Velocity-based Methods for Divide and Conquer Analysis and Design of Nonlinear Systems

 

 

A linear system (the 'velocity-based linearisation') is associated with every operating point of a nonlinear system (not just the equilibrium points).   A family of velocity-based linearisations is therefore associated with the nonlinear system.  This family embodies the entire dynamics of the nonlinear system and so is an alternative representation.  It is emphasised that this representation is valid globally and does not involve any restriction to the vicinity of the equilibrium points.  Large transients and sustained non-equilibrium operation can both be accommodated. 

 

More on this topic.

 

 

Bibliography on Velocity-based Methods and Applications

 

 

1996

 

D. J. Leith, W. E. Leithead.

Appropriate Realisation of Gain-Scheduled Controllers with Application of Wind Turbine Regulation.

International Journal of Control, Volume 65, Issue 2, 1996, Pages 223-248.

 

D. J. Leith, W. E. Leithead.

Can an appropriate gain-scheduling realisation enhance performance?
UKACC International Conference on Control‘96, (Conf. Publ. No. 427), Volume 1, 1996, Page: 563 - 568

 

 

1997

 

D. J. Leith, W. E. Leithead.

Implementation of Wind Turbine Controllers.

International Journal of Control, Volume 66, Issue 3, 1997, Pages 349-380.

 

D. J. Leith, W. E. Leithead.

Analysis of gain-scheduled and nonlinear systems by velocity-based linearisation families.
Proceedings of the 36th IEEE Conference on Decision and Control, 1997, Volume 1,  1997,  Pages: 424 – 429.

 

D. J. Leith, W. E. Leithead.

Equivalence of gain-scheduling and input-output linearisation for a class of commonly occurring plants.
Proceedings of the 36th IEEE Conference on Decision and Control, 1997, Volume 1,  1997,  Pages: 430 – 431.

 

1998

 

D. J. Leith, W. E. Leithead.

Appropriate Realisation of MIMO Gain-Scheduled Controllers. 

International Journal of Control, Volume 70, Issue 1, 1998, Pages 13-50.

 

D. J. Leith, W. E. Leithead.

Gain-Scheduled Controller Design: An Analytic Framework Directly Incorporating Non-Equilibrium Plant Dynamics.

International Journal of Control, Volume 70, Issue 2, 1998, Pages 249-269.

 

D. J. Leith, W. E. Leithead.

Gain Scheduled and Nonlinear Systems: Dynamic Analysis by Velocity-Based Linearisation Families.

International Journal of Control, Volume 70, Issue 2, 1998, Pages 289-317.

 

 

D. J. Leith, W. E. Leithead.

Comments on Gain Scheduling Dynamic Linear Controllers for a Nonlinear Plant + Response.

Automatica, Volume 34, Issue 8, 1998, Pages 1041-1043.

 

D. J. Leith, W. E. Leithead.

Towards a theory of local model networks and blended multiple model systems.
UKACC International Conference on Control '98. (Conf. Publ. No. 455)
Volume 1,  1998,  Page: 509 - 514

 

D. J. Leith, W. E. Leithead.

On incorporating non-equilibrium plant dynamics into gain-scheduling design.
UKACC International Conference on Control '98. (Conf. Publ. No. 455)
Volume 1,  1998,  Page: 816 - 821

 

D. J. Leith, W. E. Leithead.

The importance of implementation issues in achieving control goals.
IEE Colloquium on Integrated Systems in Aerospace (Digest No: 1997/015), 1997, Pages: 7/1 - 7/3

 

 

1999

 

J. Kocijan,  D. J.  Murray-Smith.

Robust nonlinear control for ship steering.

N. E. Mastorakis (edt.)., Progress in simulation, modeling, analysis and synthesis of modern electrical and electronic devices and systems. World Scientific and Engineering Society Press, 1999, Pages. 235-240.

 

D. J. Leith, W. E. Leithead.

On microprocessor-based arc voltage control for gas tungsten arc welding using gain scheduling.
IEEE Transactions on Control Systems Technology,  Volume 7,  Issue 6,  1999,  Pages: 718 - 723

 

D. J. Leith, W. E. Leithead.

Input-Output Linearisation by Velocity-Based Gain-Scheduling.

International Journal of Control, Volume 72, Issue 3, 1999, Pages 229-246.

 

D. J. Leith, W. E. Leithead.

Analytic Framework for Blended Multiple Model Systems Using Linear Local Models. International Journal of Control, Volume 72, Issue 7, 1999, Pages 605-619.

