SOS design for nonlinear H∞ control

Zhen He; Guang Xiong Wang; Fan Wei Meng

doi:10.15938/j.emc.2015.01.012

SOS design for nonlinear H_∞ control

Zhen He^*
, Guang Xiong Wang
, Fan Wei Meng

^*Corresponding author for this work

School of Astronautics, Harbin Institute of Technology
Northeastern University China

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

5 Scopus citations

Abstract

A new design method for nonlinear H_∞ control was proposed. Though sum of squares (SOS) method can be used to solve analytically unsolvable nonlinear problems, but it still cannot be used directly to solve the Hamilton-Jacobi-Issacs (HJI) inequality or the nonlinear bounded-real inequality. The restrictions of the SOS method were discussed in detail. An iterative design procedure for nonlinear H_∞ control problems was presented. There are two steps in each round of iteration. The first step is to design the nonlinear state feedback with adjustable gain matrix by using the SOS method. The second step is to solve an optimal problem in computation of the L₂-gain by using a graphical-analytical method. A nonlinear H_∞ control design for large attitude maneuvers of statellites was presented as an application example of the proposed method.

Original language	English
Pages (from-to)	82-89
Number of pages	8
Journal	Dianji yu Kongzhi Xuebao/Electric Machines and Control
Volume	19
Issue number	1
DOIs	https://doi.org/10.15938/j.emc.2015.01.012
State	Published - 1 Jan 2015
Externally published	Yes

Keywords

Attitude control
Bounded real lemma
Hamilton-Jacobi-Issacs inequality
Nonlinear H control
Sum of squares (SOS)

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10.15938/j.emc.2015.01.012

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title = "SOS design for nonlinear H∞ control",

abstract = "A new design method for nonlinear H∞ control was proposed. Though sum of squares (SOS) method can be used to solve analytically unsolvable nonlinear problems, but it still cannot be used directly to solve the Hamilton-Jacobi-Issacs (HJI) inequality or the nonlinear bounded-real inequality. The restrictions of the SOS method were discussed in detail. An iterative design procedure for nonlinear H∞ control problems was presented. There are two steps in each round of iteration. The first step is to design the nonlinear state feedback with adjustable gain matrix by using the SOS method. The second step is to solve an optimal problem in computation of the L2-gain by using a graphical-analytical method. A nonlinear H∞ control design for large attitude maneuvers of statellites was presented as an application example of the proposed method.",

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doi = "10.15938/j.emc.2015.01.012",

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AU - He, Zhen

AU - Wang, Guang Xiong

AU - Meng, Fan Wei

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N2 - A new design method for nonlinear H∞ control was proposed. Though sum of squares (SOS) method can be used to solve analytically unsolvable nonlinear problems, but it still cannot be used directly to solve the Hamilton-Jacobi-Issacs (HJI) inequality or the nonlinear bounded-real inequality. The restrictions of the SOS method were discussed in detail. An iterative design procedure for nonlinear H∞ control problems was presented. There are two steps in each round of iteration. The first step is to design the nonlinear state feedback with adjustable gain matrix by using the SOS method. The second step is to solve an optimal problem in computation of the L2-gain by using a graphical-analytical method. A nonlinear H∞ control design for large attitude maneuvers of statellites was presented as an application example of the proposed method.

AB - A new design method for nonlinear H∞ control was proposed. Though sum of squares (SOS) method can be used to solve analytically unsolvable nonlinear problems, but it still cannot be used directly to solve the Hamilton-Jacobi-Issacs (HJI) inequality or the nonlinear bounded-real inequality. The restrictions of the SOS method were discussed in detail. An iterative design procedure for nonlinear H∞ control problems was presented. There are two steps in each round of iteration. The first step is to design the nonlinear state feedback with adjustable gain matrix by using the SOS method. The second step is to solve an optimal problem in computation of the L2-gain by using a graphical-analytical method. A nonlinear H∞ control design for large attitude maneuvers of statellites was presented as an application example of the proposed method.

KW - Attitude control

KW - Bounded real lemma

KW - Hamilton-Jacobi-Issacs inequality

KW - Nonlinear H control

KW - Sum of squares (SOS)

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SOS design for nonlinear H_∞ control

Abstract

Keywords

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