no code implementations • 8 Mar 2021 • Vít Cibulka, Milan Korda, Tomáš Haniš, Martin Hromčík
These nonlinearities are approximated in a predefined subset of the state-space by the linear Koopman operator and used for a linear Model Predictive Control (MPC) design in the high-dimension state space where the nonlinear system dynamics evolve linearly.
Optimization and Control Systems and Control Systems and Control
no code implementations • 3 Feb 2021 • Milan Korda
First, we show that the stability and performance of a polynomial dynamical system controlled by a neural network with semialgebraically representable activation functions (e. g., ReLU) can be certified by convex semidefinite programming.
Optimization and Control Dynamical Systems
no code implementations • 10 Dec 2020 • Corbinian Schlosser, Milan Korda
In this paper we prove general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain structures, which we call subsystems.
Optimization and Control 90C22, 37M22
1 code implementation • 7 May 2020 • Corbinian Schlosser, Milan Korda
For systems with polynomial dynamics, a hierarchy of finite-dimensional sum-of-squares tightenings of the dual LP provides a sequence of outer approximations to the global attractor with guaranteed convergence in the sense of volume discrepancy tending to zero.
Optimization and Control Dynamical Systems 34D45 (primary), 90C22 (secondary)
2 code implementations • 15 Apr 2018 • Hassan Arbabi, Milan Korda, Igor Mezic
The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data.
Fluid Dynamics 76B75, 35Q93, 76D55, 76N25
1 code implementation • 18 Oct 2017 • Milan Korda, Mihai Putinar, Igor Mezić
We also show how to compute, from measured data, the spectral projection on a given segment of the unit circle, allowing us to obtain a finite-dimensional approximation of the operator that explicitly takes into account the point and continuous parts of the spectrum.
Dynamical Systems Numerical Analysis Spectral Theory
