Control Theory: MATH4406 / MATH7406

Teaching Staff: Yoni Nazarathy (coordinator), Artem Pulemotov (lecturer – units 6 to 10), Tim Brereton (tutor)

This is the 2012 course web-site.
The current course web-site (2016) is here.

Overview:

This is an 11 part course designed to introduce several aspects of mathematical control theory as well as some aspects of control in engineering to mathematically mature students. This web-page contains a detailed plan of the course as well as links to home work (HW) assignments and other resources. The course profile page, available to UQ students can be accessed through here.

Some HW assignments may require computation. In that case, MATLAB is a natural tool for control theory, yet other software packages may be used as well (see software).

Student: Do not let the long book list below intimidate you. It is simply serves as to give you an indication of what resources you may want to use as supplementary material and/or material for future research and/or practical work. The books vary greatly in style and level of rigour – some are mathematical books, while others were designed to serve analytic engineers.

Books:

· [AntMich07] Antsaklis PJ, Michel AN. A Linear Systems Primer. Boston, Mass: Birkhäuser Boston; 2007.   UQ Library link (online).

· [AntMich06] Antsaklis PJ, Michel AN. Linear Systems Boston, Mass: Birkhäuser Boston; 2006 .UQ Library link (online).

· [Ber00] Bertsekas DP. Dynamic Programming and Optimal Control. Vol 1. And Vol 2. Belmont, Mass: Athena Scientific; 2000.   UQ Library link.

· [Cha10] Chaparro L. Signals and Systems using MATLAB. Burlington: Elsevier Science; 2010.   UQ Library link (online).

· [Eng05] Engelberg S. A Mathematical Introduction to Control Theory. Vol 2. London: Imperial College Press; 2005.   UQ Library link.

· [FraEmaPow10] Franklin GF, Emami-Naeini A, Powell JD. Feedback Control of Dynamic Systems. Upper Saddle River [N.J.]: Pearson; 2010.   UQ Library link.

· [Fri86] Friedland B. Control System Design: An Introduction to State-Space Methods. New York: McGraw-Hill; 1986.   UQ Library link.

· [HwaBrow97] Hwang PYC, Brown RG. Introduction to Random Signals and Applied Kalman Filtering: With MATLAB Exercises and Solutions. New York: Wiley; 1997.   UQ Library link.

· [KamHec00] Kamen EW, Heck BS. Fundamentals of Signals and Systems using the Web and MATLAB. Upper Saddle River, N.J: Prentice Hall; 2000.   UQ Library link.

· [Kir70] Kirk DE. Optimal Control Theory: An Introduction. Englewood Cliffs, N.J: Prentice-Hall; 1970.   UQ Library link.

· [KwaSiv91] Kwakernaak H, Sivan R, Modern Signals and Systems. UQ Library link

· [Lue79] Luenberger DG. Introduction to Dynamic Systems: Theory, Models, and Applications. New York: Wiley; 1979.   UQ Library link.

· [Mes09] Mesterton-Gibbons M. A Primer on the Calculus of Variations and Optimal Control Theory. Vol 50. Providence, R.I: American Mathematical Society; 2009.   UQ Library link.

· [MooAnd89] Moore JB, Anderson BDO. Optimal Control: Linear Quadratic Methods. Englewood Cliffs, N.J: Prentice Hall; 1989.   UQ Library link.

· [NawOppWil97] Nawab SH, Oppenheim AV, Willsky AS. Signals & Systems. Upper Saddle River, N.J: Prentice Hall; 1997.   UQ Library link .

· [PerMar10] Albertos Pérez P, Mareels I. Feedback and Control for Everyone. Berlin: Springer Berlin Heidelberg; 2010.   UQ Library link (online).

· [PolWil98] Jan Willem Polderman, Jan C. Willems, Introduction to Mathematical Systems Theory. Vol 26. New York; Berlin: Springer-Verlag; 1998. UQ Library link.

· [SivKwa72] Sivan R, Kwakernaak H. Linear Optimal Control Systems. New York: Wiley Interscience; 1972.   UQ Library link On-line through IEEE

· [Son90] Sontag ED. Mathematical Control Theory: Deterministic Finite Dimensional Systems. Vol 6. New York ; Berlin: Springer-Verlag; 1990.   UQ Library link.

