Title: Underdetermined stochastic systems modelled by a control dependent diffusion
Authors: Joao Bosco Ribeiro do Val , Rafael Souto
Abstract: This paper presents a theoretical framework for the optimization of a class of control dependent diffusions, namely, continuous-time stochastic systems in which the absolute value of the control variations increase the state uncertainty (CVIU systems). It is shown that this class of systems can be used in the modelling of complex stochastic systems for which the dynamics are not completely known. Controlled Itˆo diffusion processes describes the state path of the systems, and it is necessary to solve the Hamilton-Jacobi-Bellman equation of a nonlinear system in order to achieve the optimal solution. In addition, tools from nonsmooth analysis indicated the existence of a region in the state space where the optimal control action is characterized by no variation , yielding periods of inaction in the control policy. This behavior is somehow expected from the cautionary nature of controlling underdetermined systems, but here it is obtained directly from optimality.
Publication date: 2012-07-16
Online entry date: 2013-05-08
Conference: CONTROLO’2012
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