State Feedback Guaranteed Cost Control of Parameter Uncertain Nonlinear System

Abstract:

In an actual system, the effects of nonlinear factors are inevitable. So in real practice, when a model for complex system is being built, all the features in it will be linearized. Though simplifying the designing and analyzing process, the model being built in this way is thought to be incapable of revealing the true characteristics of the system. In order to solve this problem, the paper analyzes a model combining both linear and nonlinear features while taking the parameter perturbation of the linear part into consideration, which enables the model to retain as many characteristics of the actual system as possible. Provided that the nonlinear function satisfies the Lipschitz constraint conditions, the robust guaranteed cost state feedback control law of nonlinear system is deduced using the Lyapunov function and then converted into the feasible solutions of linear matrix inequality (LMI). The proposed method optimizes the design of controller by modifying the previous oversimplified models that fail to reveal the real characteristics of the actual system, and the effectiveness of the proposed method is being verified through an algorithm simulation example.

• Periodical: Applied Mechanics and Materials (Volumes 58-60)
• Pages: 803-809
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.58-60.803
• Online since: June 2011
• Authors: Chuan Feng Li, Yong Ji Wang, Yun Xing Shu, Zhi Shen Wang
• Keywords: Linear Matrix Inequality (LMI), Parameter Uncertainty, Partial Linearization, Robust Guaranteed Cost Control

References

[1] W. MacKunis, P.M. Patre, W.E. Dixon: IEEE Transaction on Control Systems Technology. Vol. 18 (2010), p.1448.

[2] I.R. Petersen, D.C. MacFarlane: IEEE Transactions on Automatic Control. Vol. 39 (1994), p. (1971).

[3] S.C. Tsay, I.K. Fong, E.S. Kuo: International Journal of control Vol. 53 (1991), p.81.

[4] F.C. Qian, S.P. Zhu, D. Liu: Control Theory and Applications Vol. 27 (2010), p.1017.

[5] A.K. Xue, in: Robust Optimal Control Theory and Application, Science Press (2007).

[6] S.S.L. Chang, T.K.C. Peng: IEEE Transactions on Automatic Control Vol. 17 (1972), p.474.

[7] W.H. Chen, Z.H. Guan, X. M. Lu: Automatica Vol. 40 (2004), p.1263.

[8] G. Pujol, J. Rodellar, J.M. Rossell: IET Control Theory Application Vol. 1 (2007), p.779.

[9] Z.X. Deng, C.F. Li, L. Liu, Y. Y: Journal of Huazhong University of Science and Technology(Nature Science Edition) Vol. 38 (2010), p.92.

[10] E.F. Costa, V.A. Oliverira: Systems and Control Letters Vol. 46 (2002), p.17.

[11] I.R. Petersen: IEEE Transactions on Automatic Control Vol. 54 (2009), p.1209.

[12] J.S. Xu, Y.J. Wang: Control Theory and Applications Vol. 25 (2008), p.976.

[13] L. Yu, in: Robust Control-Linear Matrix Inequality Method, Tsinghua University Press (2002).

[14] K.J. Murphy, R.J. Nowak, R.A. Thompson, et al: Journal of Spacecraft and Rockets Vol. 38 (2001), p.670.