Main Publications (journal papers, books)

Books, co-authored and edited books(downloadable erratum and addendum)

Papers (some comments)

Springer-Verlag link to my books

## Main Publications (journal papers, books)

My research mainly focuses on non-smooth dynamical systems (control, analysis, modelling) like mechanical, electrical systems, as well as dissipative dynamical systems. Plus few things on adaptive control of some non-linear systems (a research topic I stopped many years ago). Some of these results belong to Systems and Control (among these, 8 regular papers at IEEE Trans. Automatic Control), others to Mechanics of Solids, few others to Applied Mathematics.

Systems and Control

R. Lozano, B. Brogliato,"Adaptive motion control of flexible joint manipulators", IEEE Transactions on Automatic Control, vol.37, no 2, pp.174-181, February 1992. (regular paper) pdf

B. Brogliato, R. Lozano, "Correction to "Adaptive control of robot manipulators with flexible joints"", IEEE Transactions on Automatic Control, vol.41, no 6, pp.920-922, June 1996. pdf

R. Lozano, B. Brogliato, "Adaptive control of a simple nonlinear system without a priori information on the plant parameters", IEEE Transactions on Automatic Control, vol.37, no 1, pp.30-37, January 1992. (regular paper) pdf

B. Brogliato, R. Ortega, R.Lozano,"Globally stable nonlinear controllers for flexible joint manipulators: a comparative study", Automatica, vol. 31, no 7, July 1995. (regular paper) pdf

B. Brogliato, S. Niculescu, P. Orhant, "On the control of finite-dimensional mechanical systems with unilateral constraints", IEEE Transactions on Automatic Control, vol.42, no 2, pp.200-215, February 1997. (regular paper) pdf

B. Brogliato, A. Zavala-Rio,"On the control of complementary-slackness mechanical juggling systems", IEEE Transactions on Automatic Control, vol.45, no 2, pp.235-246, February 2000. (regular paper) pdf

B. Brogliato, ``Some perspectives on the analysis and control of complementarity systems'', IEEE Transactions on Automatic Control, vol. 48, no 6, pp.918-935, June 2003. (regular paper) pdf

J.C. Avila-Vilchis, B. Brogliato, A. Dzul, R. Lozano,"Nonlinear modelling and control of helicopters", Automatica, vol. 39, no 9, pp.1583-1596, 2003. (regular paper) pdf

D. Goeleven, B. Brogliato, "Stability and instability matrices for linear evolution variational inequalities", IEEE Transactions on Automatic Control, vol.49, no 4, pp.521-534, 2004. (regular paper) pdf

Y. Hurmuzlu, F. Génot, B. Brogliato,"Modelling, stability and control of biped robots -- A general framework", Automatica, vol.40, no 10, pp.1647-1664, 2004. (survey paper) pdf

B. Brogliato, D. Goeleven, "The Krakovskii-LaSalle invariance principle for a class of unilateral dynamical systems", Mathematics of Control, Signals and Systems, vol.17, pp.57-76, 2005. pdf

B. Brogliato, "On the control of nonsmooth complementarity dynamical systems", Philosophical Transactions of the Royal Society series A (Mathematical, Physical and Engineering Sciences), spécial issueNon-smooth Mechanics,(F. Pfeiffer, Ed.), vol.359, no 1789, Issue 15th December 2001.

M. Mata-Jimenez, B. Brogliato,"Analysis of PD and nonlinear control of mechanical systems with dynamic backlash", Journal of Vibrations and Control, special issue in the honour of F. Pfeiffer (F. Vestroni, Ed.) vol.9, no 1-2, pp.119-155, January 2003. pdf

J.M. Bourgeot, B. Brogliato,"Tracking control of complementarity Lagrangian systems", International Journal of Bifurcation and Chaos, special issue on Non-smooth Dynamical Systems, vol.15, no 6, pp.1839-1866, 2005. pdf

M. Heemels, B. Brogliato, "The complementarity class of hybrid dynamical systems", European Journal of Control, vol.9, no 2-3, pp.322-360, 2003. (survey paper)

B. Brogliato, S.I. Niculescu, M. Monteiro-Marques,2000 "On tracking control of a class of complementary-slackness hybrid mechanical systems", Systems and Control Letters, vol.39, no 4, pp.255-266, March.

