等式约束非线性控制系统的时程精细计算

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。

Time Precise Integration Method for Constrained Nonlinear Control System

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.