As in signal processing, sparsity is also a useful concept in control systems.
Our paper on a sparsity-based control method has been accepted to
IEEE Transactions on Automatic Control, entitled
"Sparse Packetized Predictive Control for Networked Control over Erasure Channels"
The paper can be downloaded from arxiv.
The motivation of this study is sparse representation of control data.
In networked control systems, the data packets are transmitted through communication channels whose bit-rates are limited, and the transmitted data should be represented in fewer bits.
Sparsity then gives an attractive solution to this problem.
To reduce the data size of packets, we have proposed to adopt sparsity-promoting optimizations, namely,
- L1-L2 optimization
- L2-constrained L0 optimization
for which efficient algorithms exist (e.g., see this article).
We have shown how to design the tuning parameters to ensure (practical) stability of the resulting feedback control systems when the number of consecutive packet-dropouts is bounded.