Error analysis of spectral approximation for space–time fractional optimal control problems with control and state constraints

Abstract

In this paper, spectral discretization of optimal control problem governed by the space–time fractional diffusion equation with integral control and state constraints is investigated. The study of the optimality conditions is very important for analyzing the optimal control problem. Introducing the auxiliary equations and some important operators are to obtain a priori error estimates of spectral approximation for state, adjoint state and control variable rigorously. Additionally, reliable a posteriori error estimates are also proved for the optimal control problem carefully. The analysis results indicate that the errors decay exponentially when the data is smooth.