Model predictive control with random batch methods for a guiding problem
Ko D, Zuazua E (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 31
Pages Range: 1569-1592
Journal Issue: 8
DOI: 10.1142/S0218202521500329
Abstract
We model, simulate and control the guiding problem for a herd of evaders under the action of repulsive drivers. The problem is formulated in an optimal control framework, where the drivers (controls) aim to guide the evaders (states) to a desired region of the Euclidean space. The numerical simulation of such models quickly becomes unfeasible for a large number of interacting agents, as the number of interactions grows O(N2) for N agents. For reducing the computational cost to O(N), we use the Random Batch Method (RBM), which provides a computationally feasible approximation of the dynamics. First, the considered time interval is divided into a number of subintervals. In each subinterval, the RBM randomly divides the set of particles into small subsets (batches), considering only the interactions inside each batch. Due to the averaging effect, the RBM approximation converges to the exact dynamics in the L2-expectation norm as the length of subintervals goes to zero. For this approximated dynamics, the corresponding optimal control can be computed efficiently using a classical gradient descent. The resulting control is not optimal for the original system, but for a reduced RBM model. We therefore adopt a Model Predictive Control (MPC) strategy to handle the error in the dynamics. This leads to a semi-feedback control strategy, where the control is applied only for a short time interval to the original system, and then compute the optimal control for the next time interval with the state of the (controlled) original dynamics. Through numerical experiments we show that the combination of RBM and MPC leads to a significant reduction of the computational cost, preserving the capacity of controlling the overall dynamics.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Korea, Republic of (KR)How to cite
APA:
Ko, D., & Zuazua, E. (2021). Model predictive control with random batch methods for a guiding problem. Mathematical Models & Methods in Applied Sciences, 31(8), 1569-1592. https://dx.doi.org/10.1142/S0218202521500329
MLA:
Ko, Dongnam, and Enrique Zuazua. "Model predictive control with random batch methods for a guiding problem." Mathematical Models & Methods in Applied Sciences 31.8 (2021): 1569-1592.
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