[HTML][HTML] Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization
Chordal and factor-width decomposition methods for semidefinite programming and
polynomial optimization have recently enabled the analysis and control of large-scale linear …
polynomial optimization have recently enabled the analysis and control of large-scale linear …
An inductive synthesis framework for verifiable reinforcement learning
Despite the tremendous advances that have been made in the last decade on developing
useful machine-learning applications, their wider adoption has been hindered by the lack of …
useful machine-learning applications, their wider adoption has been hindered by the lack of …
Safety guarantees for neural network dynamic systems via stochastic barrier functions
Abstract Neural Networks (NNs) have been successfully employed to represent the state
evolution of complex dynamical systems. Such models, referred to as NN dynamic models …
evolution of complex dynamical systems. Such models, referred to as NN dynamic models …
[HTML][HTML] Sparse polynomial optimisation for neural network verification
M Newton, A Papachristodoulou - Automatica, 2023 - Elsevier
The prevalence of neural networks in applications is expanding at an increasing rate. It is
becoming clear that providing robust guarantees on systems that use neural networks is …
becoming clear that providing robust guarantees on systems that use neural networks is …
Stability of non-linear neural feedback loops using sum of squares
M Newton, A Papachristodoulou - 2022 IEEE 61st Conference …, 2022 - ieeexplore.ieee.org
Neural network controllers have the potential to improve the performance of feedback
systems compared to traditional controllers, due to their ability to act as general function …
systems compared to traditional controllers, due to their ability to act as general function …
Synthesizing stable reduced-order visuomotor policies for nonlinear systems via sums-of-squares optimization
We present a method for synthesizing dynamic, reduced-order output-feedback polynomial
control policies for control-affine nonlinear systems which guarantees runtime stability to a …
control policies for control-affine nonlinear systems which guarantees runtime stability to a …
Linear principal minor polynomials: hyperbolic determinantal inequalities and spectral containment
A linear principal minor polynomial or lpm polynomial is a linear combination of principal
minors of a symmetric matrix. By restricting to the diagonal, lpm polynomials are in bijection …
minors of a symmetric matrix. By restricting to the diagonal, lpm polynomials are in bijection …
Sum-of-squares methods for controlled invariant sets with applications to model-predictive control
We develop a method for computing controlled invariant sets of discrete-time affine systems
using Sum-of-Squares programming. We apply our method to the controller design problem …
using Sum-of-Squares programming. We apply our method to the controller design problem …
Towards optimal spatio‐temporal decomposition of control‐related sum‐of‐squares programs
This paper presents a method for calculating the Region of Attraction (ROA) of nonlinear
dynamical systems, both with and without control. The ROA is determined by solving a …
dynamical systems, both with and without control. The ROA is determined by solving a …
Sum-of-squares bounds on correlation functions in a minimal model of turbulence
We suggest a new computer-assisted approach to the development of turbulence theory. It
allows one to impose lower and upper bounds on correlation functions using sum-of …
allows one to impose lower and upper bounds on correlation functions using sum-of …