(Modified) PERT distribution

The United States navy developed in the 1950’s a program evaluation research task (PERT). It was designed to analyze the duration of a project and the tasks within the project. Each task in the project is given the following properties:

  • Name of the task
  • Predecessor, the list of tasks that have to be completed before the task can start.
  • The amount of time it will take for a task to be finished.

The duration of a task is often not fixed. It can vary between a minimum and maximum. The PERT distribution was created to give a good estimate of what the probability is of the duration of a task. It uses the same three parameters as the Triangular distribution, namely, the minimum (\text{min}), the most likely (\text{mode}) and the maximum (\text{max}). The probability density function (PDF) is given by

    \begin{equation*} f(x) = \frac{1}{B(\alpha_1,\alpha_2)}\frac{(x - \text{min})^{\alpha_1 - 1} (\text{max} - x)^{\alpha_2 - 1}}{(\text{max} - \text{min})^{\alpha_1 + \alpha_2 - 1}} \end{equation*}

where

    \begin{equation*} \alpha_1 = 6 \left( \frac{\mu - \text{min}}{\text{max} - \text{min}} \right), \quad \alpha_2 = 6 \left( \frac{\text{max} - \mu}{\text{max} - \text{min}} \right), \quad \end{equation*}

with

    \begin{equation*} \mu = \frac{\text{min} + 4\text{mode} + \text{max}}{6} \end{equation*}

being the mean.

An additional shape parameter \gamma might be added, in which case we are dealing with the modified PERT (MPERT) distribution. The parameter influences the peakness of the distribution. The only difference with PERT is the definition of \alpha_1 and \alpha_2. These are namely defined as:

    \begin{equation*} \alpha_1 = 1 + \gamma \left( \frac{\mu - \text{min}}{\text{max} - \text{min}} \right), \quad \alpha_2 = 1 + \gamma \left( \frac{\text{max} - \mu}{\text{max} - \text{min}} \right), \quad \end{equation*}

I created some Matlab code which includes functions for the PDF, the (inverse) cumulative distribution function (CDF). The inverse CDF is important for when you want to generate random numbers. The code can be download from here.

Finally, below is an interactive example of the PDF of PERT (blue) and MPERT (red) distribution.

Published articles

During and after my Master thesis I authored and co-authored three articles. Two for a scientific journals (IEEE) and one for a Dutch professional magazine (Mechatronica & Machinebouw). While it took me a lot of time writing these articles and I do think that the current publish or perfish system is completly wrong – can write a whole blog about this or maybe read this article – I am glad I took up the challenge to write them next to my thesis.

Writing a scientific article is completely different compared to writing your thesis. For your thesis you have numerous pages to explain your story for a scientific article you only have a few. As a result, you will have to be very precise in your writing and choose the words carefully. It has to be very clear, precise and short. This can be very challenging when your story touches a lot of subjects from different fields. Angel Borja wrote a three articles on writing your article and I would like to share these with you:

  1. Six things to do before writing your manuscript
  2. 11 steps to structuring a science paper editors will take seriously
  3. Writing the first draft of your science paper — some dos and don’ts

In addition, I found the UW-Madisons Writer’s Handbook and especially the page about Transitional Words and Phrases useful.

Finally, without further ado, the three articles I have written.

Frequency-domain analysis of real-time and networked control systems with stochastic delays and data drops

Abstract—We present a novel frequency-domain analysis framework for a closed-loop model capturing a wide range of real-time and networked control systems with stochastic delays and packet drops. Our results allow for inferring the mean and variance of the output response to deterministic inputs, based on a new frequency response plot. We illustrate the usefulness of our results in the context of real-time control systems with input-to-output delays resulting from the use of a shared processor.

