# Data-Driven Optimal Control Using Perron-Frobenius Operator

arXiv: https://arxiv.org/abs/1806.03649 · HTML: https://mlsanity.com/paper/1806.03649/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2018.

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

- [Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories](https://mlsanity.com/paper/2209.09977/) (2022)

## Abstract (arXiv)

In this paper, we propose a data-driven approach for control of nonlinear dynamical systems. The proposed data-driven approach relies on transfer Koopman and Perron-Frobenius (P-F) operators for linear representation and control of such systems. Systematic model-based frameworks involving linear transfer P-F operator were proposed for almost everywhere stability analysis and control design of a nonlinear dynamical system in previous works [1-3]. Lyapunov measure can be used as a tool to provide linear programming-based computational framework for stability analysis and almost everywhere stabilizing control design of a nonlinear system. In this paper, we show that those frameworks can be extended to a data-driven setting, where the finite dimensional approximation of linear transfer P-F operator and stabilizing feedback controller can be obtained from time-series data. We exploit the positivity and Markov property of these operators and their finite-dimensional approximation to provide it linear programming based approach for designing an optimally stabilizing feedback controller.