A. Zavala, B. Brogliato,2001 "Direct adaptive control of a one degree-of-freedom complementary-slackness juggler", Automatica, vol.37, no 7, pp.1117-1123. pdf

B. Brogliato, 2004 "Absolute stability and the Lagrange-Dirichlet theorem with monotone multivalued mappings", Systems and Control Letters, vol.51, pp.343-353, April. pdf

B. Brogliato, 2005 "Some results on the controllability of planar variational inequalities", Systems and Control Letters, vol.54, pp.65-71, January. pdf

S.I. Niculescu, B. Brogliato,"On force measurement time-delay in control of constrained manipulators", European Journal of Control, vol.5, pp.279-289, 1999. (see also an experimental validation by A. Tornambé, same issue, pp.290-292) EJC

A. Zavala-Rio, B. Brogliato,"On the control of a one degree-of-freedom juggling robot", Dynamics and Control, vol.9, pp.67-90, January 1999. pdf

B. Brogliato, I.D. Landau, R. Lozano, "Adaptive motion control of robot manipulators: a unified approach based on passivity", Int. J. of Robust and Nonlinear Control, vol.1, no 3, pp.187-202, July-September 1991. pdf

R. Lozano, B. Brogliato,"Adaptive hybrid force/position control for redundant manipulators", IEEE Trans. on Automatic Control, vol.37, no 10, pp.1501-1505, October 1992. pdf

B. Brogliato, R. Lozano,"Passive least-squares type estimation algorithm for direct adaptive control", Int. J. of Adaptive Control and Signal Processing, vol.6, no 1, pp.35-44, January 1992.

B. Brogliato, A. Trofino, R. Lozano, "Robust adaptive control of a class of first order nonlinear systems", Automatica, vol.28, no 4, pp.795-801, July 1992.

B. Brogliato, A. Trofino, "Practical stabilization of a class of nonlinear systems with partially known uncertainties", Automatica, vol.31, no 1, pp.145-151, January 1995. pdf

B. Brogliato, R. Lozano,"Adaptive control of first order nonlinear systems with reduced knowledge of the plant parameters", IEEE Trans. on Automatic Control, vol.39, no 8, August 1994.

Lozano R., B. Brogliato, I.D. Landau,"Passivity and global stabilization of cascaded nonlinear systems", IEEE Trans. on Automatic Control, vol.37, no 9, September 1992. pdf

B. Brogliato, R. Lozano, I.D. Landau,"New relationships between Lyapunov functions and the passivity theorem", Int. J. of Adaptive Control and Signal Processing, vol.7, pp.353-365, 1993.

C. Canudas, B. Brogliato,"Direct adaptive impedance control", Automatica, vol.33, no 4, pp.643-649, 1997.

B. Brogliato, D. Rey, A. Pastore, J. Barnier,"Experimental comparison of nonlinear controllers for flexible joint manipulators", Int. J. of Robotics Research, vol.17, no 3, pp.260-281, March 1998. ACC1998.pdf IJRR.pdf

B. Brogliato, P. Orhant,"Contact stability analysis of a one degree-of-freedom robot", Dynamics and Control, vol.8, no 1, pp.37-53, January 1998. pdf

L. Villani, C. Canudas, B. Brogliato,"An exponentially stable adaptive force/position controller for robot manipulators", IEEE Transactions on Automatic Control, vol.44, no 4, pp.798-802, 1999.

B. Brogliato, M. Mabrouk, A. Zavala Rio,2006 "A controllability criterion for linear juggling mechanical systems", Systems and Control Letters, vol.55, no 4, pp.350-367, April pdf

B. Brogliato, 2007 "Comment on "Control of a planar underactuated biped on a complete walking cycle"", IEEE Transactions on Automatic Control, vol. 52, no 5, May. pdf

B. Brogliato, R. Lozano, B. Maschke, O. Egeland, Dissipative Systems Analysis and Control, Springer London, second edition, 2007.

