Solving Sparse Differential Riccati Equations on Hybrid CPU-GPU Platforms

摘要

The numerical treatment of the linear-quadratic optimal control problem requires the solution of Riccati equations. In particular, the differential Riccati equations (DRE) is a key operation for the computation of the optimal control in the finite-time horizon case. In this work, we focus on large-scale problems governed by partial differential equations (PDEs) where, in order to apply a feedback control strategy, it is necessary to solve a large-scale DRE resulting from a spatial semi-discretization. To tackle this problem, we introduce an efficient implementation of the implicit Euler method and linearly implicit Euler method on hybrid CPU-GPU platforms for solving differential Riccati equations arising in a finite-time horizon linear-quadratic control problems. Numerical experiments validate our approach.