A Stochastic Approach for Robustness: a H-2-norm comparison

Author(s)

Silva, Vinicius L. ; do Val, Joao B. R. ; Souto, Rafael F. ; IEEE

• Document type: Journal article
• Source: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC); v. N/A, p. 6-pg., 2017-01-01.

Abstract

The design of controllers for systems whose dynamics is uncertain or poorly known is a recurrent theme in control systems theory. Usually the mathematical models for control design are approximations of the dynamics of the real systems, and uncertainties arise naturally in this context. In the field of control systems, the theory of robust control is one typical approach for such systems, where the goal is to guarantee some features for the designed controller such as stability and a satisfactory performance against a set of possible uncertainties. Other common approach in the literature is found in the theory of stochastic control, where the uncertainties affecting the system are modeled as stochastic processes. In the literature, a recent proposal to control uncertain stochastic systems is the so called CVIU - Control Variation Increases Uncertainties - approach. This approach makes use of stochastic state-and control-dependent noise, and the corresponding control problem involves minimization of a discounted quadratic function. The representation of uncertainties in the CVIU approach bears similarities with models used in robust control theory, which motivates our discussion on the relations between the two approaches. A correspondence between the H-2 stochastic norm and the expected value of a discounted functional bridges the different cost criteria. (AU)

• FAPESP's process: 16/02208-6 - Stochastic control of uncertain systems: a model in which the control increases uncertainty
• Grantee: Vinicius Lima Silva
• Support Opportunities: Scholarships in Brazil - Master
• FAPESP's process: 16/08645-9 - Interdisciplinary research activities in electric smart grids
• Grantee: João Bosco Ribeiro do Val
• Support Opportunities: Research Projects - Thematic Grants