Details
| Original language | English |
|---|---|
| Pages (from-to) | 399-404 |
| Number of pages | 6 |
| Journal | IEEE Control Systems Letters |
| Volume | 2 |
| Issue number | 3 |
| Publication status | Published - 1 Jul 2018 |
| Externally published | Yes |
Abstract
We investigate strict dissipativity and turnpike properties for indefinite discrete-time linear quadratic optimal control problems in the presence of constraints on state and input. Previous results provide a geometric characterization of these properties in case that the stage cost is convex. We generalize these results to indefinite cost functions using two approaches: First, we show that the existing framework can be extended to indefinite state weighting if the stage cost accumulated over multiple consecutive time steps is convex. As a second contribution, we study the strict dissipation inequality by taking the particular shape of the constraints into account. This allows us to state sufficient conditions for strict dissipativity and turnpike properties where the occurrence of turnpikes on the boundary of the constraints is directly related to negative eigenvalues of the cost.
Keywords
- constrained control, optimal control, Predictive control for linear systems
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Engineering(all)
- Control and Systems Engineering
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In: IEEE Control Systems Letters, Vol. 2, No. 3, 01.07.2018, p. 399-404.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Indefinite Linear Quadratic Optimal Control
T2 - Strict Dissipativity and Turnpike Properties
AU - Berberich, Julian
AU - Köhler, Johannes
AU - Allgöwer, Frank
AU - Muller, Matthias A.
N1 - Publisher Copyright: © 2017 IEEE. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - We investigate strict dissipativity and turnpike properties for indefinite discrete-time linear quadratic optimal control problems in the presence of constraints on state and input. Previous results provide a geometric characterization of these properties in case that the stage cost is convex. We generalize these results to indefinite cost functions using two approaches: First, we show that the existing framework can be extended to indefinite state weighting if the stage cost accumulated over multiple consecutive time steps is convex. As a second contribution, we study the strict dissipation inequality by taking the particular shape of the constraints into account. This allows us to state sufficient conditions for strict dissipativity and turnpike properties where the occurrence of turnpikes on the boundary of the constraints is directly related to negative eigenvalues of the cost.
AB - We investigate strict dissipativity and turnpike properties for indefinite discrete-time linear quadratic optimal control problems in the presence of constraints on state and input. Previous results provide a geometric characterization of these properties in case that the stage cost is convex. We generalize these results to indefinite cost functions using two approaches: First, we show that the existing framework can be extended to indefinite state weighting if the stage cost accumulated over multiple consecutive time steps is convex. As a second contribution, we study the strict dissipation inequality by taking the particular shape of the constraints into account. This allows us to state sufficient conditions for strict dissipativity and turnpike properties where the occurrence of turnpikes on the boundary of the constraints is directly related to negative eigenvalues of the cost.
KW - constrained control
KW - optimal control
KW - Predictive control for linear systems
UR - http://www.scopus.com/inward/record.url?scp=85057636560&partnerID=8YFLogxK
U2 - 10.1109/LCSYS.2018.2842142
DO - 10.1109/LCSYS.2018.2842142
M3 - Article
VL - 2
SP - 399
EP - 404
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
IS - 3
ER -