Keywords—Frequency-domain analysis, networked control systems, real-time systems, stochastic systems, data losses, delays

pdf

The impact of deadline misses on the control performance of high-end motion control systems

Abstract—In high-end motion control systems the real-time computational platform must execute tasks from multiple control loops operating at high sampling rates. In recent years traditional special-purpose platforms have been replaced by general purpose multi-processor platforms, which introduce significant fluctuations in execution times. While considering worst-case execution times would severely reduce the sampling rates, accepting deadline misses and assuring that the control system still meets the desired specifications is challenging. In this paper, we provide a framework to model and assert the impact of deadline misses in a real-time control loop. We consider stochastic models for deadline misses and characterize the mean and the variance of closed-loop output variables based on a time-domain analysis. We illustrate the usefulness of our framework in the control of a benchmark motion control experimental setup and in the control of a wafer stage in a lithographic machine.

Keywords—Deadline misses, data losses, packet drops, performance analysis, stochastic analysis, industrial case study, hybrid systems, cyber-physical systems, real-time systems

pdf

Smarter balancing between performance and costs in control systems

Abstract—In order to ensure the performance of control systems, the digital platforms on which they are executed are often over-dimensioned, which are unnecessary costly. State-of-the-art model based techniques make it possible to create cheaper control systems, without performance degradation.

Keywords—Deadline misses, data losses, packet drops, performance analysis, stochastic analysis, industrial case study, hybrid systems, cyber-physical systems, real-time systems

pdf

Fantasy book frame quote

A few weeks ago I saw the following tweet by Bo Marit. I really liked how the quote and the symbol reference stand out in front of the text in the frame. Since, I liked them so much I decided to be a copy-cat. However, I added also another frame with a reference to Game of Thrones.

The font that she uses for the quote is called Darleston. It is a really elegant calligraphic font created by Youssef Habchi. For the book page text I used Garamond, a standard font on most computers. I chose this font because it has an oldish style to it. While this could easily be created in Photoshop or any other graphics editor, I simply recreated it with Microsoft Word, which is maybe even easier! I simply created a two column layout, added two textboxes for the quotes and the symbol image. You can download the word file here (note: you will need the fonts Darleston and Garamond) or a pdf file here. As an frame I would recommend a simple wooden frame as Bo Marit uses, I think it gives adds elegance and makes it look more humble. Furthermore, I would not use regular A4 paper to print this on. I searched for the same type of paper you often see used in books. Most likely you will find this type of paper in your local hobby store.

Finally, my result:

Three frames with a book page and quote in front as reference.

I plan the hang the Harry Potter frame near to a light switch, the Lord of the Rings frame near to the clock and the Game of Thrones frame near to the thermostat.

GEWIS GEMOLD 2014

From 28th of May to the 1st of June GEMOLD14 takes place. GEMOLD14 is the GEWIS version of the popular Dutch television program wie is de mol?, literally translated who is the mole?. The program is about 10 candidates who have to complete several assignments with which they can earn money. However, one of the candidates is the mole, it is his solely purpose to make sure that assignments fail and the team of candidates earn as less money as possible.  At the end of each episode there is an execution, the candidates have to answer a number of questions about the identity of the mole. The candidate who answers the least amount of questions correct has to leave. Candidates can earn jokers, which turns a falsely answered question into a correct one, or free-cards with which they do not have to do the answer the questions at all and guarantees continuation to the next episode. At the end of the program there are only three candidates left, the mole and two candidates. The winner is the candidate, who is not the mole of course, who answers the most correct questions about the identity of the mole.

On the 23rd of February I got an e-mail from the GEMOLD14 committee with the message I was selected to participate as a candidate. Together with the e-mail I received a questionnaire which I immediately filled in. You can download it here, however, it is in Dutch. I also had to write a small introduction about myself for the website, which you can view here, also in Dutch. After that it was just waiting for the 28th of May.

