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Research Interests
Principal
research interests lie in Mathematical Systems Theory with particular emphasis
in Geometric Nonlinear Control and Applications in Robotics and Vision. Other interests include
Riemannian geometry, smoothing and interpolation splines on non Euclidean
spaces, Lie groups and Lie algebras, rolling motions of (pseudo) Riemannian
manifolds.
Research Experience
▪
Scientific Coordinator of the research group "Control Optimization and
Computation"
of the
Institute of
Systems and Robotics
– University of Coimbra (since
2004).
▪
Scientific Coordinator of the research group "Control Theory" of the
Institute of
Systems and Robotics
- University of Coimbra (1992-2003).
▪
Scientific
Coordinator of the research group "Mathematical Systems Theory" of the
Center of Mathematics of the University of Coimbra
- CMUC (1988-1992).
▪
Local
Representative of the Marie Curie Multipartner Training Site,
Control Training
Site, funded by European Commission (2002-2006).
▪
Scientific
Coordinator of the Portuguese Team in the Nonlinear Control
Network, under
the EU Training and Mobility of Researchers (TMR) Programme (1997-2002).
▪
Portuguese
Coordinator of the project Control and Systems Engineering, under the EC
EUROFORM Programme (1993-1994).
▪
Scientific
Coordinator of the Portuguese Team in the project Advances in Nonlinear
Systems and Applications, under the EC SCIENCE Programme (1990-1993).
Ph.
D.
thesis supervised
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F. Pina,
Smoothing and Interpolation on the Generalized Essential Manifold. University of Coimbra, June 2020. |
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A.
Marques,
Rolling Maps for Pseudo-Riemannian Manifolds.
University of Coimbra, February 2015.
|
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R.
Rodrigues,
Interpolating
Curves in Euclidean Spaces and other Riemannian Manifolds.
University of Coimbra, April 2007.
|
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L.
Machado, Least Square Problems on Riemannian Manifolds.
(Co-supervisor K. Hüper). University of Coimbra, May 2006. |
|
P. Saraiva, n-ary Lie
Algebras and Malcev Algebras.
(Co-supervisor A. Pozhidaev). University of Coimbra,
July
2004. |
|
J.
Cardoso, Matrix Logarithms – Theoretical and Numerical Considerations.
University of Coimbra,
December
2003. |
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M.
Camarinha, Geometry of Cubic Polynomials in Riemannian Manifolds, (Co-supervisor P. Crouch). University of Coimbra, September 1996. |
|
H.
Albuquerque, Contributions to the Theory of Malcěv Superalgebras,
(Co-supervisor A. Elduque). From January 1989 to March 1992.
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Post-Doc / Ph. D. advisor
|
K.
Krakowski.
Pos-doc,
under
FCT under Project
PTDC/EEA-CRO/122812/2010.
March -September 2015. |
|
I.
Yudin. Pos-doc,
under
FCT under Project
PTDC/EEA-CRO/113820/2009.
July -December 2013. |
|
S.
Rodrigues. Pos-doc,
under FCT Project PTDC/EEA-ACR/67020/2006.
March -September 2008. |
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A.
Filipescu (University of Dunarea de Jos - Galaty).
Pos-doc, under INVOTAN Research Grant.
September
2003 - February 2004. |
|
J.
Clemente Gallardo (University of Saragoza).
Pos-doc under Training and Mobility of Researchers (TMR) EC-Programme.
April-October 2002. |
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K. Hüper
(University of Wüerzburg).
Pos-doc under Training and Mobility of Researchers (TMR) EC-Programme.
April-August 2000. |
|
J.
Jakubiak
(University of Wrocław). Ph. D. Project, under Marie Curie Control
Training Site (CTS) EC-Programme. April-September 2003. |
|
M.
Kleinsteuber (University
of Wüerzburg).
Ph. D. Project, under Marie Curie Control Training Site (CTS) EC-Programme.
July-October 2003. |
|
S. Ricardo,
Geometry of Mechanical Control Systems with Applications to Systems Subject
to Second-Order Nonholonomic Constraints, University of Rouen. (Supervisor:
W. Respondek). November 2008. |
|
T.
Azevedo, Optimization Problems in Gas Networks, University of Salford.
(Supervisor: L. Fletcher). October 1999. |
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R.
