论文标题
随机线性季度控制问题与仿射约束
Stochastic Linear-quadratic Control Problems with Affine Constraints
论文作者
论文摘要
本文研究了与仿射约束的随机线性季节控制问题，其中涉及平等和不平等约束。借助Pontryagin的最大原理和Lagrangian二重性理论，确定了原始问题的二重问题，并获得了最佳控制问题解决方案的状态反馈形式。在平面条件下，在原始问题的解决方案和双重问题的解决方案之间证明了等效性，还提供了KKT条件以解决原始问题。特别是，为可逆性假设提供了新的足够条件，从而确保了解决双重问题的独特性。
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality theory, the dual problem of original problem is established and the state feedback form of the solution to the optimal control problem is obtained. Under the Slater condition, the equivalence is proved between the solutions to the original problem and the ones of the dual problem, and the KKT condition is also provided for solving original problem. Especially, a new sufficient condition is given for the invertibility assumption, which ensures the uniqueness of the solutions to the dual problem.
