Tag Archives: dynamic programming

Convergence of dynamic programming iterates

By psopasakis on July 27, 2021 | Leave a comment

We are interested in the following infinite-horizon optimal control problem

$\begin{aligned}\mathbb{P}_\infty(x): \mathrm{Minimise}_{\{u_t\}_{t=0}^{\infty}, \{x_t\}_{t=0}^{\infty}} & \sum_{t=0}^{\infty}\ell(x_t, u_t)\\ \text{s.t.}\, & x_{t+1} = f(x_t, u_t), \forall t\in\mathbb{N},\\ & x_t \in X, u_t \in U, \forall t\in\mathbb{N},\\ & x_{0} = x.\end{aligned}$

We ask under what conditions the dynamic programming value iterates converge. We will state and prove a useful convergence theorem, but first we need to state some useful definitions.

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Posted in: Control / Optimal Control | Tagged: dynamic programming, optimal control, optimization

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Convergence of dynamic programming iterates

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