Exercises and Design Problems: Solution Hints and Other Problems

(notes for the professor and student)

Kevin M. Passino

Biomimicry for Optimization, Control, and Automation,

Springer-Verlag, London, UK, 2005

E=Exercise

DP=Design Problem

Chapter 1:

E1.5: Keep in mind that that there are many correct solutions to this problem. Can you see anyway to make the process of constructing a functional architecture systematic (i.e., so that given a physical system, there is a step-by-step approach to constructing it)?

E1.7: To do this problem right requires you also to review the current literature, and to invest a significant amount of time in reading all the existing work. A good source for earlier progress in this area can be obtained from the book on Intelligent and Autonomous Control that is available for a free download by clicking here.

E1.9: This problem has never been fully solved, although I have played around with it a bit. It is challenging to to it properly!

Chapter 2:

E2.1: Additional problem: Search the current literature in the area of systems biology for other applications. For instance, what is being done at the genomic level?

E2.2(c): Provides an opportunity for a controls person to work with neuroscientists and psychologists. I feel that the stability-theoretic characterization of ADD is quite a useful way to think of that problem, and may lead to a better understanding of the scientific principles of it.

Chapter 4:

E4.3: If you are not already familiar with Lyapunov stability theory, you may want to see Khalil's book on nonlinear systems before trying this problem (see full reference in the book).

Additional problems: E4.4, E4.5, DP4.1, or DP4.2 could also be done for the cargo ship rather than the tanker ship.

Chapter 5:

E5.3 and E5.4: Teach new ideas from fuzzy sets and logic. Most often, several of these ideas are not, however, needed for control systems development.

E5.5: This is a great problem for a beginner. If they can do it by hand, they really understand it.

E5.6: Again, a great problem for a beginner.

DP5.1: Additional problem: Repeat, but for the tanker ship.

DP5.2: I generally do not like the inverted pendulum since it is over-studied, and often its difficulty is over-stated. This is, however, a reasonble first problem to solve.

DP5.3: See: Passino K.M. and A.D. Lunardhi, "Qualitative Analysis of Expert Control Systems", Chapter 16 in Gupta M.M., Sinha N.K., eds., Intelligent Control: Theory and Applications, pp. 404-442, IEEE Press, Piscataway, NJ, 1996. Also, see: Lunardhi A.D., Passino K.M., "Verification of Qualitative Properties of Rule-Based Expert Systems", Int. Journal of Applied Artificial Intelligence, Vol. 9, No. 6, pp. 587-621, Nov./Dec. 1995.

Additional problems: There are many additional problems for the topics of this chapter in the book on fuzzy control that is available for a free download by clicking here.

Chapter 6:

DP6.2: This is a nice problem for a student who wants to understand the connections between planning systems and model predictive control (MPC), and may be particularly important for someone who does not know the wealth of progress in MPC theory and applications.

DP6.3: Click here for more information and background on solving this problem in the form of an MS thesis of one of my students that I supervised. A chapter on planning systems is also in the book on Intelligent and Autonomous Control that is available for a free download by clicking here.

Chapter 7:

DP7.5: This is a nontrivial problem that if properly expanded upon could be a nice thesis. I would recommend, however, a search of the current literature as this is an active research area.

DP7.6: The chapter is only meant to provide an overview of ideas in this area; hence, to do this problem properly the reader will have to do significant additional work.

DP7.7: Part (a) has been solved, at least one version of it. The cooperative case is of significant interest in a variety of engineering applications (e.g., cooperative cross-platform sensor fusion/management or in cooperative control).

General remark: The general state of development of use of attentional strategies in control, and control theory for attentional strategies, is not well-developed as of the date of publication of this book. Hence, overall it represents an area where a number of research opportunities exist.

Chapter 9:

E9.1, E9.2: Repeat problems, but for inverted pendulum application.

DP9.1: Repeat problem, but for the inverted pendulum application.

Additional problems: There are many additional problems for the topics of this chapter in the book on fuzzy control that is available for a free download by clicking here.

Chapter 10:

E10.1, E10.2: Successful completion of these two problems will show that you understand the derviations of batch and recursive least squares. Good problems for beginners in this area.

DP10.1, DP10.2: These problems allow the student to "get their hands dirty" with the least squares methods. They are not meant to be serious industrial applications, just good first-problems to study to learn the methods.