B. Brogliato, 2008 "Some results on optimal control with unilateral constraints", Nonlinear Analysis: Theory, Methods and Applications, vol.70, 15 May, pp.3626-3657, 2009. preliminary version

V. Acary, B. Brogliato, "Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems", Systems and Control Letters, vol.59, pp.284-293, 2010. preliminary version

V. Acary, B. Brogliato, Y. Orlov, "Chattering-free digital sliding-mode control with state observer and disturbance rejection", IEEE Transactions on Automatic Control, vol.57, no 5, pp.1087-1101, 2012. (regular paper) preliminary version

B. Wang, B. Brogliato, V. Acary, A. Boubakir, F. Plestan , "Experimental comparisons between implicit and explicit implementations of discrete-time sliding mode controllers: towards input and output chattering suppression", November 2013, submitted. preliminary version

Mechanics, Dynamics, Numerical Simulation, Analysis

F. Génot, B.Brogliato,"New results on Painlevé paradoxes", European Journal of Mechanics A/Solids, vol.18, pp.653-678, 1999. F. Génot PhD thesis (ps)"Periodic motion and bifurcations induced by the Painlevé paradox", European Journal of Mechanics A/Solids, 2002, vol. 21, no 5, pp.869-896.

R. Leine, B. Brogliato, H. Nijmeijer,

D. Goeleven, B. Brogliato, "Necessary conditions of asymptotic stability for unilateral dynamical systems", Nonlinear Analysis, vol.61, no 6, pp.961-1004, 2005 (45 pages). pdf

B. Brogliato, A.A. ten Dam, L. Paoli, F. Génot, M. Abadie,"Numerical simulation of finite dimensional multibody nonsmooth mechanical systems", ASME Applied Mechanics Reviews, vol.55, no 2, March 2002, pp.107-150. (J. Telega, Ed.). (survey paper) ASME-AMR

B. Brogliato Nonsmooth Mechanics, second edition, Springer London, 1999. Nonsmooth Mechanics (Springer London)

B. Brogliato (Editor), Impacts in Mechanical Systems. Analysis and Modeling, Springer Verlag, Berlin, Lecture Notes in Physics, vol.551.

B. Brogliato, A. Daniilidis, C. Lemaréchal, V. Acary, 2006 "On the equivalence between complementarity systems, projected systems and unilateral differential inclusions", Systems and Control Letters, vol.55, no 1, pp.45-51, January. pdf

K. Addi, S. Adly, B. Brogliato, D. Goeleven, 2007 "A method using the approach of Moreau and Panagiotopoulos for the mathematical formulation of non-regular circuits in electronics", Nonlinear Analysis: Hybrid Systems, vol.1, no 1, pp.30-43.

V. Acary, B. Brogliato, D. Goeleven, 2008 "Higher order Moreau's sweeping process: Mathematical formulation and numerical simulation", Mathematical Programming Ser. A, vol.113, no 1, pp.133-217, May (85 pages). pdf

V. Acary, B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics. Springer Heidelberg, Lecture Notes in Applied and Computational Mechanics, vol.35, 2008. Numerical Methods, Springer's site

C. Liu, Z. Zhao, B. Brogliato, "Frictionless multiple impacts in multibody systems: Part I. Theoretical framework", Proceedings of the Royal Society A (Mathematical, Physical and Engineering Sciences), vol.464, no 2100, pp.3193-3211, December 2008. preliminary version

C. Liu, Z. Zhen, B. Brogliato, "Frictionless multiple impacts in multibody systems: Part II. Numerical algorithm and simulation results", Proceedings of the Royal Society A (Mathematical, Physical and Engineering Sciences), vol.465, no 2101, pp.1-23, January 2009.

C. Liu, Z. Zhao, B. Brogliato, "Energy dissipation and dispersion effects in a granular media", Physical Review E, vol.78, no 3, 031307, September 2008. pdf

Z. Zhao, C. Liu, B. Brogliato, "Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations", Proceedings of the Royal Society A, Mathematical, Physical and Engineering Sciences, vol.465, no 2107, pp. 2267-2292, July. pdf

B. Brogliato, "Inertial couplings between unilateral and bilateral holonomic constraints in frictionless Lagrangian systems", Multibody System Dynamics, vol.29, no 3, pp.289-325, March 2013, DOI: 10.1007/s11044-012-9317-8. pdf

B. Brogliato, H. Zhang, C. Liu, "Analysis of a generalized kinematic impact law for multibody-multicontact systems, with application to the planar rocking block and chains of balls", Multibody System Dynamics, vol.27, no 3, pp.351-382, March 2012. (NB: Proposition 1 in this paper is wrong. For a correction see the book with Nguyen, or my paper "Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction" pdf

B. Brogliato, "Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction", Multibody System Dynamics, DOI: 10.1007/s11044-013-9392-5 pdf

H. Zhang, B. Brogliato, C. Liu, "Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data", Multibody System Dynamics, DOI: 10.1007/s11044-013-9356-9 preliminary version1.pdf preliminary version2.pdf preliminary version3.pdf

