Stationary policies for lower bounds on the minimum average cost of discrete-time nonlinear control systems

Author(s)

Vargas, Alessandro N. ^{[1, 2]} ; Ishihara, Joao Y. ^{[2, 3]} ; do Val, Joao B. R. ^[4]

Affiliation

^[1] Univ Tecnol Fed Parana, UTFPR, BR-86300000 Cornelio Procopio, PR - Brazil

^[2] BCAM, E-48009 Bilbao, Vizcaya - Spain

^[3] Univ Brasilia, UnB, FT, BR-70910900 Brasilia, DF - Brazil

^[4] Univ Estadual Campinas, UNICAMP, FEEC DT, BR-13083852 Campinas, SP - Brazil

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL; v. 24, n. 17, p. 2943-2957, NOV 25 2014.
• Web of Science Citations: 0

Abstract

The paper deals with the control problem of discrete-time nonlinear systems. The main contribution of this note is to present conditions that assure the existence of stationary policies that generate lower bounds for the minimal long-run average cost. These lower bounds coincide with the optimal solution when a mild convergence assumption holds. To illustrate the results, the paper presents an application for the simultaneous state-feedback control problem, and the derived strategy is used to design a real-time simultaneous control for two direct current motor devices. The dynamics of these two devices are written in terms of a nonlinear algebraic matrix recurrence, which in turn represents a particular case for our general nonlinear approach. The optimal gain for the corresponding simultaneous state-feedback problem is obtained, and such a gain was implemented in a laboratory testbed to control simultaneously the two direct current motors. Copyright (c) 2013 John Wiley \& Sons, Ltd. (AU)

• FAPESP's process: 03/06736-7 - Control and filtering of Markovian jumping parameters stochastic systems
• Grantee: João Bosco Ribeiro do Val
• Support Opportunities: Research Projects - Thematic Grants