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.

L1 Control Theoretic Smoothing Splines

The control theoretic spline is a bridge between control and signal processing, as mentioned in a previous blog post. This technique is extended to robust and sparse splines via L¹ optimality:

M. Nagahara and C. F. Martin,
L1 Control Theoretic Smoothing Splines,
IEEE Signal Processing Letters, 2014. (accepted)

The robustness is against outliers in data, while the sparsity is for representation of a curve with smaller number of parameters.
The abstract reads

In this paper, we propose control theoretic smoothing splines with L1 optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that is generated as an output of a given linear dynamical system. Conventional design requires exactly the same number of base functions as given data, and the result is not robust against outliers. To solve these problems, we propose to use L1 optimality, that is, we use the L1 norm for the regularization term and/or the empirical risk term. The optimization is described by a convex optimization, which can be efficiently solved via a numerical optimization software. A numerical example shows the effectiveness of the proposed method.

The MATLAB codes are available here.
PDF is here.