 

D. J. Leith, W. E. Leithead.

Global Gain-Scheduling Control for Variable Speed Wind Turbines.

Proceedings of European Wind Energy Conference  EWEC’99, Nice, France, 1999.

 

D. J. Leith, W. E. Leithead, F., Hardan, H. Markou,

Direct Regulation of Large Speed Excursions for Variable Speed Wind Turbines.

Proceedings of European Wind Energy Conference  EWEC’99, Nice, France, 1999, Pages: 857-860.

 

 

2000

 

R. Gao, A. O’Dwyer, S. McLoone, E. Coyle.

Velocity-based multiple model networks in the discrete time domain.

Proceedings of Controlo 2000: 4th Portuguese Conference on Automatic Control, Guimaraes, Portugal, 2000, 6 pages.

 

J. Kocijan, N. Hvala, S. Strmčnik.

Multi-model control of wastewater treatment reactor.

N. Mastorakis (edt.). System and control : theory and applications, (Electrical and computer engineering series). World Scientific and Engineering Society, 2000, Pages 49-54.

 

J. Kocijan, D. Vrančić.

Multiple blended controller design for bilinear systems.

I. J. Rudas (edt.), J. K. Tar  (edt.). Preprints of IFAC Symposium on Artificial Intelligence in Real Time Control, AIRTC-2000, October 2-4, 2000, Budapest, Hungary.  Budapest: Budapest Polytechnic, 2000, Pages 187-192.

 

J. Kocijan, G. Žunič, D. Vrančić.

Fuzzy gain-scheduling control of gas-liquid separation plant.

5th On-line World Conference on Soft Computing in Industrial Applications WSC5, September 4-18, 2000, Helsinki University of Technology, Cranfield University, Nagoya University. 2000, 8 pages.

 

D. J. Leith, W. E. Leithead.

An Example of the Possible InStability of Local Controller Networks/Takagi-Sugeno Fuzzy Controllers.

I. J. Rudas (edt.), J. K. Tar  (edt.). Preprints of IFAC Symposium on Artificial Intelligence in Real Time Control, AIRTC-2000, October 2-4, 2000, Budapest, Hungary.  Budapest: Budapest Polytechnic, 2000, Pages.

 

D. J. Leith, W. E. Leithead.

Survey of Gain-Scheduling Analysis and Design.

International Journal of Control, Volume 73, Issue 11, 2000, Pages 1001-1025.

 

D. J. Leith, W. E. Leithead.

Gain-Scheduled Control of a Skid-to-Turn Missile: Relaxing Slow Variation Requirements by Velocity-Based Design.

Journal of Guidance, Dynamics and Control, Volume 23, Issue 6, 2000, Pages 988-1000.

 

D. J. Leith, W. E. Leithead.

On formulating nonlinear dynamics in LPV form
Proceedings of the 39th IEEE Conference on Decision and Control, 2000, Volume 4, Sydney, 2000,  Pages: 3526 – 3527.

 

D. J. Leith, W. E. Leithead.

Counter- Example to a common LPV Gain-Scheduling Design Approach.

CD Rom Proc., UKACC Int. Control Conference, Control'2000, 2000, Cambridge.

 

D. J. Leith, W. E. Leithead.

On The Identification of Nonlinear Systems by Combining Identified Linear Models. Proceedings third MathMod Vienna ARGESIM Report No. 15, Volume 1. Vienna, Austria, 2000. Pages: 407– 410.

 

W. E. Leithead, D. J. Leith, and R. Murray-Smith.

A Gaussian Process prior/Velocity-based Framework for Nonlinear Modelling and Control.

In Irish Signals and Systems Conference, Dublin, 2000.

 

S.C. McLoone.
Nonlinear Identification using Local Model Networks.
PhD Thesis, Queen’s University of Belfast, 2000.

 

S.C.  McLoone, G.W. Irwin.
Nonlinear identification using velocity-based local model networks.
CD Rom Proc., UKACC Int. Control Conference, Control'2000, 2000, Cambridge.

 

G. Žunič, D. Vrančić, J. Kocijan.

Nelinearno vodenje ločevalnika plina in tekočine.

B. Zajc (edt.). Zbornik devete Elektrotehniške in računalniške konference ERK 2000, 21. - 23. september 2000, Portorož, Slovenija. Ljubljana: IEEE Region 8, Slovenska sekcija IEEE, 2000, Volume. A, Pages 197-200.

