Safe Controller Synthesis for Nonlinear Switched Systems via Probabilistic Abstractions
Abstract
In this paper, we tackle the problem of computing safe controllers for nonlinear dynamical systems, extending previous work on linear systems that relied on probabilistic abstraction. Building an exact probabilistic abstraction of a nonlinear system requires computing exact reachable sets, a task that is known to be infeasible for such systems. To overcome this limitation, we rely on over-approximations of reachable sets. The probabilistic approximation is formally a Markov Decision Process (MDP). To enhance scalability, the MDP is stored as a Dynamic Bayesian Network (DBN), this formulation allows for a compact representation of the probabilistic abstraction. Controllers can then be derived using reinforcement learning (RL) techniques such as policy iteration. Their safety is ensured by using reachability over-approximations to determine which control modes are admissible. The RL problem is then restricted to these safe modes. Finally, we illustrate our framework on a path planning problem in a maze environment.
Related
- Attack-Aware Event-Triggered Impulsive Control for Switched Nonlinear Systems via Multi-Diffeomorphism
- Dynamic Quantum-Assisted Co-Design of Controller and Lyapunov Candidate Parameters for Nonlinear Systems
- Koopman--Lyapunov and Koopman--Riccati Controller Synthesis
- Numerical study of probabilistic well-posedness of one dimensional fractional nonlinear wave equations
- Probabilistic representation and Monte Carlo method for nonlinear Dirac equations
BibTeX
@misc{bahloul2026safe,
title = {{Safe Controller Synthesis for Nonlinear Switched Systems via Probabilistic Abstractions}},
author = {Yahia Bahloul and Adrien Le Coënt and Benoît Barbot and Nihal Pekergin},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05837173v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Safe Controller Synthesis for Nonlinear Switched Systems via Probabilistic Abstractions
AU - Yahia Bahloul
AU - Adrien Le Coënt
AU - Benoît Barbot
AU - Nihal Pekergin
PY - 2026
DA - 2026/10/23
PB - HAL
UR - https://hal.science/hal-05837173v1
AB - In this paper, we tackle the problem of computing safe controllers for nonlinear dynamical systems, extending previous work on linear systems that relied on probabilistic abstraction. Building an exact probabilistic abstraction of a nonlinear system requires computing exact reachable sets, a task that is known to be infeasible for such systems. To overcome this limitation, we rely on over-approximations of reachable sets. The probabilistic approximation is formally a Markov Decision Process (MDP). To enhance scalability, the MDP is stored as a Dynamic Bayesian Network (DBN), this formulation allows for a compact representation of the probabilistic abstraction. Controllers can then be derived using reinforcement learning (RL) techniques such as policy iteration. Their safety is ensured by using reachability over-approximations to determine which control modes are admissible. The RL problem is then restricted to these safe modes. Finally, we illustrate our framework on a path planning problem in a maze environment.
ER -