On the 28th of May all 14 candidates gathered at GEWIS in the Metaforum at the university. Before I went to GEWIS I made a visit to the bathroom where I wrote mole on mirror with soap just as a tease for the other male candidates who might had to go to the bathroom after I went. Later we were delegated to come to balcony of the Metaforum. After a group picture with all the candidates GEMOLD14 was finally about to start. Tim the host of GEMOLD14 showed up and welcomed us. He explained some organizational matters and how jokers and free cards looked like. We handed in our mobile phones, wallets and everything else that we were not allowed to have in our possession during the weekend. Afterwards, he told us to prepare ourselves for execution! With only the questions from questionnaire  someone was already going to leave the group. Everyone was in shock, while I only had an eye for the joker and free card which Tim showed us as an example and left on a small table. With an easy pace I walked up to the table and grabbed them while everyone was gasping and watching me. Unfortunately however, one of the other organizers came up to me and told me to give them back. As polite as I am, I gave them back. Very stupid afterwards since they really lay in the open and the organizers were only to blame themselves to leave them so in the open. In the meantime the monitor was placed. Ruben, the host who did the executions, called the first name: Rik — who I think is the mole by the way — got a green screen. He was followed by Celine, Mark, Jos, Arno and Levi who all got a green screen. Then it was Wout’s turn, he was one of the finalist of GEMOLD13. Unfortunately for him he got a red screen and we were left with 13 candidates.

Wout was executed and the remaining candidates and myself gathered between the Metaforum and the Main building. Tim showed up. He asked for two volunteers who were lazy, Jos and Annebel presented themselves after which they were escorted away from the rest. Tim asked for someone who still had to recover from the shock, Mike presented himself and he was also escorted. At the end Tim needed two more volunteers who would enjoy a little walk, Ingmar and Leroy presented themselves. The rest had to fetch our bicycles and were escorted by two people from the organisation, Merel and Serge. For clearance here a list of the people:

  • Two volunteers who were lazy: Jos and Annebel.
  • One volunteer who still had to recover from the shock: Mike
  • Two volunteers who enjoyed a walk: Ingmar and Leroy
  • The rest who were gonna travel by bicycle: Wouter (me), Jorik, Celine, Wim, Levi, Rik (mole!), Patricia and Arno.

We drove to the Opwettense Watermill. Tim was waiting for us, after we parked our bicycles Tim explained us the assignment. Two people would arrive at the Watermill in approximate 10 minutes. From there on we had to guide them within one hour to the camp location were we would spend the night. We were to act as a traffic signpost and were not allowed to communicate by any other means than that. We were given three maps in which not all roads were clearly visible. On the left side the street directions were given in plain text. After the instructions of Tim we gathered in a circle around one of the maps, discussing which positions were best to post someone as a signpost. In this discussing Levi took the lead. Celine also got hold of one of the maps, I asked her if I could have a look at it. She gave me the map, but not before saying that she wanted it back afterwards, of course I never gave it back. At the first point were we had to leave someone behind I told the group we had to leave Celine as a signpost, I took the lead in this discussion since I did not suspect her. Celine was left at the first street crossing and the rest bicycled further. During the road there was some discussion whether or not someone had to be left at a street junction however of course our logic kicked in and we decided to post no-one as long as the directions was straight ahead. Jorik was left next at a roundabout. Then Patricia was left at a crossing. After that there was some discussion if we took the correct turn. I quickly ended that discussion because from reading the map and street names I knew we were correct. It was very funny and suspicious to see that no one seemed to be bothered to actually look at the street names and the ones on the map. The discussions were more like — when you look at the scale of the map and the distance from this crossing to this crossing, this had to be the correct crossing. At the next crossing I told the group which was left, that I want to act as a signpost and to be left behind. Levi did not like that and wanted to leave someone else behind — I guess he did not trust me.  Rik (mole!) however told Levi however that we could keep discussing but that it was useless and he should accept the situation as it was. I was left behind as a signpost and the rest continued. However at the end of the road they stopped and were discussing. Later I learned that there was confusion about the map since there should have been a straight clear road ahead but there was not. However during their discussion Ingmar and Leroy arrived at my location, quickly I acted as a signpost and pointed them to the correct direction. Ingmar and Leroy were gaining upon the rest of the bicyclists, since they were still discussing. Suddenly they saw them and drove of, however, leaving Wim behind as a signpost. From this point on I could only guess and learn from others what happened further on. Suddenly however Mike arrived, I was kind of surprised and without thinking I pointed him in the correct direction, very foolish of me so it appeared afterwards.

