相关论文: A Blob Method for Mean Field Control With Terminal…
This paper contributes to the compactification approach to study mean-field control problems with Poissonian common noise. To overcome the lack of compactness and continuity issues caused by common noise, we exploit the point process…
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…
In this work, we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation approach to implement spatial dimension approximation. Our main contribution is to extend the…
Bearing-based distributed formation control is attractive because it can be implemented using vision-based measurements to achieve a desired formation. Gradient-descent-based controllers using bearing measurements have been shown to have…
Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In their general form, in absence of convexity/concavity assumptions, finding pure equilibria of the…
This work extends the concepts of algebraic flux correction and convex limiting to continuous high-order Bernstein finite element discretizations of scalar hyperbolic problems. Using an array of adjustable diffusive fluxes, the standard…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the…
For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are…
In this paper, we investigate optimal control problems governed by the parabolic interface equation, in which the control acts on the interface. The solution to this problem exhibits low global regularity due to the jump of the coefficient…
Model Predictive Control (MPC) is a widely known control method that has proved to be particularly effective in multivariable and constrained control. Closed-loop stability and recursive feasibility can be guaranteed by employing accurate…
The recent evolution of software and hardware technologies is leading to a renewed computational interest in Particle-In-Cell (PIC) methods such as the Material Point Method (MPM). Indeed, provided some critical aspects are properly…
This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
In this article, we consider a weighted mean-field control problem with jump-diffusion as its state process. The main difficulty is from the non-Lipschitz property of the coefficients. We overcome this difficulty by an $L_{p,q}$-estimate of…
In this paper, we introduce a new conservation-based approach to model traffic dynamics, and apply the model predictive control (MPC) approach to control the boundary traffic inflow and outflow, so that the traffic congestion is reduced. We…
Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this…
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress field by controlling the displacement at prescribed parts of…
We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…
We survey recent results on controlled particle systems. The control aspect introduces new challenges in the discussion of properties and suitable mean field limits. Some of the aspects are highlighted in a detailed discussion of a…