Related papers: Reduction of Necessary Conditions for the Variatio…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
We propose a distributed control algorithm for a multi-agent network whose agents deploy over a cluttered region in accordance with a time-varying coverage density function while avoiding collisions with all obstacles they encounter. Our…
This work is concerned with an optimal control problem on a Riemannian manifold, for which two typical cases are considered. The first case is when the endpoint is free. For this case, the control set is assumed to be a separable metric…
Understanding collision avoidance behavior is of key importance in traffic safety research and for designing and evaluating advanced driver assistance systems and autonomous vehicles. While existing experimental work has primarily focused…
In most modern cities, traffic congestion is one of the most salient societal challenges. Past research has shown that inserting a limited number of autonomous vehicles (AVs) within the traffic flow, with driving policies learned…
Multi-agent systems exhibit complex behaviors that emanate from the interactions of multiple agents in a shared environment. In this work, we are interested in controlling one agent in a multi-agent system and successfully learn to interact…
We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In…
We prove an existence theorem for the sliding boundary variant of the Plateau problem for $2$-dimensional sets in $\mathbb{R}^n$. The simplest case of sufficient condition is when $n=3$ and the boundary $\Gamma$ is a finite disjoint union…
Individual traffic significantly contributes to climate change and environmental degradation. Therefore, innovation in sustainable mobility is gaining importance as it helps to reduce environmental pollution. However, effects of new ideas…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…
Generalized from the concept of consensus, this paper considers a group of edge agreements, i.e. constraints defined for neighboring agents, in which each pair of neighboring agents is required to satisfy one edge agreement constraint. Edge…
In this paper, we present an on-board vision-based approach for avoidance of moving obstacles in dynamic environments. Our approach relies on an efficient obstacle detection and tracking algorithm based on depth image pairs, which provides…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was…
We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of…
Minimum circle circumnavigation is proposed in this paper, which is of special value in target monitoring, capturing and/or attacking. In this paper, a safe minimum circle circumnavigation of multiple targets based on bearing measurements…
We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus,…
In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modelling…