约束线性二次优化控制的多参数规划求解

Multi-parametric programming approach for linear constrained quadratic optimal control problems

针对求解约束线性二次优化控制问题,结合动态规划和控制时域长度为1的单步多参数二次规划,提出一种新的多参数规划方法。该方法一方面能够快速求解得到约束线性二次优化控制问题最优解与状态之间的显式函数关系,减少多参数规划问题求解的工作量;另一方面,能够同时求解得到显式分段线性状态反馈最优控制律。应用高频机械振动系统数值仿真例子,对该文的方法进行了数值仿真计算。仿真结果表明该文提出的方法是有效的。

Dynamic programming techniques were combined with one-step multi-parametric programming(control horizon 1) to create a multi-parametric programming method for linearly constrained quadratic optimal control problems.This method gives the explicit solution of the optimization problem with less computation burden and the optimal open loop explicit state feedback control law.Simulations of the vibration control of a mechanical elevator system show effectiveness of the approach.