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In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…
This work is aimed to develop a new class of methods for the BGK model of the Boltzmann equation. This technique allows to get high order of accuracy both in space and time, theoretically without CFL stability limitation. It's based on a…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
For linear and fully non-linear diffusion equations of Bellman-Isaacs type, we introduce a class of approximation schemes based on differencing and interpolation. As opposed to classical numerical methods, these schemes work for general…
Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in…
In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
This paper studies a class of linear unconditionally energy stable schemes for the gradient flows. Such schemes are built on the SAV technique and the general linear time discretization (GLTD) as well as the linearization based on the…
We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is…
Nowadays, many strategies to solve polynomial systems use the computation of a Gr{\"o}bner basis for the graded reverse lexicographical ordering, followed by a change of ordering algorithm to obtain a Gr{\"o}bner basis for the…
In this paper, a centred universal high-order finite volume method for solving hyperbolic balance laws is presented. The scheme belongs to the family of ADER methods where the Generalized Riemann Problems (GRP) is a building block. The…
Standard model-based control design deteriorates when the system dynamics change during operation. To overcome this challenge, online and adaptive methods have been proposed in the literature. In this work, we consider the class of…
We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
This paper proposes a new methodology in linear time-periodic (LTP) system identification. In contrast to previous methods that totally separate dynamics at different tag times for identification, the method focuses on imposing appropriate…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
This paper studies the robustness of reinforcement learning algorithms to errors in the learning process. Specifically, we revisit the benchmark problem of discrete-time linear quadratic regulation (LQR) and study the long-standing open…
The stability of classical semi-implicit scheme, and some more advanced iterative schemes recently proposed for Numerical Weather Prediction (NWP) purpose is examined. In all these schemes, the solution of the centred-implicit non-linear…