H. Zhang, B. Brogliato, C. Liu, "Study of the planar rocking-block dynamics with Coulomb friction: Critical kinetic angles", ASME Journal of Computational and Nonlinear Dynamics, vol.8, no 2, 021002, April 2013, http://dx.doi.org/10.1115/1.4007056. preliminary version.pdf

C. Liu, H. Zhang, Z. Zhen, B. Brogliato, "Impact/contact dynamics in a disk-ball system", Proceedings of the Royal Society A, Mathematical, Physical and Engineering Sciences, vol.469, 20120741, April 2013, doi:10.1098/rspa.2012.0741. pdf

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I authored and co-authored five monographs: one on nonsmooth mechanics, one on dissipative systems, one dedicated to numerical methods for nonsmooth dynamical systems (mainly mechanical systems), one devoted to the numerical simulation of nonsmooth electrical circuits, and the last one is about multiple impact modeling in dissipative granular chains.

•V. Acary, B. Brogliato,Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics. Springer Verlag Berlin Heidelberg, Lecture Notes in Applied and Computational Mechanics, vol.35, 2008. Erratum.ps Erratum.pdf Electronic version Springer web page

"This monograph is a valuable and concise contribution to the numerics of nonsmooth ODEs with an up-to-date reference list of 27 pages. It is clearly designed for engineering applications in computational mechanics, and the main concern is the discussion of the construction of algorithms and their properties...many parts are written in a formal mathematical style with precise definitions, followed by results stated as Lemma, Proposition, or Theorem (and references to the literature for the proofs). This makes the overall work accessible for both, researchers in mechanics and in mathematics." (C. Wieners, ZAMM-Journal of Applied Mathematics and Mechanics, vol.88, no 7, p.572, 2008) complete review

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•B. Brogliato,Nonsmooth Mechanics, Springer Verlag London, second edition, 552 + xx pages, 1999.

Addendum: ps pdf Springer web page

(first edition:B. Brogliato,Nonsmooth Impact Mechanics. Models, Dynamics and Control,1996, Springer-Verlag, Lecture Notes in Control and Information Sciences 220, 400 + xv pages)

About the first edition:

"This monograph ... is well-written and is a rich source of information on the subject treated. Even people working on the impact of deformable bodies can benefit considerably from this book.... The book is self-contained.... Reading this monograph, the reader will have a better understanding of the reality: the dynamics of systems with unilateral constraints is a difficult subject which requires very modern mathematical tools to be well understood..... The book is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers" (P.D. Panagiotopoulos, Mathematical Reviews, June 1998, issue 98f, p.3893)

"The book deals with very important phenomena in engineering and other fields of applied science, namely dynamical phenomena with impacts... To develop such a theory is the main aim of this book which focusses on the mathematical aspects in a very competent and comprehensive way.... The presentation is excellent in combining rigorous mathematics with a great number of examples ranging from simple mechanical systems to robotic systems.... The book can be strongly recommended to engineers wishing to better understand the mathematical background of impacting systems, and to applied mathematicians who will still find a great number of open mathematical questions to be attacked in the future." (H. Troger, Zentralblatt Mathematik, 861, pp.488)

"the reader is again referred to the excellent book of Brogliato.", in D. Stewart, SIAM Review, vol.42, no 1, pp.3-39, 2000.

"one may refer especially to [Brogliato 1996], where nonsmooth mechanical problems are very well introduced to the non-expert reader", in M. Kunze, M. Marques, Impacts in Mechanical Systems, Lecture Notes in Physics 551, Springer 2000.

"for an excellent review of the subject, see Brogliato (1996)", in Cortès et al, Proc. Royal Soc. London A, 2001, pp.651-670.

About the second edition:

"Nonsmooth mechanics is the study of classical mechanics, i.e., the mechanics of particles and rigid bodies moving subject to Newton's and Euler's laws, where one allows occurrences of impacts and other instantaneous changes in the dynamical behaviour of a system. This book is a survey of this intricate subject..... also points out an interesting connection between variational methods for systems with unilateral constraints and the Pontryagin maximum principle... certainly many readers will be quite comfortable with the style of presentation.... I think it is a very useful contribution to the literature. The book's two best features, in my view, are (1) its detailed survey of the literature (there are over 1000 items in the bibliography) and (2) its detailed presentation of many examples illustrating both the techniques and their limitations. I also like the way the book makes contact between the main subject matter, and other topics that are not obviously related. For readers interested in the field, this book will serve as an excellent introductory survey". (A.D. Lewis, Automatica, vol.41, pp.1105-1108, June 2005)

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•B. Brogliato, R. Lozano, B. Maschke,O. EgelandDissipative Systems Analysis and Control. Theory and Applications. Springer Verlag London, second edition, 576 + xiv pages, 2007.

