# Relaxed Actor-Critic with Convergence Guarantees for Continuous-Time Optimal Control of Nonlinear Systems

arXiv: https://arxiv.org/abs/1909.05402 · HTML: https://mlsanity.com/paper/1909.05402/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2019.

## Built on by (most cited first, 4 of 4)

- [Enhance Sample Efficiency and Robustness of End-to-end Urban Autonomous Driving via Semantic Masked World Model](https://mlsanity.com/paper/2210.04017/) (2022)
- [Deep Learning for Continuous-Time Stochastic Control with Jumps](https://mlsanity.com/paper/2505.15602/) (2025)
- [Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedback](https://mlsanity.com/paper/2310.19022/) (2023)
- [DeepPAAC: A New Deep Galerkin Method for Principal-Agent Problems](https://mlsanity.com/paper/2511.04309/) (2025)

## Abstract (arXiv)

This paper presents the Relaxed Continuous-Time Actor-critic (RCTAC) algorithm, a method for finding the nearly optimal policy for nonlinear continuous-time (CT) systems with known dynamics and infinite horizon, such as the path-tracking control of vehicles. RCTAC has several advantages over existing adaptive dynamic programming algorithms for CT systems. It does not require the ``admissibility" of the initialized policy or the input-affine nature of controlled systems for convergence. Instead, given any initial policy, RCTAC can converge to an admissible, and subsequently nearly optimal policy for a general nonlinear system with a saturated controller. RCTAC consists of two phases: a warm-up phase and a generalized policy iteration phase. The warm-up phase minimizes the square of the Hamiltonian to achieve admissibility, while the generalized policy iteration phase relaxes the update termination conditions for faster convergence. The convergence and optimality of the algorithm are proven through Lyapunov analysis, and its effectiveness is demonstrated through simulations and real-world path-tracking tasks.