* Corresponding author. Tel.:#1 219 631 8309; fax: #1 219 631
4393; e-mail: lemmon@maddog.ee.nd.edu.
This paper was not presented at any IFAC meeting. This paper was
recommended for publication in revised form by Guest Editors
J. M. Schumacher, A. S. Morse, C. C. Pantelides, and S. Sastry. The
authors gratefully acknowledge the partial financial support of the
Army Research Office (DAAH04-95-1-0600, DAAH04-96-1-0134, and
DAAAG5-98-1-0199).
Automatica 35 (1999) 491—503
Bounded amplitude performance of switched LPV systems
with applications to hybrid systems
Christopher J. Bett, Michael D. Lemmon*
Raytheon Systems Company, Missile Guidance Laboratory, Tewksbury, MA 01876, USA
Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
Received 14 October 1997; revised 1 May 1998; received in final form 24 September 1998
¹emporal characteristics of a scheduled linear parameter varying system, controlled by switching
from a finite collection of setpoint amplitude controllers, are derived and used to construct timed
automata models of the switched system.
Abstract
This paper discusses recent results on multiple linear agent control for systems satisfying a bounded amplitude performance
constraint. The plant is assumed to be a linear parameter varying (LPV) system scheduled along a nominal parameter trajectory; in
this respect, the control problem represents a plant operating between a prespecified set of operating conditions. Linear controllers are
designed at setpoints along this scheduling trajectory to satisfy bounded amplitude performance constraints. This paper discusses an
approach to analyze the switched system behavior under practical assumptions on the structure of the switching rule. The approach
combines the scheduling parameter with LPV system properties to derive bounds on the switching behavior of the system. These
estimates are then used to construct a logical model of the switched system behavior in the form of a timed automaton. In this respect,
this paper presents a way of extracting logical models of continuous time system behavior. 1999 Elsevier Science Ltd. All rights
reserved.
Keywords: Amplitude response; Automata extraction; Gain scheduling; Lyapunov methods; Parametric variation; Timed automata
1. Introduction
This paper addresses the problem of scheduling a
linear parameter varying (LPV) system between
a predefined set of operating conditions by switching
from a set of LTI controllers, called agents, so that the
controlled system satisfies constraints on signal ampli-
tude. The primary theoretical result of this study is a suf-
ficient condition for bounded amplitude performance
expressed as a dwell time, a lower bound on the time for
which an agent must be kept in feedback with the plant.
This dwell time condition is parameterized by solutions
to a set of matrix inequalities similar to those defined in
Bett and Lemmon (1997) for bounded amplitude control
of LPV systems. Analyzing the switched system for the
dwell time conditions allows the extraction of a timed
logical model of the controlled system. This result has
important implications for hybrid systems because it
provides a necessary link between continuous state and dis-
crete event representations of the switched system de-
rived from modern linear robust control methodologies.
In the area of scheduled control, this paper provides
contributions to the study of switched scheduling under
bounded amplitude performance constraints. While the
framework established in this paper describes a schedul-
ing problem, the framework is distinct from traditional
and modern gain scheduling paradigms (e.g. Apkarian
0005-1098/99/$—see front matter 1999 Elsevier Science Ltd. All rights reserved
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