Stabilization of strictly dissipative discrete time systems with discounted optimal control

Vladimir Gaitsgory; Lars Grüne; Matthias Höger; Christopher M. Kellett; Steven R. Weller

doi:10.1016/j.automatica.2018.03.076

Stabilization of strictly dissipative discrete time systems with discounted optimal control

Vladimir Gaitsgory, Lars Grüne, Matthias Höger, Christopher M. Kellett^*, Steven R. Weller

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

Abstract

We consider stabilization of an equilibrium point via infinite horizon discounted optimal control in discrete-time. In addition to applications in economics and social sciences, discounted optimal control is a commonly used numerical technique guaranteeing solvability of certain classes of optimal control problems. In this paper, we present conditions based on strict dissipativity that ensure that the optimally controlled system is asymptotically stable or practically asymptotically stable. These conditions are shown to be complementary to recently proposed conditions based on a detectability property. Illustrative examples are provided.

Original language	English
Pages (from-to)	311-320
Number of pages	10
Journal	Automatica
Volume	93
DOIs	https://doi.org/10.1016/j.automatica.2018.03.076
Publication status	Published - Jul 2018
Externally published	Yes

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title = "Stabilization of strictly dissipative discrete time systems with discounted optimal control",

abstract = "We consider stabilization of an equilibrium point via infinite horizon discounted optimal control in discrete-time. In addition to applications in economics and social sciences, discounted optimal control is a commonly used numerical technique guaranteeing solvability of certain classes of optimal control problems. In this paper, we present conditions based on strict dissipativity that ensure that the optimally controlled system is asymptotically stable or practically asymptotically stable. These conditions are shown to be complementary to recently proposed conditions based on a detectability property. Illustrative examples are provided.",

keywords = "Discounted optimal control, Lyapunov function, Stabilization, Strict dissipativity",

author = "Vladimir Gaitsgory and Lars Gr{\"u}ne and Matthias H{\"o}ger and Kellett, \{Christopher M.\} and Weller, \{Steven R.\}",

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AU - Gaitsgory, Vladimir

AU - Grüne, Lars

AU - Höger, Matthias

AU - Kellett, Christopher M.

AU - Weller, Steven R.

PY - 2018/7

Y1 - 2018/7

N2 - We consider stabilization of an equilibrium point via infinite horizon discounted optimal control in discrete-time. In addition to applications in economics and social sciences, discounted optimal control is a commonly used numerical technique guaranteeing solvability of certain classes of optimal control problems. In this paper, we present conditions based on strict dissipativity that ensure that the optimally controlled system is asymptotically stable or practically asymptotically stable. These conditions are shown to be complementary to recently proposed conditions based on a detectability property. Illustrative examples are provided.

AB - We consider stabilization of an equilibrium point via infinite horizon discounted optimal control in discrete-time. In addition to applications in economics and social sciences, discounted optimal control is a commonly used numerical technique guaranteeing solvability of certain classes of optimal control problems. In this paper, we present conditions based on strict dissipativity that ensure that the optimally controlled system is asymptotically stable or practically asymptotically stable. These conditions are shown to be complementary to recently proposed conditions based on a detectability property. Illustrative examples are provided.

KW - Discounted optimal control

KW - Lyapunov function

KW - Stabilization

KW - Strict dissipativity

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VL - 93

SP - 311

EP - 320

JO - Automatica

JF - Automatica

ER -

Stabilization of strictly dissipative discrete time systems with discounted optimal control

Abstract

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