Sistemas Dinâmicos e Optimização
Diploma de Estudos Avançados em Engenharia Electrotécnica e de Computadores
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.