Interpolation-based robust constrained model predictive output feedback control

Abstract

In this paper, a problem of output feedback robust control of polytopic uncertain discrete-time systems is addressed. The output feedback control law proposed is a function of estimated state determined by mapping of the current output measured. An appropriate estimator is defined, and a sequence of feedback gains is computed by solving off-line a series of optimal control optimization problems. A sequence of nested polyhedral invariant sets associated with each feedback gain pre-computed is then constructed as a mapping on a system output. At each control iteration, a smallest polyhedral invariant set containing the current output is determined. A corresponding feedback gain is then implemented to the process. Further, an interpolation algorithm is proposed to improve control performance. In the interpolation scheme, a feedback gain is computed from convex combination between a feedback gain associated with the current invariant set and that of the adjacent smaller invariant set, where a parameter used in the combination is minimized subjected to a set of constraints associated with the current invariant set. The controller design is illustrated with a case study of nonlinear two-tank system formulated as a polytopic uncertain system. The simulation results showed that the proposed algorithms can drive the system to the origin without input and output constraints violation. The interpolation algorithm proposed can improve control performances while on-line computation is still tractable.