Description
Objectives
Capacity to formulate well posed optimal control problems associated to ordinary differential equations and linear partial differential equations. Proficiency in deriving necessary and sufficient conditions for optimality. Master standard numerical methods used to approximate the optimal solution of different types of control problems.
Syllabus
Optimal control problems: terminology and basic concepts. Well posedness of nonlinear control problems governed by ordinary differential equations.The Pontriagyn Maximum Principle. Discretization of the boundary value problem. Global error and convergence of the numerical scheme. The direct discretization approach and the principle of dynamic programming in the case of linear quadratic problems. Feedback control; Optimal control problems governed by elliptic partial differential equations (PDEs): existence of solution, one shot approach versus gradient approaches. First and second order optimality conditions for distributed and boundary control. Finite Element (FE) based discretization. Error analysis. The direct approach: first discretize, then optimize, advantages and disadvantages; Optimal control of the heat equation. Optimality conditions. The time stepping scheme and FE space discretization. Error estimates. Introduction to feedback control of PDEs.
Prerequisites
Differential and Integral Calculus III, Numerical Analysis.
Cross Competence Component
The UC allows the development of transversal competences on Critical Thinking, Creativity and Problem Solving Strategies, in class, in autonomous work and in the several evaluation components. The percentage of the final grade associated with these competences should be around 15%.
Programming And Computing Component
Computational project (30% of the evaluation).
Ethical Principles
All members of a group are responsible for the group’s work. In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.