Optimal Control of Constrained and
Hybrid Nonlinear Systems

Institutions involved

• Faculty of Engineering, University of Porto - FEUP  
• University of Minho - UM  
• Engineering School of Porto Polytechnic Institute - ISEP  
• Institute of Systems and Robotics of Porto - ISR  
• Centre of Mathematics of University of Minho  

Meet the people behind the project.

Team

• Amélia C.D. Caldeira (ISEP) 
• Ana Filipa Ribeiro (FEUP) 
• Dimitri Karamzin (FEUP) 
• Fernando A.C.C. Fontes (FEUP), Coordinator 
• F. Lobo Pereira (FEUP) 
• Luís Tiago Paiva (FEUP) 
• M. Margarida A. Ferreira (FEUP) 
• Maria do Rosário de Pinho (FEUP) 
• Md. Haider Ali Biswas (FEUP) 
• Sofia O. Lopes (UM) 

In this section you will find a selection of team Publications.

• [AKP05]  A. Arutyunov, D. Karamzin, F. Lobo Pereira, A Nondegenerate Maximum Principle for the Impulsive Control Problem with State Constraints, SIAM Journal of Control and Optimization, vol. 43, No. 5, pp. 1812–1843, 2005.
• [dPFF05]  M.d.R. de Pinho, M.M.A. Ferreira, and F.A.C.C. Fontes, Unmaximized inclusion necessary condutions for nonconvex constrained optimal control problems, ESAIM Control Optim. Calc. Var., 11 (2005), pp. 614–632.
• [dPR08]  M.d.R. de Pinho and J. Rosenblueth, Necessary Conditions for Constrained Problems under Mangasarian-Fromowitz Conditions, SIAM J. Control Optim. 47 (2008), pp. 535–552.
• [F01]  F.A.C.C. Fontes. A general framework to design stabilizing nonlinear model predictive controllers”, Systems and Control Letters , 42(2) pp 127--143, 2001
• [FM03]  F.A.C.C. Fontes, L. Magni. Min-Max Model Predictive Control of Nonlinear Systems Using Discontinuous Feedbacks, IEEE Transactions on Automatic Control, Vol. 48, no. 10, pp. 1750-1755, 2003.

In this section you will find a selection of bibliographic references in the scope of this project.

