I think you can start with MATLAB's documentation on nonlinear model predictive control.

Suggested text:1. Control Systems Engineering by Norman Nise 2. Modern Control Engineering by P.N Paraskevopoulos

you can aslo read, Applied Nonlinear Control by Slotine

A good book for nonlinear control is :

Nonlinear Systems by Hassan K. Khalil

but it is not simple. The book that Edi introduced is almost simple.

Finite time stabilization : the main paper in this area is

S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM J. CONTROL OPTIM., vol. 38, no. 3, pp. 751–766, 2000.

another good paper is:

Y. Hong and Z.-P. Jiang, “Finite-Time Stabilization of Nonlinear Systems With Parametric and Dynamic Uncertainties,” IEEE TRANSACTIONS ON AUTOMATIC CONTROL, vol. 51, no. 12, pp. 1950–1956, 2006.

Hi. You are looking for the answer of how to obtain the controller for nonlinear systems. In this context I suggest there are books to design controller based on Adaptive Techniques, Lyapunov Theory, Passivity based control and many more. For this you refer NONLINEAR SYSTEMS, Second Edition by Hassan K. Khalil, Michigan State University , Nonlinear Systems Analysis by M. Vidyasagar, SIAM, 2002, Nonlinear Process Control by Michael A. Henson, and Dale E. Seborg, Prentice Hall, Englewood Cliffs, New Jersey and many more Books.

Method of Localization only.

Hi,

A very good starting point is the book Nonlinear Systems by Hassan K. Khalil.

You will find many examples and courses material on his web pages also.

I think Slotine is a good one to begin studying Nonlinear Control. But, also i can recommend Khalil's Nonlinear Systems Book.

Hi, Have you any system in mind or your question is general?

(1) Lecture Notes and Textbooks on Nonlinear Controller Design

Nonlinear Control Design, Lund University, 2014.

* Exact-linearization

* Lyapunov-based design

* Sliding modes control

Literature: [Khalil, ch.s 13, 14.1,14.2] and [Glad-Ljung,ch.17]

http://www.control.lth.se/media/Education/EngineeringProgram/FRTN05/2014/lec09_2014eight.pdf

[Khalil02] H.K. Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall, 2002.

[GL00] T. Glad and L. Ljung, Control theory : multivariable and nonlinear methods, CRC Press, 2000.

(2) Iterative feedback tuning (IFT) was proposed to tune controller parameters for system with unknown parameters. A linear control model can be used to approximate non-linear system with unknown parameters roughly, and such control plant approximation may exist large deviation from the real non-linear system. IFT was proposed to solve controller tuning issues caused by plant uncertainty. The goal of IFT is similar to Quantitative Feedback Theory proposed by Isaac Horowitz.

http://en.wikipedia.org/wiki/Isaac_Horowitz

H. Hjalmarsson, M. Gevers, S. Gunnarsson, and O. Lequin, "Iterative feedback tuning: theory and applications," IEEE Control Systems Magazine, vol.18, no.4, Aug 1998, pp .26-41,

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=710876

H. Hjalmarsson was elected to the Class of 2013 IEEE fellow last year due to his fundamental contribution to iterative feedback tuning. The key contribution of IFT is tuning controller parameters for those control model (or control plant) whose parameters are difficult to be identified relatively accurately.

By cooperating with his peer researchers including Stanford University researcher, H. Hjalmarsson integrated iterative feedback tuning with PID controller to minimize a given quadratic cost function of the system output error and control effort, thus solving the controller tuning issues caused by plant uncertainty.

WK Ho, Y Hong, A Hansson, H Hjalmarsson, and JW Deng, "Relay auto-tuning of PID controllers using iterative feedback tuning," Automatica 39 (1), January 2003, pp. 149-157. Available from the following RG Link.

https://www.researchgate.net/publication/223504459_Relay_auto-tuning_of_PID_controllers_using_iterative_feedback_tuning

Only PID Control and Smith Predictor were listed in the “Leaders of the Pack” InTech’s 50 most influential industry innovators since 1774. Available from the following link.

http://archive.today/2RoSK 

PID Control was listed twice (the dominant control method in the industrial applications) -- (1) John G. Ziegler and Nathaniel B. Nichols and classical PID Control; (2) Karl Johan Åström and modern PID Control (IEEE Medal of Honor, 1993)

http://en.wikipedia.org/wiki/IEEE_Medal_of_Honor

The next popular method is Smith Predictor: Otto J.M. Smith and Smith Predictor.

http://en.wikipedia.org/wiki/Otto_J._M._Smith

A typical PID tuning procedure: (1) Use relay control to estimate the control model (or control plant); (2) Use Z-N formula to initialize Kp and Ki; (3) use trial and error to adjust Kp and Ki or other method such as iterative feedback tuning (IFT), internal model control (IMC), etc.

