(Sub)Optimal feedback control of mean field multi-population dynamics

Abstract

We study a multiscale approach for the control of agent-based, two-population models. The control variable acts over one population of leaders, which influence the population of followers via the coupling generated by their interaction. We cast a quadratic optimal control problem for the large-scale microscale model, which is approximated via a Boltzmann approach. By sampling solutions of the optimal control problem associated to binary two-population dynamics, we generate sub-optimal control laws for the kinetic limit of the multi-population model. We present numerical experiments related to opinion dynamics assessing the performance of the proposed control design.

Controlling swarms towards flocks and mills

“…Remark 2 (The role of the assumptions). The condition (5) means that the control can counteract the natural tendency of the system to stabilize |v| to α β . The value M α,β corresponds to the maximum of the function s → αs − βs 3 on the half line s 0, which is attained at v = α 3β .…”

“…Imposing consensus in velocity has also been analysed from the point of view of control [14,17,18,38]. These consensus models also have applications in swarm robotics [27,28], social and pedestrian dynamics [3,2,42,59] where control theory is applied with different regulation objectives expressed in both ad-hoc and optimal control designs [4,5,8,15].…”

Optimization Problems for Interacting Particle Systems and Corresponding Mean‐field Limits

“…Interacting particle systems and their kinetic descriptions were extensively studied in the last decades. The applications range from formation of swarms of birds or schools of fish to dogs herding sheep, consensus formation and follower-leader dynamics [1][2][3][4][5][6]. Recently, even various particle swarm schemes for global optimization were proposed [7,8].…”

Optimal consensus control of the Cucker-Smale model

“…To circumvent this difficulty, we propose a numerical realisation of the control synthesis via metaheuristics related to particle swarm optimisation (PSO), and to nonlinear model predictive control (NMPC). Finally, based on the works Carrillo et al (2010a,b);Fornasier and Solombrino (2014); Bongini et al (2017); Albi et al (2017aAlbi et al ( , 2016; Albi and Kalise (2018), we discuss the resulting mean-field optimal control problem: that obtained as the number of agents N tends to ∞ and the microstate (x i (t), v i (t)) of the population is replaced by an agent density function f (t, x, v).…”