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. To reduce the computational cost, we use the Random Batch Method (RBM), which provides a computationally feasible approximation of the dynamics. At each time step, 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 as the time discretization gets finer. We propose an algorithm that leads to the optimal control of a fixed RBM approximated trajectory using a classical gradient descent. The resulting control is not optimal for the original complete system, but rather for the reduced RBM model. We then adopt a Model Predictive Control (MPC) strategy to handle the error in the dynamics. While the system evolves in time, the MPC strategy consists in periodically updating the state and computing the optimal control over a long-time horizon, which is implemented recursively in a shorter time-horizon. This leads to a semi-feedback control strategy. 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.
Reinforcement Learning for Batch Bioprocess Optimization
The University of Manchester（曼彻斯特大学）；University College London（伦敦大学学院）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Norwegian University of Science and Technology（挪威科技大学）；Imperial College London（帝国理工学院）
WarpMPC: Large-Batch MPC on GPU via ADMM with Unrolled $LDL^\top$ Factorization
Institute for Data Science in Mechanical Engineering (DSME), RWTH Aachen University（亚琛工业大学机械工程数据科学研究所）；Department of Mechanical Engineering, Massachusetts Institute of Technology（麻省理工学院机械工程系）
Predictive and Prescriptive AI toward Optimizing Wildfire Suppression
Michael G. Foster School of Business and Paul G. Allen School of Computer Science & Engineering, University of Washington（迈克尔·G·福斯特商学院和保罗·G·阿伦计算机科学与工程学院，华盛顿大学）