 

 

2001

 

D. J. Leith, W. E. Leithead.

Gain-Scheduled Control of a Skid-to-Turn Missile: Relaxing Slow Variation Requirements by Velocity-Based Design.

Proceedings of the 2001 American Control Conference, Volume 1, Issue , 2001 Pages 500 – 505.

 

D. J. Leith, W. E. Leithead.

Input-Output Linearisation of Nonlinear Systems with Ill-Defined Relative Degree: The Ball and Beam Revisited.

Proceedings of the 2001 American Control Conference, Volume 4,  2001 Pages:2811 – 2816.

 

D. J. Leith, W. E. Leithead.

Velocity-Based Gain-Scheduled Lateral Auto-Pilot For An Agile Missile.

Control Engineering Practice, Volume 9, Issue 10, 2001, Pages 1079-1093.

 

S.C. McLoone, G.W. Irwin.

On nonlinear modelling using velocity-based multiple model networks.

Proceedings of the 2001 American Control Conference, Volume 4,  2001.

 

S.C. McLoone, G.W. Irwin, S.F. McLoone.
Blending local models within a velocity-based multiple model network.
Proc. IFAC Conf. on Emerging Computing Technologies, Hong Kong, Nov. 2001, Pages: 117-122.

 

S.C. McLoone, G.W. Irwin, S.F. McLoone.
Constructing networks of continuous-time velocity-based local models.
IEE Proc.on Control theory and Applications, Volume 148, Issue 5, 2001, Pages: 397-405.

 

A. Tsourdos, D. J. Leith, W. E. Leithead, B. A. White.
A velocity-based framework for the robust stability analysis of dynamic inversion flight controllers.
Proceedings of the A merican Control Conference, 2001, Volume 5,  2001,  Pages: 3341 – 3345

 

 

2002

 

F. Bruzelius, C. Breitholtz, S. Pettersson.

LPV-based gain scheduling technique applied to a turbo fan engine model.

Proceedings of the 2002 International Conference on Control Applications, 2002, Volume 2,  Pages 713 – 718.

 

B. Čokan, J. Kocijan.

Some realisation issue of fuzzy gain-scheduling controllers: a robotic manipulator case study. 

[presented at the 6th On-line World Conference on Soft Computing in Industrial Applications, September 10-24, 2001 on the Internet]. R. Roy (edt.). Soft computing and industry : recent applications. New York: Springer, 2002, Pages 191-199.

 

J. Kocijan, G. Žunič, S. Strmčnik, D. Vrančić.

Fuzzy gain-scheduling control of a gas-liquid separation plant implemented on a PLC.

International Journal of Control, Volume 75, Issue 14, 2002, Pages 1082-1091.

 

D. J. Leith, W. E. Leithead,

Global Reconstruction Of Nonlinear Systems From Families Of Linear Systems.

Preprints of the 15th Triennial World Congress of the IFAC, Barcelona, 2002, 6 pages.

 

S.C. McLoone, G.W. Irwin, S.F. McLoone.

On Gaussian Weighting Functions For Velocity-Based Local Model Networks.

Irish Signals and Systems Conference, Cork, 24th-26th June 2002, Pages: 135-140.

 

S.C. McLoone, S. McGinnity,  G.W. Irwin.

Comparison of two construction algorithms for local model networks.

International Journal of Systems Science, Volume 33, Number 13, 2002 , Pages: 1059-1072.

 

R. H. Nyström,  B. M. Åkesson, H. T. Toivonen.

Gain-Scheduling Controllers Based on Velocity-Form Linear Parameter-Varying Models Applied to an Example Process.

Ind. Eng. Chem. Res. Volume 41, 2002, Pages: 220-229.

 

S. Peršin, B. Tovornik, N. Muškinja.

Detekcija napake na pretočnem grelniku s pomočjo hitrostne linearizacije.

Zbornik enajste mednarodne Elektrotehniške in računalniške konference ERK 2002, Portorož, Volume A, Pages. 311-314.

 

Q. Rong, S. McLoone, G. W. Irwin.

On hidden coupling in multiple model based PID controller networks.

Preprints of the 15th Triennial World Congress of the IFAC, Barcelona, 2002, 6 pages.

 

 

2003

 

M. Halas, M. Huba, K. Žakova.

The exact velocity linearization method.

Proceedings of IFAC Conference Control Systems Design '03, Bratislava, 2003, 7 pages.