· [You69] Young LC. Lectures on the Calculus of Variations and Optimal Control Theory. Philadelphia: Saunders; 1969.   UQ Library link.

Schedule:

· The course is split up into 11 parts, where some parts build upon others where as some parts are “stand alone”.

· There are 13 weeks and 4 hourly meetings per week, they are referenced as x.y, where x is in {1,…,13} and y is in {1,2,3,4}. Note that parts are NOT directly mapped to weeks. It is often that the HW and/or quiz associated with a part, is handled a few weeks later. Due to PUBLIC HOLIDAY, meetings 10.1 and 10.2 are not taking place.

· There are 4 in class quizzes (45 min each), 7 HW assignments and an additional assignment “course summary” assignment.

· Meetings of the form x.4 are typically (but not always) tutorial meetings where students may either ask questions about the HW or participate in a quiz.

· The teaching format varies based on the material and the speed and depth in which it is to be covered.

Part	Teaching Format and Key Resources	Outline	Lecture Meetings	HW/Quiz Meetings	Home Assignments	Quizzes	Relevant Literature	Comments and Additional Resources
1	Presentation (2h) SlidesUnit1.pdf	Introduction: “Control Theory” defined. The various aspects of control are be outlined.	1.1, 1.2	-	-	-	[PerMar10] Ch1, Ch2, Ch3, Ch11 [FraEmaPow10] Ch1 [Son91] Ch1	Note: The “tutorial” class is taking place on week 1!!! You Tube Watt's fly ball governor WolframDemo: InvertedPendulumControls
2	Lecture Notes + Board (4h) Part2_v20120808.pdf Photos_1_3and1_4.pdf Photos_2_1and2_2.pdf	SISO Linear Systems and Math Background: This is essentially a crash course covering the essentials of an engineering “Signals and Systems” course as well as related applied math background dealing with integral transforms, convolutions and generalized functions.	1.3, 1.4, 2.1, 2.2	2.4 (HW1), 3.4 (HW1)	HW1.pdf Example solutions by students (as most things on this web-page – perhaps not 100% perfect – but very very good): HW1_LukeMarshallSolution.pdf HW1_MitchGoodingSolution.pdf	Quiz1prep.pdf Quiz1.pdf Quiz1Solution.pdf	[FraEmaPow10] Ch3 [Eng05] Ch1, Ch2 [KwaSiv91] All book [NawOppWil97] All book [Cha10] All book [KamHec00] All book	Related on-line lectures from Stanford
3	Presentation (4h) SlidesUnit3.pdf Photos_2_3.pdf Photos_3_1and3_2.pdf Photos_3_3.pdf NyquistExample.nb	Elements of “Classic” Engineering Control. The objectives facing control engineers are taught together with an illustration of PID controllers as well as the Nyquist stability criterion.	2.3, 3.1, 3.2, 3.3,	4.4 (HW2), 5.4 (Quiz1)	HW2.pdf HoaggBernsteinNonMinimumPhaseZero.pdf Example solutions by students (as most things on this web-page – perhaps not 100% perfect – but very very good): HW2_MitchGoodingSolution.pdf HW2_LukeMarshallSolution.pdf		[FraEmaPow10] [Eng05] [KwaSiv91] Ch11 [NawOppWil97] Ch11 [Cha10] Sec 6.3 [KamHec00] Ch10	WolframDemo: SecondOrder WolframDemo: SecondOrder PID Control Systems with Mathematica
