Sparse Packetized Predictive Control for Networked Control over Erasure Channels

A new paper on sparsity-based control has been published:

M. Nagahara, D. E. Quevedo, and J. Ostergaard,
Sparse Packetized Predictive Control for Networked Control over Erasure Channels,
IEEE Transactions on Automatic Control, vol. 59, no. 7, pp. 1899-1905, July 2014. 

PDF can be downloaded from arxiv.

The abstract reads:

We study feedback control over erasure channels with packet-dropouts. To achieve robustness with respect to packet-dropouts, the controller transmits  data packets   containing plant input predictions, which minimize a finite horizon cost function. To reduce the data size of packets, we propose to adopt sparsity-promoting optimizations, namely, ell-1/ell-2 and  ell-2-constrained ell-0 optimizations,  for which efficient algorithms exist. We show 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.

A corresponding blog post is here.

Sparse Packetized Predictive Control

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, 

1. L1-L2 optimization
2. 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.

Enjoy!

Compressed sensing meets control systems

After I had a lecture on compressed sensing (CS) in 2010 given by Prof. Toshiyuki Tanaka , I had a vague idea to apply CS to control systems.

CS is not so popular in control systems community as in signal processing. Although L1 optimal control is a relatively classical problem (see, e.g., a work by Dahleh and Pearson here), they have not cared about the sparsity-promoting property of L1 optimization.

On the other hand, networked control have recently attracted a lot of attention in control systems community.  In networked control, a controller is placed away from a controlled plant and the controller should communicate with the plant over rate-limited networks, such as wireless networks (imagine controlling this for example).  In this situation,  the data should be compressed to satisfy the rate-limiting constraint.

My idea is to use a technique of CS for compressing data of signals in networked control systems.  More precisely, we use L1 optimization for sparse representation of control signals to be transmitted through rate-limited and erasure networks.  I discussed the subject with Dr. Daniel E. Quevedo and presented the work at a conference:

M. Nagahara and D. E. Quevedo,
Sparse Representations for Packetized Predictive Networked Control,
IFAC 18th World Congress, pp. 84-89, Aug 2011.

and also a journal version

M. Nagahara, D. E. Quevedo, and J. Ostergaard,
Sparse Packetized Predictive Control for Networked Control over Erasure Channels,
IEEE Transactions on Automatic Control, Vol. 59, No. 7, Jul 2014.


I believe this is the first-ever paper to apply CS (more precisely, sparse representation or sparse approximation) to networked control systems. However, there remain a couple of difficulties:

1. The term "Ax-b" where A is highly structured (not randomized) and x is unknown whether it is sparse or not.
2. The matrix "A" includes model error (e.g., error from linearization).
3. The vector "b" is subject to noise (e.g., quantization noise).
4. Computation should be extremely fast since computational delay may cause instability of the closed-loop system.
5. Only cheap quantization (e.g., a uniform scalar quantizer) can be used.

To see these difficulties, imagine again controlling the helicopter to make it fly stably along a desired trajectory. The problem is very challenging.

For recent papers on CS for control systems, see this entry.