W.K. Ho, T.H. Lee, H.P. Han, and Y. Hong, "Self-Tuning IMC-PID Control with Interval Gain and Phase Margin Assignment," IEEE Transactions on Control Systems Technology, 9(3), May 2001, pp. 535-541. Available from the following RG Link.

https://www.researchgate.net/publication/3332273_Self-tuning_IMC-PID_control_with_interval_gain_and_phase_marginsassignment

C.C. Hang, K.J. Astrom, and W.K. Ho, "Refinements of the Ziegler-Nichols tuning formula," IEE Proceedings on Control Theory and Applications, 138(2), March 1991, pp.111-118.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=67610

This paper and selected classic PID tuning methods (co-invented by K.J. Astrom and his student W.K. Ho) have been implemented by Maplesoft Inc. for MapleSim Control Design Toolbox

http://www.maplesoft.com/support/help/MapleSim/view.aspx?path=ControlDesign/GainPhaseMargin

K.J. Åström, T. Hägglund, C.C. Hang, and W.K. Ho, "Automatic tuning and adaptation for PID controllers - a survey," Control Engineering Practice, 1(4), August 1993, pp.699-714.

http://www.sciencedirect.com/science/article/pii/096706619391394C

K.J. Åström, C.C. Hang, P. Persson, and W.K. Ho, "Towards intelligent PID control," Automatica, 28(1), January 1992, pp.1-9.

http://www.sciencedirect.com/science/article/pii/000510989290002W

Control theoretic approaches have been applied to model the interactions between an overloaded SIP server and its upstream servers as a feedback control system in two different scenarios - round trip delay control (IEEE ICC 2011) and redundant retransmission ratio control (IEEE Globecom 2010).

Round-Trip Delay Control (RTDC, implicit SIP overload control) algorithm: Y. Hong, C. Huang, and J. Yan, "Design Of A PI Rate Controller For Mitigating SIP Overload," Proceedings of IEEE ICC, Kyoto, Japan, June 2011.

https://www.researchgate.net/publication/224249824_Design_of_a_PI_Rate_Controller_for_Mitigating_SIP_Overload

RTDC implicit SIP overload control algorithm has been recommended as White Paper by TechRepublic (CBS Interactive)

http://www.techrepublic.com/whitepapers/design-of-a-pi-rate-controller-for-mitigating-sip-overload/25142469

IEEE ICC 2011 presentation slides for RTDC implicit SIP overload control can be downloaded from the following RG link.

https://www.researchgate.net/publication/257945199_Round-Trip_Delay_Control_(RTDC)_For_Mitigating_SIP_Overload_(IEEE_ICC_2011_Slides)

Redundant Retransmission Ratio Control (RRRC, implicit SIP overload control) algorithm: Y. Hong, C. Huang, and J. Yan, "Mitigating SIP Overload Using a Control-Theoretic Approach," Proceedings of IEEE Globecom, Miami, FL, U.S.A, December 2010.

https://www.researchgate.net/publication/221284946_Miigating_SIP_Overload_Using_a_Control-Theoretic_Approach

RRRC implicit SIP overload control algorithm has been quickly adopted by The Central Weather Bureau of Taiwan for their early earthquake warning system.

T.Y. Chi, C.H. Chen, H.C. Chao, and S.Y. Kuo, "An Efficient Earthquake Early Warning Message Delivery Algorithm Using an in Time Control-Theoretic Approach", 2011.

http://link.springer.com/chapter/10.1007%2F978-3-642-23641-9_15#

http://www.ipv6.org.tw/docu/elearning8_2011/1010004798p_3-7.pdf

Short review and comments on this implicit SIP overload control algorithm by former IEEE TAC Associate Editor S. Mascolo: 

L. De Cicco, G. Cofano, and S. Mascolo,"Local SIP Overload Control: Controller Design and Optimization by Extremum Seeking", IEEE Transactions on Control of Network Systems, Vol. 2, Issue 3, September 2015, pp. 267-277.

