Existence of SDRE stabilizing feedback

J. S. Shamma; J. R. Cloutier

doi:10.1109/acc.2001.945645

Existence of SDRE stabilizing feedback

J. S. Shamma^*, J. R. Cloutier

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

9 Scopus citations

Abstract

The state-dependent Riccati equation (SDRE) approach to nonlinear system stabilization relies on representing a nonlinear system's dynamics in a manner to resemble linear dynamics, but with state-dependent coefficient matrices that can then be inserted into state-dependent Riccati equations to generate a feedback law. Although stability of the resulting closed loop system need not be guaranteed a priori, simulation studies have shown that the method can often lead to suitable control laws. In this paper, we consider the non-uniqueness of such a representation. In particular, we show that if there exists any stabilizing feedback leading to a Lyapunov function with star-shaped level sets, then there always exists a representation of the dynamics such that the SDRE approach is stabilizing. The main tool in the roof is a novel application of the S-procedure for quadratic forms.

Original language	English (US)
Pages (from-to)	4253-4257
Number of pages	5
Journal	Proceedings of the American Control Conference
Volume	6
DOIs	https://doi.org/10.1109/acc.2001.945645
State	Published - 2001
Externally published	Yes
Event	2001 American Control Conference - Arlington, VA, United States Duration: Jun 25 2001 → Jun 27 2001

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/acc.2001.945645

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title = "Existence of SDRE stabilizing feedback",

abstract = "The state-dependent Riccati equation (SDRE) approach to nonlinear system stabilization relies on representing a nonlinear system's dynamics in a manner to resemble linear dynamics, but with state-dependent coefficient matrices that can then be inserted into state-dependent Riccati equations to generate a feedback law. Although stability of the resulting closed loop system need not be guaranteed a priori, simulation studies have shown that the method can often lead to suitable control laws. In this paper, we consider the non-uniqueness of such a representation. In particular, we show that if there exists any stabilizing feedback leading to a Lyapunov function with star-shaped level sets, then there always exists a representation of the dynamics such that the SDRE approach is stabilizing. The main tool in the roof is a novel application of the S-procedure for quadratic forms.",

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year = "2001",

doi = "10.1109/acc.2001.945645",

language = "English (US)",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "2001 American Control Conference ; Conference date: 25-06-2001 Through 27-06-2001",

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T1 - Existence of SDRE stabilizing feedback

AU - Shamma, J. S.

AU - Cloutier, J. R.

PY - 2001

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N2 - The state-dependent Riccati equation (SDRE) approach to nonlinear system stabilization relies on representing a nonlinear system's dynamics in a manner to resemble linear dynamics, but with state-dependent coefficient matrices that can then be inserted into state-dependent Riccati equations to generate a feedback law. Although stability of the resulting closed loop system need not be guaranteed a priori, simulation studies have shown that the method can often lead to suitable control laws. In this paper, we consider the non-uniqueness of such a representation. In particular, we show that if there exists any stabilizing feedback leading to a Lyapunov function with star-shaped level sets, then there always exists a representation of the dynamics such that the SDRE approach is stabilizing. The main tool in the roof is a novel application of the S-procedure for quadratic forms.

AB - The state-dependent Riccati equation (SDRE) approach to nonlinear system stabilization relies on representing a nonlinear system's dynamics in a manner to resemble linear dynamics, but with state-dependent coefficient matrices that can then be inserted into state-dependent Riccati equations to generate a feedback law. Although stability of the resulting closed loop system need not be guaranteed a priori, simulation studies have shown that the method can often lead to suitable control laws. In this paper, we consider the non-uniqueness of such a representation. In particular, we show that if there exists any stabilizing feedback leading to a Lyapunov function with star-shaped level sets, then there always exists a representation of the dynamics such that the SDRE approach is stabilizing. The main tool in the roof is a novel application of the S-procedure for quadratic forms.

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U2 - 10.1109/acc.2001.945645

DO - 10.1109/acc.2001.945645

M3 - Conference article

AN - SCOPUS:0034841486

SN - 0743-1619

VL - 6

SP - 4253

EP - 4257

JO - Proceedings of the American Control Conference

JF - Proceedings of the American Control Conference

T2 - 2001 American Control Conference

Y2 - 25 June 2001 through 27 June 2001

ER -

Existence of SDRE stabilizing feedback

Abstract

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