利用H-J-B方程的粘性逼近求解非线性最优控制

Approximation to Nonlinear Optimal Control by Viscosity Approximation of H-J-B Equations

利用李级数离散控制系统,逼近最优轨道,并利用H-J-B方程的粘性逼近估计值函数.进而借助动态规划原理,把非线性最优控制的数值求解转化为一组正定二次规划的求解.对一个非线性的动态规划过程进行线性化的逼近,这在理论上简化了非线性最优控制问题求解的困难,从实际计算数学的角度看,这也将加快非线性最优控制数值解的计算速度.

In this article,we introduce the idea of using Lie series to give an approximation of the optimal tra- jectory of a nonlinear optimal control problem by a discrete process.The dynamic programming equation is solved by means of the viscosity approximation of value functions and a positive quadratic programming.By this way,a nonlinear dynamic programming is transformed to a linear approximation.The difficulty of solving an op- timal control problem is simplified.