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7035079 http://c3lab.poliba.it/images/f/f4/Dcm-tcns15.pdf 

IEEE GLOBECOM 2010 presentation slides for RRRC implicit SIP overload control can be downloaded from the following RG link.

https://www.researchgate.net/publication/258555827_Mitigating_SIP_Overload_Using_a_Control-Theoretic_Approach

Journal paper (SIP Overload Control) not only conducts more theoretical analysis of Round trip delay control (RTDC) and Redundant retransmission ratio control (RRRC), but also discusses how to apply RTDC algorithm to mitigate SIP overload for both SIP over UDP and SIP over TCP (with TLS).

Y. Hong, C. Huang, and J. Yan, "Applying control theoretic approach to mitigate SIP overload", Telecommunication Systems, 54(4), 2013, pp. 387-404.

https://www.researchgate.net/publication/257667871_Applying_control_theoretic_approach_to_mitigate_SIP_overload

http://link.springer.com/article/10.1007/s11235-013-9744-8

Survey on SIP overload control algorithms: Y. Hong, C. Huang, and J. Yan, "A Comparative Study of SIP Overload Control Algorithms", IGI Global, 2012, pp. 1-20.

http://www.researchgate.net/publication/231609451_A_Comparative_Study_of_SIP_Overload_Control_Algorithms

http://www.igi-global.com/chapter/comparative-study-sip-overload-control/67496

Open-source SIP/VoIP project discussion archive

http://lists.sip-router.org/pipermail/sr-users/2013-April/077596.html

IETF-RFC "SIP Overload Control" discussion archive

http://www.ietf.org/mail-archive/web/sip-overload/current/msg00919.html

API-RCP(TCP Congestion Control):Y. Hong and O.W.W. Yang, "Design of Adaptive PI Rate Controller for Best-Effort Traffic in the Internet Based on Phase Margin," IEEE Transactions on Parallel and Distributed Systems, 18(4), April 2007, pp. 550-561.

http://www.researchgate.net/publication/3301176_Design_of_Adaptive_PI_Rate_Controller_for_Best-Effort_Traffic_in_the_Internet_Based_on_Phase_Margin

Review, comments, and extensive evaluation on API-RCP:

H. Zhou, C. Hu, and L. He, "Improving the Efficiency and Fairness of eXplicit Control Protocol in Multi-Bottleneck Networks", Elsevier Computer Communications, 36(10-11), June 2013, pp. 1193-1208.

http://www.sciencedirect.com/science/article/pii/S0140366413001059

(3) Control Theory developed in the twentieth century: 25 Seminal Papers (1932-1981) Selected by IEEE Control Society in 2000.

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0780360214,descCd-tableOfContents.html

http://ieeeexplore.com/xpl/bkabstractplus.jsp?bkn=5265919

http://www.ebay.com/itm/Control-Theory-Twenty-Five-Seminal-Papers-1932-1981-New-Book-/400696796391

IEEE Control Systems Award

http://en.wikipedia.org/wiki/IEEE_Control_Systems_Award

IFAC Giorgio Quazza Medal

http://www.ifac-control.org/awards/major-medals

4 co-authors of 25 Seminal Papers (1932-1981) awarded IEEE Medal of Honor (the highest IEEE award): Nyquist(1960), Kalman(1974), Bellman(1979), Astrom(1993).

http://www.ieee.org/about/awards/medals/medalofhonor.html

R.E. Bellman and K.J. Astrom, "On structural identifiability," Mathematical Biosciences, 7(3-4), 1970, pp. 329–339.

http://www.sciencedirect.com/science/article/pii/002555647090132X

Richard E. Bellman Control Heritage Award for US control systems engineers and scientists (US citizenship)

http://a2c2.org/awards/richard-e-bellman-control-heritage-award

Ragazzini's notable students are Rudolf Kalman (see Kalman filters), Eliahu Ibraham Jury (see Z-transform) and Lotfi Asker Zadeh (see Fuzzy sets and Fuzzy logic).

https://en.wikipedia.org/wiki/John_Ragazzini

K. Astrom, E.I. Jury, and R. Agniel, "A numerical method for the evaluation of complex integrals," IEEE Transactions on Automatic Control, vol.15, no.4, Aug 1970, pp.468-471.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1099492

 "To control theorists, Nyquist is no doubt best known as the inventor of the Nyquist diagram, defining the conditions for stability of negative feedback systems. This has become a foundation stone for control theory the world over, applicable in a much wider range of situations than that for which it was orignally enunciated." Hendrik W. Bode, Harvard University, USA, 1977.

