Comparing Data-Driven Models for Forecast and Control

Abstract

Greenhouses offer the promise to mitigate the challenges faced by traditional open field agri- culture. Operating these systems on a commercial scale demands effective control and forecast models. This thesis contributes to the increasing field of research that applies methods from systems and control to greenhouse systems. The primary objective was to evaluate various cli- mate prediction models for their applicability in forecast and predictive control within green- houses. Comparative analyses were conducted on linear and non-linear data-driven models across one week and one hour time horizons. The linear models include an autoregressive with exogenous input (ARX) model, subspace identification using the Multivariable Output-Error State-space algorithm (MOESP), and dynamic mode decomposition with control (DMDc). Of the linear methods, MOESP performed the best on both time horizons. The nonlinear methods included several long-short term memory (LSTM) models with different architec- tures. A stacked LSTM model was found to outperform the other LSTM models as well as all linear models over the one-week time horizon. The Koopman with inputs and control (KIC) framework, a novel nonlinear approach, was also examined. The choice of lifting func- tions proved to be a challenge, yielding only partial improvements over linear methods on the training set. For the short-term one-hour time horizon, the data-enabled predictive control (DeePC) algorithm was also implemented and yielded the most accurate results. Notably, the stacked LSTM predictor did not show any advantages on the one-hour timescale. Finally, a novel approach combining Koopman theory with DeePC was introduced and compared to the regular DeePC algorithm. No improvement was observed with this proposed method for one hour-ahead predictions. The comparison concluded with the insight that for the one hour time-horizon, the nonlinear methods that were investigated did not show advantages over linear methods in the greenhouse system. On the one week time horizon, nonlinear methods outperform linear ones. It affirmed the challenges around finding observables that fully span a Koopman invariant subspace. Further investigation on the proposed extension to DeePC should be the focus of future work.