Almeida, Regulator Problems for Descriptor Systems, University of
Salford. (Supervisor: L. Fletcher). July 1998. |
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C. Simões, Stability
and Stabilization of Nonlinear Systems, University of Twente.
(Supervisor: H. Nijmeijer). April 1996.
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M.Sc. theses supervised
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S.
Seco, Applications of Quadratic Equations.
University of Coimbra, September 2012. |
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I.
Guilherme, Applications of the Harmonic Oscillator.
University of Coimbra, September 2012. |
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L.
Freitas, Exotic Roads and Wheels.
University of Coimbra, September 2012. |
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A.
Paiva, Fractals.
University of Coimbra,
September 2011. |
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A.
Rodrigues, Coloring Problems.
University of Coimbra,
July 2011. |
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C.
Medeiros, Applications of Differential Equations in Health Problems.
University of Coimbra,
July 2011. |
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E.
Bizarro, The Cycloid.
University of Coimbra,
July 2011. |
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C.
Monteiro, The geometry of Origami. University of Coimbra,
July 2010. |
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R. Minuça, Non-Euclidean Geometry in the Art of Dressmaking.
University of Coimbra, July 2010. |
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A.
Rodrigues, Polar Flowers.
University of Coimbra, July 2010. |
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J.
Sintra,
The Path of the Cycloid. University of Coimbra, February
2009. |
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F. Pina,
Nonholonomy of the Unit n-Sphere.
University of Coimbra, March 2008. |
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D. Couto,
Semisimples Lie Algebras – an Introduction. University of Coimbra,
April 2006. |
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O.
Ribeiro, Wavelets Theory.
University of Coimbra, July 2002. |
|
S.
Ricardo, Controllability on Lie Groups. University of Coimbra, July
2000. |
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R.
Rodrigues, Splines and Control Theory. University of Coimbra, January
1999. |
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L.
Machado, Geodesic Flows, Toda Flows and Optimal Control. University
of Coimbra, January 1999. |
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C.
Costa, Variational Problems in Non - Euclidean Spaces. University of
Coimbra, February 1997. |
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P.
Saraiva, Algebras with Cross Products. University of Coimbra, October
1996. |
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R.
Almeida, Fast Fourier Transform and Applications. University of
Coimbra, September 1992. |
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M.
Camarinha, Regular Automorphisms of Semisimple Lie Algebras.
University of Coimbra, April 1991. |
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C.
Simões, Controllability of Bilinear Systems. University of Coimbra,
July 1990. |
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H.
Albuquerque, Finite Generation of Semisimple Lie Algebras over a Field of
Characteristic 0. University of Coimbra, September 1988.
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Scientific and Organizing Committees Membership
Member of the
International Program Committee
of the following events:
▪
APCA International Conference on Automatic Control and Soft-Computing (CONTROLO'2022)
6-8 July, 2022. Lisbon - Portugal.
▪
Dynamic Control and Optimization Conference (DCO'2021), in honor of the 65th birthday of Andrey Sarychev.
3-5 February, 2021. Aveiro - Portugal.
▪
Portuguese Meeting on Optimal Control 2020-2021 (EPCO'2020-2021)
July, 2021. Lisbon - Portugal.
▪
APCA International Conference on Automatic Control and Soft-Computing (CONTROLO'2020)
1-3 July, 2020. Bragança - Portugal.
▪
Portuguese Meeting on Optimal Control 2019 (EPCO'2019)
25
June, 2019. Porto - Portugal.
▪
APCA International Conference on Automatic Control and Soft-Computing (CONTROLO'2018)
4-7
June, 2018. Ponta Delgada, Azores - Portugal.
▪
Portuguese Meeting on Optimal Control 2018 (EPCO'2018)
18
June, 2018. Coimbra - Portugal.
▪
3rd Conference on Geometric Science of
Information (GSI 2017)
7-9
November, 2017. Mines ParisTech, Paris - France.
▪
Portuguese Meeting on Optimal Control 2017 (EPCO 2017).
June 12, 2017. ISEG, Lisbon - Portugal.
▪
The Cape Verde International Days on Mathematics 2017 (CVIM'2017).
8-11
Maio, 2017. Praia - Cape Verde.
