Output model predictive control for a wave equation

We present an observer-based model predictive control scheme for a wave equation with non-collocated boundary control and observation. The design comprises a Luenberger-type state estimator combined with a model predictive controller which we show to stabilize the considered wave equation in the sense that the energy of the system decays asymptotically to zero. Moreover, if the initial state estimation error is sufficiently small, the controller is guaranteed to robustly satisfy given input constraints. The performance of the proposed design is demonstrated on a numerical simulation.

I. INTRODUCTION

This paper considers output model predictive control (MPC) for a one-dimensional wave equation with non-collocated control and observation. The proposed control scheme is motivated by the classical output MPC design for constrained finite-dimensional linear systems [1], [2], [Sect. 5.3] which has received recent attention, e.g., in terms of reduced conservatism [3], [4]. However, for simplicity we assume that the system is not subject to external disturbances so that we can focus solely on the output MPC design. Regardless, the state estimation error will cause some un-certainty which the proposed control design will take into account. We note that while MPC algorithms are generally capable of handling (e.g. affine) state and input constraints, for simplicity and brevity we restrict our consideration to input constraints.