Related papers: A Simple Solution for Maximum Range Flight
For a general optimal control problem for dynamical systems with hybrid dynamics, we study the dependency of the optimal cost and of the value function on the initial conditions, parameters, and perturbations. We show that upper and lower…
We consider the problem of multiple agents or robots searching for a target in the plane. This is motivated by Search and Rescue operations (SAR) in the high seas which in the past were often performed with several vessels, and more…
In this paper, we address the problem of finding the optimal trajectory for an unmanned aerial vehicle (UAV) for improving the wireless coverage of a terrestrial cellular network. In particular, we consider a UAV that is tasked to travel…
We first formulate the problem of optimally scheduling air traffic low with sector capacity constraints as a mixed integer linear program. We then use semidefinite relaxation techniques to form a convex relaxation of that problem. Finally,…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve a diffusion process and its running maximum. Besides, a new feature includes absorbing boundaries that vary with the value of the running…
Guaranteeing stringent data freshness for low-altitude unmanned aerial vehicles (UAVs) in shared spectrum forces a critical trade-off between two operational costs: the UAV's own energy consumption and the occupation of terrestrial channel…
The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear…
In this paper, we consider a trajectory planning problem arising from a lunar vertical landing with minimum fuel consumption. The vertical landing requirement is written as a final steering angle constraint, and a nonnegative regularization…
Engine failure is a recurring emergency in General Aviation and fixed-wing UAVs, often requiring the pilot or remote operator to carry out carefully planned glides to safely reach a candidate landing strip. We tackle the problem of…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…
We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward…
We consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the…
We study the problem of controlling the initial condition of a vibrating beam. The optimal control problem seeks to determine solutions of initial velocity that assure the approach of the state of the beam to a given target function in the…
We study the approximation of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H>1/2$. For the mean-square error at a single point we derive the optimal rate of convergence that can be achieved…
We consider a single Unmanned Aerial Vehicle (UAV) routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot. The objective of the problem is to find a path for the UAV such that each target is…
Unmanned aerial vehicles (UAVs) are increasingly utilized in global search and rescue efforts, enhancing operational efficiency. In these missions, a coordinated swarm of UAVs is deployed to efficiently cover expansive areas by capturing…
As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal…
We present an analytic solution of a differential-difference equation that appears when one solves an optimal stopping time problem with state process following a jump-diffusion process. This equation occurs in the context of real options…
This study proposes an algorithm to synthesize controllers for the power management on board hybrid vehicles that allows the vehicle to reach its maximum range along a given route. The algorithm stems from a level-set approach that computes…