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Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At the same time, in some applications…
Simulation is an efficient tool in the design and control of power electronic systems. However, quick and accurate simulation of them is still challenging, especially when the system contains a large number of switches and state variables.…
Many contemporary applications in signal processing and machine learning give rise to structured non-convex non-smooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to…
We consider output-feedback stabilization problems for a class of two-component linear parabolic systems with boundary actuation and measurement. The state-feedback control laws are obtained using backstepping method and require measurement…
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
A combination of a steady-state preserving operator splitting method and a semi-implicit integration scheme is proposed for efficient time stepping in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical…
We propose algorithms for efficient time integration of large systems of oscillatory second order ordinary differential equations (ODEs) whose solution can be expressed in terms of trigonometric matrix functions. Our algorithms are based on…
We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
Gradient descent and its variants are widely used in machine learning. However, oracle access of gradient may not be available in many applications, limiting the direct use of gradient descent. This paper proposes a method of estimating…
We propose a reformulation for the integral equations approach of Jain, Breunung \& Haller [Nonlinear Dyn. 97, 313--341 (2019)] to steady-state response computation for periodically forced nonlinear mechanical systems. This reformulation…
Difference control schemes for controlling unstable fixed points become important if the exact position of the fixed point is unavailable or moving due to drifting parameters. We propose a memory difference control method for stabilization…
Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…
This paper addresses the local stabilization problem for semilinear single-track vehicle models with distributed tire friction dynamics, represented as interconnections of ordinary differential equations (ODEs) and hyperbolic partial…
The paper presents a new control algorithm for unstable linear systems with input delay. In comparison with known analogues, the control law has been designed, which is a modification of the Smith predictor, and is the simplest one to…
In this article we present three robust instability mechanisms for linear and nonlinear inverse problems. All of these are based on strong compression properties (in the sense of singular value or entropy number bounds) which we deduce…
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
A non-relativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between…