2022/04/23 by Alexander Krolicki, Krolicki, Alexander, Sarang Sutavani +3 · 3 citations
Physics and Astronomy · Computer Science · Engineering · #Model Reduction and Neural Networks #Adversarial Robustness in Machine Learning #Nuclear reactor physics and engineering
paper · pdf · doi:10.48550/arxiv.2204.10987
Classically, the optimal control problem in the presence of an adversary is formulated as a two-player zero-sum differential game or an H_∞ control problem. The solution to these problems can be obtained by solving the Hamilton-Jacobi-Issac equation (HJIE). We provide a novel Koopman-based expression of the HJIE, where the solutions can be obtained through the approximation of the Koopman operator itself. In particular, we developed a data-driven and model based policy iteration algorithm for approximating the optimal value function using a finite-dimensional approximation of the Koopman operator and generator.