Related papers: Optimal linear response for expanding circle maps
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason - the problem of "super…
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…
Traditional stochastic optimal control methods that attempt to obtain an optimal feedback policy for nonlinear systems are computationally intractable. In this paper, we derive a decoupling principle between the open loop plan, and the…
We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations.…
We develop a computationally tractable method for estimating the optimal map between two distributions over $\mathbb{R}^d$ with rigorous finite-sample guarantees. Leveraging an entropic version of Brenier's theorem, we show that our…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
The Circle Packing Theorem states that every planar graph can be represented as the tangency graph of a family of internally-disjoint circles. A well-known generalization is the Primal-Dual Circle Packing Theorem for 3-connected planar…
For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case, such as: given a fixed interaction between the system…
Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating…
This paper is concerned with finding an optimal path for an observer, or sensor, moving at a constant speed, which is to estimate the position of a stationary target, using only bearing angle measurements. The generated path is optimal in…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
We introduce a model of infinite horizon linear dynamic optimization with linear constraints and obtain results concerning feasibility of trajectories and optimal solutions necessarily satisfying conditions that resemble the Euler condition…
In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a…
In this short and elementary note, we study some ergodic optimization problems for circle expanding maps. We first make an observation that if a function is not far from being convex, then its calibrated sub-actions are closer to convex…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal…
The following optimization problem is considered. For a linear vector Ito equation. it is required to find an optimal deterministic control vector which minimizes a quadratic the functional. A necessary and sufficient condition for the…