On Model Predictive Funnel Control with Equilibrium Endpoint Constraints

TL;DR

This paper introduces a new model predictive funnel control method that combines error boundary optimization with predictive control, enhancing robustness and efficiency in output regulation tasks.

Contribution

It presents a novel MPC scheme based on funnel control principles, offering improved stability, feasibility, and reduced decision variables independent of horizon length.

Findings

Ensures stability through MPC theory with terminal constraints.

Achieves initial and recursive feasibility.

Reduces optimization complexity by fewer decision variables.

Abstract

We propose model predictive funnel control, a novel model predictive control (MPC) scheme building upon recent results in funnel control. The latter is a high-gain feedback methodology that achieves evolution of the measured output within predefined error margins. The proposed method dynamically optimizes a parameter-dependent error boundary in a receding-horizon manner, thereby combining prescribed error guarantees from funnel control with the predictive advantages of MPC. On the one hand, this approach promises faster optimization times due to a reduced number of decision variables, whose number does not depend on the horizon length. On the other hand, the continuous feedback law improves the robustness and also explicitly takes care of the inter-sampling behavior. We focus on proving stability by leveraging results from MPC stability theory with terminal equality constraints. Moreover, we rigorously show initial and recursive feasibility.