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1101666

Biography of Harry Nyquist, University of Cambridge, UK, 2003.

"Between 1920 and 1940 he published a series of papers on research in telecommunications which are arguably the most outstanding set of scientific contributions since Newton (apart from Einstein!)."

http://babylon.acad.cai.cam.ac.uk/students/study/engineering/engineer03l/cenyquist.htm

http://babylon.acad.cai.cam.ac.uk/students/study/engineering/engineer03l/ceframes.htm

K.J. Åström, "Harry Nyquist (1889-1976): A Tribute to the Memory of an Outstanding Scientist," Royal Swedish Academy of Engineering Sciences, 2003.

American Society of Mechanical Engineers (ASME) Nyquist Lecturer Award

https://www.asme.org/about-asme/get-involved/honors-awards/unit-awards/nyquist-lecturer

8 wonderful presentations in control symposium "Paths Ahead in the Science of Information and Decision Systems", Massachusetts Institute of Technology (MIT), USA, November 12 – 14, 2009.

http://paths.lids.mit.edu/papers_mitter.html

Panel on Future Directions in Control, Dynamics, and Systems, Richard M. Murray (chair), California Institute of Technology, April 2002

http://www.cds.caltech.edu/~murray/cdspanel/

R. Murray, K. Astrom, S. Boyd, R. Brockett, and G. Stein, "Future Directions in Control in an Information-Rich World," IEEE Control Systems Magazine, 23(2), April 2003, pp.20-33.

http://www.stanford.edu/~boyd/papers/cds_panel.html

To celebrate the golden anniversary, IFAC Automatica will publish in the 50th volume throughout the year 2014, special survey/overview papers, on selected topics, some tracing the history on some mature topics and areas, others focusing on newly emerging areas, with forecasts into the future. The survey paper published by the 1st issue provides an overview of the developments in the control field from its early days.

K.J. Astrom and P.R. Kumar, "Control: A Perspective," Automatica, 50(1), January 2014, pp. 3-43.

http://www.sciencedirect.com/science/article/pii/S0005109813005037

Article Design of Adaptive PI Rate Controller for Best-Effort Traffi...

Article Self-tuning IMC-PID control with interval gain and phase mar...

Conference Paper Mitigating SIP Overload Using a Control-Theoretic Approach.

Article Relay auto-tuning of PID controllers using iterative feedback tuning

Conference Paper Design of a PI Rate Controller for Mitigating SIP Overload

Article A Comparative Study of SIP Overload Control Algorithms

Article Applying control theoretic approach to mitigate SIP overload

Data Round-Trip Delay Control (RTDC) For Mitigating SIP Overload ...

Data Mitigating SIP Overload Using a Control-Theoretic Approach

a good book for analysing nonlinear control systems is "Nonlinear Systems - H.KHalil 3rd"

a good book for design is "Applied Nonlinear Control Systems - Slotine"

another new good book is "Nonlinear Control Systems - Horacio J.Marquez"

Matlab help is too informative for your work

you can read 1. Applied Nonlinear Control by Slotine

2. Nonlinear Control Systems - Horacio J.Marquez"

The simple techniques for nonlinear controller design are given in brief in "modern control engg.", by D Roy Choudhary

Slotine / Li "Nonlinear Control Systems" will give you a very easily readable introduction.

If memory serves, the book by Khalil is heavy(ier) on mathematics. If you're not afraid of that it is a good one.

problem control engineering is heavy mathematics. You need to be good in maths.

You can read our articles on synthes problem controllers for nolinear nonstationary

objects.

My small revu in attachment.

Please refer to these articles:

https://www.researchgate.net/publication/313576646_From_PID_to_Nonlinear_State_Error_Feedback_Controller

https://www.researchgate.net/publication/312046377_Improved_Sliding_Mode_Nonlinear_Extended_State_Observer_based_Active_Disturbance_Rejection_Control_for_Uncertain_Systems_with_Unknown_Total_Disturbance

https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design

Article From PID to Nonlinear State Error Feedback Controller

Article Improved Sliding Mode Nonlinear Extended State Observer base...

Article On the Improved Nonlinear Tracking Differentiator based Nonl...