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一个全局隐函数定理及计算隐函数的迭代算法

Keywords: 全局隐函数,全局存在性,迭代算法

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Abstract:

利用Banach压缩映射原理,证明了高维空间中的一个全局隐函数定理,给出计算隐函数近似解的迭代算法,并证明迭代序列收敛于隐函数的精确解,改进和推广了某些文献中已知的结果.

References

[1]  Ge S S,HangC C,ZhangT.Nonlinear adaptive control using neural networks and its application to CSTR systems[J].JProcess Control,1999,9:313ˉ323.
[2]  Ge S S,Hang C C,ZhangT.Adaptive neural network control ofnonlinear systems by state and output feedback[J].IEEE Trans SystMan Cybernetics PartB,1999,29:818ˉ828.
[3]  Ge S S,Hang C C,Lee TH,et al.Stable Adaptive NeuralNetwork Control[M].Boston:KluwerAcademic,2001.
[4]  Jittorntrum K.An implicit function theorem[J].JOptim Theory Appl,1978,25:575ˉ577.
[5]  ButlerG J,FreedmanH I.Further critical cases of the scalar implicit function theorem[J].AequationesMath,1972,8:203ˉ211.
[6]  Ge S S,W ang C.Adaptive NN control of uncertain nonlinear pureˉfeedback systems[J].Automatica,2002,38:671ˉ682.
[7]  ZhangW N,Ge S S.A global implicit function theorem without initial point and its applications to control ofnonˉaffine systems of high dimensions[J].JMath AnalAppl,2006,313:251ˉ261.
[8]  Ortega JM.Matrix Theory[M].New York:Plenum,1987.
[9]  丁协平.解非线性混合似变分不等式的预测ˉ校正迭代算法[J].四川师范大学学报:自然科学版,2003,26(1):1ˉ5.
[10]  李林珂,丁协平.解变分不等式的超梯度Mann迭代算法[J].四川师范大学学报:自然科学版,2005,28(5):514ˉ517.
[11]  罗春林,姚益民.不具Lipschitz条件的Browder变分不等式解的Ishikawa迭代算法[J].四川师范大学学报:自然科学版,2005,28(1):58ˉ60.
[12]  Bridges D,Calude C,Pavlov B,et al.Chaos Solitons Fractals,1999,10:927ˉ934.
[13]  Datko R.An implicit function theorem with an application to control theory[J].MichiganMath J,1964,11:345ˉ351.
[14]  AlexandrovV.Implicit function theorem for systems ofpolynomial equationswith vanishing Jacobian and its application to flexible polyhedra and frameworks[J].MonatshMath,2001,132:269ˉ288.
[15]  Craven B D,NashedM Z.Generalized implicit function theoremswhen the derivative has no bounded inverse[J].NonlinearAˉnal,1982,6:375ˉ387.
[16]  P les Z.Inverse and implicit function theorems for nonsmoothmaps in Banach spaces[J].JMath AnalAppl,1997,209:202ˉ220.

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