Adaptive Control Design of High-order Nonlinear Systems with Unknown Control Coefficients and Zero Dynamics
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摘要: 主要研究一类控制系数未知和有不可测零动态的高阶非线性系统的全局自适应镇定问题. 进一步放宽了对零动态的约束条件, 通过定义一个恰当的未知参数, 把连续自适应状态反馈控制器的动态阶数降到最低(仅一维). 通过结合增加幂次积分方法, 相关的自适应技术以及交换能量函数思想, 给出控制器的设计步骤. 所设计的控制器确保闭环系统的所有状态是全局一致有界的, 且原系统的状态收敛到零.Abstract: This paper focuses on the adaptive stabilization problem for a class of high-order nonlinear systems with uncertain control coefficients and unmeasurable zero dynamics. Restriction on zero dynamics is further relaxed, and the dynamic order of a continuous adaptive state-feedback controller reduces to the minimum (only one dimension) through delicately defining an appropriate unknown parameter. The design procedures of the controller are provided by flexibly incorporating the method of adding a power integrator with the related adaptive technique and the idea of changing supply functions. The designed controller guarantees that all the closed-loop system states are globally uniformly bounded, and that the original state converges to zero.
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[1] Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design. New York: John Wiley and Sons, 1995. 140-150[2] Khalil H K. Nonlinear Systems (3rd edition). New Jersey: Prentice Hall, 2002. 323-323[3] Ye X D, Jiang J P. Adaptive nonlinear design without a priori knowledge of control directions. IEEE Transactions on Automatic Control, 1998, 43(11): 1617-1621[4] Jiang Z P. A combined backstepping and small-gain approach to adaptive output feedback control. Automatica, 1999, 35(6): 1131-1139[5] Ge S S, Hong F, Lee T H. Adaptive neural network control of nonlinear systems with unknown time delays. IEEE Transactions on Automatic Control, 2003, 48(11): 2004-2010[6] Zhou J, Wen C Y, Zhang Y. Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity. IEEE Transactions on Automatic Control, 2006, 51(3): 504-511[7] Deng H, Krstic M. Output-feedback stochastic nonlinear stabilization. IEEE Transactions on Automatic Control, 1999, 44(2): 328-333[8] Liu Y G, Pan Z G, Shi S J. Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost. IEEE Transactions on Automatic Control, 2003, 48(3): 509-513[9] Liu Y G, Zhang J F. Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zero-dynamics. SIAM Journal on Control and Optimization, 2006, 45(3): 885-926[10] Wu Z J, Xie X J, Zhang S Y. Adaptive backstepping controller design using stochastic small-gain theorem. Automatica, 2007, 43(4): 608-620[11] 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[12] Lin W, Qian C J. Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework. IEEE Transactions on Automatic Control, 2002, 47(5): 757-774[13] Lin W, Pongvuthithum R. Nonsmooth adaptive stabilization of cascade systems with nonlinear parameterization via partial-state feedback. IEEE Transactions on Automatic Control, 2003, 48(10): 1809-1816[14] Xie X J, Tian J. Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization. Automatica, 2009, 45(1): 126-133[15] Sun Z Y, Liu Y G. State-feedback adaptive stabilizing control design for a class of high-order nonlinear systems with unknown control coefficients. Journal of Systems Science and Complexity, 2007, 20(3): 350-361[16] Sun Z Y, Liu Y G. Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems. Automatica, 2007, 43(10): 1772-1783[17] Sun Z Y, Liu Y G. Adaptive stabilisation for a large class of high-order uncertain non-linear systems. International Journal of Control, 2009, 82(7): 1275-1287[18] Zhang J, Liu Y G. A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems. Science China Information Sciences, 2011, 54(7): 1419-1429[19] Lin W, Pongvuthithum R. Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization. IEEE Transactions on Automatic Control, 2003, 48(10): 1737-1749[20] Sun Z Y, Liu Y G. Adaptive practical output tracking control for high-order nonlinear uncertain systems. Acta Automatica Sinica, 2008, 34(8): 984-988[21] Sontag E, Teel A. Changing supply functions in input/state stable systems. IEEE Transactions on Automatic Control, 1995, 40(8): 1476-1478[22] Hale J K. Ordinary Differential Equations. New York: Huntington, 1980. 17-18
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