Metrics for ergodicity and design of ergodic dynamics for multi-agent systems |
| |
| Authors: | George Mathew Igor Mezić |
| |
| Institution: | 1. Embedded Systems and Networks Group, United Technologies Research Center (UTRC), Inc., Berkeley, CA, USA;2. Department of Mechanical Engineering, University of California, Santa Barbara, CA, USA;1. Department of Mathematics and Mechanics, Saint Petersburg University, Universitetskii 28, Petrodvoretz, St.Petersburg, 198504, Russia,;2. School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney 2052, Australia;1. Mathematics Institute and Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Germany;2. ITEP, 25 B. Cheremushkinskaya, Moscow 117218, Russia;3. Imperial College, London SW7 2AZ, United Kingdom;4. Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia;5. Institute of Biochemical Physics, 4 Kosygina st., Moscow 119334, Russia;6. National Research University, Higher School of Economics, International Laboratory of Representation Theory and Mathematical Physics, 20 Myasnitskaya Ulitsa, Moscow 101000, Russia |
| |
| Abstract: | In this paper we propose a metric that quantifies how far trajectories are from being ergodic with respect to a given probability measure. This metric is based on comparing the fraction of time spent by the trajectories in spherical sets to the measure of the spherical sets. This metric is shown to be equivalent to a metric obtained as a distance between a certain delta-like distribution on the trajectories and the desired probability distribution. Using this metric, we formulate centralized feedback control laws for multi-agent systems so that agents trajectories sample a given probability distribution as uniformly as possible. The feedback controls we derive are essentially model predictive controls in the limit as the receding horizon goes to zero and the agents move with constant speed or constant forcing (in the case of second-order dynamics). We numerically analyze the closed-loop dynamics of the multi-agents systems in various scenarios. The algorithm presented in this paper for the design of ergodic dynamics will be referred to as Spectral Multiscale Coverage (SMC). |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
