Bennet Outland | Searcharxiv

arXiv2026

A Fast Convergent Algorithm for Solving Non-convex Partially-Decoupled Generalized Nash Equilibrium Problems

Solving multi-agent optimal control problems in aerospace such as pursuit-evasion and contested space operations can be modeled as non-convex differential games for which, there are limited algorithms. In this work, a relaxation of generalized Nash Equilibrium problems (GNEPs) to exclude inter-agent control coupling in dynamics, which is representative of many multi-agent systems is introduced. The main contribution is an algorithm for solving a broad class of differential games named FALCON: Fast Augmented Lagrangian Convexification for Open-loop Nash equilibria is presented. Methodologically, sequential convex programming (SCP) is utilized to create tractable convex sub-games which can then be solved via standard convex programming methods involving a potential game reformulation. FALCON is demonstrated to have global convergence guarantees to an open-loop Nash equilibrium for non-convex differential games under mild assumptions. This is numerically shown through both cooperative and competitive differential games.

cs.MA↗

arXiv2026

Orbital Stability of Closely-Spaced Four-planet Systems

We investigate the orbital dynamics of four-planet systems consisting of Earth-mass planets on initially-circular, coplanar orbits around a star of one solar mass. In our simulations, the innermost planet's semimajor axis is set at 1 AU, with subsequent semimajor axes spaced equally in terms of planets' mutual Hill radii. Several sets of initial planetary longitudes are investigated, with integrations continuing for up to $10^{10}$ orbits of the innermost planet, stopping if a pair of planets pass within 0.01 AU of each other or if a planet is ejected from the system. We find that the simulated lifetimes of four-planet systems follow the general trend of increasing exponentially with planetary spacing, as seen by previous studies of closely-spaced planets. Four-planet system lifetimes are intermediate between those of three- and five-planet systems and more similar to the latter. Moreover, as with five-planet systems, but in marked contrast to the three-planet case, no initial semimajor axes spacings are found to yield systems that survive several orders of magnitude longer than other similar spacings. First- and second-order mean-motion resonances (MMRs) between planets correlate with reductions in system lifetimes. Additionally, we find that third-order MMRs between planets on neighboring orbits also have a substantial, though smaller, destabilizing effect on systems very near resonance that otherwise would be very long-lived. Local extrema of system lifetimes as a function of planetary spacing occur at slightly smaller initial orbital separation for systems with planets initially at conjunction relative to those in which the planets begin on widely-separated longitudes. This shift is produced by the asymmetric mutual planetary perturbations as the planets separate in longitude from the initial aligned configuration that cause orbits to spread out in semimajor axis.

astro-ph.EP↗