4	Lecture Notes + Board (9h) Part4_v20120902.pdf Photos_4_1and4_2.pdf Photos_5_1and5_2.pdf Photos_5_3.pdf Photos_6_1and6_2.pdf Pendulum_inClass_Unit4.nb	Linear State-Space Systems and Control. MIMO Linear Systems are studied together with controllability, observability and their generalizations. State feedback controllers and the Luenberger observers are studied in depth.	4.1, 4.2, 4.3, 5.1, 5.2, 5.3, 6.1, 6.2, 6.3	6.4 (HW3), 7.4 (Quiz2), 8.4 (HW4/HW5),	HW3.pdf, due 10/9 Example solutions by students (as most things on this web-page – perhaps not 100% perfect – but very very good): HW3_MitchGoodingSolution.pdf HW4.pdf due 8/10 (Note: it is recommended to do HW5 first for those who are doing Quiz 3). Example solutions by students (as most things on this web-page – perhaps not 100% perfect – but very very good): HW4_MitchGoodingSolution.pdf	Quiz2.pdf Quiz2Solution.pdf	[Fri86] Ch2, Ch3, Ch4, Ch5, Ch6, Ch7, Ch8 [Lue79] Ch 4, Ch 5, Ch 8 [AntMich07] All book	Stephen Boyd's Introduction to Linear Dynamical Systems Video Lectures are fun and useful background WolframDemo: 2 state system Wolfram Demo: 2nd Order ODE WolframDemo: Phase Portraits
5	Board (3h) Photos_7_1and7_2.pdf Photos_7_3.pdf MarkovChainQueueControl.nb	Lyapunov stability theory. This unit deals with both the notion of linearization about an equilibrium point and (equally or more important) with the notion of Lyapunov functions. There is no “control” in this unit per say.	7.1, 7.2, 7.3	9.4 (Quiz3), 10.4 (HW4/HW5)	Quiz 3 during first hour of 20/9. The best practice for it is HW5!!! HW5.pdf, due 8/10 Example solutions by students (as most things on this web-page – perhaps not 100% perfect – but very very good): HW5_MitchGoodingSolution.pdf HW5_LukeMarshallSolution.pdf	Quiz3.pdf Quiz3Solution.pdf	[Lue79] Ch 9 [PolWil98] Ch7 Bruce Hajek's Notes(book) - see Section 6.9 for Foster Lyapunov of Markov Chains
6	Presentation (3h) SlidesUnit6.pdf Additional MPC-LQR Slides by Erjen Lefeber: ErjenLefeberconstrainedMPC.pdf	Linear Quadratic Regulator (LQR) + LQ-MPC (Model Predictive Control). This unit only presents the results of LQR optimal control problems (without proving). It then introduces the notion of Model Predictive Control and focuses on stability results of MPC problems based on LQR.	8.1, 8.2, 8.3	11.4 (HW6)	HW6.pdf, due 22/10 BemporadMorariDuaPistikopoulos2002.pdf	-	[Fri86] Ch9 [Ber00] [SivKwa72] [MooAnd89]	Wolfram Demo: LQR A highly cited survey paper on MPC
7	Board (3h) 9_1and9_2.pdf No one took photos during 9.3	Dynamic Programming. The Hamilton-Jacobi-Bellman PDE is derived and studied together with examples.	9.1, 9.2, 9.3,	None. 12.4 (HW7)	HW7.pdf, due 9/11.		[Ber00] [Kir70] Part II	Richard Weber's Optimization and Control Course (useful notes in pdf)
8	Board (3h)	The Calculus of Variations and Pontryagin’s Minimum Principle	10.3, 11.1,11.2				[You69] Vol II [Kir70] Part III [Mes09] All book	Wolfram Demo: Moon Landing
9	Board (2h)	LQR proofs - Derivations of the LQR Riccati Results by means of both Dynamic Programming and Pontryagin.	11.3, 12.1				[Ber00] [SivKwa72] [MooAnd89]
10	Lecture Notes + Board (3h) Part10_v20121910.pdf	Linear Quadratic Gaussian (LQG) and Kalman Filtering	12.2, 12.3, 13.1	13.4 (Quiz4)	Quiz 4 during first hour of 25/10.		[Fri86] Ch10, Ch11 [HwaBrow97] [Ber00] [SivKwa72] [MooAnd89]	Link to a full course on this subject (and generalizations) by Nahum Shimkin
11	Presentation (2h) SlidesUnit11.pdf	Summary and outlook to further theory and practice	13.2, 13.3		CourseSummaryAssignment.pdf Course summary due 16/11 Some nice course summaries of students: MitchGoodingSummary.pdf RobinPearceSummary.pdf LukeMarshallSummary.pdf ThomasPlevnikSummary.pdf TinosNitsopoulosSummary.pdf AndrewBarnesSummary.pdf		[PerMar10]	Go Non-Linear: Sontag’s Mathematical Control Theory Book. A workshop to attend...