Approximation of continuous-time infinite-horizon optimal control problems arising in model predictive control

This article presents two different approximations to linear infinite-horizon optimal control problems arising in model predictive control. The dynamics are approximated using a Galerkin approach with parametrized state and input trajectories. It is shown that the first approximation represents an upper bound on the optimal cost of the underlying infinite dimensional optimal control problem, whereas the second approximation results in a lower bound. We analyze the convergence of the costs and the corresponding optimizers as the number of basis functions tends to infinity. The results can be used to quantify the approximation quality with respect to the underlying infinite dimensional optimal control problem.