Simple Adaptive Control for Positive Linear Systems with Applications to Pest Management

Chris Guiver,Christina Edholm,Richard Rebarber,Markus Mueller,Yu Jin,Jim Powell,Stuart Townley,Brigitte Tenhumberg

doi:10.1137/140996926

Chris Guiver, Christina Edholm + Show 6 more

Open Access

https://doi.org/10.1137/140996926

Copy DOI

Abstract

Pest management is vitally important for modern arable farming, but models for pest species are often highly uncertain. In the context of pest management, control actions are naturally described by a nonlinear feedback that is generally unknown, which thus motivates a robust control approach. We argue that adaptive approaches are well suited for the management of pests and propose a simple high-gain adaptive tuning mechanism so that the nonlinear feedback achieves exponential stabilization. Furthermore, a switched adaptive controller is proposed, cycling through a set of given control actions, that also achieves global asymptotic stability. Such a model in practice allows for the possibility of rotating between different courses of management action. In developing our control strategies we appeal to comparison and monotonicity arguments. Interestingly, componentwise nonnegativity of the model, combined with an irreducibility assumption, implies that several issues typically associated with high-gain adapt...

Highlights

The 21st century is likely to see increasing pressure on world food production because of growing population and per capita consumption, greater competition for land use, and climate change [1]
Simple adaptive control has been considered for discrete-time positive state linear systems, motivated by potential applications in pest management
Pest management is a timely and hugely important societal challenge that shall significantly contribute to the future success of economically and environmentally viable agriculture and horticulture

Summary

Introduction

The 21st century is likely to see increasing pressure on world food production because of growing population and per capita consumption, greater competition for land use, and climate change [1]. The present mathematical investigation is motivated by the observation that existing simple adaptive controllers are typically not designed for models where the state variables are constrained to take nonnegative values, as is the case in applied pest management contexts, and in models for harvesting, scavenging, culling, or predation. In a pest management context, the input variable is naturally allowed to take negative values, provided that a nonnegative number or distribution of pests remains, leading to the concept of so-called positive state systems [41] Such a framework allows the modelling of control actions that are essential for pest management but, importantly, fall outside the existing positive input systems theory.

Adaptive control schemes for pest management

Findings

Discussion