Abstract
We are concerned with Model Predictive Control (MPC) of constrained linear systems governed by regular differential-algebraic equations. The contribution is twofold: First, we provide a characterization of the set of admissible control functions to clarify what the actual input is. This is essential for the design of numerical algorithms. Secondly, we present a blueprint for the construction of suitable terminal costs and terminal constraints such that asymptotic stability of the origin w.r.t. the MPC closed-loop is guaranteed provided initial feasibility. To this end, we exploit recent results on the unconstrained linear quadratic regulator problem using recently introduced concepts of input index and an augmented system.
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