• [AA97]  A.V. Arutyunov, S. M. Aseev, Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints, SIAM Journal of Control and Optimization, vol. 35, pp. 930–952, 1997.
• [Aru00]  A.V. Arutyunov, Optimality Conditions: Abnormal and Degenerate Problems, Kluwer Academic Publishers, Dordrecht/Boston/London, 2000.
• [AKP05]  A. Arutyunov, D. Karamzin, F. Lobo Pereira, A Nondegenerate Maximum Principle for the Impulsive Control Problem with State Constraints, SIAM Journal of Control and Optimization, vol. 43, No. 5, pp. 1812–1843, 2005.
• [AP06]  A. Arutyunov, Lobo Pereira, Second-order necessary optimality conditions for nproblems without a priori normality assumptions, Mathematics of Operations Research, INFORMS, vol. 31, nº 1, pp 1-12, February 2006.
• [AUB02]  AUBIN Jean-Pierre, LYGEROS John, QUINCAMPOIX Marc, SASTRY Shankar, SEUBE Nicolas, Impulse differential inclusions: A viability approach to hybrid systems, IEEE transactions on automatic control, 2002, vol. 47, no1, pp. 2-20.
• [BF07]  P. Bettioli, H. Frankowska, Normality of the maximum principle for nonconvex constrained Bolza problems, in Journal of Differential Equations, vol. 243, no. 2, pp.256-259, 2007.
• [C83]  F.H. Clarke, Optimization and Nonsmooth Analysis, John Wiley, New York, 1983 (Reprinted in 1990: Vol. 5, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia.
• [C05]  F.H. Clarke, Necessary Conditions in Dynamic Optimization, Memoirs Amer. Math. Soc. 816, vol. 178 (2005).
• [CCLV06]  F.H. Clarke, P. Caines, X. Liu, R. Vinter, A maximum principle for hybrid optimal control problems with pathwise constraints, Proc. 45th Conf. on Dec. and Control, pp. 4821-4825, IEEE, 2006.
• [CLSS97]  F.H. Clarke, Y.S. Ledyaev, E.D. Sontag, A.I. Subbotin, Asymptotic controllability implies feedback stabilization, IEEE Trans. Automat.Contr., vol. 42, pp. 1394–1407, Oct. 1997.
• [CV89]  F.H. Clarke, R. Vinter, Optimal Multiprocesses, SIAM J. Cont. Optim., vol. 27, n 5, pp. 1072-1091 (1989).
• [dPFF02]  M.d.R. de Pinho, M.M.A. Ferreira, F.A.C. C. Fontes, An Euler-Lagrange Inclusion for Optimal Control Problems with State Constraints, Journal of Dynamical and Control Systems, 8, pp. 23-45, 2002.
• [dPFF09]  M.d.R. de Pinho, M.M.A. Ferreira, F.A.C.C.Fontes, On Possibly Nonregular Mixed Constrained Optimal Control Problems, International Journal of Mathematics and Statistics, ISSN 0973-8347, vol. 5, n. A09, pp. 42-51, 2009.
• [dPI02]  M.d.R. de Pinho, A. Ilchmann, Weak maximum principle for optimal control problems with mixed constraints, Nonlinear Anal., 48 (2002), pp. 1179–1196.
• [dPSL08]  M.d.R. de Pinho, G.N. Silva, P. Loewen, A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints, Preprint 2008.
• [dPV95]  M.d.R. de Pinho, R. Vinter, An Euler-Lagrange inclusion for optimal control problems, IEEE Trans. Automat. Control, 40 (1995), pp. 1191–1198.
• [dPV97]  M.d.R. de Pinho, R. Vinter, Necessary conditions for optimal control problems involving nonlinear differential algebraic equations, J. Math. Anal. Appl., 212 (1997), pp. 493–516.
• [dPVZ01]  M.d.R. de Pinho, R. Vinter, H.Zheng, A maximum principle for optimal control problems with mixed constraints, IMA J. Math. Control Inform., 18 (2001), pp. 189–205.
• [dPFF05]  M.d.R. de Pinho, M.M.A. Ferreira, F.A.C.C.Fontes, Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems, ESAIM Control Optim. Calc. Var., 11 (2005), pp. 614–632.
• [dPR08]  M.d.R. de Pinho, J. Rosenblueth, Necessary Conditions for Constrained Problems under Mangasarian-Fromowitz Conditions, SIAM J. Control Optim. 47 (2008), pp. 535–552.
• [F01]  F.A.C.C. Fontes, A general framework to designstabilizing nonlinear model predictive controllers, Systems and Control Letters , 42(2) pp 127--143, 2001.
• [FM03]  F.A.C.C. Fontes, L. Magni, Min-Max Model Predictive Control of Nonlinear Systems Using Discontinuous Feedbacks, IEEE Transactions on Automatic Control, Vol. 48, no. 10, pp. 1750-1755, 2003.
• [F02]  F.A.C.C. Fontes, Nondegenerate Necessary Conditions of Optimality for Control Problems with State Constraints, In Nonlinear Control Systems, A.B. Kurzhanski, A.L. Fradkov editors, pp. 45-50, 2002.
• [F03]  F.A.C.C. Fontes, Discontinuous Feedbacks, Discontinuous Optimal Controls, and Continuous-Time Model Predictive Control, International Journal of Robust and Nonlinear Control, vol. 13 (3-4), pp. 191--209, 2003.
• [FFV99]  M.M.A. Ferreira, F.A.C.C. Fontes, R. Vinter, Nondegenerate necessary conditions for nonconvex optimal control problems with state constraints, Journal of Mathematical Analysis and Applications, vol. 233, pp. 116–129, 1999.
• [FV94]  M.M.A. Ferreira, R. Vinter, When is the maximum principle for state constrained problems nondegenerate?, Journal of Mathematical Analysis and Applications, vol. 187, no. 2, pp. 438–467, 1994.
• [L09]  S.O. Lopes, Nondegenerate forms of the Maximum Principle for Optimal Control Problems with State Constraints, PhD thesis, Univ. Minho. January 2009.
• [M01]  J.M. Maciejowski, Predictive Control with Constraints, Prentice Hall, 2001.
• [M95]  B.S. Mordukhovich, Discrete approximations and refined Euler-Lagrange conditions for non-convex differential inclusions, SIAM J. Control Optim. 33, 882-915 (1995).
• [M06]  B.S. Mordukhovich, Variational Analysis and Generalized Differentiation, Volumes I and II. Grundlehren Math. 330, Springer-Verlag, Berlin, 2006.
• [P97]  E. Polak, Optimization: Algorithms and Consistent Approximation, Springer, New York, 1997.
• [PS00]  F. Lobo Pereira, G. Silva, Necessary Conditions of Optimality for Vector-valued Impulsive Control Problems, Systems & Control Letters, 40, pp. 205-215, 2000.
• [PS04]  F. Lobo Pereira, G. Silva, Lyapounov Stability of Measure Driven Differential Inclusions, Journal of Differential Equations, Volume 40, Number 8, pp. 1122–1130, August 2004.
• [RV99]  F. Rampazzo, R. Vinter, A theorem on the existence of neighbouring feasible trajectories with application to optimal control, IMA Journal o Mathematical Control and Information 16, (1999), 335-351.
• [V00]  R. Vinter, Optimal Control, Birkhauser, Boston (2000).

