Optimal Control:
Health, Energy and Robotics Applications

Institutions involved

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

Objectives

1. Research and application of optimization and optimal control methods.  

2. Analyze, simulate and numerically solve various problems modeling situations in areas as different as health, energy and robotics.  

3. Obtain new optimal control methods useful to characterize solutions of problems.    

The applications are here used as a driving force behind the theoretical developments. Although their choice is based on their societal interest, some problems are nevertheless chosen to ascertain that their analytical and numerical treatments trigger the need for new and improvements of theoretical and numerical results. Driven by applications it is our aim to contribute with theoretical results in areas like normality of the maximum principle, regularity of solutions and multipliers associated with the solutions of our problems and optimization based control.

Meet the people behind the project.

Team

• Adriano Carvalho (FEUP) 
• Amélia C.D. Caldeira (ISEP) 
• Ana Filipa Ribeiro (FEUP) 
• António Paulo Moreira (FEUP) 
• Delfim F.M. Tores (UAveiro) 
• Fernando A.C.C. Fontes (FEUP) 
• Fernando Lobo Pereira (FEUP) 
• Igor Kornienko (FEUP) 
• José Lima (FEUP) 
• Luís Tiago Paiva (FEUP) 
• Luís Roque (ISEP) 
• M. Margarida A. Ferreira (FEUP), Coordinator 
• Maria do Rosário de Pinho (FEUP) 
• Md. Haider Ali Biswas (FEUP) 
• Paulo Costa (FEUP) 
• LShakoor Pooseh (UA) 
• Sofia O. Lopes (UM) 
• Tatiana Odzijewicz (UA) 

Research Grants

• Ana Filipa Ribeiro (BI, 6 months) 
• Filipa Nogueira (BPD,12 months) 
• Igor Kornienko (BI, 6 months) 
• Luís Tiago Paiva (BI, 6 months) 
• Tatiana Martins Pinho (BI, 6 months) 

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

• [PFFPT11]  Maria do Rosario de Pinho, M.M.A. Ferreira, F. A. C. C. Fontes, F. Lobo Pereira, Delfim F. M. Torres, 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- Serie A, Vol.29 nº2, pp.i-ii, 2011. doi: 10.3934/dcds.2011.29.2i
• [Cd10]  F Clarke and MdR de Pinho, Optimal Control with Mixed Constraints, SIAM J. Control Optimization, Vol.48, n. 7, pp. 4500-4524, 2010.
  
• [LSFd05]  MdR de Pinho, M. M. Ferreira, U. Ledzewicz and H. Schaettler. A model for cancer chemotherapy with state-space constraints. Nonlinear Analysis 63, e2591–e2602, 2005.
  
• [GLV11]  Gavriel, C., Lopes, S., Vinter, R., “Regularity of minimizers for higher order variational problems is one independente variable", Annual Reviews in Control 35 (2), 172-177, 2011.
  
• [AP06]  A.V. Arutyunov and F. Lobo Pereira, Second-order necessary optimality conditions for problems without a priori normality assumptions, Mathematics of Operations Research, INFORMS, vol. 31, nº 1, pp 1-12, 2006.
  

