Backstepping Mean-Field Density Control for Large-Scale Heterogeneous Nonlinear Stochastic Systems

TL;DR

This paper introduces a backstepping control method for large-scale heterogeneous stochastic systems, enabling density regulation beyond simple homogeneous models, with applications demonstrated on mobile robots.

Contribution

It extends mean-field density control to heterogeneous and higher-order stochastic systems using a backstepping approach, overcoming limitations of previous density feedback methods.

Findings

Proposed a backstepping control algorithm for complex stochastic systems.

Validated the approach with simulations on nonholonomic mobile robots.

Demonstrated improved density regulation in heterogeneous systems.

Abstract

This work studies the problem of controlling the mean-field density of large-scale stochastic systems, which has applications in various fields such as swarm robotics. Recently, there is a growing amount of literature that employs mean-field partial differential equations (PDEs) to model the density evolution and uses density feedback to design control laws which, by acting on individual systems, stabilize their density towards a target profile. In spite of its stability property and computational efficiency, the success of density feedback relies on assuming the systems to be homogeneous first-order integrators (plus white noise) and ignores higher-order dynamics, making it less applicable in practice. In this work, we present a backstepping design algorithm that extends density control to heterogeneous and higher-order stochastic systems in strict-feedback forms. We show that the strict-feedback form in the individual level corresponds to, in the collective level, a PDE (of densities) distributedly driven by a collection of heterogeneous stochastic systems. The presented backstepping design then starts with a density feedback design for the PDE, followed by a sequence of stabilizing design for the remaining stochastic systems. We present a candidate control law with stability proof and apply it to nonholonomic mobile robots. A simulation is included to verify the effectiveness of the algorithm.