.02$ ( $\pm 5.48$ )
RCPO w/o KAN	$3.755$ ( $\pm 0.165$ )	$-0.71$ ( $\pm 4.39$ )	$0.710$ ( $\pm 0.025$ )	$-17.25$ ( $\pm 3.52$ )
KAN-RCPO-PPO	$3.892$ ( $\pm 0.147$ )	$+2.91$ ( $\pm 3.78$ )	$0.698$ ( $\pm 0.029$ )	$-18.65$ ( $\pm 4.15$ )

Table 7: Performance comparison under different controller configurations.

Figure 3: Ablation study on policy representation enhancements. Training performance comparison between baseline PPO, PPO with cyclic time features, and PPO with KAN-based policy networks. All methods are trained without RCPO constraint regulation.

Figure 4: Normalized cumulative climate constraint violations for different climate variables achieved by the proposed RCPO-PPO controller relative to the baseline PPO controller. The baseline PPO result is normalized to $100\%$ .

Figure 5: Normalized cumulative operation costs associated with heating and $\mathrm{CO}_{2}$ input achieved by the proposed RCPO-PPO controller relative to the baseline PPO controller. The baseline PPO result is normalized to $100\%$ .

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Parameter	Value	Parameter	Value	Parameter	Value
$p_{1}$	0.544	$p_{11}$	$7.50\times 10^{-6}$	$p_{21}$	$3.60\times 10^{-3}$
$p_{2}$	$2.65\times 10^{-7}$	$p_{12}$	8.31	$p_{22}$	9348
$p_{3}$	53	$p_{13}$	273.15	$p_{23}$	8314
$p_{4}$	$3.55\times 10^{-9}$	$p_{14}$	101325	$p_{24}$	273.15
$p_{5}$	$5.11\times 10^{-6}$	$p_{15}$	0.044	$p_{25}$	17.4
$p_{6}$	$2.30\times 10^{-4}$	$p_{16}$	$3.00\times 10^{4}$	$p_{26}$	239

Appendix

Table 8: Nominal parameter values of the lettuce greenhouse model.

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Group Relative Policy Optimization (GRPO) remains the dominant critic-free approach for fine-tuning LLMs and VLMs, but its compatibility with constrained policy optimization (e.g. for safety-critical domains) has not been carefully examined. In this work, we introduce Constrained GRPO, a Lagrangian-based extension of GRPO for constrained policy optimization. We show that the standard practice of scalarizing rewards before normalization introduces a critical Lagrangian-specific failure mode: GRPO's within-group normalization makes constrained optimization highly sensitive to how multi-component learning signals are aggregated. We show that scalarizing rewards before normalization introduces shared-denominator coupling, so that changing one multiplier alters not only the emphasis on its corresponding constraint, but also the relative weighting of the reward and other constraints. We address this with a simple but crucial modification: scalarizing standardized advantages rather than rewards. This yields a better-conditioned update by addressing the coupling induced by reward scalarization, resulting in better-behaved multiplier dynamics and more stable constraint enforcement in practice. Empirically, across a controlled gridworld, a real-world autonomous driving benchmark, and a mathematical reasoning task, Constrained GRPO consistently achieves better adherence to specified constraints while maintaining or improving task performance.

Abstract

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