Publications 2011

In this section you will find a selection of recent publications from our team.

In Jornals

• Sofia O. Lopes, F.A.C.C. Fontes, M.d.R. de Pinho, On Constraint Qualifications for Nondegenerate Necessary Conditions Of Optimality Applied to Optimal Control Problems, Discrete and Continuous Dynamical Systems series A, AIMS, vol. 29, n. 2, 2011.
• M.d.R. de Pinho, F.A.C.C. Fontes, D.F.M. Torres, editores convidados, Special section Nonsmooth Analysis, Control and Optimization, European Journal of Control, Volume 17, No. 1, 2011.
• M.d.R. de Pinho, M.M.A. Ferreira, F.A.C.C. Fontes, F. Lobo Pereira, G. Smirnov, D.F.M. Torres, editores convidados. Special Issue of the Discrete and Continuous Dynamical Systems - Series A, In celebration of the 60th birthday of Francis Clarke and Richard Vinter, Discrete and Continuous Dynamical Systems - Series A, vol. 29, n. 2, 2011.
• Christos Gavriel, Sofia O. Lopes, Richard Vinter, Regularity of minimizers for higher order variational problems is one independente variable, Annual Reviews in Control, vol 35, n. 2, 2011.
• M.d.R. de Pinho, Ilya Shvartsman, Lipschitz continuity of optimal control and Lagrange multipliers in a problem with mixed and pure state constraints, Discrete and Continuous Dynamical Systems- Serie A, Vol.29 nº 2, pp.505-521, 2011.
• Francis Clarke, Yuri Ledyaev, MdR de Pinho, An extension of the Schwarzkopf multiplier rule in optimal control, SIAM J. Control and Optim, Vol.49 nº 2, pp.599-610, 2011.
• Md. Haider Ali Biswas, M.d.R de Pinho, A nonsmooth maximum principle for optimal control problems with state and mixed constraints - convex case, Dynamical Systems and Differential Equations, 174 - 183, Issue Special, September 2011.
• Aram V. Arutyunov, Dmitry Karamzin, F. Lobo Pereira, A Generalization of the Impulsive Control Concept: Controlling System Jumps, Discrete and Continuous Dynamical Systems- Serie A, Vol.29 nº 2, pp.403-415, 2011.
• Aram Arutyunov, Dmitry Karamzin, F. Lobo Pereira, The maximum principle for optimal control problems with bounded phase coordinates by R.V. Gamkrelidze and its relations with other optimality conditions, Doklady Mathematics, Vol.436 nº 6, pp.738-742, 2011.
• Aram Arutyunov, Dmitry Karamzin, F. Lobo Pereira, The maximum principle for optimal control problems with state constraints by R.V. Gamkrelidze: Revisited, Journal of Optimization Theory and Applications, pp.5-20, 2011.
• Sofia O. Lopes, F.A.C.C. Fontes, Normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints, (Submetido em Outubro 2011).
• Luís A.C. Roque, Dalila B.M.M. Fontes, and Fernando A.C.C. Fontes, An Improved Biased Random Key Genetic Algorithm Approach to the Unit Commitment Problem, (Submetido em Dezembro 2011).
• Marta S.R. Monteiro, Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, Concave Minimum Cost Network Flow Problems Solved with a Colony of Ants, (Submetido em Dezembro 2011).
• Sofia O. Lopes, F.A.C.C. Fontes, Rui M. S. Pereira, Gaspar J. Machado and A. Manuela Gonçalves, An optimal control approach to irrigation planning problems, (Submetido em Dezembro 2011).

