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Designing spacecraft trajectories remains challenging in the presence of stochastic effects such as maneuver execution errors and observation uncertainties. Although covariance control and belief-space planning provide useful tools for…
Future multi-spacecraft missions require robust autonomous trajectory optimization capabilities to ensure safe and efficient rendezvous operations. This capability hinges on solving non-convex optimal control problems in real-time, although…
Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all…
In 1934, Reinhardt conjectured that the shape of the centrally symmetric convex body in the plane whose densest lattice packing has the smallest density is a smoothed octagon. This conjecture is still open. We formulate the Reinhardt…
This paper presents a framework to jointly optimize the design and control of an electric race car equipped with a multiple-gear transmission, specifically accounting for the discrete gearshift dynamics. We formulate the problem as a…
We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin…
The minimum-fuel orbital transfer is analyzed in the case of a launcher upper stage using a constantly thrusting engine. The thrust level is assumed to be constant and its value is optimized together with the thrust direction. A closed-loop…
The minimum-fuel low-thrust transfer between circular orbits is formulated using the Edelbaum's averaged dynamics with the addition of the nodal precession due to the first zonal term. The extremal analysis shows that an optimal transfer is…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
Second-order necessary conditions for optimal control problems are considered, where the ``second-order" is in the sense of that Pontryagin's maximum principle is viewed as a first-order necessary optimality condition. A sufficient…
We consider a problem on maximizing the height of vertical flight of a material point ("meteorological rocket") in the presence of a nonlinear friction and a constant flat gravity field under a bounded thrust and fuel expenditure. The…
We study the reduction of degrees of freedom for the equations that determine necessary optimality conditions for extrema in an optimal control problem for a multiagent system by exploiting the physical symmetries of agents, where the…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
Space robotics applications, such as Active Space Debris Removal (ASDR), require representative testing before launch. A commonly used approach to emulate the microgravity environment in space is air-bearing based platforms on flat-floors,…
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
This paper aims to devise the shape of the external electromagnetic field that drives the spin dynamics of radical pairs to a quantum coherent state through maximization of the triplet-born singlet yield in biochemical reactions. The model…
This paper presents a comparative study of the applicability and accuracy of optimal control methods and neural network-based estimators in the context of porkchop plots for preliminary asteroid rendezvous mission design. The scenario…
We consider trajectory optimal control problems in which parameter uncertainty limits the applicability of control trajectories computed prior to travel. Hence, efficient trajectory adjustment is needed to ensure successful travel. However,…
The basic module for the solution of the minimum time optimal control of a car-like vehicle is herein presented. The vehicle is subject to the effect of laminar (linear) and aerodynamic (quadratic) drag, taking into account the asymmetric…