A sub-optimal receding horizon control strategy for constrained linear systems

We present a novel receding horizon control strategy for constrained linear systems, based on a suboptimal solution to the fixed horizon optimization problem considered in Model Predictive Control (MPC). The proposed strategy relies on a basis function expansion of the unconstrained optimal solution in terms of the singular vectors of the Hessian of the performance index. At each sampling time, the strategy ensures that the constraints are not violated by considering a variable subset of the basis representation. For cases in which the Hessian is ill-conditioned, the proposed strategy delivers a feasible solution without excessively compromising performance. We also show that the singular values of the Hessian are related to the frequency response of the plant.