Compressive Sampling for Remote Control Systems

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.