Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 964742, 28 pages
http://dx.doi.org/10.1155/2012/964742
Research Article

MPC Schemes Guaranteeing ISDS and ISS for Nonlinear (Time-Delay) Systems

Sergey Dashkovskiy1 and Lars Naujok2

1Department of Civil Engineering, University of Applied Sciences Erfurt, P.O. Box 450155, 99051 Erfurt, Germany
2Centre of Industrial Mathematics, University of Bremen, P.O. Box 330440, 28334 Bremen, Germany

Received 22 June 2012; Accepted 3 October 2012

Academic Editor: Hamid Reza Karimi

Copyright © 2012 Sergey Dashkovskiy and Lars Naujok. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

New directions in model predictive control (MPC) are introduced. On the one hand, we combine the input-to-state dynamical stability (ISDS) with MPC for single and interconnected systems. On the other hand, we introduce MPC schemes guaranteeing input-to-state stability (ISS) of single systems and networks with time delays. In both directions, recent results of the stability analysis from the mentioned areas are applied using Lyapunov function(al)s to show that the corresponding cost function(al) of the MPC scheme is a Lyapunov function(al). For networks, we show that under a small-gain condition and with an optimal control obtained by an MPC scheme for networks, it has the ISDS property or ISS property, respectively.