Simple adaptive control for positive linear systems with applications to pest management

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 adaptive controllers do not arise and usual high-gain structural assumptions are not required

Mitigating ground effect on mini quadcopters with model reference adaptive control

Mitigating ground effect becomes a big challenge for autonomous aerial vehicles when they are flying in close proximity to the ground. This paper aims to develop a precise model of ground effect on mini quadcopters, provide an advanced control algorithm to counter the model uncertainty and, as a result, improves the command tracking performance when the vehicle is in the ground effect region. The mathematical model of ground effect has been established through a series of experiments and validated by a flight test. The experiments show that the total thrust generated by rotors increases linearly as the vehicle gets closer to the ground, which is different from the commonly-used ground effect model for a single rotor vehicle. In addition, the model switches from a piecewise linear to a quadratic function when the rotor to rotor distance is increased. A control architecture that utilizes the model reference adaptive controller (MRAC) has also been designed, where MRAC is added to the altitude loop. The performance of the proposed control algorithm has been evaluated through a set of flight tests on a mini quadcopter platform and compared with a traditional proportional–integral–derivative (PID) controller. The results demonstrate that MRAC dramatically improves the tracking performance of altitude command and can reduce the rise time by 80 % under the ground effect

STABILIZATION BY ADAPTIVE FEEDBACK CONTROL FOR POSITIVE DIFFERENCE EQUATIONS WITH APPLICATIONS IN PEST MANAGEMENT

An adaptive feedback control scheme is proposed for stabilizing a class of forced nonlinear positive difference equations. The adaptive scheme is based on so-called high-gain adaptive controllers and contains substantial robustness with respect to model uncertainty as well as with respect to persistent forcing signals, including measurement errors. Our results take advantage of the underlying positive systems structure and ideas from input-to-state stability from nonlinear control theory. Our motivating application is to pest or weed control, and in this context the present work substantially strengthens previous work by the authors. The theory is illustrated with examples

Modeling Complex Systems

Abstract Empirical observations suggest that linear dynamics are not an adequate representa- tion of ecological systems and that a realistic representation would require adoption of complex nonlinear dynamical systems with characteristics encountered in complex adaptive systems (CAS). Adequate modelling should include and combine, among others, strategic interactions among economic agents, nonconvexities induced by non-linear feedbacks, separate spatial and temporal scales and modeling of spatiotempo-ral dynamics, and allowance of alternative time scales. Ignoring these characteristics might obscure very important features that we observe in reality such as bifurcations and irreversibilities or hysteresis. As a consequence, the design of policies that do not take CAS characteristics into account might lead to erroneous results and undesirable states of managed economic-ecological systems.Complex adaptive systems, differential games, spatiotemporal dynamics, fast-slow variables.

ADDITIVE VERSUS PROPORTIONAL PEST DAMAGE FUNCTIONS: WHY ECOLOGY MATTERS

Economic analyses of pests typically assume damage is either additively separable from pest free yield or proportional to it. This paper describes the ecological assumptions required for additive and proportional damage functions to demonstrate that both specifications are reasonable. Ecological research supports a proportional damage function for competitive pests such as weeds, while for insect pests the appropriate damage function depends on the level of pest free yield. Theoretical analysis identifies differences between additive and proportional damage functions in terms of the impact of pest control on output variance and the concavity of output in the pest control input.Pest Economics, Damage Function, Damage Control, Risk Reducing Input, Increasing Returns, Functional Response, Crop Production/Industries, Environmental Economics and Policy,

Practical guidelines for modelling post-entry spread in invasion ecology

In this article we review a variety of methods to enable understanding and modelling the spread of a pest or pathogen post-entry. Building upon our experience of multidisciplinary research in this area, we propose practical guidelines and a framework for model development, to help with the application of mathematical modelling in the field of invasion ecology for post-entry spread. We evaluate the pros and cons of a range of methods, including references to examples of the methods in practice. We also show how issues of data deficiency and uncertainty can be addressed. The aim is to provide guidance to the reader on the most suitable elements to include in a model of post-entry dispersal in a risk assessment, under differing circumstances. We identify both the strengths and weaknesses of different methods and their application as part of a holistic, multidisciplinary approach to biosecurity research

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research

An exploration of the potential benefits of integrated pest management systems and the use of insect resistant potatoes to control the Guatemalan Tuber Moth (Tecia solanivora Povolny) in Ventaquemada, Colombia:

"CORPOICA and IFPRI implemented a research project in Ventaquemada, Colombia. The project's goal was to asses the benefits of Integrated Pest Management (IPM) practices and the potential of Genetically Modified insect resistant (Bt) potatoes to manage damage caused by the Guatemalan Tuber Moth (Tecia solanivora Povolny). The Guatemalan Tuber Moth is particularly destructive because field spraying on the adult stage is ineffective and there exists damage specificity to the tubers. Excessive pesticide sprays have resulted in resistance to several insecticides. Insect resistant (Bt) potatoes has been shown an effective means to control other members of the Tuber Moth complex. Thus a Bt potato may play a role in managing Tecia in Colombia. This is an ex ante study as there are no Bt potatoes currently under field conditions in Colombia.. To examine this issue, we conducted a survey in 2003 of 78 farmers in the region to estimate a baseline of traditionally and IPM managed systems. The first year survey was supplemented with focus groups to examine damage and production costs in 2003 and 2004. We also implemented activities such as field verification of IPM practices and damage, a Farmer Field School and other participatory methods. Our analysis uses methods such partial budgeting analysis, a production function input abatement expectations model, and an economic surplus model augmented by stochastic simulations. Results of the analysis presented here outlines estimated losses under field and storage conditions, likely range of benefits accrued by farmers in the region due to the potential adoption of a portfolio of IPM management practices and Bt potatoes. Results from the survey conducted in 2003 show that producers in the area have endured significant field and storage losses within the previous 10 years, but were low in that particular year. Initial results where confirmed by results of focus groups in 2003 and 2004 which show very low field and storage damage. Sustained precipitation explains the observed low levels of damage by the Tuber Moth. Low levels of damage induced zero (or even negative) cost differences between conventional and IPM management. In contrast, using the proposed expectation model to estimate expected payoffs to IPM investments show that even with low levels of damage it still pays for producers to invest in IPM practices. The economic surplus estimates show that even considering variability of field and storage losses, as well as of other critical parameters, the use of Bt potatoes in Colombia creates a positive return to investment to Bt potato research, assuming that damage is present under field conditions. We finalize by discussing some of the institutional and strategic considerations for the potential use of Bt potatoes in the country." Authors' abstractPotatoes Economic aspects, Genetically modified crops, Economic surplus model, Risk, Research and development, Bt-potatoes,