Compressive Sampling for Remote Control Systems

TL;DR

This paper introduces a compressive sampling-based method for sparse control signal representation in remote control systems, reducing data transmission and computational complexity while maintaining control performance.

Contribution

It formulates sparse control signal optimization as an L1-L2 problem and provides theoretical analysis using RIP, demonstrating effectiveness through numerical experiments.

Findings

Sparse control signals can be effectively generated with reduced computation.

The method maintains control performance despite compression.

Numerical experiments confirm the approach's efficiency and accuracy.

Abstract

In remote control, efficient compression or representation of control signals is essential to send them through rate-limited channels. For this purpose, we propose an approach of sparse control signal representation using the compressive sampling technique. The problem of obtaining sparse representation is formulated by cardinality-constrained L2 optimization of the control performance, which is reducible to L1-L2 optimization. The low rate random sampling employed in the proposed method based on the compressive sampling, in addition to the fact that the L1-L2 optimization can be effectively solved by a fast iteration method, enables us to generate the sparse control signal with reduced computational complexity, which is preferable in remote control systems where computation delays seriously degrade the performance. We give a theoretical result for control performance analysis based on the notion of restricted isometry property (RIP). An example is shown to illustrate the effectiveness of the proposed approach via numerical experiments.