 

D. J. Leith, W. E. Leithead.

Necessary and Sufficient Conditions for the Minimal State-Space Realisation of Nonlinear Systems from Input-Output Information.

Proceedings of the 2003 American Control Conference, Volume 4,  2003, Pages 2937 – 2942.

 

S.C. McLoone, G.W. Irwin.

On velocity-based local model networks for nonlinear identification.

Asian Journal of Control, Volume 5, Issue 2, 2003,  Pages: 309-315.

 

 

H. T. Toivonen.

State-dependent parameter models of non-linear sampled-data systems: a velocity-based linearization approach.

International Journal of Control, Volume 76, Issue 18, 2003, Pages 1823–1832.

 

H. T. Toivonen, K. V. Sandström, R. H. Nyström.

Internal model control of nonlinear systems described by velocity-based linearizations.

Journal of Process Control. Volume 13, Issue 3, 2003, Pages 215-224.

 

 

2004

 

J. L. Diez, J. L. Navarro, A. Sala.

Control por Planificacion de Ganancia con Modelos Borrosos.

Revista Iberoamericana de Automatica e Informatica. Volume 1, Issue 1, 2004, Pages 32-43.

 

R. Gao, A. O’Dwyer, S. McLoone, E. Coyle.

State Feedback Integral Control by Velocity-Based Multiple Model Networks.

Proceedings of the 2004 American Control Conference,  2004, Pages 2039 – 2044.

 

 

2005

 

B. M. Åkesson, H. T. Toivonen.

Identification of Quasi-ARMAX models of nonlinear stochastic sampled-data systems.

Preprints of the 2005 IFAC World Congress, Prague, 2005, 6 pages.

 

B. M. Åkesson, H. T. Toivonen, J. B. Waller, R. H. Nyström.

Neural network approximation of a nonlinear model predictive controller applied to a pH neutralization process.

Computers & Chemical Engineering, Volume 29, Issue 2, 2003, Pages 323–335.

 

S. Persin, B. Tovornik.

Real-time implementation of fault diagnosis to a heat exchanger.

Control engineering practice. Volume 13, Issue 8, 2005, Pages 1061-1069.

 

L. Reberga, D. Henrion, J. Bernussou, F. Vary.

LPV modeling of a turbofan engine.

Preprints of the 2005 IFAC World Congress, Prague, 2005, 6 pages.

 

 

2006

 

B. M. Åkesson, H. T. Toivonen.

State-dependent parameter modelling and identification of stochastic non-linear sampled-data systems.

Journal of Process Control, Volume 16, Issue 8, 2006, Pages 877-886.

 

K. Ažman, J. Kocijan.

An application of Gaussian process models for control design.

International Control Conference (ICC2006) : Glasgow, Scotland, United Kingdom, 30th August to 1st September 2006, 2006, 6 pages.

 

S. Gerkšič,  G. Dolanc, D. Vrančić,  J. Kocijan,  S. Strmčnik, S. Blažič, I. Škrjanc, Z. Marinšek, M. Božiček, A. Stathaki, R. E. King, M. B. Hadjiski, K. Boshnakov.

Advanced control algorithms embedded in a programmable logic controller.

Control engineering practice. Volume 14, Issue 8, 2006, Pages 935-948.

 

 

2007

 

 

G. Bevan, S.J. O'Neill, H. Gollee, J. O'Reilly.

Automatic lateral emergency collision avoidance for a passenger car

International Journal of Control. Volume 80, Issue 11, Pages 1751-1762.

 

G. Bevan, H. Gollee, J. O'Reilly.

Performance comparison of collision avoidance controller designs

2007 IEEE Intelligent Vehicles Symposium, June 2007,  Pages: 468 – 473.

 

J. Kocijan.

Mreže lokalnih modelov in zliti večmodelni sistemi, Načrtovanje vodenja z razvrščanjem ojačenj.

Modeliranje dinamičnih sistemov z umetnimi nevronskimi mrežami in sorodnimi metodami.

Univerza v Novi Gorici, 2007, Pages 51-72. (in Slovene).

 

 

2008

 

A. Santafe-Moros, J. L. Diez, F. Barcelo-Rico, J. M. Gozalvez-Zafrilla.

Modelling, control and optimization of a continuous distillation tower through

fuzzy techniques.

Proceedings of the 17th World Congress IFAC Seoul, Korea, July 6-11, 2008, Pages 7052-7057.

