Robust Economic Model Predictive Control without Terminal Conditions

TL;DR

This paper introduces a robust tube-based economic MPC scheme for uncertain systems that does not rely on terminal costs or constraints, extending undisturbed case results to systems with bounded disturbances.

Contribution

It presents a novel MPC approach that guarantees robustness without terminal conditions, using modified stage costs and turnpike arguments.

Findings

Robust closed-loop performance and stability are proven.

The method extends undisturbed case results to systems with disturbances.

Numerical example demonstrates effectiveness.

Abstract

In this paper, a novel tube-based economic Model Predictive Control (MPC) scheme for uncertain systems that uses neither terminal costs nor terminal constraints is investigated. We show that the results from the undisturbed case can be extended to systems with bounded disturbances by using similar turnpike arguments and a properly modified stage cost. We prove robust guarantees on the closed-loop performance, convergence, and stability under suitable dissipativity and controllability conditions and discuss them in a numerical example.