While I was waiting to be picked up by one of the organizers I started to write in my mole booklet. After a while the group reappeared and we drove back to the starting point to pick up everyone after which we drove straight to the camp location. At the camp location we had to step off from our bicycles and one by one we had to go to the gates from the encampment. Jorik went first, he however came back and told us that he did not get in. He told us that we were getting a yes or no question about if we wanted to get into the encampment for -500 mole money. In the meantime Arno did went to the gate and got in. At first I thought he told yes. Then Wim and Celine got in as well. I got to the gate and got the question which Jorik told me I would get, I clearly said no and got in. From what I learned afterwards Jorik told not clearly no but said “euh no. Inside the main building of the encampment I learned that while there was some confusion on the road, after I was left behind, we succeeded with the assignment. When every candidate was inside Tim greeted us. He told us that Ingmar and Leroy were inside the encampment in time with which we earned 500 mole money. However, Mike also made it also into the encampment with which he earned a free-card. This did however cost -1000 mole money. So actually we did fail with the assignment, since we got -500 mole money in the end. The mole had succeeded and we went to sleep.

The next morning all candidates gathered in a small room. Tim joined and explained the lie and cheat assignment. The moles of the three previous editions of GEMOLD would join us they would act as a jury. Tim would then ask each candidate two questions, one had to be answered truthfully the other with a lie. The jury would then try to guess which answer was a lie. Each candidate could earn mole money when the jury did not manage to find out which answer was a lie. When a previously candidate managed to fool the jury the next candidate could choose to call. The mole money earned by the previous candidate would then be safe. If he continued and the jury would guess correctly which answer was a lie then the previously earned mole money would be gone. The amount of mole money earned would raise by:

  • 10 mole
  • 30 mole
  • 100 mole
  • 200 mole
  • 500 mole
  • 1000 mole
  • 1500 mole

First Ingmar and Patrice who both did not manage to fool the jury. Then other candidates told me I had to go, I resisted a bit but gave in to the pressure. Tim asked me two questions, if I had a part-time job and what my favorite book was. Since I did not quiet understand the game at that moment, I was wondering if the question which were asked stood in the questionnaire, I decided to answer the first question falsely and the second truthfully. The jury then guessed wrong. The next candidate did not decide to call and unfortunately he did not fool the jury. The 10 mole earned by me were gone. After my question, I gave the assignment some more thought and I believed that we could have lied always regardless what type of question we were asked because the questions did not actually come from the questionnaire. Hence it could never be checked if the candidate was actually lying towards the jury. After I got executed, I looked it up and indeed both questions which I was asked were not in the questionnaire. As such I think I was correct during the game and we could all just have lied towards the jury. Unfortunately everyone was to truthfully towards the jury and we only managed to obtain 100 mole. We could have earned a lot of mole money very easily. This time the mole was not clever, we were dumb.

After the next assignment, I unfortunately got executed. I wrote this blog almost immediately after I was executed. However, I did not describe the events during the last assignment, I did plan to finish it at a later stage. However, as you can see that never happened. Because the episodes are being aired now, I decided not describe these events anymore from my point of view.

Mole booklet

Simyo – Vriendendeal

Simyo is a mobile virtual network operator (MVNO), which is active in several countries. Namely, Netherlands, Belgium, Germany, France and Spain. Simyo, as a MVNO, does not own any network infrastructure. In the Netherlands it uses the infrastructure of KPN. KPN is namely its parent company. Furthermore the company has no offices and solely operates by using the internet.