Chapter 11:

E11.1, E11.2: Personally, I feel that every person that first learns these methods ought to write out the gradient descent formulas via the calculus; however, I do not recommend doing that each time you want to solve one of these interpolation problems. There are excellent computational toolboxes for optimization (e.g., Matlab, or others available for free on the web), and these should be used so that you can get to solutions faster.

DP11.2: Proper solution of this problem would require an effort the size of doing a thesis. Elements of this problem could be a project for a class. It does, however, require a relatively high level of indepence on the part of the student to come up with a good solution.

Chapter 12:

E12.2: Doing this problem shows the student how to develop the theory on stable adaptive control in the chapter.

E12.2: And, this problem shows how to apply the theory from E12.2 to an application (you need to do E12.2 in order to solve this problem).

DP12.3: This provides the opportunity for the student to do yet another problem on this topic. Basically, the results come out like the one in the chapter.

Additional theory and problems: If you are interested in a much more detailed and complete treatment of the theory and application of the theory of this chapter, and many additional problems for the topics of this chapter, see the book by J. Spooner et al. on stable adaptive estimation and control by clicking here.

Chapter 14:

E14.1: Doing one of these problems helps the student learn about the GA.

DP12.2: This problem is only meant to provide a complex landscape over which to perform optimization. If you want, you could go to the web and get data for the region of Earth where you live and do the problem for that case (but, if you live in western Kansas that may not be so interesting since it is as flat as a pancake, really).

DP14.3: Caution: For this problem do not just come up with a GA that succeeds via random search!

Chapter 15:

E15.2-E15.4: Relatively easy problems to give the student practice in applying the methods to easy optimization problems.

E15.5: The last part was contributed by J. Spall and is not trivial, but is quite interesting. You might want to see his recent book on SPSA and other related topics to learn more.

DP15.1: I want to emphasize the limitations of this approach to design! What are they? What are the problems with the approach when it comes to higher-dimensional problems (i.e., when there are many parameters to tune)?

Chapter 16:

DP16.5: These are difficult problems; however, they will lead the reader to understand the advantages and disadvantages of RSM.

DP16.8: This was not intended to be a well-formulated problem. It was only intended to move the reader in a general direction. I know of no work at the time of the publication of this book that addresses the points that I raise in this problem.

Chapter 18:

E18.3: For part (c) you need to add some nonlinearities to the ODE so that its solution better matches Seeley's data. Focus on simply doing better than what their ODE model did for the data that the compared to. However, keep in mind that this model then only matches one set of experimental conditions.

DP18.1: One approach to this problem is to simply add other effects, while another is to really try to match the experiments shown in the literature. To do this problem in a complete way would involve getting a microbiologist involved to verify your model/simulations.

DP18.2: This is currently an active area of research. Simulation methods based on PDEs and cellular automata have been used.

DP18.4: This is a problem that integrates foraging approaches into adaptive control so this problem integrates ideas from Parts III and V.

DP18.7: This is a theoretically challenging problem, but it does have solutions.

DP18.8: One could use the current literature to produce simulations that are reasonable, but verifying the simulations against actual biological experiments would be very challenging. As of the writing of this book that has not been completed.

DP18.9: This is a fun toy problem that is illustrative of some swarming principles.

DP18.10: Well, this problem is very challenging, but its solution is of interest in a wide variety of areas (e.g. physics, chemistry, and biology).

DP18.11: In our Distributed Dynamical Systems laboratory I had a group of undergraduates construct these circuits, simulate the fireflies, and it works quite well. The mathematical analysis is a topic of current research. At the time of the publication of this book new results were still appearing.

Additional problems: This is an active area of research. For more problems in this area see the papers on swarms and foraging in my list of publications; many of those papers could be used for teaching or additional problems.

Chapter 19:

DP19.2: This is a fun problem, really. There has been a significant amount of work done on extensions to this area of research, in biology, economics, and mathematics.

DP19.4, DP19.5: These challenge problems are for trying to integrate methods from earlier parts of the book into the framework of Part V to achieve intelligent and social foraging. These problems are not well-formulated; however, if you really understood earlier parts of the book you will easily see problems to study and solutions. These problems should be viewed as "capstone design" experiences for the topics of the book. They could serve very nicely as final projects for a class.

Last updated: 9/10/04