一类非线性系统的全局渐近稳定和有限时间镇定

周映江; 王莉; 孙长银

doi:10.3724/SP.J.1004.2013.00664

一类非线性系统的全局渐近稳定和有限时间镇定

doi: 10.3724/SP.J.1004.2013.00664

1.
东南大学自动化学院南京 210096;
2.
扬州大学能源与动力工程学院扬州 225127

详细信息

通讯作者:
孙长银

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出版历程
- 收稿日期: 2012-05-15
- 修回日期: 2012-08-28
- 刊出日期: 2013-05-20

Global Asymptotic and Finite-time Stability for Nonlinear Systems

1.
School of Automation, Southeast University, Nanjing 210096;
2.
School of Energy and Power Engineering, Yangzhou University, Yangzhou 225127

摘要

摘要: 针对一类全矩阵形式的非线性系统, 研究其全局稳定性及有限时间镇定问题. 首先, 全矩阵形式非线性系统被分成上三角形式和下三角形式非线性系统的加和, 并针对下三角形式非线性系统, 利用加幂积分方法, 自上而下地设计系统的全局稳定控制器; 其次, 在上面控制器作用下, 证明全矩阵形式系统在一个给定领域内是局部渐近稳定的; 最后, 运用自下而上的顺序, 一种嵌套饱和方法被用到上述控制器中, 通过调节饱和度, 使得闭环系统全局渐近稳定. 此外, 在适当的条件下, 可以得到全矩阵形式非线性系统的全局有限时间稳定性.
- 全局稳定 /
- 非线性系统 /
- 加密积分方法 /
- 有限时间镇定
Abstract: In this paper, the problems of global asymptotic and finite-time stability of a class of nonlinear systems are considered. The control law is designed in the following three steps: First, the full matrix form nonlinear system is divided into a lower-triangular form plus a upper-triangular form. And for the lower-triangular systems, the generalized adding a power integrator technique is used to design the global stabilization controller from top to bottom. Next, we proof that the whole system is locally asymptotically stabile in a given region under the above controller. Finally, a series of nested saturations are imposed on the above controller. And by adjusting the saturation level, the global asymptotic stability of the closed-loop systems is ensured. In addition, we can also obtain the global finite-time stability of the whole nonlinear system under appropriate conditions.
- Global stabilization /
- nonlinear system /
- adding a power integrator /
- finite-time stability

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参考文献(1)

[1]

Isidori A. Nonlinear Control Systems II. Berlin: Springer, 1995[2] Kokotovic P V, Freeman R A. Robust Nonlinear Control Design: State-Space and Lyapunov Techniques. Berlin: Springer, 1996[3] Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design. New York: Wiley-Interscience, 1995[4] Lin W, Qian C J. Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems. Systems Control Letters, 2000, 39(5): 339-351[5] Qian C J, Lin W. A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Transactions on Automatic Control, 2001, 46(7): 1061-1079[6] Polendo J, Qian C J. A universal method for robust stabilization of nonlinear systems: unification and extension of smooth and non-smooth approaches. In: Proceedings of the 2006 American Control Conference. Minneapolis, MN: IEEE, 2006. 4285-4290[7] Polendo J, Qian C J. An expanded method to robustly stabilize uncertain nonlinear systems. Communications in Information and Systems, 2008, 8(1): 55-70[8] Mazenc F, Praly L. Adding integrations, saturated controls, and stabilization for feedforward systems. IEEE Transactions on Automatic Control, 1996, 41(11): 1559-1578[9] Sepulchre R, Jankovic M, Kokotovic P V. Integrator forwarding: a new recursive nonlinear robust design. Automatica, 1997, 33(5): 979-984[10] Teel A R. A nonlinear small gain theorem for the analysis of control systems with saturation. IEEE Transactions on Automatic Control, 1996, 41(9): 1256-1270[11] Teel A R. Global stabilization and restricted tracking for multiple integrators with bounded controls. Systems and Control Letters, 1992, 18(3): 165-171[12] Lin W, Li X J. Synthesis of upper-triangular non-linear systems with marginally unstable free dynamics using state-dependent saturation. International Journal of Control, 1999, 72(12): 1078-1086[13] Isidori A. Nonlinear Control Systems, vol.II: Communications and Control Engineering Series. Springer: London, 1999[14] Ye X D. Universal stabilization of feedforward nonlinear systems. Automatica, 2003, 39(1): 141-147[15] Chen T S, Huang J. Disturbance attenuation of feedforward systems with dynamic uncertainty. IEEE Transactions on Automatic Control, 2008, 53(7): 1711-1717[16] Qian C J, Lin W. Using small feedback to stabilize a wider class of feedforward systems. In: Proceedings of the 14th IFAC World Congress. Beijing, China, 1999. 309-314[17] Ding S H, Qian C J, Li S H. Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations. International Journal of Robust and Nonlinear Control, 2011, 21(3): 271-294[18] Qian C J, Li J. Global output feedback stabilization of upper-triangular nonlinear systems using a homogeneous domination approach. International Journal of Robust and Nonlinear Control, 2006, 16(9): 441-463[19] Rui C L, Reyhanoglu M, Kolmanovsky I, Cho S, McClamroch N H. Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system. In: Proceedings of the 36th Conference on Decision Control. San Diego, California, USA: IEEE, 1997. 3998-4003

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