Core Concepts
The author aims to develop a method for inferring stable quadratic control dynamical systems by investigating stability characteristics and applying them to the learning process. The main thesis is to ensure bounded-input bounded-state stability in inferred models through a data-driven approach.
Abstract
This content discusses a methodology for learning stable quadratic control systems through data-driven approaches. It focuses on stability guarantees, energy-preserving nonlinearities, and parametrizations of matrices to ensure stability. The efficacy of the proposed framework is demonstrated through numerical examples.
Significant developments have been made in learning dynamical systems from data, driven by various applications such as robotics and climate science. Operator inference methodologies are utilized for constructing low-dimensional dynamical models based on prior knowledge and expert insights.
The content emphasizes the importance of stability in dynamical systems and addresses challenges related to ensuring stability while learning dynamical systems. By leveraging parametrizations for stable matrices and energy-preserving Hessians, the proposed methodology ensures stable behavior in learned models.
Theoretical concepts such as Hurwitz matrices, Lyapunov functions, and energy-preserving nonlinearities are discussed in the context of stability certification for quadratic control systems. The methodology extends to more general quadratic Lyapunov functions for enhanced stability guarantees.
Numerical examples illustrate the effectiveness of the proposed approach compared to traditional methods. Stability-certified learning ensures robust performance and opens avenues for further research in data-driven modeling of complex systems.
Stats
A = (J − R)Q
H ∈ Rn×n2 is an energy-preserving Hessian.
r = ∥B∥2∥u∥L∞ / σmin(R)
D = X X ˜⊗ X U
Quotes
"Learning stability-certified control systems with quadratic nonlinearities."
"Bounded-input bounded-state stability for quadratic systems with control is shown under parametrization assumptions."