一类p规范型非线性系统自适应有限时间镇定
|
摘要
研究一类虚拟控制系数未知且带有不确定参数的p规范型非线性系统自适应有限时间镇定问题.结合自适应技术、加幂积分技术及有限时间Lyapunov稳定理论,设计该类系统的自适应有限时间控制器,使闭环系统有限时间稳定.在已有的未考虑不确定参数的p规范型非线性系统中加入一个不确定参数,考虑系统的幂p为奇整数之比的形式.设计的控制器能够调整系统的停息时间.仿真结果表明该设计方案具有有效性.
The adaptive finite-time stabilization problem was studied for a class of p-normal form nonlinear systems with unknown virtual control coefficients and uncertainty parameters in this paper.The adaptive finite-time controller of the system was designed by combining the adaptive technology,the adding power integrator technique with the Lyapunov finite-time stability theory,so that the closed-loop system was finite-time stable.An uncertainty parameter was added into the existed p-normal form nonlinear system without considering any uncertainty parameter,and the power pof the system was considered as a ratio of two odd integers.Specially,the designed controller could adjust the settling-time of the studied system.The simulation results demonstrated the effectiveness of the proposed control scheme.
The adaptive finite-time stabilization problem was studied for a class of p-normal form nonlinear systems with unknown virtual control coefficients and uncertainty parameters in this paper.The adaptive finite-time controller of the system was designed by combining the adaptive technology,the adding power integrator technique with the Lyapunov finite-time stability theory,so that the closed-loop system was finite-time stable.An uncertainty parameter was added into the existed p-normal form nonlinear system without considering any uncertainty parameter,and the power pof the system was considered as a ratio of two odd integers.Specially,the designed controller could adjust the settling-time of the studied system.The simulation results demonstrated the effectiveness of the proposed control scheme.
引文
[1]蒲明,周蓉,熊皑,等.一类非匹配不确定非线性系统快速加幂积分控制[J].控制与决策,2018,33(6):1017-1025.
[2]李世华,丁世宏,田玉平.一类二阶非线性系统的有限时间状态反馈镇定方法[J].自动化学报,2007,33(1):101-104.
[3]赵灵冬,胡建兵,包志华,等.分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步[J].物理学报,2011,60(10):93-97.
[4]程桂芳,丁志帅,慕小武.自治非光滑时滞系统的有限时间稳定[J].应用数学学报,2013,36(1):14-22.
[5] BHAT S P.Finite-time stability of continuous autonomous systems[J].SIAM Journal on Control and Optimization,2000,38(3):751-766.
[6] WANG H,CHEN B,LIN C,et al.Adaptive finite-time control for a class of uncertain high-order non-linear systems based on fuzzy approximation[J].IET Control Theory&Applications,2017,11(5):677-684.
[7] ZHENG S,LI W.Fuzzy finite time control for switched systems via adding a barrier power integrator[J].IEEE Transactions on Cybernetics,2018,99:1-14.
[8] HUANG X,LIN W,YANG B.Global finite-time stabilization of a class of uncertain nonlinear systems[J].Automatica,2005,41(5):881-888.
[9] DING S,LI S,LI Q.Stability analysis for a second-order continuous finite-time control system subject to a disturbance[J].Journal of Control Theory&Applications,2009,7(3):271-276.
[10] MAO J,HUANG S,XIANG Z.Adaptive practical finite-time stabilization for switched nonlinear systems in pure-feedback form[J].Journal of the Franklin Institute,2017,354(10):3971-3994.
[11] ZHU Z,XIA Y,FU M.Attitude stabilization of rigid spacecraft with finite-time convergence[J].International Journal of Robust&Nonlinear Control,2015,21(6):686-702.
[12] HOU M,WANG S,DUAN G,et al.Practical finite-time control of missiles:a terminal sliding mode approach[C]//Proceedings of IEEE 36th Chinese Control Conference,2017:1238-1242.
[13]刘万海,沈艳军,任欣军.一类单输入单输出非线性系统全局有限时间输出反馈控制[J].山东大学学报(理学版),2012,47(7):106-116.
[14]曹智茹,牛玉刚,宋军,等.Markov跳变系统有限短时间控制研究综述[J].安徽大学学报(自然科学版),2018,42(2):32-40.
[15]何舒平,沈浩.随机Markov跳变系统的有限短时间控制与综合[M].北京:科学出版社,2016.
[16] LIN W,QIAN C.Adding apower integrator:a tool for global stabilization of high-order lower-triangular systems[J].Systems&Control Letters,2000,39(5):339-351.
[17]常霞.非线性系统停息时间可调的有限时间控制设计[D].济南:山东大学控制科学与工程学院,2009.
[18] BHAT S P,BERNSTEIN D S.Continuous finite-time stabilization of the translational and rotational double integrators[J].IEEE Transactions on Automatic Control,2002,43(5):678-682.
[19] ZHANG X,FENG G,SUN Y.Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems[J].Automatica,2012,48(3):499-504.
[20] HAIMO V T.Finite time controllers[J].Society for Industrial and Applied Mathematics,1986,24(4):760-770.
