Control of uncertain stochastic systems: the CVIU approach and the H infinity control

Abstract

The MSc research project "Stochastic control of uncertain systems: a model in which the control increases uncertainty" studies the control of uncertain systems by means of the CVIU approach, short for Control Variation Increases Uncertainties. This approach originates from the idea that, for systems with highly uncertain or unknown dynamics, a forceful control action may lead the system to a region in which the uncertainty about the exact state of the system may be higher than the one induced by a mild action. The idea is captured by the introduction of multiplicative stochastic noise terms dependent on the absolute values of the system state and control, and the resulting model is used to formulate an optimal stochastic control problem. The solution of the control problem via dynamic programming shows the existence of a region around the equilibrium point, the inaction region, for which the optimal control policy is to keep the equilibrium control action unchanged.This is a theoretical result, and yet relates to the call for cautionary control policies in fields such as economy and biology. The representation of uncertainties in the CVIU model, on the other hand, bears similarities to the way uncertainties are portrayed in the theory of robust control. This motivates our study on the relation between the two approaches and how their performances can be compared. Preliminary results which enable the comparison of the CVIU approach with that of a controller designed by minimization of the H2 norm were developed during the research project carried at the University of Campinas. Here we propose to develop a similar comparison result with the H infinity case. The characterization of the relations between the CVIU approach and classical models from the theory of control systems, as well as the study of possible applications of the proposed control strategy, will enhance the description of the CVIU approach and help to place it among the general literature of control of uncertain systems. (AU)