相关论文: Optimal Constraint Projection for Hyperbolic Evolu…

Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems.…

High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…

A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…

Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…

This paper presents a unified approach for inverse and direct dynamics of constrained multibody systems that can serve as a basis for analysis, simulation, and control. The main advantage of the formulation of the dynamic is that it does…

We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent…

We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…

The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do…

A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…

In this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection one can assign a particular multi-objective convex optimization problem, such that the…

This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…

This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…

Motivated by the initial-boundary value problem for the Einstein equations, we propose a definition of symmetric hyperbolicity for systems of evolution equations that are first order in time but second order in space. This can be used to…

The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls.…

The vast majority of mesh-based modelling applications iteratively transform the mesh vertices under prescribed geometric conditions. This occurs in particular in methods cycling through the constraint set such as Position-Based Dynamics…

The constraint equations for smooth $[n+1]$-dimensional (with $n\geq 3$) Riemannian or Lorentzian spaces satisfying the Einstein field equations are considered. It is shown, regardless of the signature of the primary space, that the…

Accurate tracking of planned trajectories in the presence of perturbations is an important problem in control and robotics. Symmetry is a fundamental mathematical feature of many dynamical systems and exploiting this property offers the…

New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike…

Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…