Self-triggered MPC robust to bounded packet loss via a min-max approach: extended version

TL;DR

This paper introduces a robust self-triggered MPC scheme that accounts for bounded packet loss in networked control systems, ensuring stability and constraint satisfaction through a min-max optimization approach.

Contribution

It presents a novel self-triggered MPC method resilient to packet loss, with proven recursive feasibility and convergence guarantees.

Findings

Ensures stability despite packet loss

Maintains constraint satisfaction under bounded packet loss

Demonstrates effectiveness through numerical example

Abstract

Networked Control Systems typically come with a limited communication bandwidth and thus require special care when designing the underlying control and triggering law. A method that allows to consider hard constraints on the communication traffic as well as on states and inputs is self-triggered model predictive control (MPC). In this scheme, the optimal length of the sampling interval is determined proactively using predictions of the system behavior. However, previous formulations of self-triggered MPC have neglected the widespread phenomenon of packet loss, such that these approaches might fail in practice. In this paper, we present a novel self-triggered MPC scheme which is robust to bounded packet loss by virtue of a min-max optimization problem. We prove recursive feasibility, constraint satisfaction and convergence to the origin for any possible packet loss realization consistent with the boundedness constraint, and demonstrate the advantages of the proposed scheme in a numerical example.