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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).

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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.

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P. Saraiva, n-ary Lie Algebras and Malcev Algebras. (Co-supervisor A. Pozhidaev). University of Coimbra, July 2004.

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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.

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H. Albuquerque, Contributions to the Theory of Malcěv Superalgebras, (Co-supervisor A. Elduque). From January 1989 to March 1992.
 

Post-Doc / Ph. D. advisor
 

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K. Krakowski. Pos-doc, under FCT under Project PTDC/EEA-CRO/122812/2010. March -September 2015.

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I. Yudin. Pos-doc, under FCT under Project PTDC/EEA-CRO/113820/2009. July -December 2013.

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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.

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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.

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J. Jakubiak (University of Wrocław).  Ph. D. Project, under Marie Curie Control Training Site (CTS) EC-Programme. April-September 2003.

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M. Kleinsteuber (University of Wüerzburg). Ph. D. Project, under Marie Curie Control Training Site (CTS) EC-Programme. July-October 2003.

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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.

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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.
 

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.

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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.

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Invited Presentations

▪ Invited Lectures:

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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.

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"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.

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"On the Interpolation Problem for the Essential Manifold" at the Conference Optimization 2011, 24-27 july , Lisbon - Portugal.

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"Least Squares Problems on Riemannian Manifolds" at the Workshop The Interface Between Mathematics, Science and Engineering, 10-11 February, 2011, Lisbon - Portugal.

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"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. 

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 "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.

Invited Sessions:

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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.

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 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).

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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


029266-02/SAICT/2017 - FCT

"D4 - Deep Drug Discovery and Deployment"


2012-2015

 

 

 PTDC/EEA-CRO/122812/2010 - FCT
"DG2CVPR - Differential Geometry for Computer Vision and Pattern Recognition"

2011-2014

 

PTDC/EEA-CRO/113820/2009 - FCT
"CONAV: COoperative NAvigation and Control of Multiple Autonomous Vehicles"

 

2007-2010

 


PTDC/EEA-ACR/67020/2006 - FCT
"DENO: DEvelopment of NOnlinear Observers"

 

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"

 

2002-2005

 


TSM02 – FCT
"Trajectory Planning for Nonholonomic Mechanical Systems"

 

2002-2006

 


EU Marie Curie Multipartner Training Site
"Control Training Site"

 

2002-2004

 


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

 


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".

 

 

 

Sabbatical grants and travel grants on several occasions from:
Calouste Gulbenkian Foundation, INIC, JNICT, INVOTAN, Fullbright, FLAD, FCT.

 

  Other activities             

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 30 invited seminars and short courses at several universities abroad.

Regular visits to universities abroad.

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