Addendum: Addendum_Erratum.ps Addendum_Erratum.pdf Springer web page

(first edition:R. Lozano, B. Brogliato, O. Egeland, B. Maschke,2000Dissipative Systems Analysis and Control. Theory and Applications, Springer Verlag, Communications and Control Engineering Series)

About the first edition:

"The current text is a recent contribution to this growing body of literature. The book provides an extensive exposition of both mathematics, physics motivations and control applications of passivity and dissipativity....the richness of a very impressive inventory of illustrating examples stands out as a point of excellence.... Also outstanding is the large number of journal article results (as compared with basic textbooks style facts) and inventory of methods contained and, indeed, elaborated in detail in the book..." (G. Tadmor, Automatica, vol.41, pp.177-179, 2005)

"The book... is a unique monograph on characterizations of dissipative dynamic systems and control design for such systems...The book presents a comprehensive and rigorous coverage of dissipative systems theory, passivity-based feedback control designs...including a collection of interesting experimental results.... The contents of this book is very rich in terms of both theoretical results and practical considerations, its analysis very rigorous, and its presentation very clear. It is an excellent reference for graduate students, engineers and researchers." (G. Tao, Int. Journal of Adaptive Control and Signal Processing, vol.18, pp.423-426, 2004)

"The book excellently combines the theoretical outline including mathematical foundations with lots of elaborate examples. There is almost no concept or consideration which is not illustrated by some calculation for a given system. This is the real strength of this monograph... The solutions found by the authors are very instructive for readers interested in applications.. In summary, this book is really to be recommended to those who seek a sound, well written and far reaching introduction." (H. Kantz, IoP Electronic Journals, Measurement Science and Tehcnology, vol.12, December 2001, 2211; http://www.iop.org/EJ/abstract/0957-0233/12/12/70 )

"The monograph is a self contained advanced introduction to the theory which is consistently supplied with numerous physical examples... It will be suitable for graduate students interested in the control of linear and nonlinear systems as well as for researchers and practicing control engineers who are interested in applying this theory in their applications". (L. Bakule, Zentralblatt Mathematik, 0958.93002, 2003)

About the second edition:

"The main value of the book is that it is an up to date reference of dissipative systems in the framework of many system description. It is a good roadmap to the many contributions on the subject.... the book is a good reference for dissipative systems for advanced engineering students and researchers in control...is to be recommended for its vast amount of up to date information and indications to the literature." (F.M. Callier, IEEE Transactions on Automatic Control, July 2007)

"The monograph under review gives a comprehensive mathematical introduction to the analysis and control of systems with dissipative properties The book concludes with an appendix summarizing essential mathematical background material and a rather comprehensive bibliography containing over 500 references In summary, this book is a highly readable, authoritative, and comprehensive introduction to the theory of dissipative input-output systems. The authors make regular and recurring references to physical examples so as to effectively motivate the material." Mathematical Reviews 2007k (Reviewer: Kevin A. Grasse)

"This book is focused to the development of direct Lyapunov method using input-output properties of controlled complex systems. The investigations are very useful to see how the dissipativity properties can be used to design stable and robust feedback controllers basing on the fundament classical Lyapunov stability and Lyapunov functions. For graduate students, researchers and practicing engineers." (Yuri N. Sankin, Zentralblatt MATH, Vol. 1121 (23), 2007)

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•N.S. Nguyen, B. Brogliato,2014Multiple Impacts in Dissipative Granular Chains, Springer Verlag, Berlin, Lecture Notes in Applied and Computational Mechanics, vol.72; ISBN 978-3-642-39298-6.

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•V. Acary, O. Bonnefon, B. Brogliato, 2011Nonsmooth Modeling and Simulation for Switched Circuits, Springer Verlag, Berlin, Lecture Notes in Electrical Engineering, vol.69; ISBN 978-90-481-9680-7.

