Print Email Facebook Twitter Comparing Two Approaches of Modelling Fish Harvesting Strategies Using Optimal Control Title Comparing Two Approaches of Modelling Fish Harvesting Strategies Using Optimal Control Author in 't Veld, Niels (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Sandberg, Mattias (mentor) Vuik, Cornelis (graduation committee) Degree granting institution Delft University of TechnologyKTH Royal Institute of Technology Programme Computer Simulations for Science and Engineering (COSSE) Date 2022-06-10 Abstract Optimal control is a paradigm for solving optimization problems involving dynamical systems, which are to be controlled. It is able to solve fish harvesting problems, in which we want to optimize harvesting out-take by considering fishing as a control function that acts on the state of the dynamical system, which represents the growth of fish species in the environment. Other modelling aspects of optimal control are defining terminal costs and running costs, e.g. maximizing profit. We keep the terminal condition comparable for a different number of species. It is based on the initial population.By using the optimal control Hamiltonian and Pontryagin's Maximum Principle we can calculate the optimal state trajectories corresponding to suitable optimal controls. The Hamiltonian is dependent on the state equation and the running costs. We present two approaches of modelling the running costs. An approach that is not directly translatable to the fish harvesting problem, but it leads to a smooth Hamiltonian, which greatly simplifies derivation and computation. The other, which is equivalent to maximizing profit, leads to a non-smooth Hamiltonian. This leads to jump-discontinuous derivatives needed for computation. We propose to regularize the derivatives of the Hamiltonian using suitable smooth functions, such that it is equivalent to regularizing the Hamiltonian directly. We give details for implementing both approaches up to systems of n competing species. After which we go into detail on algorithms and programming structure implemented. Finally, in modest numerical experiments, for one and two species, we show the relation between the optimal control and the terminal costs. But more interestingly, that the smooth Hamiltonian models are inadequate and regularized Hamiltonian models are the preferred choice. Intriguingly, the latter approach results in steady state solution, where the control acts as a stabilizer. Subject Optimal ControlNumerical AnalysisFish HarvestingHarvesting Strategies To reference this document use: http://resolver.tudelft.nl/uuid:fa7e731d-2348-4fc0-bedb-6f7c0f99427f Part of collection Student theses Document type master thesis Rights © 2022 Niels in 't Veld Files PDF main.pdf 3.39 MB Close viewer /islandora/object/uuid:fa7e731d-2348-4fc0-bedb-6f7c0f99427f/datastream/OBJ/view