▪
12th Portuguese Control
Conference (CONTROLO'2016)
14-16
September, 2016. Guimarães - Portugal.
▪
The International Meeting on Applied Mathematics in Errachidia
9-12 May, 2016. Errachidia - Marocco.
▪
The Cape Verde International Days on Mathematics 2015 (CVIM'2015).
27-30 April 2015. University of Cape Verde, São Vicente.
▪
11th Portuguese Control
Conference (CONTROLO'2014)
21-13 July, 2014. Porto - Portugal.
▪
Portuguese Meeting on Optimal Control 2014 (EPCO 2014).
June 6, 2014, University of Aveiro - Portugal.
▪
The Cape Verde International Days on Mathematics 2013 (CVIM'2013).
22-25
April, 2013. Praia - Cape Verde.
▪
CIM International Conferences and Advanced Schools Mathematics of Planet Earth
2013.
2013. Lisbon - Portugal.
▪
International Conference on Pure and Applied Mathematics (ICPAM’12)
28-30 May, 2012. Guelma - Algeria.
▪
The International Meeting on Applied Mathematics in Errachidia
April 23-26, 2012. Errachidia - Marocco.
▪
10th Portuguese Control
Conference (CONTROLO'2012)
July
16-18, 2012. Funchal, Madeira - Portugal.
▪
Trimester in Combinatorics and Control
April-June 2010.
Madrid and Zaragoza - Spain.
▪
6th International Conference on Informatics in Control, Automation and Robotics
(ICINCO 2009)
2-5 July 2009. Milan - Italy
▪
8th Portuguese Control
Conference (CONTROLO'2008)
21-23 July, 2008. Vila Real - Portugal.
▪
7th Portuguese Control
Conference (CONTROLO'2006)
11-14
September, 2006.
Lisbon - Portugal.
▪
7th Inter. Conference on
Adaptive and Natural Computing Algorithms (ICANNGA'2005)
21-23
March, 2005.
Coimbra - Portugal.
▪
IFAC Symposium on Nonlinear
Control Systems (NOLCOS'2004)
1-3
September, 2004.
Stuttgard - Germany.
▪
Inter. Conference on Informatics in Control, Automation and Robotics (ICINCO'04)
25-28 August, 2003.
Setúbal – Portugal.
▪
Portuguese Control Conference (CONTROLO'2004)
7-9 June, 2004.
Algarve –
Portugal.
▪
Seventh European Control Conference (ECC'03)
1-4 September, 2003. Cambridge University – England.
▪
Mediterranean Control and Automation Conference (MED'02)
9-12 July, 2002. Lisbon – Portugal.
▪
Fifth Portuguese Control Conference (CONTROLO'2002)
4-6 October, 2002. University of Aveiro – Portugal.
▪
Fourth Portuguese Control Conference (CONTROLO’2000)
4-6 October, 2000. Guimarães – Portugal.
▪
8th International Linear Algebra Society (ILAS) Conference
17-21 July, 1999. Barcelona – Spain.
▪
Meeting on Matrix Analysis and Applications
10-12
September, 1997. Seville – Spain.
▪
Second Portuguese Control Conference (CONTROLO’96)
11-13 September, 1996. Porto – Portugal.
▪
Third European Control Conference (ECC’95)
5-8 September, 1995. Rome – Italy.
▪
First Portuguese Control Conference (CONTROLO’94)
14-16 September, 1994. Lisbon – Portugal.
▪
Second European Control Conference (ECC'93)
28 June - 1 July, 1993. Groningen - Holand.
Member of the
Organizing Committee
of the following events:
▪
APCA International Conference on Control and Soft-Computing (CONTROLO'2018)
4-7
June, 2018. Ponta Delgada, Azores
- Portugal.
Workshop
"The Work of Peter Crouch", within CDC-ECC 2011
December 11, 2011. Orlando - USA.
▪
CIM Workshop
on Mathematical Control Theory and Finance
10-14 April, 2007. Lisbon – Portugal.
▪
Inter.
Conference on Adaptive and Natural Computing Algorithms (ICANNGA'05)
21-23 March, 2005.
Coimbra - Portugal.
▪
First Control Training Site Workshop
1-3 July, 2004.
Coimbra - Portugal.
