论文标题
Minkowski-Bellman方程
The Minkowski-Bellman Equation
论文作者
论文摘要
该手稿研究了Minkowski-Bellman方程，该方程是由有限或无限的地平线最佳控制不受约束的线性离散时间系统，具有阶段和终端成本函数，指定为适当C-set的Minkowski函数。关于有限的视野最佳控制，可以很好地确定，在自然条件下，Minkowski-Bellman方程及其迭代良好。得出了值函数和优化图图的表征。关于无限的地平线最佳控制，证明在相同的自然条件下，Minkowski-Bellman方程的固定点在价值函数方面是独一无二的，在适当C-set的Minkowski函数的空间上。报告了固定点值函数和优化器图的表征。
This manuscript studies the Minkowski-Bellman equation, which is the Bellman equation arising from finite or infinite horizon optimal control of unconstrained linear discrete time systems with stage and terminal cost functions specified as Minkowski functions of proper C-sets. In regards to the finite horizon optimal control, it is established that, under natural conditions, the Minkowski-Bellman equation and its iteration are well posed. The characterization of the value functions and optimizer maps is derived. In regards to the infinite horizon optimal control, it is demonstrated that, under the same natural conditions, the fixed point of the Minkowski-Bellman equation is unique, in terms of the value function, over the space of Minkowski functions of proper C-sets. The characterization of the fixed point value function and optimizer map is reported.
