Uncertainty propagation for nonlinear dynamics: A polynomial optimization approach
Covella F, Fantuzzi G (2023)
Publication Type: Conference contribution
Publication year: 2023
Conference Proceedings Title: 2023 American Control Conference (ACC)
Event location: San Diego, CA
URI: https://arxiv.org/abs/2209.07432
DOI: 10.23919/ACC55779.2023.10156169
Open Access Link: https://arxiv.org/abs/2209.07432
Abstract
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation, producing rigorous bounds on the expected future value of a quantity of interest even when only limited statistics of the initial condition (e.g., mean and variance) are known. For dynamical systems evolving in compact sets, the best upper (lower) bound coincides with the largest (smallest) expectation among all initial state distributions consistent with the known statistics. For systems governed by polynomial equations and polynomial quantities of interest, one-sided estimates on the optimal bounds can be computed using tools from polynomial optimization and semidefinite programming. Moreover, these numerical bounds provably converge to the optimal ones in the compact case. We illustrate the approach on a van der Pol oscillator and on the Lorenz system in the chaotic regime.
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APA:
Covella, F., & Fantuzzi, G. (2023). Uncertainty propagation for nonlinear dynamics: A polynomial optimization approach. In IEEE (Eds.), 2023 American Control Conference (ACC). San Diego, CA, US.
MLA:
Covella, Francesca, and Giovanni Fantuzzi. "Uncertainty propagation for nonlinear dynamics: A polynomial optimization approach." Proceedings of the American Control Conference (ACC), San Diego, CA Ed. IEEE, 2023.
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