Estudo e desenvolvimento de sistemas de controle ótimo com filtragem estocástica

Abstract

Optimal control theory and stochastic filtering, especially with respect to their intrinsic relationship to problems of optimization that may or may not be subject to uncertainties of the system have always been what many mathematicians and engineers consider theories of wide application together. The present work provides a motivation to study these areas, covering the key concepts of both the theory of didactic form. Deals with the study of the dynamic programming proposed by Richard Bellman and, at the same time, the optimization problem develops the study of State estimators using the Kalman filter, emphasizing the problem in discrete domain. This paper proposes applications for optimization problems modeled for a quadratic cost, divided into finite and infinite horizon problems in discrete and continuous domain. Finally, it proposes a methodology for implementation of optimal control systems with stochastic filtering in a didactic prototype (helicopter 2DOF of fixed base), whose purpose begins with the development of the mathematical model of the prototype and ends with the realization of optimal control.