A fast second-order parareal solver for fractional optimal control problems

作者：Wu, Shu-Lin^*; Huang, Ting-Zhu

来源：Journal of Vibration and Control, 2018, 24(15): 3418-3433.

DOI：10.1177/1077546317705557

• Parareal algorithm
• fractional optimal control
• convergence analysis
• parameter optimization
• numerical computation

The gradient projection technique has recently been used to solve the optimal control problems governed by a fractional diffusion equation. It lies in repeatedly solving the state and co-state equations derived from the optimality conditions, and the Crank-Nicolson (CN) scheme, which gives a second-order numerical solution, is a widely used method to solve these two equations. The goal of this paper is to implement the CN scheme in a parallel-in-time manner in the framework of the parareal algorithm. Because of the stiffness of the approximation matrix of the fractional operator, direct use of the CN scheme results in a convergence factor satisfying 1 as x0 for the parareal algorithm, where x denotes the space step-size. Here, we provide a new idea to let the parareal algorithm use the CN scheme as the basic component possessing a constant convergence factor approximate to 1/5, which is independent of x. Numerical results are provided to show the efficiency of the proposed algorithm.

• 出版日期2018-8
• 单位电子科技大学; 四川轻化工大学