Related papers: Multitime hybrid differential games with curviline…
A multiple integral functional is equivalent to a curvilinear integral functional, if the domain is a hyper-parallelepiped, but equivalence is only theoretical. The introduction of this kind of functionals in multitime optimal control…
Our original results are associated to a multitime hybrid game, with two equips of players, based on a multiple integral functional and an m- ow as constraint. The aim of this paper is three-fold: (i) to define the multitime lower or upper…
In a multitime hybrid differential game with mechanical work payoff, the multitime upper value function and the multitime lower value function are viscosity solutions of original PDEs of type Hamilton-Jacobi-Isaacs.
This article introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features…
Some optimization problems coming from the Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control problems.…
This paper develops an algorithm for upper- and lower-bounding the value function for a class of linear time-varying games subject to convex control sets. In particular, a two-player zero-sum differential game is considered where the…
Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles.…
This paper considers a formulation of a differential game with constrained dynamics, where one player selects the dynamics and the other selects the applicable cost. When the game is considered on a finite time horizon, its value satisfies…
In this paper an N-pursuer vs. M-evader team conflict is studied. The differential game of border defense is addressed and we focus on the game of degree in the region of the state space where the pursuers are able to win. This work extends…
A multifractal-like representation for multi-time multi-scale velocity correlation in turbulence and dynamical turbulent models is proposed. The importance of subleading contributions to time correlations is highlighted. The fulfillment of…
Hamilton-Jacobi (HJ) partial differential equations (PDEs) have diverse applications spanning physics, optimal control, game theory, and imaging sciences. This research introduces a first-order optimization-based technique for HJ PDEs,…
Coordination games with explicit spatial or relational structure are of interest to economists, ecologists, sociologists, and others studying emergent global properties in collective behavior. When assemblies of individuals seek to…
In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…
In this work we discuss an Mean Field Games approach to traffic management on multi-lane roads. Such approach is particularly indicated to model self driven vehicles with perfect information of the domain. The mathematical interest of the…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
We propose a neural physics system for real-time, interactive fluid simulations. Traditional physics-based methods, while accurate, are computationally intensive and suffer from latency issues. Recent machine-learning methods reduce…
In this paper we consider an infinite horizon zero-sum differential game where the dynamics of each player and the running cost are also depending on the evolution of some discrete (switching) variables. In particular, such switching…
This paper investigates the boundary behaviour of potential-type integrals for the multi-term time-fractional diffusion equation (MTFDE) across the moving boundary. First, we establish the jump relation for the integral operator associated…
Modern control systems are featured by their hierarchical structure composing of cyber, physical, and human layers. The intricate dependencies among multiple layers and units of modern control systems require an integrated framework to…
Hybrid games are games played on a finite graph endowed with real variables which may model behaviors of discrete controllers of continuous systems. The synthesis problem for hybrid games is decidable for classical objectives (like LTL…