I joined Simyo in august 2013. Because I wanted to switch to a SIM-only subscription, since my phone, from my previous subscription, was still working fine. From my invoices I figured out that I did not call or text that much. I spent around +/-70 minutes calling or texting and around +/- 600 MB of internet traffic. For this reason I decided that I only needed a subscription which could offer 100 min/sms with 1000 MB internet traffic for a reasonable price. After searching and searching for a subscription, I came across Simyo. I then decided to join Simyo for the following reasons.

  1. It was the cheapest (it really was, my subscription is 13 euro’s, I should note however that it nowadays is 14 euro’s)
  2. It was already at that time, called one of the best providers in the Netherlands by a non-profit organization which promotes consumer protection, the “consumentenbond“.
  3. It uses the KPN network, which, by reputation, is know to be very reliable

A while ago my parents told me that they needed a new mobile subscription and they asked me if I could be of help. Since I am a happy Simyo customer, I advised to go for a subscription at Simyo. At the same time Simyo had started an advertising campaign, called the “Vriendendeal” or in English “Offer for friends”. This campaign was about getting existing customers to tell friends to join Simyo. As an existing Simyo customer it was made possible to start your own shop. If people would then register for a Simyo subscription, using your shop, both the shop owner and the subscriber would earn 10 euro discount on theirs subscription fee.

Naturally my parents did obtain a Simyo subscription using my shop. A few days later my brother also called me, if I could be of help with his mobile subscription. Again, I pointed him to my Simyo shop. Because of these three subscriptions my shop, apparently, was one of the best in attracting new customers towards Simyo. For this reason Simyo asked me, as well as a few others, who also ranked high in selling subscriptions, if they could put a link to my Simyo shop on their main website. I replied that I did not had any objection, however I was skeptical since I thought “oh well, I guess my link just appears somewhere at the bottom of the webpage, but everything is better than nothing.”. The nice thing was, was that I was completely wrong. Namely on Sunday, the 13th of September, the Simyo website looked as follows.

Appearance of the Simyo on the 13th of September 2014.
Appearance of the Simyo on the 13th of September 2014.

They actually had removed the links to their own subscription form and replaced it with a link to my Simyo shop. When I saw it I was really exited. At the end of the day a total of 36 people ordered a subscription at Simyo using my shop. Of those 36, 12 people also activated their SIM card which did boil down to 120 euro’s in discount. As you can imagine I was, and am still, very happy because of this. It is for this reason and the fact that I am just a happy customer at Simyo, I wrote this blog. To thank them for putting my shop on their main website.

In the end I managed to obtain 160 euro’s in discount. Below is the list, I removed the names for privacy reasons.

Duck Tales theme song with real ducks

The Oh My Disney youtube channel created a funny video in which they recreated the original Duck Tales intro with real ducks. The Duck Tales is an animated television series, which I watched a lot when I was a child.

After watching the video I was wondering how it compared to the real intro. Luckily they a few days back they also uploaded a side-by-side comparison, which I think is also amusing to watch.

Testimonial Master’s program TU/e Systems & Control

In November 2013 I was asked by the PR of the Mechanical Engineering department of the TU/e to write a story about myself and how I perceived the master Systems & Control. It would be used as a testimonial on the TU/e website. In the end only a part of my full story was incorporated, below is the full-text which I submitted.

TUe - Testimonial
Testimonial on the TU/e website.

Hello, my name is Wouter Geelen. Currently I am following the Master Systems & Control at the Eindhoven University of Technology. First I will tell you something about why I decided for the Master System & Control, then something about how I experience the Master track and what currently keeps my life occupied.

When I was finished with my Bachelor in Mechatronics (HBO) it was clear to me that I wanted to continue studying. Choosing at which University I wanted to do my Master was a really easy choice for myself for 2 main reasons. Firstly, since I was raised in a small town in the province of Limburg and did not yet wanted to drift off to far from my roots and secondly I did two years of my Bachelor in Germany near Düsseldorf and at that time I still went regularly to Germany to visit friends. Therefor I decided that the University in Eindhoven was best the best choice. However, choosing the master was a really hard and difficult decision. After a Bachelor in Mechatronics there are several possible Masters which you can choose from. In my case there were basically two options: i) Embedded Systems or ii) Systems & Control.

