等式约束非线性控制系统的时程精细计算

基金项目: 国家自然科学基金资助(19872057;19732020);霍英东青年教师基金资助(71005);航空科学基金资助(00B53006);大连理工大学工业装备结构分析国家重点实验室开放基金资助项目

Time Precise Integration Method for Constrained Nonlinear Control System

1.
Department of Civil Engineering, Northwestern Polytechnical University, Xi'an 710072, P R China;
2.
State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, P R China

摘要: 针对等式约束非线性最优控制问题,通过一阶Taylor级数展开,得到线性化的动力学方程,进而在方程原变量的基础上,引入对偶向量(Lagrange乘子向量),将动力学方程从Lagrange体系引入到了Hamilton体系,在全状态下,从一个新的角度对等式约束非线性控制问题进行了描述,进一步基于时程精细积分理论,对其方程进行了有效的精细求解,并通过算例说明了文中方法的有效性。
- 非线性控制系统 /
- 等式约束 /
- 时程精细积分
Abstract: For the constrained nonlinear optimal control problem,by taking the first term of Taylor series,the dynamic equation is linearized.Thus by introducing into the dual variable(Lagrange multiplier vector),the dynamic equation can be transformed into Hamilton system from Lagrange system on the basis of the original variable.Under the whole state,the problem discussed can be described from a new view,and the equation can be precisely solved by the time precise integration method established in linear dynamic system.A numerical example shows the effectiveness of the method.
- nonlinear control system /
- constraint equation /
- time precise integration

[1]	钟万勰,欧阳华江,邓子辰.计算结构力学与最优控制[M].大连:大连理工大学出版社,1993.
[2]	钟万勰.暂态历程的精细计算方法[J].计算结构力学及其应用,1995,12(1):1-6.
[3]	邓子辰.飞行器控制系统的高精度计算方法[J].飞行力学,1997,15(2):46-51.
[4]	钟万勰.H_∞控制状态反馈与瑞利商精细积分[J].计算力学学报,1999,16(1):1-7.
[5]	邓子辰.基于子结构消元法的柔性结构主动控制的研究,航空学报,1997,18(5):559-562.
[6]	DENG Zi-chen.Theoptimal solution of the constraimed nonlinear control system[J].Computers&Structures,1994,53 (5): 1115-1121.