SVD based receding horizon control for constrained linear systems: stability results

A stability result for a recently proposed sub-optimal receding horizon control (RHC) strategy for constrained linear systems is presented. The strategy is based on a singular value decomposition (SVD) of the Hessian of the quadratic performance index generally minimized in Model Predictive Control. A basis function expansion of the unconstrained optimal control vector in terms of the Hessian´s singular vectors is considered. At each sampling time, the strategy computes a feasible control sequence by selecting a variable subset of the basis representation. Stability is analysed in the framework of optimal RHC: a final set constraint is used in combination with a stability enforced algorithm that implements the SVD-RHC strategy.