Related papers: Distributionally Robust Lyapunov Function Search U…
In this paper, we develop a dynamical system counterpart to the term sparsity sum-of-squares (TSSOS) algorithm proposed for static polynomial optimization. This allows for computational savings and improved scalability while preserving…
Leveraging a stochastic extension of Zubov's equation, we develop a physics-informed neural network (PINN) approach for learning a neural Lyapunov function that captures the largest probabilistic region of attraction (ROA) for stochastic…
We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to…
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
One of the proposed solutions to the equilibrium selection problem for agents learning in repeated games is obtained via the notion of stochastic stability. Learning algorithms are perturbed so that the Markov chain underlying the learning…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
We present several new easy ways of generating smooth one-dimensional maps displaying robust chaos, i.e., chaos for whole intervals of the parameter. Unlike what happens with previous methods, the Lyapunov exponent of the maps constructed…
In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…
This book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically…
Deep learning methods have been widely used in robotic applications, making learning-enabled control design for complex nonlinear systems a promising direction. Although deep reinforcement learning methods have demonstrated impressive…
Most of nonlinear robust control methods just consider the affine nonlinear nominal model. When the nominal model is assumed to be affine nonlinear, available information about existing non-affine nonlinearities is ignored. For non-affine…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
Lyapunov functions are fundamental to establishing the stability of Markovian models, yet their construction typically demands substantial creativity and analytical effort. In this paper, we show that deep learning can automate this process…
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…
The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with…
In this paper, we study the problem of control of discrete-time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the…
Motivated by robust and quantile regression problems, we investigate the stochastic gradient descent (SGD) algorithm for minimizing an objective function $f$ that is locally strongly convex with a sub--quadratic tail. This setting covers…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…