▪
Third Nonlinear Control Network Pedagogical School, on Optimal Control
10-14 September, 2001. Coimbra - Portugal.
▪
Sixth European Control Conference (ECC'01)
4-7 September, 2001. Porto - Portugal.
▪
Portuguese Mathematicians in Control (COPO'2000)
19-20 May 2000. Aveiro - Portugal.
▪
Third Portuguese Control Conference (CONTROLO'98)
9-11
September, 1998. Coimbra - Portugal.
▪
Second Portuguese Control Conference (CONTROLO'96)
11-13 September 1996, Porto - Portugal.
▪ Methods of Geometry and Analysis in Variational Problems and their Applications
11
March, 1996. Coimbra - Portugal.
▪
First Portuguese Control Conference (CONTROLO'94)
11-16 September 1994. Lisbon - Portugal.
▪ Workshop H-infinity Control Theory
11-12 March, 1993. Coimbra - Portugal.
Invited Presentations
▪ Invited
Lectures:
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"The de Casteljau algorithm on symmetric spaces" in the Special Session "Modeling and Approximation with Manifold-Valued Data" at the 10th International Congress of Industrial and Applied Mathematics, Tokyo - Japan, 20-25 August, 2023.
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"Applied differential geometry" at the 3rd Women in Mathematics Meeting, Coimbra - Potugal, 24-26 July, 2023.
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"A unified framework for studying extremal curves on real Stiefel manifolds" at the Dynamical Systems, Mechanics and Control, a Workshop to honor Anthony Bloch, Madrid - Spain, 10-14 July, 2023.
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"Endpoint geodesics on symmetric spaces with applications" at the Mini-Symposium Matrix and Operator Means, 25th ILAS Conference 2023, Madrid - Spain, 12-16 June, 2023.
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"Dynamic interpolation on Riemannian manifolds" at the French German Portuguese Conference in Optimization, Porto - Potugal, 3-6 May, 2022. (Jointly with M. Camarinha.)
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"Sub-Riemannian structures on Stiefel manifolds" at the SIAM Conference on Control and its Applications (CT21), held virtually 19-21 July, 2021.
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"Sub-Riemannian structures on homogeneous manifolds" at the Dynamic Control and Optimization Conference (DCO'2021), University of Aveiro, 3-5 February, 2021, Portugal.
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"Least squares problems on Riemannian manifolds" at the Differential Geometry and Applications Workshop, University of Würzburg, 15 January 2020, Germany.
|
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"Geometric Control and Sub-Riemannian Problems" at the Coloquio-ICMAT,
Instituto de Ciências Matemáticas, 28 November 2018, Madrid.
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"Left-invariant sub-Riemannian systems on Lie groups and extremal curves on Stiefel manifolds" at the Differential Geometry and Applications Workshop, University of Würzburg, 1-2 October 2018, Germany.
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"Exotic wheels and roads" at The Cape Verde
International Days on Mathematics (CVIM'2015), University of Cape
Verde, 27-30 April, 2015, S. Vicente, Cape Verde.
|
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"Rolling Lorentzian spheres and quadratic Lie groups"
at the Thematic Day on Sub-Loretzian Geometry, within the Trimester
"Geometry, Analysis and Dynamic on Subriemannian Manifolds" 12 November
2014, Institut Henri Poincaré, Paris - France.
|
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"Solving interpolation problems on manifolds using
rolling motions" at the Thematic Day on Rolling Manifolds, within the
Trimester "Geometry, Analysis and Dynamic on Subriemannian Manifolds" 19
November 2014, Institut Henri Poincaré, Paris - France.
|
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"Fitting
problems on Riemannian Manifolds" at the IV Iberoamerican Meeting on
Geometry, Mechanics and Control, 7-11 April, 2014, IMPA, Rio de Janeiro -
Brasil.
|
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"Rolling motion of ellipsoids - constructive proof of
controllability" at the International Conference on Dynamics, Games and
Science III, 17-18 February, 2014, Porto - Portugal. |
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"Generalizing
least square problems on Grassmann manifolds"at
the International Conference on Applied Mathematics and Informatics (ICAMI
2013), 22 November -1 December, 2013, San Andrés - Colombia.
|
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"Smooth
interpolation on ellipsoids via rolling motions"
at the 6th International Scientific Conference on Physics and Control
(PhysCon2013), 24-31 August, 2013, San Luís de Potosí - Mexico.
