# Optimal feedback control of dynamical systems via value-function approximation

arXiv: https://arxiv.org/abs/2302.13122 · HTML: https://mlsanity.com/paper/2302.13122/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2023.

## Built on by (most cited first, 2 of 2)

- [Neural Network Approaches for Parameterized Optimal Control](https://mlsanity.com/paper/2402.10033/) (2024)
- [Nonuniform random feature models using derivative information](https://mlsanity.com/paper/2410.02132/) (2024)

## Abstract (arXiv)

A self-learning approach for optimal feedback gains for finite-horizon nonlinear continuous time control systems is proposed and analysed. It relies on parameter dependent approximations to the optimal value function obtained from a family of universal approximators. The cost functional for the training of an approximate optimal feedback law incorporates two main features. First, it contains the average over the objective functional values of the parametrized feedback control for an ensemble of initial values. Second, it is adapted to exploit the relationship between the maximum principle and dynamic programming. Based on universal approximation properties, existence, convergence and first order optimality conditions for optimal neural network feedback controllers are proved.