# Approximate Dynamic Programming For Linear Systems with State and Input Constraints

arXiv: https://arxiv.org/abs/1906.11369 · HTML: https://mlsanity.com/paper/1906.11369/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2019.

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

- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [Reinforcement Learning for Adaptive Optimal Stationary Control of Linear Stochastic Systems](https://mlsanity.com/paper/2107.07788/) (2021)

## Abstract (arXiv)

Enforcing state and input constraints during reinforcement learning (RL) in continuous state spaces is an open but crucial problem which remains a roadblock to using RL in safety-critical applications. This paper leverages invariant sets to update control policies within an approximate dynamic programming (ADP) framework that guarantees constraint satisfaction for all time and converges to the optimal policy (in a linear quadratic regulator sense) asymptotically. An algorithm for implementing the proposed constrained ADP approach in a data-driven manner is provided. The potential of this formalism is demonstrated via numerical examples.