In Books

• Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, Amélia Caldeira, Optimal formation switching with collision avoidance and allowing variable agent velocities, In Dynamics of Information Systems: Mathematical Foundations. A. Sorokin, P.M. Pardalos, R. Murphey, M.T. Thai (eds.) Springer, 2012.(Aceite Junho 2011).
• Paulo A. Pereira, Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, A Hybrid Genetic Algorithm for Constrained Combinatorial Problems: An Application to Promotion Planning Problems, In Operations Research Proceedings 2010, Springer Verlag, 2011.
• Luís Roque, Dalila B.M.M. Fontes, Fernando A. C. C. Fontes, A biased random key genetic algorithm approach for the unit commitment problem, In Experimental Algorithms. Panos M. Pardalos and Steffen Rebennack editors. Lecture Notes in Computer Science, Volume 6630 , pp.327-339, 2011.

In Proceedings (full articles)

• Luís Roque, Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, BRKGA Adapted To Multiobjective Unit Commitment, ICORES 2012, Algarve, Fevereiro 2012, Accepted.
• Sofia O. Lopes, Fernando A.C.C. Fontes, Rui M.S. Pereira, Gaspar J. Machado, Irrigation Planning in the context of Climate Change, International Conference on Mathematical Models for Engineering Science (MMES '11), Tenerife,10-12 Dez 2011.
• Sofia O. Lopes, Fernando A.C.C. Fontes and M.d.R. de Pinho, On the Relation Between Inward Pointing Velocity Condition, ICNAAM, Halkidiki, Greece, 21 September 2011.
• Marta S.R. Monteiro, Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, An Ant Colony Optimization Approach for Minimum Spanning Tree Problems in Nonlinear Costs Network Flows, International Conference on Operations Research - OR2011, Zurich, Switzerland, August 30 - September 2 2011.
• Marta S.R. Monteiro, Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, An Ant Colony Optimization Algorithm to Solve the Minimum Cost Network Flow Problem with Concave Cost Functions, GECCO'11, Dublin, Ireland, 12-16 Julho 2011
• Tiago Pereira do Nascimento, Fernando A.C.C. Fontes, António Paulo Moreira, André Gustavo Scolari Conceição, Leader Following Formation Control For Omnidirectional Mobile Robots: The Target Chasing Problem, 8th International Conference on Informatics in Control, Automation and Robotics - ICINCO 2011, Noordwijkerhout, The Netherlands, July 28 - 31, 2011.
• Tiago Nascimento, Hugo Alves, André Gustavo Scolari Conceição, Fernando A.C.C. Fontes, António Paulo Moreira. A Generic Framework for Multi-Robot Formation Control, RoboCup Symposium 2011.
• Luís Roque, Dalila B.M.M. Fontes, Fernando A. C. C. Fontes, A Biased Random Key Genetic Algorithm approach for Unit Commitment Problem, International Symposium on Experimental Algorithms, Crete, Greece, April 2011.

In Proceedings (abstracts)

• Amélia Caldeira, Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, Optimal Switching of Agent Formations with Collision Avoidance and Allowing Variable Path Curvatures, Optimization 2011, Lisbon (Caparica), Portugal July 24-27, 2011.
• Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, Amélia Caldeira, Changing the geometry of agent formations in Minimal time: collision avoidance and variable agent velocities, 3rd Porto Meeting on Mathematics for Industry, porto, 28-30 April 2011.
• Marta S.R. Monteiro, Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, Um algoritmo das formigas para a resolução de problemas de transportes com custos fixos, 15º Congresso da Associação Portuguesa de Investigação Operacional - IO2011, Coimbra, April, 18-20, 2011.
• Fernando A.C.C. Fontes, Model Predictive Control of Nonholonomic Vehicle Formations, 1st SADCO industrial workshop & kick off meeting, March 2-4 , Paris.
• Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, Amélia Caldeira, Switching of agent formations with collision avoidance and allowing variable agent velocities, DIS 2011 – Int. Conference on the Dynamics of Information Systems Gainesville, FL U.S.A., February 16-18, 2011.
• Christos Gavriel, Sofia O. Lopes, Richard Vinter, Regularity of Minimizers for Higher Order Variational Problems, Workshop SADCO Summer School, London, UK, 5-9 September 2011.
• M.d.R. de Pinho, Necessary Conditions for Constrained Optimal Control Problems, First SADCO Industrial workshop & kick off meeting of the project 264735-SADCO, the European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN, ENSTA, Paris, France, March, 2011.
• M.M.A. Ferreira, Optimal Control Problems in the Management of Hydroelectric Resources, Summer School and Workshop of the project 264735-SADCO, the European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN, Imperial College, London, UK, September 5-9, 2011.

Contact information

To request information or send a general comment/question about this project, please send an email to faffe.up.pt. Please include your full name, affiliation and workfield.

Grant opportunities

Please find our available positions below. Click on the link to see the full job description and contact information to apply.

• Research Grant (BI) for MSc holders (M/F)  

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