基于动态规划的约束优化问题多参数规划求解方法及应用

结合动态规划和单步多参数二次规划, 提出一种新的约束优化控制问题多参数规划求解方法. 一方面能得到约束线性二次优化控制问题最优控制序列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状态反馈最优控制律. 应用本文提出的多参数二次规划求解方法, 建立无限时间约束优化问题状态反馈显式最优控制律. 针对电梯机械系统振动控制模型做了数值仿真计算.

Dynamic-programming-based multi-parametric programming method for constrained optimal control problem and its applications

By combining the dynamic programming techniques with one-step multi-parametric programming (control horizon 1), a new multi-parametric programming method for linear constrained quadratic optimal control problems is proposed. With this new method, the explicit solution of the optimization problem can be calculated with less computation burden, and the state feedback optimal control laws are obtained simultaneously. Applying the proposed multi-parametric programming method, an explicit algorithm for obtaining the state feedback optimal control law for the constrained linear infinite-time optimal control problem is established. At the end of the paper, simulations of a vibration control for the mechanical system of an elevator are performed.