Stabilising quasi-time-optimal nonlinear model predictive control with variable discretisation

This paper deals with novel time-optimal point-to-point model predictive control concepts for nonlinear systems. Recent approaches in the literature apply a time transformation, however, which do not maintain recursive feasibility for a piecewise constant control parameterisation. The key idea in this paper is to introduce uniform grids with variable discretisation. A shrinking-horizon grid adaptation scheme ensures convergence to a specific region around the target state and recursive feasibility. The size of the region is configurable by design parameters. This facilitates the systematic dual-mode design for quasi-time-optimal control to restore asymptotic stability and establish a smooth stabilisation. Two nonlinear programme formulations with different sparsity patterns are introduced to realise and implement the underlying optimal control problem. For a class of numerical integration schemes, even nominal asymptotic stability and true time-optimality are achieved without dual-mode. A comparative analysis as well as experimental results demonstrate the effectiveness of the proposed techniques.