Infinite-Horizon Continuous-Time NMPC via Time Transformation

In this note, a solution method is presented for nonlinear model-predictive control of open-loop stable systems on an infinite horizon. The proposed method first reformulates the infinite-horizon continuous-time problem by a time-coordinate transformation as a finite horizon problem and computes the solution after discretization of the control variables. This method aims to ensure stability without imposing a terminal constraint set. The adaptive discretization algorithm allows an efficient and accurate solution of the infinite-horizon problem with a moderate number of discrete decision variables. The time transformation function is adapted such that the important dynamics of the system can be captured and the control variables can be discretized appropriately. An illustrative case study is presented.