Mean Field Analysis of Controlled Cucker-Smale Type Flocking: Linear Analysis and Perturbation Equations

Nourian, Mojtaba; Caines, Peter E.; Malhamé, Roland P.

doi:10.3182/20110828-6-it-1002.03639

Cited by 36 publications

(42 citation statements)

References 11 publications

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“…For 1) travel time minimization, it is intended to minimize the remaining travel distance r i (t) 2 , while maximizing the velocity towards the destination, i.e., minimizing the projected velocity v i (t) · r i (t)/ r i (t) towards the opposite direction to the destination. For 2) motion energy minimization, it is planned to minimize the kinetic energy and the acceleration control energy that are proportional to v i (t) 2 and a i (t) 2 , respectively [12], [13]. The global term φ G (s Ni (t)) in (3) refers to 3) collision avoidance, and is intended to form a flock of UAVs moving together [14].…”

Section: ) Collision Avoidance and Connectivity Guaranteementioning

confidence: 99%

Massive Autonomous UAV Path Planning: A Neural Network Based Mean-Field Game Theoretic Approach

Shiri

Park

Bennis

2019

2019 IEEE Global Communications Conference (GLOBECOM)

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This paper investigates the autonomous control of massive unmanned aerial vehicles (UAVs) for mission-critical applications (e.g., dispatching many UAVs from a source to a destination for firefighting). Achieving their fast travel and low motion energy without inter-UAV collision under wind perturbation is a daunting control task, which incurs huge communication energy for exchanging UAV states in real time. We tackle this problem by exploiting a mean-field game (MFG) theoretic control method that requires the UAV state exchanges only once at the initial source. Afterwards, each UAV can control its acceleration by locally solving two partial differential equations (PDEs), known as the Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations. This approach, however, brings about huge computation energy for solving the PDEs, particularly under multi-dimensional UAV states. We address this issue by utilizing a machine learning (ML) method where two separate ML models approximate the solutions of the HJB and FPK equations. These ML models are trained and exploited using an online gradient descent method with low computational complexity. Numerical evaluations validate that the proposed ML aided MFG theoretic algorithm, referred to as MFG learning control, is effective in collision avoidance with low communication energy and acceptable computation energy.Index Terms-Autonomous UAV, communication-efficient online path planning, mean-field game, machine learning. … destination source shortest path energy saving collision avoiding wind perturbations communication 3 1 2Related works. The problem of UAV placement for supporting communication systems has been studied in [7]. Under wind perturbations, the real-time placement of massive UAVs without collision has been investigated in [1]. Path planning is a more challenging problem wherein UAVs are controlled to reach a destination. In offline control, a multiple-UAV scenario arXiv:1905.04152v1 [cs.SY]

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Section: ) Collision Avoidance and Connectivity Guaranteementioning

confidence: 99%

Massive Autonomous UAV Path Planning: A Neural Network Based Mean-Field Game Theoretic Approach

Shiri

Park

Bennis

2019

2019 IEEE Global Communications Conference (GLOBECOM)

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“…Furthermore, the algorithm is unable to take into account its corresponding energy efficiency. We overcome these limitations by leveraging a noncooperative game theoretic approach, as done in [17]- [21]. In our modified CS flocking algorithm, each UAV tries to minimize its long-term energy cost and its flocking cost.…”

Section: A Flocking Problem Formulationmentioning

confidence: 99%

“…The flocking cost follows from [17]. Denoting v(t) = {v 1 (t), ..., v N (t)} as the set of UAV velocities and z(t) = {z 1 (t), ..., z N (t)} as the set of their locations at time t, the flocking cost F i (v(t), z(t)) is given as:…”

Section: A Flocking Problem Formulationmentioning

confidence: 99%

Massive UAV-to-Ground Communication and its Stable Movement Control: A Mean-Field Approach

Kim

Park

Bennis

et al. 2018

2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

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This paper proposes a real-time movement control algorithm for massive unmanned aerial vehicles (UAVs) that provide emergency cellular connections in an urban disaster site. While avoiding the inter-UAV collision under temporal wind dynamics, the proposed algorithm minimizes each UAV's energy consumption per unit downlink rate. By means of a mean-field game theoretic flocking approach, the velocity control of each UAV only requires its own location and channel states. Numerical results validate the performance of the algorithm in terms of the number of collisions and energy consumption per data rate, under a realistic 3GPP UAV channel model.

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“…Equivalently, mean field games must be regarded as the continuum limit of games with a large number of symmetric players, each of them having a small effect on the dynamics of the whole group. The applications of mean field games are numerous, and spread across many disciplines, including social science (congestion [25] [19] [3], cyber attacks [12]), biology (flocking [28] [29]), and economics (systemic risk [11], production of exhaustible resources [23] [13]), just to name a few. As explained in [8,9], solutions to mean field games can be characterized through a coupled system of two forward and backward stochastic differential equations of mean field type, like those we address in this note.…”

Section: Introductionmentioning

confidence: 99%

Cemracs 2017: numerical probabilistic approach to MFG

Angiuli

Graves

et al. 2019

ESAIM: ProcS

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This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [27], and by Huang, Caines, and Malhamé, see [24]. Generally speaking, the purpose is to understand the continuum limit of optimizers or of equilibria (say in Nash sense) as the number of underlying players tends to infinity. When approached from the probabilistic viewpoint, solutions to these control problems (or games) can be described by coupled mean field FBSDEs, meaning that the coefficients depend upon the own marginal laws of the solution. In this note, we detail two methods for solving such FBSDEs which we implement and apply to five benchmark problems. The first method uses a tree structure to represent the pathwise laws of the solution, whereas the second method uses a grid discretization to represent the time marginal laws of the solutions. Both are based on a Picard scheme; importantly, we combine each of them with a generic continuation method that permits to extend the time horizon (or equivalently the coupling strength between the two equations) for which the Picard iteration converges.

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Mean Field Analysis of Controlled Cucker-Smale Type Flocking: Linear Analysis and Perturbation Equations

Cited by 36 publications

References 11 publications

Massive Autonomous UAV Path Planning: A Neural Network Based Mean-Field Game Theoretic Approach

Massive Autonomous UAV Path Planning: A Neural Network Based Mean-Field Game Theoretic Approach

Massive UAV-to-Ground Communication and its Stable Movement Control: A Mean-Field Approach

Cemracs 2017: numerical probabilistic approach to MFG

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