相关论文: Fast algorithms for optimal control, anisotropic f…
The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the…
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…
- In this paper we introduce a new method to solve fixed-delay optimal control problems which exploits numerical homotopy procedures. It is known that solving this kind of problems via indirect methods is complex and computationally…
We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general…
We consider a general family of nonlocal in space and time diffusion equations with space-time dependent diffusivity and prove convergence of finite difference schemes in the context of viscosity solutions under very mild conditions. The…
We formulate a class of velocity-free finite-particle methods for mass transport problems based on a time-discrete incremental variational principle that combines entropy and the cost of particle transport, as measured by the Wasserstein…
This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a class of nonlocal Hamilton--Jacobi equations and establish a…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…
Optimal control problems are crucial in various domains, including path planning, robotics, and humanoid control, demonstrating their broad applicability. The connection between optimal control and Hamilton-Jacobi (HJ) partial differential…
In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…
In this article, the notion of viscosity solution is introduced for the path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with the optimal control problems for path-dependent stochastic differential equations. We identify…
We consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV). Assuming a traffic intensity map of users to be served, the UAV must travel from a given initial location to a final position within a given duration…
In this work, we design and analyze a Hybrid High-Order (HHO) discretization method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. We work under general assumptions on the viscosity and convection…
We study some optimal control problems on networks with junctions, approximate the junctions by a switching rule of delay-relay type and study the passage to the limit when $\varepsilon$, the parameter of the approximation, goes to zero.…
We present a splitting-free variant of the vorticity redistribution method. Spatial consistency and stability when combined with a time-stepping scheme are proven. We propose a new strategy preventing excessive growth in the number of…
We consider a controlled reaction-diffusion equation, motivated by a pest eradication problem. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. In this direction, the first part of the paper…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…
This work develops an efficient and accurate optimization algorithm to study the optimal mixing problem driven by boundary control of unsteady Stokes flows, based on the theoretical foundation laid by Hu and Wu in a series of work. The…
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically prove that all traveling waves, especially the critical…