During my graduation project for my Bachelor I created a double inverted pendulum (video) which would be a typical project for students from Systems & Control, but with the knowledge at that time it was a difficult problem for myself. However, I successfully completed the project. After a lot of talking with my former teachers and a graduate from Systems & Control, who helped me with my graduation project, I decided to start with the Master Embedded Systems and that I would choose several Systems & Control courses in my free electives. When you come from a University of Applied Sciences you will have to do a pre Master first, before you can actually start with the “real” Master. I did the pre Master of Embedded Systems, it had a lot of fun and interesting courses. After I finished the pre Master and had started with the real Master it started nagging me that the control courses which I wanted to do for my electives where really hard because of a knowledge gap. Furthermore, the master Embedded Systems also focused really on energy-efficient chip design which I really did not find interesting at all. I am the type of person which just wants to pick a chip from the shelve after which I work my magic on it. For those two reasons I decided to switch to Systems & Control. Luckily most of the courses of the pre Master of Systems & Control where the same as the pre Master of Embedded Systems so I finished it quickly. Furthermore, after asking the examination board of Systems & Control for permission, I could take 3 courses from Embedded Systems with me to the Systems & Control. So luckily that detour of half a year Embedded Systems was not a complete waste.

The core program of Systems & Control covers really all the basics about control engineering and the whole cycle of model based design. There are very theoretical courses but also very practical courses, which, I think is perfect for a University of Technology. You can then namely apply what you learnt in your theoretical courses in your practical courses. You also have a lot of freedom in choosing your electives: i) there are a lot of elective courses from which you can choose from and ii) if there is a course which you really like but is unfortunately not on the list then, if you have good arguments, you can ask the examination board for permission. Which I did as you have read earlier.

For a lot of courses you have to work together with another student or a group of students. Which is nice since most students in System & Control all have a different background, as well in study, as in culture. As such groups get really mixed up, which is good for learning how to work with a very diverse group of people. Also all the Professors excel in their field of expertise, they really challenge you during college. Since the TU/e is a small University you really get to know them and can almost always ask them anything if you don’t understand something. So the distance between you as a student and the Professor is really small.

Inside the master Systems & Control there are several specialization groups. At first I did choose for the Hybrid Systems group. However , during the summer they did merge with the Control Systems Technology group, which made them one of the strongest groups at the TU/e and one of the strongest in control theory worldwide. The reason why I did choose for this group is very simple. During my graduation presentation of the double inverted pendulum I was asked if I could compute the best possible transition between the two controllers. The system namely consisted out of two controllers one for bringing the pendulum in upwards position and one for stabilizing it. At that time I could not answer that question yet, but now and thanks to the help of Hybrid Systems, which combines continuous and discrete systems, I can answer that question! Which makes me feel kind of proud of myself.

Nowadays I am busy with a literature survey about several Matlab toolboxes which help in analyzing and simulation of systems in which wireless networks are involved. Wireless networks are namely increasingly more being used for control systems. To give an example where one could have used a wireless network inside a control system is my double inverted pendulum, namely at the encoder where the two pendulums meet. In that case the encoder at the connection of the two pendulums is not wired anymore. Wireless networks however bring all kind of nasty behavior with them which influences the stability of the system. Furthermore, wireless networks combined with control systems are still hard to analyze mathematically. Therefore there are still a lot of open questions to be answered around this subject.

Smuggling Game (Dutch: Smokkelspel)

The Smuggling Game is another running game which can be played inside the forest. The game takes place inside the forest. The group is divided into two teams. One team is called the smugglers and the other the police or customs. The goal of the smugglers is to smuggle goods (cards) from one part of the forest to another part. In both parts of the forest is a game leader, one who hands out and one who collects cards. The goal of the police is to make sure that the smugglers fail at their goal. The smuggler has to hand over his card to the police when he is tapped by them. The police then hands out the collected card to a third game leader who is located in the middle of the two other game leaders. The game leader who hands out cards to the smugglers has a fixed number of cards. Shortly after the game leader is out of cards the smugglers become the police and vica versa. Of course this team switching can also be time dependent.

