31 research outputs found
Declarative vs Rule-based Control for Flocking Dynamics
The popularity of rule-based flocking models, such as Reynolds' classic
flocking model, raises the question of whether more declarative flocking models
are possible. This question is motivated by the observation that declarative
models are generally simpler and easier to design, understand, and analyze than
operational models. We introduce a very simple control law for flocking based
on a cost function capturing cohesion (agents want to stay together) and
separation (agents do not want to get too close). We refer to it as {\textit
declarative flocking} (DF). We use model-predictive control (MPC) to define
controllers for DF in centralized and distributed settings. A thorough
performance comparison of our declarative flocking with Reynolds' model, and
with more recent flocking models that use MPC with a cost function based on
lattice structures, demonstrate that DF-MPC yields the best cohesion and least
fragmentation, and maintains a surprisingly good level of geometric regularity
while still producing natural flock shapes similar to those produced by
Reynolds' model. We also show that DF-MPC has high resilience to sensor noise.Comment: 7 Page
Convergence to consensus of the general finite-dimensional Cucker-Smale model with time-varying delays
We consider the celebrated Cucker-Smale model in finite dimension, modelling
interacting collective dynamics and their possible evolution to consensus. The
objective of this paper is to study the effect of time delays in the general
model. By a Lyapunov functional approach, we provide convergence results to
consensus for symmetric as well as nonsymmetric communication weights under
some structural conditions
Local sensitivity analysis for the Cucker-Smale model with random inputs
We present pathwise flocking dynamics and local sensitivity analysis for the
Cucker-Smale(C-S) model with random communications and initial data. For the
deterministic communications, it is well known that the C-S model can model
emergent local and global flocking dynamics depending on initial data and
integrability of communication function. However, the communication mechanism
between agents are not a priori clear and needs to be figured out from observed
phenomena and data. Thus, uncertainty in communication is an intrinsic
component in the flocking modeling of the C-S model. In this paper, we provide
a class of admissible random uncertainties which allows us to perform the local
sensitivity analysis for flocking and establish stability to the random C-S
model with uncertain communication.Comment: 32 page
Mean-Field Pontryagin Maximum Principle
International audienceWe derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ordinary differential equations and a partial differential equation of Vlasov-type with smooth interaction kernel. Such problems arise naturally as Gamma-limits of optimal control problems constrained by ordinary differential equations, modeling, for instance, external interventions on crowd dynamics by means of leaders. We obtain these first-order optimality conditions in the form of Hamiltonian flows in the Wasserstein space of probability measures with forward-backward boundary conditions with respect to the first and second marginals, respectively. In particular, we recover the equations and their solutions by means of a constructive procedure, which can be seen as the mean-field limit of the Pontryagin Maximum Principle applied to the optimal control problem for the discretized density, under a suitable scaling of the adjoint variables