[21] MOULAY E,PERRUQUETTI W.Finite time stability of nonlinear systems[C]//Proceedings of IEEE Conference on Decision and Control,2003:3641-3646.
[22]洪奕光,王剑魁.一类非线性系统的非光滑有限时间镇定[J].中国科学,2005,35(6):663-672.
[23] HONG Y, WANG J,CHENG D.Adaptive finite-time control of nonlinear systems with parametric uncertainty[J].IEEE Transactions on Automatic Control,2006,51(5):858-862.
[24]高芳征,谢晶,袁付顺.一类不确定高阶非线性系统有限时间镇定[J].安徽大学学报(自然科学版),2012,36(4):13-17.
[25]谢晶,陈宝凤.一类非线性系统的有限时间输出反馈镇定问题[J].常熟理工学院学报,2013,27(4):9-12.
[26] HUANG J,WEN C,WANG W,et al.Design of adaptive finite-time controllers for nonlinear uncertain systems based on given transient specifications[J].Automatica,2016,69:395-404.
[2]李世华,丁世宏,田玉平.一类二阶非线性系统的有限时间状态反馈镇定方法[J].自动化学报,2007,33(1):101-104.
[3]赵灵冬,胡建兵,包志华,等.分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步[J].物理学报,2011,60(10):93-97.
[4]程桂芳,丁志帅,慕小武.自治非光滑时滞系统的有限时间稳定[J].应用数学学报,2013,36(1):14-22.
[5] BHAT S P.Finite-time stability of continuous autonomous systems[J].SIAM Journal on Control and Optimization,2000,38(3):751-766.
[6] WANG H,CHEN B,LIN C,et al.Adaptive finite-time control for a class of uncertain high-order non-linear systems based on fuzzy approximation[J].IET Control Theory&Applications,2017,11(5):677-684.
[7] ZHENG S,LI W.Fuzzy finite time control for switched systems via adding a barrier power integrator[J].IEEE Transactions on Cybernetics,2018,99:1-14.
[8] HUANG X,LIN W,YANG B.Global finite-time stabilization of a class of uncertain nonlinear systems[J].Automatica,2005,41(5):881-888.
[9] DING S,LI S,LI Q.Stability analysis for a second-order continuous finite-time control system subject to a disturbance[J].Journal of Control Theory&Applications,2009,7(3):271-276.
[10] MAO J,HUANG S,XIANG Z.Adaptive practical finite-time stabilization for switched nonlinear systems in pure-feedback form[J].Journal of the Franklin Institute,2017,354(10):3971-3994.
[11] ZHU Z,XIA Y,FU M.Attitude stabilization of rigid spacecraft with finite-time convergence[J].International Journal of Robust&Nonlinear Control,2015,21(6):686-702.
[12] HOU M,WANG S,DUAN G,et al.Practical finite-time control of missiles:a terminal sliding mode approach[C]//Proceedings of IEEE 36th Chinese Control Conference,2017:1238-1242.
[13]刘万海,沈艳军,任欣军.一类单输入单输出非线性系统全局有限时间输出反馈控制[J].山东大学学报(理学版),2012,47(7):106-116.
[14]曹智茹,牛玉刚,宋军,等.Markov跳变系统有限短时间控制研究综述[J].安徽大学学报(自然科学版),2018,42(2):32-40.
[15]何舒平,沈浩.随机Markov跳变系统的有限短时间控制与综合[M].北京:科学出版社,2016.
[16] LIN W,QIAN C.Adding apower integrator:a tool for global stabilization of high-order lower-triangular systems[J].Systems&Control Letters,2000,39(5):339-351.
[17]常霞.非线性系统停息时间可调的有限时间控制设计[D].济南:山东大学控制科学与工程学院,2009.
[18] BHAT S P,BERNSTEIN D S.Continuous finite-time stabilization of the translational and rotational double integrators[J].IEEE Transactions on Automatic Control,2002,43(5):678-682.
[19] ZHANG X,FENG G,SUN Y.Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems[J].Automatica,2012,48(3):499-504.
[20] HAIMO V T.Finite time controllers[J].Society for Industrial and Applied Mathematics,1986,24(4):760-770.
[21] MOULAY E,PERRUQUETTI W.Finite time stability of nonlinear systems[C]//Proceedings of IEEE Conference on Decision and Control,2003:3641-3646.
[22]洪奕光,王剑魁.一类非线性系统的非光滑有限时间镇定[J].中国科学,2005,35(6):663-672.
[23] HONG Y, WANG J,CHENG D.Adaptive finite-time control of nonlinear systems with parametric uncertainty[J].IEEE Transactions on Automatic Control,2006,51(5):858-862.
[24]高芳征,谢晶,袁付顺.一类不确定高阶非线性系统有限时间镇定[J].安徽大学学报(自然科学版),2012,36(4):13-17.
[25]谢晶,陈宝凤.一类非线性系统的有限时间输出反馈镇定问题[J].常熟理工学院学报,2013,27(4):9-12.
[26] HUANG J,WEN C,WANG W,et al.Design of adaptive finite-time controllers for nonlinear uncertain systems based on given transient specifications[J].Automatica,2016,69:395-404.