Optimal economic planning and control for the management of ecosystems

In recent years the interest on sustainable systems has increased significantly. Among the many interested problems, creating and restoring sustainable ecosystems is a challenging and complex problem. One of the fundamental problems within this area is the imbalance between species that have a predator-prey relationship. Solutions involving management have become an integral player in many environments. Management systems typically use ad hoc methods to develop harvesting policies to control the populations of species to desired numbers. In order to amalgamate intelligence and structure, ecological systems require a diverse research effort from three primary fields: ecology, economics, and control theory. In this thesis, all three primary fields aforementioned are researched to develop a theoretical framework that includes an optimal trajectory planning system that exploits an ecosystem to maximize profits for the supporting community, and a robust control system design to track the optimal trajectories subjected to exogenous disturbances. Population ecology is used to select a model that identifies the key characteristics a management system needs to understand the behavior of the natural environment. A bioeconomic model is developed to relate the species populations to revenue. The nonlinear ecosystem is transformed into a linear parameter-varying (LPV) system that is then controlled using hinf synthesis and the gain scheduling methodology. The consequences of the results in this thesis are that optimal trajectories of an ecosystem can be obtained by constructing and solving a nonlinear programming problem (NLP), and the LPV based gain scheduling approach produces a robust controller that rejects disturbances and advises quality control policies to the manager an ecosystem. The LPV controller achieves comparable profits with satisfactory tracking performance while minding the induced costs of its high frequency output. Implications of constraining the control effort when designing for robustness are observed. Overall, the theoretical framework provides a solid foundation for future research on the understanding and improvement of ecosystem management