# High-Relative Degree Stochastic Control Lyapunov and Barrier Functions

arXiv: https://arxiv.org/abs/2004.03856 · HTML: https://mlsanity.com/paper/2004.03856/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM](https://mlsanity.com/paper/2202.10658/) (2022)

## Abstract (arXiv)

We introduce High-Relative Degree Stochastic Control Lyapunov functions and Barrier Functions as a means to ensure asymptotic stability of the system and incorporate state dependent high relative degree safety constraints on a non-linear stochastic systems. Our proposed formulation also provides a generalisation to the existing literature on control Lyapunov and barrier functions for stochastic systems. The control policies are evaluated using a constrained quadratic program that is based on control Lyapunov and barrier functions. Our proposed control design is validated via simulated experiments on a relative degree 2 system (2 dimensional car navigation) and relative degree 4 system (two-link pendulum with elastic actuator).