Nice restaurants in Cape Town

IFAC world congress 2014 was held at Cape Town International Convention Centre (CTICC), Cape Town, South Africa. I attended this congress in this summer and enjoyed restaurants around CTICC. Today's post is on nice restaurants around CTICC that I recommend to go.

TASCA
If you stay near CTICC, then basically Waterfront gives you nice restaurants. I went to this restaurant twice, because they offer quite nice seafoods. Also, this restaurant has a great view of the table mountain from tables outside (see the picture above).

Sevruga
This restaurant is also situated in Waterfront. Nice seafoods and wines. In particular, I recommend KingKlip, one of the most popular eating fish in South Africa.

NV80
Daniel, a friend of mine, invited 18 people including me to this restaurant. Meat is absolutely nice, in fact, this was the best meat I've ever had. At the time, I met Song from Hong Kong, who is also a friend of Daniel, and a reader of this blog! Amazing!! This restaurant is located in Sea Point, which approximately five minutes' drive from CTICC.

Bon appetit!

Maximum Hands-Off Control

Sparsity is also important in control systems.

In particular, sparse control, called hands-off control, is proposed for saving energy and reducing CO2 emissions in control systems. For example, a hybrid vehicle, Toyota Prius (displayed above), uses this control. The internal combustion engine is stopped (control = zero; sparse control) when the vehicle is at a stop or the speed is lower than a preset threshold, and the electric motor is alternatively used. See also Hands-off Control as Green Control.

Recently, it has been proved that the sparsest (or L0 optimal) control among all admissible controls is L1 optimal (see L0/L1 Equivalence in Optimal Control). Based on this, hands-off control is extended to feedback control in

M. Nagahara, D. E. Quevedo, D. Nesic, Maximum Hands-Off Control: A Paradigm of Control Effort Minimization, IEEE Transactions on Automatic Control, Vol. 61, No. 4, 2016 (to appear) (PDF is here).

The abstract reads:

In this paper, we propose a new paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon control, we show the equivalence between the maximum hands-off control and L1-optimal control under a uniqueness assumption called normality. This result rationalizes the use of L1 optimality in computing a maximum hands-off control. We also propose an L1/L2-optimal control to obtain a smooth hands-off control. Furthermore, we give a self-triggered feedback control algorithm for linear time-invariant systems, which achieves a given sparsity rate and practical stability in the case of plant disturbances. An example is included to illustrate the effectiveness of the proposed control.

A MATLAB code for the simulation is available here.

Enjoy!

Textbooks on Compressed Sensing

Today, I'd like to list textbooks on compressed sensing and related topics.
This list is far from complete, but I believe this helps a beginner take the first step.

Compressed Sensing: Theory and Applications

Y. C. Eldar and G. Kutyniok (Editors),

Cambridge University Press, June, 2012

ISBN-13: 978-1107005587
My comment: The introduction chapter (Chapter 1) is especially nice.

Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing

M. Elad (Author)

Springer, August, 2010.

ISBN-13: 978-1441970107
My comment: A nice introduction to sparse representation in signal and image processing.

A Wavelet Tour of Signal Processing: The Sparse Way

S. Mallat (Author)

Academic Press, 3rd edition, December, 2008.

ISBN-13: 978-0123743701

My comment: Read this book and be a master of wavelet. You can!

A Mathematical Introduction to Compressive Sensing

S. Foucart and H. Rauhut (Authors)

Birkhäuser, August, 2013.

ISBN-13: 978-0817649470
My comment: If you are interested in the theory of compressed sensing, this book will be of help.

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

H. H. Bauschke, R. S. Burachik, P. L. Combettes, V. Elser, D. R. Luke, H. Wolkowicz (Editors)

Springer, June, 2011.

ISBN-13: 978-1441995681
My comment: This book gives you fancy methods to solve sparse optimizations (e.g. L1/L2 optimization)

Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity

J.-L. Starck, F. Murtagh, and J. M. Fadili (Authors)

Cambridge University Press, May 2010.

ISBN-13: 978-0521119139

My comment: Sparsity has many applications in image and signal processing.

Enjoy!

A related blog entry is here.

MIT's Visual Microphone System

I can understand the theory, but the technology is quite unbelievable!
See Your Candy Wrappers are Listening.

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.

L0/L1 Equivalence in Optimal Control

One of the fundamental results of compressed sensing is that L¹ optimization gives the sparsest (or L⁰-optimal) solution of an inverse problem under some assumptions.

Is it also true with L¹ optimal control?
Is L¹ optimal control the sparsest one among all admissible controls?

The answer is YES (under some assumptions, of course).
Our recent research

M. Nagahara, D. E. Quevedo, and D. Nesic,
Maximum Hands-Off Control and L1 Optimality,
52nd IEEE Conference on Decision and Control (CDC),
pp. 3825-3830, Dec. 2013.

has revealed that.

It is interesting that the L⁰ norm in this article is defined for continuous-time signals while most compressed sensing methods uses one for vectors. We call a control with small L⁰ norm a hands-off control.

The abstract reads:

In this article, we propose a new paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a much shorter support than the horizon length. The maximum hands-off control is the minimum support (or sparsest) control among all admissible controls. We first prove that a solution to an L¹-optimal control problem gives a maximum hands-off control, and vice versa. This result rationalizes the use of L¹ optimality in computing a maximum hands-off control. The solution has in general the "bang-off-bang" property, and hence the control may be discontinuous. We then propose an L¹/L²-optimal control to obtain a continuous hands-off control. Examples are shown to illustrate the effectiveness of the proposed control method.