Related papers: Computing Robustly Forward Invariant Sets for Mixe…

A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large…

Automating design minimizes errors, accelerates the design process, and reduces cost. However, automating robot design is challenging due to recursive constraints, multiple design objectives, and cross-domain design complexity possibly…

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…

We introduce a persistence-type invariant for finite weighted graphs based on combinatorial multivector dynamics. For each threshold parameter, a relation matrix determines a graph multivector field, whose induced directed dynamics admits a…

We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…

We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic…

Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the central…

We present theory and algorithms for the computation of probability-weighted "keep-out" sets to assure probabilistically safe navigation in the presence of multiple rigid body obstacles with stochastic dynamics. Our forward stochastic…

This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…

Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…

Robust control problems have significant practical implications since external disturbances can significantly impact the performance of control methods. Existing robust control methods excel at control-affine systems but fail at neural…

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we…

Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…

We revisit the concept of constraint embedding as a means for dealing with kinematic loop constraints during dynamics computations for rigid-body systems. Specifically, we consider the local loop constraints emerging from common actuation…

We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that…

Harmonic instability occurs frequently in the power electronic converter system. This paper leverages multi-resolution dynamic mode decomposition (MR-DMD) as a data-driven diagnostic tool for the system stability of power electronic…

In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…

For better explore the relations of inter-modal and inner-modal, even in deep learning fusion framework, the concept of decomposition plays a crucial role. However, the previous decomposition strategies (base \& detail or low-frequency \&…

Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…