Optimal Crop Rotations subject to Weed Dynamics: Exponential Stability and Nonlinear Programming
Maarten de Jong (TU Delft - Team Tamas Keviczky)
Koty McAllister (TU Delft - Team Koty McAllister)
Giulia Giordano (Università degli Studi di Trento)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
Agricultural production of annual crops is often hampered by annual weeds, which compete with planted crops and persist through the collection of dormant seeds in the soil called the weed seed bank. Conventional weed management relies heavily on chemical herbicides, which are not sustainable. A complementary method that reduces the need for herbicides is ‘cultural control’, in which the crop rotation is designed in part to manage the weed population. We propose a methodology that optimizes the crop rotation, here defined as periodic crop planting densities, subject to periodic weed dynamics. We adopt a well-established model of discrete-time annual weed seed bank dynamics with crop planting density inputs, and show that any periodic weed seed bank trajectory corresponding to a periodic crop rotation is globally exponentially stable. This guarantees convergence to the optimal periodic trajectory obtained by solving a nonlinear optimal control problem with periodic constraints, which we formulate as a nonlinear program.