Sparse Representations for Packetized Predictive Networked Control

TL;DR

This paper introduces a robust networked control method using sparse, predictive control packets designed via compressed sensing techniques, reducing bit-rate needs over unreliable networks while maintaining stability.

Contribution

It proposes a novel sparse control packet design for packetized predictive control using on-line L1/L2 minimization, enhancing robustness and efficiency over unreliable networks.

Findings

Sparsity reduces bit-rate requirements.

Control stability is maintained under bounded packet dropouts.

Numerical example demonstrates effectiveness in unreliable networks.

Abstract

We investigate a networked control architecture for LTI plant models with a scalar input. Communication from controller to actuator is over an unreliable network which introduces packet dropouts. To achieve robustness against dropouts, we adopt a packetized predictive control paradigm wherein each control packet transmitted contains tentative future plant input values. The novelty of our approach is that we seek that the control packets transmitted be sparse. For that purpose, we adapt tools from the area of compressed sensing and propose to design the control packets via on-line minimization of a suitable L1/L2 cost function. We then show how to choose parameters of the cost function to ensure that the resultant closed loop system be practically stable, provided the maximum number of consecutive packet dropouts is bounded. A numerical example illustrates that sparsity reduces bit-rates, thereby making our proposal suited to control over unreliable and bit-rate limited networks.