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Parametrized infinite-horizon model predictive control for linear time-invariant systems with input and state constraints

In this work we propose a parametric description of input and state trajectories in order to approximate infinte-horizon optimal control problems encountered in model predictive control. The consequences of applying the parametric description to receding horizon control (model predictive control) are discussed. In particular, recursive feasibility and closed-loop stability are shown. In contrast to the standard, discrete-time finite-horizon model predictive control formulation, the parametric approach provides inherent stability guarantees and has typically fewer optimization variables. A numerical example is used to illustrate the proposed control algorithm.