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Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the…
This paper is concerned with monotone (time-explicit) finite difference schemes associated with first order Hamilton-Jacobi equations posed on a junction. They extend the schemes recently introduced by Costeseque, Lebacque and Monneau…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
Flow control has been the subject of numerous experimental and theoretical works. In this numerical study, we analyse full-order, optimal controllers for large dynamical systems in presence of multiple actuators and sensors. We start from…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
Presented is a method to compute certain classes of Hamilton-Jacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the…
The paper deals with path-dependent Hamilton-Jacobi equations with a coinvariant derivative which arise in investigations of optimal control problems and differential games for neutral-type systems in Hale's form. A viscosity (generalized)…
Nondominated sorting is a discrete process that sorts points in Euclidean space according to the coordinatewise partial order, and is used to rank feasible solutions to multiobjective optimization problems. It was previously shown that…
We present a simple algorithm to approximate the viscosity solution of Hamilton-Jacobi (HJ) equations by means of an artificial deep neural network. The algorithm uses a stochastic gradient descent-based method to minimize the least square…
In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…
We introduce stabilized spline collocation schemes for the numerical solution of nonlinear, hyperbolic conservation laws. A nonlinear, residual-based viscosity stabilization is combined with a projection stabilization-inspired linear…
Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of viscosity solution, featured by absence of B-continuity, is…
We consider stochastic impulse control problems when the impulses cost functions are arbitrary. We use the dynamic programming principle and viscosity solutions approach to show that the value function is a unique viscosity solution for the…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the…
This book is organized into eight chapters. The first three gently introduce the basic principles of hybrid high-order methods on a linear diffusion problem, the key ideas underlying the mathematical analysis, and some useful variants of…
The fast growing scale and heterogeneity of current communication networks necessitate the design of distributed cross-layer optimization algorithms. So far, the standard approach of distributed cross-layer design is based on dual…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
In this paper, we present an application of the optimal control theory to orbital transfer of Low Earth Orbit satellites. The optimal control problem is treated with Dynamic Programming techniques which require solving the…