Mathematical Problems in Engineering
Volume 2004 (2004), Issue 3, Pages 197-208
doi:10.1155/S1024123X04404050
Robust control of discrete-time hybrid systems with uncertain modal dynamics
School of Electrical and Computer Engineering, University of Oklahoma, Norman 73019, OK, USA
Received 26 April 2004
Copyright © 2004 Thordur Runolfsson. 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
We study systems that are subject to sudden structural changes
due to either changes in the operational mode of the system or
failure. We consider linear dynamicalsystems that depend on a
modal variable which is either modeled as a finite-state Markov
chain or generated by an automaton that is subject to an external
disturbance. In the Markov chain case, the objective of the
control is to minimize a risk-sensitive cost functional. The
risk-sensitive cost functional measures the risk sensitivity of
the system to transitions caused by the random modal variable. In
the case when a disturbed automaton describes the modal variable,
the objective of the control is to make the system as robust to
changes in the external disturbance as possible. Optimality
conditions for both problems are derived and it is shown that the
disturbance rejection problem is closely related to a certain
risk-sensitive control problem for the hybrid system.