To actually play the Smuggling Game there is one required accessories and one optional.

  • required: game cards (see below)
  • optional: sash, for identification of both teams

A few alterations can be made to the game to make it more difficult or exiting.

  1. If the police taps a smuggler, they do rock-paper-scissors or another simple game, to determine if the police wins the card from the smuggler. If the police loses he has, for instance, to stand still for at least 5 seconds.
  2. Instead of one location where the smugglers can bring their cards towards to, there are multiple locations.
  3. First the smugglers bring their cards to the first location. They can then decide to double the value of the card by bringing it to a second, more difficult to reach, location. Then they can bring to a third, et cetera.

Game cards

Click on the figure to go to the Google drawing. You can download a A4 paper sheets here with the cards in the correct ratio, to be printed on colored paper. The Dutch version can be found here.

Smuggling Game - Cards

High quality interesting freely publicly available e-books

During my studies at the Eindhoven University of Technology some professors have been referring to freely available e-books. Some of these are mentioned here, others I just did find useful for other reasons. I tend to expand this list whenever I find an freely publicly e-book which I think is worth sharing.

Please contact me if one of the links is broken.

A Mathematical Introduction to Robotic Manipulation

By Richard Murray, Zexiang Li and Shankar Sastry

A Mathematical Introduction to Robotic Manipulation presents a mathematical formulation of the kinematics, dynamics, and control of robot manipulators. It uses an elegant set of mathematical tools that emphasizes the geometry of robot motion and allows a large class of robotic manipulation problems to be analyzed within a unified framework. The foundation of the book is a derivation of robot kinematics using the product of the exponentials formula. The authors explore the kinematics of open-chain manipulators and multifingered robot hands, present an analysis of the dynamics and control of robot systems, discuss the specification and control of internal forces and internal motions, and address the implications of the nonholonomic nature of rolling contact are addressed, as well. The wealth of information, numerous examples, and exercises make A Mathematical Introduction to Robotic Manipulation valuable as both a reference for robotics researchers and a text for students in advanced robotics courses.

Link

Mathematical Control Theory

By Eduardo Sontag

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein force the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematics Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. v Preface to the Second Edition The most significant differences between this edition and the first are as follows: Additional chapters and sections have been written, dealing with: nonlinear controllability via Lie-algebraic methods, variational and numerical approaches to nonlinear control, including a brief introduction to the Calculus of Variations and the Minimum Principle, – time-optimal control of linear systems, feedback linearization (single-input case), nonlinear optimal feedback, controllability of recurrent nets, and controllability of linear systems with bounded controls.

Link

Synchronization and Linearity : An Algebra for Discrete Event Systems

By François Baccelli, Guy Cohen, Geert Jan Olsder and Jean-Pierre Quadrat

This book proposes a unified mathematical treatment of a class of ‘linear’ discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the ‘max-plus algebra’. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide ‘discrete event system theory’, which is shown to parallel the classical linear system theory in several ways. This class of synchronized systems finds its main current industrial applications in the modeling, optimization and control of communications networks, computer architectures, manufacturing and transportation systems. The book should hence appeal to students and researchers in probability-statistics, applied mathematics, (industrial and electrical) engineering, operations research, as well as computer and management scientists.

Link

Convex Optimization

By  Stephen Boyd and Lieven Vandenberghe

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

Link

Linear Matrix Inequalities in System and Control Theory

By Stephen Boyd, Laurent El Ghaoui, Eric Feron, and Venkataraman Balakrishnan

In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.

