Stabilizing Quasi-Time-Optimal Nonlinear Model Predictive Control with Variable Discretization

Abstract: This paper deals with the development and analysis of 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 piecewise constant control parameterization. The key idea in this paper is to introduce uniform grids with variable discretization. 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 stabilization. Two nonlinear program formulations with different sparsity patterns are introduced to realize 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.