2024/03/23 by Max Emerick, Emerick, Max, Jared Jonas +3 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #93C25 #FOS: Electrical engineering #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Stochastic processes and financial applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2403.15702
openalex publication_date 2024/03/23 · openalex created_date 2024/03/27 · openalex updated_date 2026/07/28
We consider a problem of optimal swarm tracking which can be formulated as a tracking problem for distributions in the Wasserstein space. Optimal solutions to this problem are non-causal and require knowing the time-trajectory of the reference distribution in advance. We propose a scheme where these non-causal solutions can be used together with a predictive model for the reference to achieve causal tracking of a priori-unknown references. We develop a model-predictive control scheme built around the simple case where the reference is constant-in-time. A computational algorithm based on particle methods and discrete optimal mass transport is presented, and numerical simulations are provided for various classes of reference signals. The results demonstrate that the proposed control algorithm achieves reasonable performance even when using simple predictive models.