Link

A Brief Introduction to Neural Networks

By David Kriesel

Neural networks are a bio-inspired mechanism of data processing, that enables computers to learn technically similar to a brain and even generalize once solutions to enough problem instances are tought. The manuscript “A Brief Introduction to Neural Networks” is divided into several parts, that are again split to chapters. Part I: From Biology to Formalization — Motivation, Philosophy, History and Realization of Neural Models. Part II: Supervised learning Network Paradigms. Part III: Unsupervised learning Network Paradigms. Part IV: Excursi, Appendices and Registers.

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The Feynman Lectures on Physics

By Richard Phillips Feynman, Robert Benjamin Leighton and Matthew Sands

This revised edition of Feynman’s legendary lectures includes extensive corrections Feynman and his colleagues received and Caltech approved, making this the definitive edition of The Feynman Lectures on Physics. For all readers interested in physics.

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Motion Mountain the adventure of physics

By Christoph Schiller

Motion Mountain is an entertaining and free e-book in six pdf files introducing physics – the science of motion. Explore the motion of wheels, birds, lightning, planets, light and empty space itself! Be fascinated by the beauty of nature and by the concepts of modern physics, from the principle of cosmic laziness – least action – to gauge symmetry!

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Stratego Alive (Dutch: Levend Stratego)

One week in the Summer I work voluntary as a camp leader at a summer camp for children. Each year there are at least three summer camps for different ages. The camp accommodation is located in the Veluwe which is a forest-rich ridge of hills in the province of Gelderland in the Netherlands. Hence a lot of the activities take place inside the forest. Every camp leader organizes some games/events for the children. This year I organized four events.

The last two games I want to share with you. In this blogpost I explain the details of Stratego Alive. In another blog I will give the details about the Smuggling game.

Stratego Alive

Stratego Alive is a variation on the strategy board game Stratego. It is a running game and is to be played in the forest. The group is divided in two or more teams. All teams have their own playing field, i.e. part of the forest, in which they hide their flag, note that the flag must still be, partially, visible . The flag can be for instance a colored towel or an old ripped bed sheet with some colored paint on it. The goal of the game is to capture the flag of the opposing teams.

Every team has at least one game leader. The game leader sits on a fixed location somewhere in the part of the forest of that particular team. The game leader hands out every player a card. On the card the rank is shown and depending on the card also some extra info. The table below shows the ranks. In general it holds that the card with the highest rank wins. If a player wins the player who lost gives his card to the winning player. Both players must then return to their respective game leader, the winning player is to hand in the card of the losing player. The losing player is to obtain a new card.

Ratio Name Rank Info
1 Marshal 10 Loses against the Spy if Spy taps first.
4 General 9
5 Colonel 8
6 Major 7
7 Captain 6
8 Lieutenant 5
9 Sergeant 4
6 Miner 3 Wins against Bomb
10 Scout 2
2 Spy 1 Wins against the Marshal if Spy taps first.
6 Bomb 0 Loses against the Miner. Cannot tap anyone

The Marshal is the highest rank and wins from all other cards, except if it is tapped by the Spy. The Spy is the only character which wins from the Marshal if he taps first. It is to be noted that sometimes children fight over who tapped first regarding the Marshal and Spy, therefore the rule can also be changed such that the Marshal always losses against the Spy regardless of who taps first. The Bomb is somewhat similar to the Marshal it also wins from almost every card accept that the Bomb cannot tap other players by himself and loses against the Miner.

If the rank is equal there are two rules which one can enforce, (i) either the two players exchange cards and return to their game leader or (ii) the two players ignore each other and continue playing.

This is Stratego Alive. This game can easily be themed when the game is to be played into a certain setting, for instance, pirates. You simply change the name of the Marshal to Captain Hook, General to Jack Sparrow, et cetera.

To actually play Stratego Alive there are two required accessories and one optional.

  • required: game cards for every team (see below)
  • required: flag for every team
  • optional: sash, for identification of each team

Game cards

Click on the figure to go to the Google drawing. You can download a A4 paper sheets here with the cards in the correct ratio, to be printed on colored paper. The Dutch version can be found here. Credits regarding the graphics of the cards go to Sjoerd.

Stratego Alive - Cards