# Closed Form HJB Solution for Continuous-Time Optimal Control of a Non-Linear Input-Affine System

arXiv: https://arxiv.org/abs/2511.21593 · HTML: https://mlsanity.com/paper/2511.21593/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 1 of its 27 references that are in the map.
- First posted on arXiv 26 Nov 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 1 of 1)

- [Inverse Optimal Control with Discount Factor for Continuous and Discrete-Time Control-Affine Systems and Reinforcement Learning](https://mlsanity.com/paper/2211.09917/) (2022)

## Abstract (arXiv)

Designing optimal controllers for nonlinear dynamical systems often relies on reinforcement learning and adaptive dynamic programming (ADP) to approximate solutions of the Hamilton Jacobi Bellman (HJB) equation. However, these methods require iterative training and depend on an initially admissible policy. This work introduces a new analytical framework that yields closed-form solutions to the HJB equation for a class of continuous-time nonlinear input-affine systems with known dynamics. Unlike ADP-based approaches, it avoids iterative learning and numerical approximation. Lyapunov theory is used to prove the asymptotic stability of the resulting closed-loop system, and theoretical guarantees are provided. The method offers a closed-form control policy derived from the HJB framework, demonstrating improved computational efficiency and optimal performance on state-of-the-art optimal control problems in the literature.