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In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…

A prey animal surveying its environment must decide whether there is a dangerous predator present or not. If there is, it may flee. Flight has an associated cost, so the animal should not flee if there is no danger. However, the prey animal…

Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the…

The fundamental goal assignment problem for a multi-robot application aims to assign a unique goal to each robot while ensuring collision-free paths, minimizing the total movement cost. A plausible algorithmic solution to this NP-hard…

Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…

We introduce and study the problem of dueling optimization with a monotone adversary, which is a generalization of (noiseless) dueling convex optimization. The goal is to design an online algorithm to find a minimizer $\mathbf{x}^{*}$ for a…

Divide and Conquer is a well known algorithmic procedure for solving many kinds of problem. In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. Finding the distance of the closest pair is an…

In this paper, we present an approach to optimizing the last-mile delivery route of a truck using coordination with unmanned aerial vehicles (UAVs). First, a traveling salesman problem is formulated to determine the truck's route. Then, a…

The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This…

This work shows the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional mission space and derives explicit solutions. The underlying performance metric consists of minimizing the total…

This paper addresses the problem of target detection and localisation in a limited area using multiple coordinated agents. The swarm of Unmanned Aerial Vehicles (UAVs) determines the position of the dispersion of stack effluents to a gas…

This paper addresses a UAV path planning task that seeks to observe a set of objects while satisfying the observation quality constraint. A dynamic programming algorithm is proposed that enables the UAV to observe the target objects with…

Reinforcement learning is an effective way to solve the decision-making problems. It is a meaningful and valuable direction to investigate autonomous air combat maneuver decision-making method based on reinforcement learning. However, when…

We introduce a dynamic vehicle routing problem in which a single vehicle seeks to guard a circular perimeter against radially inward moving targets. Targets are generated uniformly as per a Poisson process in time with a fixed arrival rate…

This paper is concerned with determining the shortest path for a pursuer aiming to intercept a moving target travelling at a constant speed. To address this challenge, we introduce an efficient mathematical model outlined as an optimal…

We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. Both the defender and the intruders have non-holonomic dynamics. The intruders' objective is to breach the…

This paper explores a scenario in which a malicious actor employs a multi-armed attack strategy to manipulate data samples, offering them various avenues to introduce noise into the dataset. Our central objective is to protect the data by…

Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among $n$ discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at…

The practical problem of tracking a maneuvering aircraft during flight has always been a crucial task in order to safeguard airborne assets from unknown threats. Therefore, the need for an efficient target detection and identification…

In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…