Discrete-time, near optimal control of a cotton crop-boll weevil system

Vita.This dissertation presents a general method of optimizing simulated systems and demonstrates the procedure for maximizing the single period benefits of an entrepreneur. The method is applied to the problem of maximizing the profit of a Brazos Bottom (Texas) cotton producer faced with controlling boll weevil infestations. A plant-pest simulation model, developed by a team of bio-engineers at Texas A&M University, is used as a sub-system within a comprehensive system model to determine the impact of pesticides on boll weevil mortality and consequential changes in cotton output and producer's profit. The systems model can be visualized as a black box that generates cotton output, an economic sub-system which computes profit and an optimization algorithm which links the two components. The optimization algorithm repeatedly activates the black box generating each time an input vector yielding a higher objective function value, and stops when prescribed termination conditions are satisfied. The economic sub-system is characterized by an objective function whose analytical form is a well-defined function of cotton output; however, the explicit functional form of output as related to pesticide applications is not known because of its dependence on complex factors like plant growth characteristics and pest damage. Therefore, simulation procedures, which enable us to obviate the need for explicit functions, are used to generate the output. The complexity of the simulation relations involved in generating the output makes the objective function nonlinear in input and output variables. The systems model is amenable to solution by nonlinear optimization methods. Because of the absence of explicit objective function and constraints in this formulation, numerical solution methods are adopted. Towards this objective, the Davidson-Fletcher-Powell algorithm is utilized with some modifications aimed at increasing the efficiency of the linear searches involved in the algorithm. The algorithm repeatedly calls the output from the black box, computes the gradients and Hessian matrices numerically and returns the locally optimal value of the objective function when the criteria set for termination are satisfied..