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•B. Brogliato (Editor),2000Impacts in Mechanical Systems. Analysis and Modeling, Springer Verlag, Berlin, Lecture Notes in Physics, vol.551. Springer web page

"These lectures are so well selected that the book can be considered as a monograph comprising the mathematical analysis, the modelling, and the numerical simulation of rigid multibody systems including the stability of periodic motions with impacts, elasto-plastic contacts, and multiple impacts. .... The book presents an excellent survey on advanced methods required for the understanding of the complexity of impacts in mechanical systems and presents analytical and numerical methods verified by experimental results for the efficient solution of engineering problems. The book is recommended to graduate and postgraduate students, researchers in mechanical engineering, and scientists who are interested in established methods and new ideas for non-smooth dynamical systems." (W. Schielen, ZAMM. Z. Angew. Math. Mech., 85, no 3, p.223, 2005)

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•Zodiac,Theory of robot control,1996, Communications and Control Engineering Series, Springer-Verlag. (co-author with 11 European colleagues), C. Canudas, G. Bastin, B. Siciliano (Editors).

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Papers (comments on)

R. Lozano, B. Brogliato,"Adaptive motion control of flexible joint manipulators", IEEE Transactions on Automatic Control, vol.37, no 2, pp.174-181, February 1992.(the first and unique state feedback controller for global tracking of flexible joint manipulators, which can now be embeded into so-called "passivity-based" schemes: our basic idea was to extend the adaptive Slotine and Li scheme to another class of systems, and that's what we did. This was considered as a challenge at the end of the eighties. This is certainly also one of the very first instances of what has been called afterwards "backstepping schemes", and was published almost simultaneously with Kanellakopoulos' paper which is now remembered as "the" paper which introduced backstepping.... A flaw was present in the proof of stability and we have corrected it, see the note 33 in IEEE TAC in the above list)

R. Lozano, B. Brogliato, "Adaptive control of a simple nonlinear system without a priori information on the plant parameters", IEEE Transactions on Automatic Control, vol.37, no 1, pp.30-37, January 1992.(a scheme that deals with global stabilisation of a simple NL system whose "control gain" sign is unknown)

B. Brogliato, R. Ortega, R.Lozano,"Globally stable nonlinear controllers for flexible joint manipulators: a comparative study", Automatica, vol. 31, no 7, July 1995.(essentially a comparison between various techniques for global tracking: passivity-based, backstepping-based, singular perturbation techniques, PD; we made experimental comparisons also, see the above paper 36 published in a robotics journal. It aimed also at clarifying the structure of the scheme presented in the above paper R1 of IEEE TAC)

B. Brogliato, S. Niculescu, P. Orhant, "On the control of finite-dimensional mechanical systems with unilateral constraints", IEEE Transactions on Automatic Control, vol.42, no 2, pp.200-215, February 1997.(the first paper that deals with Lagrangian systems with unilateral constraints and their tracking control; essentially limited to the one degree-of-freedom case)

F. Génot, B. Brogliato,"New results on Painlevé paradoxes", European Journal of Mechanics A/Solids, vol.18, pp.653-678, 1999.(an analysis of what happens in the neighborhood of singular points where the contact force may tend to infinity; contrary to what many think since the problem has been raised by Painlevé one century ago, that does not call the modelling into question! J.J. Moreau does not like to call this Painlevé paradoxes, and prefers "frictional paroxysms". Such phenomena have been experimentally verified in Zhao-Liu-Chen_ASMEJAM2007.pdf)

B. Brogliato, A. Zavala-Rio,"On the control of complementary-slackness mechanical juggling systems", IEEE Transactions on Automatic Control, vol.45, no 2, pp.235-246, February 2000.(here we deal with a specific class of complementarity mechanical systems that we call jugglers because of their special structure; some results on controllability and on stabilisation)

R. Leine, B. Brogliato, H. Nijmeijer,"Periodic motion and bifurcations induced by the Painlevé paradox", European Journal of Mechanics A/Solids, 2002, vol. 21, no 5, pp.869-896.(a study on how the Painlevé paradoxes may influence the bifurcation phenomena in simple mechanical systems with unilateral constraints and Coulomb friction)

B. Brogliato, ``Some perspectives on the analysis and control of complementarity systems'', IEEE Transactions on Automatic Control, vol. 48, no 6, pp.918-935, June 2003.(in this paper I provide an overview of complementarity systems which can be viewed as hybrid systems but also as differential inclusions; the main properties of such dynamical systems are explained; some open problems are pointed out: they may not all be relevant, and many must be missing! But some of them may be of interest...)

