Robust Receding Horizon Control - analysis & synthesis

In this paper, a combined Receding Horizon Control (RHC) analysis and synthesis technique for constrained linear time-invariant systems subject to polytopic or additive uncertainty is introduced. The proposed method consists of two components. First, the maximum robust control invariant set C_∞ is computed along with the associated piecewise affine (PWA) state feedback law. This computation is based on an iterative solution of multi-parametric Quadratic Programs (mp-QP). Second, the obtained PWA feedback law is analyzed for robust stability. This analysis is based on linear matrix inequalities (LMI). The combination of these two components guarantees robust stability and constraint satisfaction for all time. Extensive numerical examples show a decrease in controller complexity by a factor of up to 250 versus established controller design methods at the cost of a degradation in performance of less than 0.5% on average.