Related papers: A $\mu$-Analysis and Synthesis Framework for Parti…
Parametric uncertainty in nonlinear dynamical systems can fundamentally alter bifurcation behaviour, leading to qualitative response changes. Predicting operating margins/envelopes under such uncertainties is critical but challenging:…
A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using…
The rigorous stability analysis of high-order implicit-explicit multistep (IEMS) methods for nonlinear parabolic equations by using discrete energy arguments is a long standing open issue due to their non-A-stable property. A novel…
We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration.…
Partial Integral Equations (PIEs) have been used to represent both systems with delay and systems of Partial Differential Equations (PDEs) in one or two spatial dimensions. In this paper, we show that these results can be combined to obtain…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to…
The structured singular value $\mu$ was introduced independently by Doyle and Safanov as a tool for analyzing robustness of system stability and performance in the presence of structured uncertainty in the system parameters. While the…
Disordered materials are attracting considerable attention because of their enhanced properties compared to their ordered analogs, making them particularly suitable for high-temperature applications. The feasibility of incorporating these…
In this paper, we develop an optimization-based framework for solving coupled forward-backward stochastic differential equations. We introduce an integral-form objective function and prove its equivalence to the error between consecutive…
This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle…
We provide a unified analysis of a posteriori and a priori error bounds for a broad class of discontinuous Galerkin and $C^0$-IP finite element approximations of fully nonlinear second-order elliptic Hamilton--Jacobi--Bellman and Isaacs…
This work solves suboptimal mixed-integer quadratic programs recursively for feedback control of dynamical systems. The proposed framework leverages parametric mixed-integer quadratic programming (MIQP) and hybrid systems theory to model a…
Iteration limited model predictive control (MPC) can stabilize a feedback control system under sufficient conditions; this work explores combining a low iteration limit MPC with a high iteration limit MPC for mixed-integer quadratic…
In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
We develop an approach to incorporate additional knowledge, in the form of general purpose integrity constraints (ICs), to reduce uncertainty in probabilistic databases. While incorporating ICs improves data quality (and hence quality of…
We investigate the analytic structure of functions defined by integrals with integrands singular on a finite union of quadrics. The main motivation comes from Feynman integrals which belong to this class. Using isotopy techniques we derive…
Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problems are proposed and tested. In particular, the algorithms are proposed and tested in the context of an optimization problem formulation arising in semi-supervised…