A new framework for solving dynamic scheduling games

Zazo, Santiago; Valcarcel, Sergio; Sanchez-Fernandez, Matilde; Zazo, Javier

doi:10.1109/icassp.2015.7178335

Cited by 7 publications

(10 citation statements)

References 18 publications

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“…This makes the statetransition equations (and the utility for the equal rate problem) depend not only on the current state, but also on time. This problem was introduced in the preliminary paper [19].…”

Section: B Simulation Resultsmentioning

confidence: 99%

Dynamic Potential Games With Constraints: Fundamentals and Applications in Communications

Zazo

Macua

Sanchez-Fernandez

et al. 2016

IEEE Trans. Signal Process.

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In a noncooperative dynamic game, multiple agents operating in a changing environment aim to optimize their utilities over an infinite time horizon. Time-varying environments allow to model more realistic scenarios (e.g., mobile devices equipped with batteries, wireless communications over a fading channel, etc.). However, solving a dynamic game is a difficult task that requires dealing with multiple coupled optimal control problems. We focus our analysis on a class of problems, named dynamic potential games, whose solution can be found through a single multivariate optimal control problem. Our analysis generalizes previous studies by considering that the set of environment's states and the set of players' actions are constrained, as it is required by most of the applications. We also show that the theoretical results are the natural extension of the analysis for static potential games. We apply the analysis and provide numerical methods to solve four key example problems, with different features each: i) energy demand control in a smartgrid network, ii) network flow optimization in which the relays have bounded link capacity and limited battery life, iii) uplink multiple access communication with users that have to optimize the use of their batteries, and iv) two optimal scheduling games with nonstationary channels.

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Section: B Simulation Resultsmentioning

confidence: 99%

Dynamic Potential Games With Constraints: Fundamentals and Applications in Communications

Zazo

Macua

Sanchez-Fernandez

et al. 2016

IEEE Trans. Signal Process.

Self Cite

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“…Later, potential games were also introduced in [5]. Because of the appealing properties of potential games, potential games have had applications in various control and resource allocation problems [24,25,26,27,28,29]. We argue that potential games, in the form of potential differential games, can be further utilized for trajectory planning in multi-agent settings.…”

Section: Potential Gamesmentioning

confidence: 99%

Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectories

Kavuncu¹,

Ayberk²,

Mehr³

2021

Robotics: Science and Systems XVII

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Many robotic applications involve interactions between multiple agents where an agent's decisions affect the behavior of other agents. Such behaviors can be captured by the equilibria of differential games which provide an expressive framework for modeling the agents' mutual influence. However, finding the equilibria of differential games is in general challenging as it involves solving a set of coupled optimal control problems. In this work, we propose to leverage the special structure of multi-agent interactions to generate interactive trajectories by simply solving a single optimal control problem, namely, the optimal control problem associated with minimizing the potential function of the differential game. Our key insight is that for a certain class of multi-agent interactions, the underlying differential game is indeed a potential differential game for which equilibria can be found by solving a single optimal control problem. We introduce such an optimal control problem and build on single-agent trajectory optimization methods to develop a computationally tractable and scalable algorithm for planning multi-agent interactive trajectories. We will demonstrate the performance of our algorithm in simulation and show that our algorithm outperforms the state-of-the-art game solvers. To further show the real-time capabilities of our algorithm, we will demonstrate the application of our proposed algorithm in a set of experiments involving interactive trajectories for two quadcopters.

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“…We will discuss methods for static games, including general Nash equilibrium problems (GNEP) [30], Newton's method [29], Nikaido-Isoda relaxation algorithms [8,15,41,42,44] and extremum seeking [32][33][34]. We will also discuss methods for special dynamic games, such as linear-quadratic games [11,20,24,25,40,45], potential games [35][36][37]49,61,63] and zero-sum games [58,59]. Finally, we will discuss general methods based on Pontryagin's maximum principle [4,7,43].…”

Section: Related Workmentioning

confidence: 99%

Newton’s Method, Bellman Recursion and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games

Lamperski

2021

Dyn Games Appl

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Dynamic games arise when multiple agents with differing objectives control a dynamic system. They model a wide variety of applications in economics, defense, energy systems and etc. However, compared to single-agent control problems, the computational methods for dynamic games are relatively limited. As in the single-agent case, only specific dynamic games can be solved exactly, so approximation algorithms are required. In this paper, we show how to extend the Newton step algorithm, the Bellman recursion and the popular differential dynamic programming (DDP) for single-agent optimal control to the case of fullinformation nonzero sum dynamic games. We show that the Newton's step can be solved in a computationally efficient manner and inherits its original quadratic convergence rate to open-loop Nash equilibria, and that the approximated Bellman recursion and DDP methods are very similar and can be used to find local feedback O(ε 2 )-Nash equilibria. Numerical examples are provided. KeywordsNoncooperative dynamic games • Open-loop Nash equilibrium • Feedback Nash equilibrium • Newton's method • Differential dynamic programming B Bolei Di

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A new framework for solving dynamic scheduling games

Cited by 7 publications

References 18 publications

Dynamic Potential Games With Constraints: Fundamentals and Applications in Communications

Dynamic Potential Games With Constraints: Fundamentals and Applications in Communications

Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectories

Newton’s Method, Bellman Recursion and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games

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