Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers
The Hamilton–Jacobi–Issacs (HJI) inequality is the most basic relation in nonlinear H∞ design, to which no effective analytical solution is currently available. The sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to solve analytically, but it still cannot solve...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/5124108 |
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| author | Fanwei Meng Dini Wang Penghui Yang Guanzhou Xie |
| author_facet | Fanwei Meng Dini Wang Penghui Yang Guanzhou Xie |
| author_sort | Fanwei Meng |
| collection | DOAJ |
| description | The Hamilton–Jacobi–Issacs (HJI) inequality is the most basic relation in nonlinear H∞ design, to which no effective analytical solution is currently available. The sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to solve analytically, but it still cannot solve HJI inequalities directly. In this paper, an HJI inequality suitable for SOS is firstly derived to solve the problem of nonconvex optimization. Then, the problems of SOS in nonlinear H∞ design are analyzed in detail. Finally, a two-step iterative design method for solving nonlinear H∞ control is presented. The first step is to design an adjustable nonlinear state feedback of the gain array of the system using SOS. The second step is to solve the L2 gain of the system; the optimization problem is solved by a graphical analytical method. In the iterative design, a diagonally dominant design idea is proposed to reduce the numerical error of SOS. The nonlinear H∞ control design of a polynomial system for large satellite attitude maneuvers is taken as our example. Simulation results show that the SOS method is comparable to the LMI method used for linear systems, and it is expected to find a broad range of applications in the analysis and design of nonlinear systems. |
| format | Article |
| id | doaj-art-a88c797d77c943b5948c7488e252b7c1 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-a88c797d77c943b5948c7488e252b7c12025-02-03T01:06:40ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/51241085124108Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude ManeuversFanwei Meng0Dini Wang1Penghui Yang2Guanzhou Xie3School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, ChinaSchool of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, ChinaSchool of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, ChinaSchool of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, ChinaThe Hamilton–Jacobi–Issacs (HJI) inequality is the most basic relation in nonlinear H∞ design, to which no effective analytical solution is currently available. The sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to solve analytically, but it still cannot solve HJI inequalities directly. In this paper, an HJI inequality suitable for SOS is firstly derived to solve the problem of nonconvex optimization. Then, the problems of SOS in nonlinear H∞ design are analyzed in detail. Finally, a two-step iterative design method for solving nonlinear H∞ control is presented. The first step is to design an adjustable nonlinear state feedback of the gain array of the system using SOS. The second step is to solve the L2 gain of the system; the optimization problem is solved by a graphical analytical method. In the iterative design, a diagonally dominant design idea is proposed to reduce the numerical error of SOS. The nonlinear H∞ control design of a polynomial system for large satellite attitude maneuvers is taken as our example. Simulation results show that the SOS method is comparable to the LMI method used for linear systems, and it is expected to find a broad range of applications in the analysis and design of nonlinear systems.http://dx.doi.org/10.1155/2019/5124108 |
| spellingShingle | Fanwei Meng Dini Wang Penghui Yang Guanzhou Xie Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers Complexity |
| title | Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers |
| title_full | Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers |
| title_fullStr | Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers |
| title_full_unstemmed | Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers |
| title_short | Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers |
| title_sort | application of sum of squares method in nonlinear h∞ control for satellite attitude maneuvers |
| url | http://dx.doi.org/10.1155/2019/5124108 |
| work_keys_str_mv | AT fanweimeng applicationofsumofsquaresmethodinnonlinearhcontrolforsatelliteattitudemaneuvers AT diniwang applicationofsumofsquaresmethodinnonlinearhcontrolforsatelliteattitudemaneuvers AT penghuiyang applicationofsumofsquaresmethodinnonlinearhcontrolforsatelliteattitudemaneuvers AT guanzhouxie applicationofsumofsquaresmethodinnonlinearhcontrolforsatelliteattitudemaneuvers |