# A Model-Free Optimal Control Method With Fixed Terminal States and Delay

arXiv: https://arxiv.org/abs/2409.10722 · HTML: https://mlsanity.com/paper/2409.10722/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 16 Sep 2024.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 4 of 4)

- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [A Convex Approach to Data-driven Optimal Control via Perron-Frobenius and Koopman Operators](https://mlsanity.com/paper/2010.01742/) (2020)
- [NOSNOC: A Software Package for Numerical Optimal Control of Nonsmooth Systems](https://mlsanity.com/paper/2203.11516/) (2022)
- [Jump Law of Co-State in Optimal Control for State-Dependent Switched Systems and Applications](https://mlsanity.com/paper/2209.12775/) (2022)

## Abstract (arXiv)

Model-free algorithms are brought into the control system's research with the emergence of reinforcement learning algorithms. However, there are two practical challenges of reinforcement learning-based methods. First, learning by interacting with the environment is highly complex. Second, constraints on the states (boundary conditions) require additional care since the state trajectory is implicitly defined from the inputs and system dynamics. To address these problems, this paper proposes a new model-free algorithm based on basis functions, gradient estimation, and the Lagrange method. The favorable performance of the proposed algorithm is shown using several examples under state-dependent switches and time delays.