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

• [Aru00]  A.V. Arutyunov, Optimality Conditions: Abnormal and Degenerate Problems, Kluwer Academic Publishers, Dordrecht/Boston/London, 2000.
• [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.
• [BTFR12]  Piernicola Bettiol and Hélène Frankowska, Lipschitz regularity of solution map of control systems with multiple state constraints, Discrete and Continuous Dynamical Systems - Series A, AIMS, 32 (1), pp. 1-26, 2012.
• [BTFRVT12]  Piernicola Bettiol, Hélène Frankowska and Richard Vinter, L∞ estimates on trajectories confined to a closed subset, Journal of Differential Equations, Elsevier, 252 (2), pp. 1912-1933, 2012.
• [BFZ10]  O. Bokanowski, N. Forcadel, H. Zidani, Reachability and minimal times for state constrained nonlinear problems without any controllability assumption. SIAM J. Control Optim. 48(7), 4292—4316, 2010.
• [BZ11]  Ariela Briani and Hasnaa Zidani, Characterization of the value function of final state constrained control problems with BV trajectories, Communication on Pure and Applied Analysis, AIMS, 10 (6), pp. 1567-1587, 2011.
• [CCG11]  Jean-Baptiste Caillau, Olivier Cots and Joseph Gergaud, Differential pathfollowing for regular optimal control problems, Optim. Methods Softw., pp. 1-20, 2011.
• [CCCDH11]  Yair Censor, Wei Chen, P.L. Combettes, Ran Davidi, Gabor Herman. On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints, Computational Optimization and Applications, Springer, 2011.
• [Cd10]  F Clarke and MdR de Pinho, Optimal Control with Mixed Constraints, SIAM J. Control Optimization, Vol.48, n. 7, pp. 4500-4524, 2010.
• [C05]  F.H. Clarke, Necessary Conditions in Dynamic Optimization, Memoirs Amer. Math. Soc. 816, vol. 178 (2005).
• [C90]  F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley, NewYork. (Reprinted in 1990: Vol. 5, Classics in Applied Mathematics,Society for Industrial and Applied Mathematics, Philadelphia, Pa.), 1983.
• [dS11] MdR 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.
• [dFF02] M.d.R. de Pinho, M.M.A. Ferreira and 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.
• [FFV99]  M. M. A. Ferreira, F. A. C. C. Fontes, and R. B. Vinter, Nondegenerate necessary conditions for nonconvex optimal control problems with state constraints, Journal of Mathematical Analysis and Applications, vol. 233, pp. 116–129, 1999.
• [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.
• [Fon01]  F.A.C.C. Fontes, A General Framework to Design Stabilizing Nonlinear Model Predictive Controllers. Systems & Control Letters, Vol. 42, pp 127-143, 2001.
• [FLM97]  KR Fister, S. Lenhart, JS Mc Nally. Optimizing chemotherapy in an HIV model. Electronic Journal of Differential Equations; 32:1–12, 1998.
• [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.
• [FRMA11]  Hélène Frankowska and Marco Mazzola, Optimal Synthesis and Normality of the Maximum Principle for Optimal Control Problems with Pure State Constraints, 2011 9th IEEE International Conference on Control and Automation (ICCA), Santiago, Chile. pp. 945-950, 2011.
• [FFC09]  Fernando A. C. C. Fontes , Dalila B. M. M. Fontes, Amélia C. D. Caldeira Model Predictive Control of Vehicle Formations. in Optimization and Cooperative Control Strategies, Springer, pp.371-384, 2009.
• [HOE11]  Daniel Hoehener, Second-Order Optimality Conditions for a Bolza Problem with Mixed Constraints, 18th IFAC World Congress, Milano, Italy. World Congress, 18, Part 1, pp. 2594 – 2599, 2011.
• [KK91]  WO Kermackand A.G. McKendrick. Contributions to the mathematical theory of epidemics. Bulletin of Mathematical Biology 53, 35–55, 1991.
• [L04]  J. W. Labadie, Optimal operation of multireservoir systems: State-of-the-art review, Journal of Water Resources Planning and Management, 130(2):93-111, 2004.
• [LEMASC11]  Urszula Ledzewicz, Helmut Maurer and Heinz Schaettler, Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy, Mathematical Biosciences and Engineering, AIMS, 8 (2), pp. 307-323, 2011.
• [LFd11] Sofia O. Lopes, F. A. C. C. Fontes, MdR 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, pp.559-575, 2011.
• [PBGM63] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, John Wiley & Sons, New York, 1963.
• [RGSV12] A.F.Ribeiro, M.C.M. Guedes, G.V. Smirnov, S. Vilela, On the optimal control of a cascade of hydro-electric power stations, Electric Power Systems Research, 2012.
• [RFF11] 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.
• [Sim2] Paulo G. Costa, SimTwo - A Realistic Simulator for Robotics. SimTwo, 2012.
• [V00]  R. Vinter, Optimal Control, Birkhauser, Boston (2000).

