A receding horizon framework for stabilization of a class of infinite-dimensional controlled systems is presented. No terminal costs and constraints are used to ensure asymptotic stability of the controlled system. The key assumption is a stabilizability assumption, which can be guaranteed, for example, for the Burgers' equations with periodic and with homogeneous Neumann boundary conditions. Numerical experiments validate the theoretical results. Comparisons to the case with terminal penalties acting as control Lyapunov functions are included.

Stabilization of the wave equation by the receding horizon framework is investigated. Distributed control, Dirichlet boundary control, and Neumann boundary control are considered. Moreover for each of these control actions, the well-posedness of the control system and the exponential stability of Receding Horizon Control (RHC) with respect to a proper functional analytic setting are investigated. Observability conditions are necessary to show the suboptimality and exponential stability of RHC. Numerical experiments are given to illustrate the theoretical results.

The present work is concerned with the stabilization of a general class of time-varying linear parabolic equations by means of a finite-dimensional receding horizon control (RHC). The stability and suboptimality of the unconstrained receding horizon framework is studied. The analysis allows the choice of the squared 1-norm as control cost. This leads to a nonsmooth infinite-horizon problem which provides stabilizing optimal controls with a low number of active actuators over time. Numerical experiments are given which validate the theoretical results and illustrate the qualitative differences between the 1-and 2-control costs.

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Stabilization of the nonlinear Korteweg-de Vries (KdV) equation on a bounded interval by model predictive control (MPC) is investigated. This MPC strategy does not need any terminal cost or terminal constraint to guarantee the stability. The semi-global stabilizability is the key condition. Based on this condition, the suboptimality and exponential stability of the model predictive control are investigated. Finally, numerical experiment is presented which validates the theoretical results.