Related papers: Riemannian optimal control
We study a continuous-time system that solves optimization problems over the set of orthonormal matrices, which is also known as the Stiefel manifold. The resulting optimization flow follows a path that is not always on the manifold but…
We present new geometric intuition on dynamical versions of regularized optimal transport. We introduce two families of variational problems on Riemannian manifolds which contain analogues of the Schr\"odinger bridge problem and the Yasue…
This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…
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…
We study a time-optimal control problem of a two-peakon collision. First, we state the controllability. Next, we find the time-optimal strategy. This is done via the HamiltonJacobi-Bellman equation and the dynamic programming method. We…
In this paper, we consider the optimal control problem for a class of evolution inclusions with Volterra type operators, which can be history-dependent. We establish the existence of a solution to the stated optimal control problem under…
We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…
A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear…
The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous…
We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the…
In this paper, we study mechanical optimal control problems on a given Riemannian manifold $(Q,g)$ in which the cost is defined by a general cometric $\tilde{g}$. This investigation is motivated by our studies in robotics, in which we…
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…
The problem of incompressible fluid mixing arises in numerous engineering applications and has been well-studied over the years, yet many open questions remain. This paper aims to address the question "what do efficient flow fields for…
In a canonical Stokes flow geometry, the Hele-Shaw cell, we show that tunable circulations induced by Lorentz forces in a conducting fluid enable particle control. We reveal that energy-optimal control paths correspond to geodesics of an…
We propose an optimal control framework for persistent monitoring problems where the objective is to control the movement of mobile nodes to minimize an uncertainty metric in a given mission space. For multi agent in a one-dimensional…
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution…
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
We investigate optimal control problems governed by the elliptic partial differential equation $-\Delta u=f$ subject to Dirichlet boundary conditions on a given domain $\Omega$. The control variable in this setting is the right-hand side…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
Flow matching has emerged as a powerful framework for generative modeling through continuous normalizing flows. We investigate a potential topological constraint: when the prior distribution and target distribution have mismatched topology…