Publications 2013 - 2015

Theses (PhD)

• [BT13]  M. Haider Ali Biswas, Necessary Conditions for Optimal Control Problems with State Constraints: Theory and Applications, Universidade do Porto, Fac. Eng., PDEEC, PhD Thesis, 2013.
• [KT15]  Igor V. Kornienko, First order optimality conditions under state constraints, PDEEC, Universidade do Porto, Fac. Engenharia, PhD Thesis, 2015.
• [PT14]  Luis Tiago Paiva, Numerical Methods in Optimal Control and Model Predictive Control,PDMA, Universidade do Porto, PhD Thesis, December 2014.
• [RT14]  Ana Filipa C. A. Ribeiro, Mathematical problems of hydro-electric power stations management, PDMA, Universidade do Porto, PhD Thesis, December 2014.
• [R14]  Luis Roque, , Optimization Methods for the Unit Commitment Problem in Electric Power Systems,PDMA, Universidade do Porto, PhD Thesis, December 2014.
• [SP13]  Shakoor Pooseh, Computational Methods in the Fractional Calculus of Variations and Optimal Control, University of Aveiro, PhD Thesis, 2013.
• [TO13]  Tatiana Odzijewicz, Generalized Fractional Calculus of Variations, University of Aveiro, PhD Thesis, 2013.

Theses (MSc)

• [AAAA14] António Alberto Assunção Araújo, Análise e tratamento numérico de problemas de controlo ótimo na gestão de energia hidroelétrica. Universidade do Porto, Fac. Eng., Mestrado Integrado em Engenharia Electrotécnica e de Computadores, MSc Thesis, 2013
• [AGS14]  Armando Gonçalo Silva, Análise, simulação e resolução numérica de problemas de controlo ótimo considerando modelos de gestão de recursos hidroeléctricos. Universidade do Porto, Fac. Eng., Mestrado Integrado em Engenharia Electrotécnica e de Computadores, MSc Thesis, 2014.
• [DBM15]  Diogo Marques Bastos, Computer Aid for Dieting and Weight Control Using Model Predictive Control, Universidade do Porto, Fac. Eng., Mestrado Integrado em Engenharia Electrotécnica e de Computadores, MSc Thesis, 2015.
• [PS14]  Pedro Diogo Pinto da Silva, Planeamento otimizado de movimento de robô submarino Universidade do Porto, Fac. Eng., Mestrado Integrado em Engenharia Electrotécnica e de Computadores, MSc Thesis, 2015.
• [TCMM14]  Tiago Costa Moreira Maia, Optimal control of power kites for wind power production. Universidade do Porto, Fac. Eng., Mestrado Integrado em Engenharia Electrotécnica e de Computadores, MSc Thesis, 2014.
• [APLP]   Ana Pedro Lemos Paião, Introduction to Optimal Control Theory and its Application to Diabetes, University of Aveiro, MSc Thesis, 2015.

Books

• [APT15] R. Almeida, S. Pooseh and D. F. M. Torres, Computational Methods in the Fractional Calculus of Variations, Imperial College Press, London, 2015.
• [MOT15] A. B. Malinowska, T. Odzijewicz and D. F. M. Torres, Advanced methods in the fractional calculus of variations, Springer Briefs in Applied Sciences and Technology, Springer, Cham, 2015.

