Efficient and accurate computation of model predictive control using pseudospectral discretization

The model predictive control (MPC) is implemented by repeatedly solving an open loop optimal control problem (OCP). For the real-time implementation, the OCP is often discretized with evenly spaced time grids. This evenly spaced discretization, however, is accurate only if sufficiently small sampling time is used, which leads to heavy computational load. This paper presents a method to efficiently and accurately compute the continuous-time MPC problem based on the pseudospectral discretization, which utilizes unevenly spaced collocation points. The predictive horizon is virtually doubled by augmenting a mirrored horizon such that denser collocation points can be used towards the current time step, and sparser points can be used towards the end time of predictive horizon. Then, both state and control variables are approximated by Lagrange polynomials at only a half of LGL (Legendre-Gauss-Lobatto) collocation points. This implies that high accuracy can be achieved with a much less number of collocation points, which results in much reduced computational load. Examples are used to demonstrate its advantages over the evenly spaced discretization.