J.C. Avila-Vilchis, B. Brogliato, A. Dzul, R. Lozano,"Nonlinear modelling and control of helicopters", Automatica, vol. 39, no 9, pp.1583-1596, 2003.(this work deals with the derivation of a new model that is suitable for the control of helicopters; we also present a controller -- an I/O feedback linearisation -- ; some experiments led on the scale helicopter of the Compiègne University of Technology are presented)

D. Goeleven, B. Brogliato, "Stability and instability matrices for linear evolution variational inequalities", IEEE Transactions on Automatic Control, vol.49, no 4, pp.521-534, 2004.

(we derive a general framework for the study of Lyapunov stability of a class of dynamical variational inequalities, which often can also be written as complementarity systems, or a special type of differential inclusions. Lyapunov's second method is extended to such non smooth systems, and various criteria are proposed to check the stability of equilibria. One central idea is to replace positive definiteness of Lyapunov functions matrices, by co-positiveness on convex sets K. This seems to be the first instance of the use of co-positivity in this framework)

Y. Hurmuzlu, F. Génot, B. Brogliato,"Modelling, stability and control of biped robots -- A general framework", Automatica, vol.40, no 10, pp.1647-1664, 2004.

(this is a survey in which we introduce the complementarity modelling framework in the field of biped robots; we discuss various aspects of the stability problem for bipeds and how the rigid body unilateral constraints model can be useful to this aim)

B. Brogliato, D. Goeleven, "The Krakovskii-LaSalle invariance principle for a class of unilateral dynamical systems", Mathematics of Control, Signals and Systems, vol.17, pp.57-76, 2005.

(studies Lyapunov stability for a class of evolution variational inequalities, and the extension of the invariance lemma; the name is Krasovskii, not Krakovskii, which is an unforgivable mistake... )

D. Goeleven, B. Brogliato, "Necessary conditions of asymptotic stability for unilateral dynamical systems", Nonlinear Analysis Theory Methods and Applications, vol.61, no 6, pp.961-1004, 2005.

(in this paper the stability of a class of evolution variational inequalities is studied. The notion of Brouwer degree of a mapping is used to characterize a necessary condition for the asymptotic stability. Indeed for an ODE wth continuous vector field F(x), it is known that a necessary condition of asymptotic stability of an equilibirum is that the degree of F(.) is equal to 1. Here this is extended to such nonsmooth systems. Applications are given in the field of feedback control, where it especially appears that the classical implication: Kalman matrix full rank ----> asymptotic stabilisation, no longer holds. The proof is quite technical and uses suitable homotopies to compute the degree)

V. Acary, B. Brogliato, D. Goeleven, 2008 "Higher order Moreau's sweeping process: Mathematical formulation and numerical simulation", Mathematical Programming A, vol.113, no 1, pp.133-217.

(in this paper we extend the second order Moreau's sweeping process, that is a specific measure differential inclusion which models, in particular, Lagragian systems subject to complementarity conditions, to what may be called a distribution differential inclusion, i.e. an inclusion whose solutions are ditributions of degree larger than 2. The framework is settled with a precise definition of the space of solutions, then well-posedness is studied, and finally we propose a numerical algorithm whose properties are analysed. Simulations illustrate the theoretical developments. The applications may be found in feedback control of nonsmooth electrical circuits, and in optimal control with unilateral state constraints -- see below-- .)

B. Brogliato, 2008 "Some results on optimal control with unilateral constraints", Nonlinear Analysis: Theory, Methods and Applications.

(in this work the higher order sweeping process -- see paper just above -- is used as a dynamical framework to represent the necessary condition of optimal control under state inequality constraints. In the first part it is shown that one may handle a multiplier that is not a measure but a higher degree distribution, at the price of modifying the action integral to be extremized. In the second part the qualitative study of optimal trajectories is studied using ten Dam's geometric approach publisehd in IEEE TAC in 1997, hence improving the seminal work of Jacobson and Lele in 1965. In particular it is shown that the widely spread fact that odd order constrained systems cannot have optimal trajectories with boundary arcs, is wrong. This has also been shown in a paper published at SIAM Control Optimization by Bonnans and Hermand in 2007, in which an example is exhibited. The case of mulitple constraints is discussed and some results extended to this case.)