Modeling and control of stochastic systems with poorly known dynamics

Author(s)

Rafael Fontes Souto

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2015-08-18

Examining board members

João Bosco Ribeiro do Val; Marcelo Dutra Fragoso; Oswaldo Luiz do Valle Costa; Ricardo Coração de Leão Fontoura de Oliveira; José Cláudio Geromel

• Advisor: João Bosco Ribeiro do Val

Abstract

This doctorate thesis is concerned with controlling poorly known systems, for which only a simplified and uncertain model is avaliable for control design purposes. There are many systems that cannot be reasonably probed for the sake of identification, yet they are important for areas such economy, biology or medicine. The ideas are developed around an alternative way to account for the rough modeling in a stochastic based setting, and to heighten the control features for such a modified model. The mathematical framework for the optimal control reveals important features, worthy to mention, the raising of a cautionary feedback policy of "keep the action unchanged" (inaction, for short), on a certain state space region. This feature is not seen in the robust approach, but has been pointed out and permeates part of the economics literature. Convexity characterization of the value function and the generalized gradient provide the means and the use of the Hamilton-Jacobi-Bellman equation for the general problem. When specialized to the infinite horizon problem with discounted quadratic running cost, the asymptotic behavior is identified, in such a manner that the optimal solution of the multidimensional case is given inside the inaction region by a Lyapunov type of equation, and far apart, by a Riccati like equation. Thus, the complete solution is composed of an analytical part and a numerical one, and it is derived for the scalar case. The control design proposed here is compared with the standard and robust LQG solutions, exploring the fact that the model can be quite distinct of the actual system. It is verified that in some mismatched situations the novel approach presented in this thesis yields better performance than the LQG strategies (AU)

• FAPESP's process: 10/15135-0 - Analysis of Systems in which the Control Variation Increases Uncertainty
• Grantee: Rafael Fontes Souto
• Support Opportunities: Scholarships in Brazil - Doctorate