基于T-S模型方法的非线性随机时滞金融系统的多目标优化
|
摘要
主要研究了不确定随机时滞金融系统的多目标H_2/H_∞的投资策略问题,多目标H_2/H_∞投资策略能够使得投资成本和投资风险尽可能达到最小.通过运用T-S模糊方法将多目标模糊投资策略问题转化为线性矩阵不等式(Linear Matrix Inequality,简写为LMI)约束的多目标优化问题(Multiobjective Optimization Problem,简写为MOP).另外,基于线性矩阵不等式的多目标进化算法(Multiobjective Evolution Algorithm,简写为MOEA)寻找多目标优化问题的Pareto最优解,最后投资者可以根据他们自己的喜好选择一个互惠策略.
This paper is concerned with the multiobjective H_2/H_∞ investment policy for uncertain nonlinear stochastic financial systems with state-delay.The multiobjective H_2/H_∞ investment policy can solve the problems of uncertain nonlinear stochastic financial systems with a state-delay to reach a desired state with minimum the investment cost and risk.By applying T-S fuzzy approach,the multiobjective H_2/H_∞ fuzzy investment problem can be replaced by a linear matrix inequality(LMI)-constrained multiobjective problem(MOP).In addition,we use a LMI-based multiobjective evolution algorithm(MOEA)to efficiently find Pareto optimal solutions for the MOP of multiobjective fuzzy investment policy.The managers can select a mutual benefit policy according to their preference.
This paper is concerned with the multiobjective H_2/H_∞ investment policy for uncertain nonlinear stochastic financial systems with state-delay.The multiobjective H_2/H_∞ investment policy can solve the problems of uncertain nonlinear stochastic financial systems with a state-delay to reach a desired state with minimum the investment cost and risk.By applying T-S fuzzy approach,the multiobjective H_2/H_∞ fuzzy investment problem can be replaced by a linear matrix inequality(LMI)-constrained multiobjective problem(MOP).In addition,we use a LMI-based multiobjective evolution algorithm(MOEA)to efficiently find Pareto optimal solutions for the MOP of multiobjective fuzzy investment policy.The managers can select a mutual benefit policy according to their preference.
引文
[1]Lorenz H W,Nusse H E.Chaotic attractors,chaotic saddles,and fractal basin boundaries:goodwins nonlinear accelerator model reconsidered[J].Chaos Solitons Fractals,2002,13:957-965.
[2]Chian A C,Rempel E L,Rogers C.Complex economic dynamics:chaotic saddle,crisis and intermittency[J].Chaos Solitons Fractals,2006,29:1194-1218.
[3]Cesare L D,Sportelli M.A dynamic is-lm model with delayed taxation revenues[J].Chaos Solitons Fractals,2005,25:233-244.
[4]He X,Li K,Wei J,et al.Market stability switches in a continuous-time financial market with heterogeneous beliefs[J].Economic Modelling,2009,26:1432-1442.
[5]Gao Q,Ma J.Chaos and hopf bifurcation of a finance system[J].Nonlinear Dynamics,2009,58:209-216.
[6]Chen W.Dynamics and control of a financial system with time-delayed feedbacks[J].Chaos Solitons Fractals,2008,37:1198-1207.
[7]Wu C F,Chen B S,Zhang W H.Multiobjective investment policy for a nonlinear stochastic financial system:a fuzzy approach[J].IEEETrans Fuzzy Syst,2017,25(2):460-474.
[8]丁宇婷.时滞微分方程高余维分支的规范型约化研究[D].哈尔滨:哈尔滨工业大学,2012.
[9]张慧慧.一类不确定随机多时滞神经网络时滞区间相关的鲁棒指数稳定分析[J].聊城大学学报(自然科学版),2013,26(4):16-23.
[10]陈国梁.多定常时滞离散系统的时滞相关稳定性分析[J].聊城大学学报(自然科学版),2014,27(4):16-21
[11]陈国梁.马尔科夫跳跃系统时滞相关无源性分析[J].聊城大学学报(自然科学版),2015,28(1):15-18.
[12]Khasminskii R,Milstein G N.Stochastic Stability of Differential Equations[M],2nd ed.Berlin Germany:Springer,2011.
[13]Boyd S,Ghaoui L,Feron E.Linear Matrix Inequalities in System and Control Theory[M].Philadelphia,PA,USA:SIAM,1994.
[14]Tanaka K,Wang H O.Fuzzy Control Systems Design and Analysis:A Linear Matrix Inequality Approach[M].New York,NY,USA:Wiley,2001.
[15]Wang Y,Xie L,de Souza C E.Robust control of a class of uncertain nonlinear systems[J],Systems and Control Letters.1992,19:139-149.
[16]俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京:清华大学出版社,2002.
[2]Chian A C,Rempel E L,Rogers C.Complex economic dynamics:chaotic saddle,crisis and intermittency[J].Chaos Solitons Fractals,2006,29:1194-1218.
[3]Cesare L D,Sportelli M.A dynamic is-lm model with delayed taxation revenues[J].Chaos Solitons Fractals,2005,25:233-244.
[4]He X,Li K,Wei J,et al.Market stability switches in a continuous-time financial market with heterogeneous beliefs[J].Economic Modelling,2009,26:1432-1442.
[5]Gao Q,Ma J.Chaos and hopf bifurcation of a finance system[J].Nonlinear Dynamics,2009,58:209-216.
[6]Chen W.Dynamics and control of a financial system with time-delayed feedbacks[J].Chaos Solitons Fractals,2008,37:1198-1207.
[7]Wu C F,Chen B S,Zhang W H.Multiobjective investment policy for a nonlinear stochastic financial system:a fuzzy approach[J].IEEETrans Fuzzy Syst,2017,25(2):460-474.
[8]丁宇婷.时滞微分方程高余维分支的规范型约化研究[D].哈尔滨:哈尔滨工业大学,2012.
[9]张慧慧.一类不确定随机多时滞神经网络时滞区间相关的鲁棒指数稳定分析[J].聊城大学学报(自然科学版),2013,26(4):16-23.
[10]陈国梁.多定常时滞离散系统的时滞相关稳定性分析[J].聊城大学学报(自然科学版),2014,27(4):16-21
[11]陈国梁.马尔科夫跳跃系统时滞相关无源性分析[J].聊城大学学报(自然科学版),2015,28(1):15-18.
[12]Khasminskii R,Milstein G N.Stochastic Stability of Differential Equations[M],2nd ed.Berlin Germany:Springer,2011.
[13]Boyd S,Ghaoui L,Feron E.Linear Matrix Inequalities in System and Control Theory[M].Philadelphia,PA,USA:SIAM,1994.
[14]Tanaka K,Wang H O.Fuzzy Control Systems Design and Analysis:A Linear Matrix Inequality Approach[M].New York,NY,USA:Wiley,2001.
[15]Wang Y,Xie L,de Souza C E.Robust control of a class of uncertain nonlinear systems[J],Systems and Control Letters.1992,19:139-149.
[16]俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京:清华大学出版社,2002.