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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.6 P.833~839

10.1631/jzus.A071486


Control synthesis for polynomial nonlinear systems and application in attitude control


Author(s):  Chang-fei TONG, Hui ZHANG, You-xian SUN

Affiliation(s):  Institute of Industrial Process Control, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   cftong@iipc.zju.edu.cn, zhanghui@iipc.zju.edu.cn

Key Words:  Nonlinear control, Attitude control, Polynomial systems


Chang-fei TONG, Hui ZHANG, You-xian SUN. Control synthesis for polynomial nonlinear systems and application in attitude control[J]. Journal of Zhejiang University Science A, 2008, 9(13): 833~839.

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author="Chang-fei TONG, Hui ZHANG, You-xian SUN",
journal="Journal of Zhejiang University Science A",
volume="9",
number="6",
pages="833~839",
year="2008",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A071486"
}

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%T Control synthesis for polynomial nonlinear systems and application in attitude control
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%A Hui ZHANG
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%J Journal of Zhejiang University SCIENCE A
%V 9
%N 6
%P 833~839
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer

TY - JOUR
T1 - Control synthesis for polynomial nonlinear systems and application in attitude control
A1 - Chang-fei TONG
A1 - Hui ZHANG
A1 - You-xian SUN
J0 - Journal of Zhejiang University Science A
VL - 9
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SP - 833
EP - 839
%@ 1673-565X
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PB - Zhejiang University Press & Springer
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Abstract: 
A method for positive polynomial validation based on polynomial decomposition is proposed to deal with control synthesis problems. Detailed algorithms for decomposition are given which mainly consider how to convert coefficients of a polynomial to a matrix with free variables. Then, the positivity of a polynomial is checked by the decomposed matrix with semidefinite programming solvers. A nonlinear control law is presented for single input polynomial systems based on the Lyapunov stability theorem. The control synthesis method is advanced to multi-input systems further. An application in attitude control is finally presented. The proposed control law achieves effective performance as illustrated by the numerical example.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[3] Chesi, G., 2007. Estimating the domain of attraction via union of continuous families of Lyapunov estimates. Syst. Control Lett., 56(4):326-333.

[4] Chesi, G., Garulli, A., Tesi, A., Vicino, A., 2005. Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach. IEEE Trans. on Automatic Control, 50(3):365-370.

[5] Dimarogonas, D.V., Tsiotras, P., Kyriakopoulos, K.J., 2006. Laplacian Cooperative Attitude Control of Multiple Rigid Bodies. Proc. IEEE Int. Symp. on Intelligent Control. Munich, Germany, p.3064-3069.

[6] Fisher, J., Bhattacharya, R., 2007. Construction of Lyapunov Certificates for Partial Stability Problems Using Sum of Squares Techniques. Proc. American Control Conf., p.4823-4828.

[7] Jarvis-Wloszek, Z., 2003. Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems Using Sum-of-Squares Optimization. Ph.D Thesis, University of California, Berkeley.

[8] Papachristodoulou, A., Prajna, S., 2005. A Tutorial on Sum of Squares Techniques for Systems Analysis. Proc. American Control Conf. Portland, OR, USA, p.2686-2700.

[9] Parrilo, P.A., 2000. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. Ph.D Thesis, California Institute of Technology, Pasadena, CA.

[10] Prajna, S., Parrilo, P.A., Rantzer, A., 2004. Nonlinear control synthesis by convex optimization. IEEE Trans. on Automatic Control, 49(2):310-314.

[11] Rantzer, A., 2001. A dual to Lyapunov’s stability theorem. Syst. Control Lett., 42(3):161-168.

[12] Sturm, J.F., 1999. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, p.625-653.

[13] Tsiotras, P., 1998. Further passivity results for the attitude control problem. IEEE Trans. on Automatic Control, 43(11):1597-1600.

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