Design of a Class of Nonlinear Controllers via State Dependent Riccati Equations

Evrin B. Erdem; Andrew G. Alleyne

doi:10.1109/TCST.2003.819588

Design of a Class of Nonlinear Controllers via State Dependent Riccati Equations

Evrin B. Erdem, Andrew G. Alleyne

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

89 Scopus citations

Abstract

In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered. By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by a combination of Lyapunov analysis and LaSalle's Principle. Accordingly, a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived. This is one of the first global results available for this class of systems controlled by SDRE methods. The stability results are demonstrated on an experimental magnetic levitation setup and are found to provide a great deal of flexibility in the control system design.

Original language	English (US)
Pages (from-to)	133-137
Number of pages	5
Journal	IEEE Transactions on Control Systems Technology
Volume	12
Issue number	1
DOIs	https://doi.org/10.1109/TCST.2003.819588
State	Published - Jan 2004
Externally published	Yes

Keywords

Magnetic levitation
nonlinear control design
State Dependent Riccati Equation (SDRE)

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10.1109/TCST.2003.819588

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abstract = "In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered. By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by a combination of Lyapunov analysis and LaSalle's Principle. Accordingly, a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived. This is one of the first global results available for this class of systems controlled by SDRE methods. The stability results are demonstrated on an experimental magnetic levitation setup and are found to provide a great deal of flexibility in the control system design.",

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AU - Erdem, Evrin B.

AU - Alleyne, Andrew G.

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N2 - In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered. By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by a combination of Lyapunov analysis and LaSalle's Principle. Accordingly, a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived. This is one of the first global results available for this class of systems controlled by SDRE methods. The stability results are demonstrated on an experimental magnetic levitation setup and are found to provide a great deal of flexibility in the control system design.

AB - In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered. By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by a combination of Lyapunov analysis and LaSalle's Principle. Accordingly, a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived. This is one of the first global results available for this class of systems controlled by SDRE methods. The stability results are demonstrated on an experimental magnetic levitation setup and are found to provide a great deal of flexibility in the control system design.

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KW - nonlinear control design

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Design of a Class of Nonlinear Controllers via State Dependent Riccati Equations

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