Sistemas Dinâmicos e Optimização SDO
Diploma de Estudos Avançados em Engenharia Electrotécnica e de Computadores - DEAEEC2006
Grupo: DEAEEC2006 > 3º Ciclo
6.0 (para cálculo da média)
The purpose of this course is twofold: to give the student a solid background in linear dynamical system theory and to expose him to the foundations of optimal control.
Basic mathematical concepts: Norms, metric spaces, complete spaces, fixed point theorem. State equation solutions: existence and uniqueness. The state transition matrix: computation and properties. Spectral decomposition with applications to linear system analysis. Stability: the Lyapunov criterion. Internal and input-output stability. Controllability and observability: key concepts, criteria, and geometrical interpretation. Realizability and minimal realizations. State feedback and pole placement. Asymptotic observers. Separation theorem. Examples of control problems with an optimality criterion. Time optimal control for linear processes: a geometric approach. Basic theory of the optimal regulator. Dynamic programming and the Hamilton-Jacobi equation. Solution of the regulator problem with a quadratic criterion.
Metodologia de avaliação
Problem sets will be issued once every week or two weeks with specific due dates. These will be graded and the grade on the problem sets will be 50% of the final grade. A final exam will be given at the end of the semester. The final exam grade will correspond to 40% of the final grade. 10% of the final grade will depend on regular class attendance and participation in class discussions.