|
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"Geometric
nonliner control through rolling motions" at the Cape Verde International
Days on Mathematics 2013, 20-27 April, 2013, Praia - Cape Verde.
|
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"A
Variational Approach to Riemannian Least Squares Problems" at the
International Conference on Pure and Applied Mathematics (ICPAM'12), 28-30
May, 2012, Guelma - Algeria. |
|
"A Tour
Through Several Aspects of Geometric Nonlinear Control Driven by Rolling
Motions" at the International Meeting on Applied Mathematics in Errachidia,
20-29 April, 2012, Errachidia - Marrocos. |
|
"On the Interpolation Problem for the Essential Manifold" at the Conference
Optimization
2011, 24-27 july , Lisbon - Portugal. |
|
"Least
Squares Problems on Riemannian Manifolds" at the Workshop The Interface
Between Mathematics, Science and Engineering, 10-11 February, 2011, Lisbon -
Portugal. |
|
"An Overview of Geometric Nonlinear Control Through
Rolling Motions"
at the 9th Portuguese Conference on
Automatic Control (CONTROLO’2010), Coimbra, Portugal, 8-10
September 2010. |
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"Least
Squares Problems on Riemannian Manifolds" at the Workshop CoCo 2010,
Trimester in Combinatorics and Control, April 6-9, 2010, Madrid - Spain.
|
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"Rolling Motions" at the
Workshop on The Interface Between Mathematics, Science, and Engineering, 28
May, 2009, Porto - Portugal. |
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"The Geometry of Rolling Maps" at the XVII Fall Workshop on Geometry and
Physics, 3-6 September, 2008, Castro Urdiales - Spain. |
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"Geometric Nonlinear Control and Applications" at the First Iberoamerican
Meeting on Geometry, Mechanics, and Control, 23-27 June, 2008, Santiago de
Compostela - Spain. |
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"The Geometry of Rolling" at the First Joint Meeting of the American
Mathematical Society and Sociedade Brasileira de Matemática, 2-9 June, 2008,
IMPA; Rio de Janeiro - Brasil. |
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"The Geometry of Smoothing Splines on Lie Groups" at the Workshop on
Geometric Methods for Interpolation and Problems in Statistics, 21 February,
2005, Canberra - Australia. |
|
"Interpolation
curves on Riemannian manifolds" at the Workshop on Nonlinear Control Systems,
16-20 June, 2003, Warsaw - Poland. |
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"Splines
on Lie Groups" at the Workshop on Geometric Nonlinear Control,
23-26 July, 2003, Campinas - Brasil. |
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"On the
generation of smooth splines and optimal control" at the Nonlinear Control
Network Pedagogical School, 6-10 September, 1999, Athens - Greece.
|
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"Splines - a Manifestation of Optimal Control" at the Conference
Optimization 2001, July 23-25, 2001, Aveiro - Portugal.
|
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"Splines on Lie Groups" at the Workshop on Lie Theory and Applications,
August 2-5, 1999, Wuerzburg - Germany. |
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"Spline Interpolation on Matrix Lie Groups" at the 8th ILAS Conference,
July 19-22, 1999, Barcelona - Spain. |
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"Geometric Splines" at the 14th World Congress of IFAC - International
Federation of Automatic Control, July 5-9 July, 1999, Beijing - China.
|
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"Splines and Optimal Control" at the Workshop on Future Directions in
Systems and Control Theory, June 23-26, 1999, Cascais - Portugal.
|
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"Control Systems on Matrix Lie Groups" at the Meeting on Matrix Analysis
and Applications, September 10-12, 1997, Seville - Spain. |
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"Dynamic Interpolation" at the Workshop in Nonlinear Control, Banach
Center, Polish Acad. of Sciences, May 31 - June, 1993, Warsaw - Poland.
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▪
Invited
Sessions:
|
Organizer of special
session
"SS-04 Geometric and Analytic Methods for Nonlinear Data" at the APCA International Conference on Automatic Control and Soft-Computing (CONTROLO'2022), 6-8 July, 2022. Lisbon - Portugal. (Co-organizer K. Hueper). |
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Organizer of special
session on
"Optimization and Dynamical Systems on Manifolds" at the International
Conference on Dynamics, Games and Science III, 17-18 February, 2014, Porto -
Portugal. |
|
Mini-Symposium Organizer "Control Theoretical Splines" at the Fifth SIAM
Conference on Control and Applications, July 11-14, 2001, San Diego - USA.