 

 

2009

 

K. Ažman,  J. Kocijan

Fixed-structure Gaussian process model.

International Journal of Systems Science. Volume 40, Issue 12, Pages 1253–1262.

 

K. Ažman,  J. Kocijan

Applications of varying parameters modelling with Gaussian processes.

2nd IFAC International Conference on Intelligent Control Systems and Signal Processing, ICONS 2009,  September 2009, Istanbul, Turkey, 6 pages.

 

 

2010

 

G.-B. Cai,  G.-R. Duan, C.-H. Hu

A velocity-based LPV modeling and control framework for nonlinear tracking.

Proceedings of the 29th Chinese Control Conference, CCC'10 , art. no. 5573337, Pages. 286-291.

 

M. Herrnberger, B. Lohmann.

Nonlinear control design for an active suspension using velocity-based linearisations.

6th IFAC Symposium Advances in Automotive Control, Munich, Germany, July 12-14, 2010, 6 pages.

 

 

2011

 

G.-B. Cai,  G.-R. Duan, C.-H. Hu

A velocity-based LPV modeling and control framework for an airbreathing hypersonic vehicle.

International Journal of Innovative Computing, Information and Control.

Volume 7, Issue 5 A, May 2011, Pages 2269-2281.

 

 

2013

 

Samo Gerkšič,  Gregor Dolanc,  Damir Vrančić,  Juš Kocijan,  Stanko Strmčnik,  Sašo Blažič, Igor Škrjanc,  Zoran Marinšek,  Miha Božiček,  Anna Stathaki, Robert King, Mincho Hadjiski, Kosta Boshnakov

A PLC-based system for advanced control.

In: Case Studies in Control, Eds: Stanko Strmčnik, Đani Juričić, Springer London, 2013, Pages 327-361.

 

J. Kocijan

The divide-and-conquer method for modelling and control of nonlinear systems: Some important issues concerning its application.

In: Case Studies in Control, Eds: Stanko Strmčnik, Đani Juričić, Springer London, 2013, Pages 101-126.

 

 

2014

 

Qing Wang, Tong Wang, De-long Huo, Chao-yang Dong

Robust LPV control for morphing vehicles via velocity-based linearization

Systems Engineering and Electronics, Volume 36, Issue 6, 2014, Pages 1130 – 1136.

 

 

2016

 

H.A. Bashar

Meta-Modelling of Intensive Computational Models.

PhD Thesis, University of Sheffield, 2016.

 

Peter Gaspar, Zoltan Szabo, Jozsef Bokor, Balazs Nemeth

Robust Control Design for Active Driver Assistance Systems: A Linear-Parameter-Varying Approach.

Springer International Publishing, Switzerland 2017.

 

J. Kocijan

Incorporation of Prior Knowledge

In: Juš Kocijan, Modeling and Control of Dynamic Systems Using Gaussian Process Models, Springer International Publishing, Cham, 2016, Pages 103-146.

 

J. Kocijan

Control with GP Models

In: Juš Kocijan, Modeling and Control of Dynamic Systems Using Gaussian Process Models, Springer International Publishing, Cham, 2016, Pages 147-208.

 

Xiaofeng Liu, Naiyu Xue

An improved hybrid Kalman filter design for aircraft engine based on a velocity-based LPV framework.

28th Chinese Control and Decision Conference (CCDC), 2016, Pages 1873-1878.

 

Mateus Paresqui Berruezo

Projeto de Controladores para Sistemas Não Lineares via Técnicas Baseadas em Escalonamento de Ganhos

M.Sc. Thesis, Universidade Federal de Minas Gerais, Belo Horizonte, 2016.

 

 

2017

 

Ahmed Adebowale Adeniran, Sami El Ferik

Modeling and Identification of Nonlinear Systems: A Review of the Multimodel Approach—Part 1

IEEE Transactions On Systems, Man, And Cybernetics: Systems, Volume ?, Number ?, 2017.

 

Boyi Chen, Yanbin Liu, Hao Lei, Haidong Shen, Yuping Lu

Ascent Trajectory Tracking For An Air-Breathing Hypersonic Vehicle With Guardian Maps

International Journal of Advanced Robotic Systems, May-June 2017, Pages 1–11

 

 

 

 

 

 

Software support for Velocity-based methods and applications

 

Matlab Velocity-based gain-scheduling demo

 

 

E-mail:  jus[dot]kocijan[at]ijs[dot]si