Homothetic Tube-Based Robust Economic MPC with Integrated Moving Horizon Estimation

This article considers homothetic tube-based economic model predictive control synthesis for constrained linear discrete-time systems. Since, in practical systems, full-state measurement is seldom available, the proposed method integrates a moving horizon estimator to achieve closed-loop stability and constraint satisfaction despite system disturbances and output measurement noise. In contrast to existing approaches, the worst cost within a single homothetic tube around the solution of the associated nominal system is minimized, which, at the same time, tightens the bound on the set of potential states compatible with past output and input data. We show that the designed optimization problem is recursively feasible and adoption of homothetic tubes leads to less conservative economic performance bounds. Thanks to the use of strict dissipativity of the nominal system with a suitable supply rate, the closed-loop system is shown to be asymptotically stable, in the sense that the state trajectory is driven to an optimal robust invariant set.