(Co-organizer C. Martin). |
|
Organizer
of special session on "Novel Applications of Geometric Systems" at the 14th World
Congress of IFAC - International Federation of Automatic Control, July 5-9,
1999, Beijing - China. |
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Organizer
of special session on "Mechanical Systems" at the 3rd Portuguese Conference on
Automatic Control, September 9-11, 1998, Coimbra, Portugal. (Co-organizer H. Nijmeijer).
|
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Organizer
of special session on "Nonlinear Control Systems" at the 2nd Portuguese Control
Conference, September 11-13, 1996, Porto - Portugal. |
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Organizer
of special session on "Trajectory Planning in Mechanical Systems" at the 2nd
European Control Conference, June 23 - July 1, 1993, Groningen - The
Netherlands.
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Research Projects and Grants
2018-2021
|
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029266-02/SAICT/2017 - FCT
"D4 - Deep Drug Discovery and Deployment"
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2012-2015 |
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PTDC/EEA-CRO/122812/2010 - FCT
"DG2CVPR - Differential Geometry for Computer Vision and Pattern Recognition"
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2011-2014 |
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PTDC/EEA-CRO/113820/2009
- FCT
"CONAV: COoperative
NAvigation and Control of Multiple Autonomous Vehicles"
|
2007-2010 |
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PTDC/EEA-ACR/67020/2006 - FCT
"DENO: DEvelopment of NOnlinear Observers"
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2005-2006 |
|
POSC/EEA-SRI/58016/2004
- FCT "Nonlinear Control Techniques Applied in Path Following of WMRs and
Autonomous Vehicles with high Precision Localization System"
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2002-2005 |
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TSM02 – FCT
"Trajectory Planning for Nonholonomic Mechanical Systems"
|
2002-2006 |
|
EU
Marie Curie Multipartner Training Site "Control Training Site"
|
2002-2004 |
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SAPIENS - FCT "Trajectory Planning for Nonholonomic Mechanical Systems"
|
1997-2002 |
|
EU
Training and Mobility of Researchers Programme "Nonlinear Control Network"
|
1990-1993 |
|
EC
SCIENCE Programme Project: "Advances in Nonlinear Systems and Applications"
|
1994-1997 |
|
Research grant from CRUP (Conselho
de Reitores das Universidades Portuguesas) Project: "Methods of Geometry and Analysis in Variational Problems and
its Applications"
|
1994-1997 and 1999-2000
|
|
JNICT
(PRAXIS XXI Programme) Project: "Mathematical Physics"
|
1993-1994 |
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EC
EUROFORM Programme Project: "Control and Systems Engineering"
|
1992-1997 |
|
NATO
Collaborative Research Grant Project: "The Foundations of Dynamic Interpolation"
|
1988-1990 |
|
Research Grant
from JNICT (Junta
Nacional de Investigação Científica e Tecnológica) Project 87/62: "Mathematical Theory of Systems and Control"
|
1985-1987 |
|
Research Grant from CRUP (Conselho
de Reitores das Universidades Portuguesas) Project N2/85: "The Mathematics of Control and Systems".
|
|
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Sabbatical grants and travel grants on several occasions from: Calouste Gulbenkian Foundation, INIC, JNICT, INVOTAN, Fullbright, FLAD,
FCT. |
Other
activities
▪
Guest Editor of Special Issue "New Trends in Geometric Mechanics", in Communications in Analysis and Mechanics (CAM).
▪
Member of Ph.D. Hiring Committee in Pure Mathematics. University of Bergen, June 2022.
▪
Referee of research papers submitted to various Journals in Control Theory and
Mathematics.
▪
Reviewer for
Mathematical Reviews since July 1986, and for
Zentralblatt für Mathematik since
January 1987, having reviewed more than 50 papers and 2 books.
▪
Participation
in more than sixty International Conferences and Meetings.
▪
More than 50
invited seminars and short courses at several universities abroad.
▪
Regular
visits to universities abroad.
|