# Model Predictive Control of Hybrid Dynamical Systems

arXiv: https://arxiv.org/abs/2604.21989 · HTML: https://mlsanity.com/paper/2604.21989/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 59 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Builds on (most cited first, 2 of 2)

- [On the Relation between the Minimum Principle and Dynamic Programming for Classical and Hybrid Control Systems](https://mlsanity.com/paper/1609.03158/) (2016)
- [Regularity of Optimal Solutions and the Optimal Cost for Hybrid Dynamical Systems via Reachability Analysis](https://mlsanity.com/paper/2112.10891/) (2021)

## Abstract (arXiv)

The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid equations, involving a differential equation and a difference equation with inputs and constraints. The proposed hybrid MPC algorithm uses a suitable prediction and control horizon construction inspired by hybrid time domains. Structural properties of the hybrid optimization problem, its feasible set, and its value function are provided. Checkable conditions to guarantee asymptotic stability of a set are provided. These conditions are given in terms of properties on the stage cost, terminal cost, and the existence of static state-feedback laws, related through a control Lyapunov function condition. Examples illustrate the results throughout the paper.