Book Chapters

• [FFR14]   Dalila B.M.M. Fontes, Fernando A.C.C. Fontes, Luís A.C. Roque. “Optimal Control Formulations for the Unit Commitment Problem”. In “Dynamics of Information Systems - Computational and Mathematical Challenges”. C. Vogiatzis, R. Murphey, P. M. Pardalos (eds.). Volume 105 of the series Springer Proceedings in Mathematics & Statistics pp 109-127, Springer, 2014.
• [MFF14b] M.S.R. Monteiro, D.B.M.M. Fontes, F. A.C.C. Fontes; ,Hop-constrained tree-shaped networks,Examining Robustness and Vulnerability of Networked Systems,,"S. Butenko, E.L. Pasiliao, V. Shylo",192-208,2014,"NATO Science for Peace and Security Series: Information and Communication Security, IOS Press".
• [RMT14]  H. S. Rodrigues, M. T. T. Monteiro and D. F. M. Torres, Optimal Control and Numerical Software: An Overview. In: Systems Theory: Perspectives, Applications and Developments (Editor: Francisco Miranda), Nova Science Publishers, New York, 2014, 93--110. Preprint: http://arxiv.org/abs/1401.7279.
• [ST15b]  C. J. Silva and D. F. M. Torres, Optimal Control of Tuberculosis: A Review. In: J. P. Bourguignon et al. (eds.), Dynamics, Games and Science, CIM Series in Mathematical Sciences 1, Springer, 2015, 701--722. Preprint: http://arxiv.org/abs/1406.3456.

Papers in International Journals with Reviewing

• [AKP15]  Arutyunov, A.V., Karamzin, D.Y., Pereira, F.L., “State Constraints in Impulsive Control Problems: Gamkrelidze-Like Conditions of Optimality”, Journal of Optimization Theory and Applications, Volume 166 Issue 2, 2015, pp. 440-459.
• [AT15a]  R. Almeida and D. F. M. Torres, Computing Hadamard type operators of variable fractional order, Appl. Math. Comput. 257 (2015), 74--88. Preprint: http://arxiv.org/abs/1412.5229.
  
• [AT15b]  R. Almeida and D. F. M. Torres, A discrete method to solve fractional optimal control problems, Nonlinear Dynam. 80 (2015), no. 4, 1811--1816. Preprint: http://arxiv.org/abs/1403.5060.
  
• [BOT14]  L. Bourdin, T. Odzijewicz and D. F. M. Torres, Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition -- Application to fractional variational problems, Differential Integral Equations 27 (2014), no. 7/8, 743--766. Preprint: http://arxiv.org/abs/1403.3937
• [BPP14]  M. H. A. Biswas, L. T. Paiva and Maria do Rosario de Pinho. A SEIR Model for Control of Infectious Diseases with Constraints, Mathematical Biosciences and Engineering, 11(4): 761-784, 2014. doi:10.3934/mbe.2014.11.761.
• [CT15]  M. C. Caputo and D. F. M. Torres, Duality for the left and right fractional derivatives, Signal Process. 107 (2015), 265--271. Preprint: http://arxiv.org/abs/1409.5319.
• [DMT14]  M. Dryl, A. B. Malinowska and D. F. M. Torres, An Inverse Problem of the Calculus of Variations on Arbitrary Time Scales, Int. J. Difference Equ. 9 (2014), no. 1, 53--66.
• [dP15]   M. H. A. Biswas and MdR de Pinho. A Nonsmooth Maximum Principle for Optimal Control Problems with State and Mixed Constraints, ESAIM- COCV, Volume 21, Number 4, October-December 2015, pp. 939 – 957
• [DRMCEST15]  R. Denysiuk, H. S. Rodrigues, M. T. T. Monteiro, L. Costa, I. Espírito Santo and D. F. M. Torres, Multiobjective approach to optimal control for a dengue transmission model, Stat. Optim. Inf. Comput. 3 (2015), no. 3, 206--220. Preprint: http://arxiv.org/abs/1506.08019.
• [DST15]  R. Denysiuk, C. J. Silva and D. F. M. Torres, Multiobjective approach to optimal control for a tuberculosis model, Optim. Methods Softw. 30 (2015), no. 5, 893--910. Preprint: http://arxiv.org/abs/1412.0528.
• [DT14]  M. Dryl and D. F. M. Torres, Necessary condition for an Euler -Lagrange equation on time scales, Abstr. Appl. Anal. 2014 (2014), Art. ID 631281, 7 pp.
• [FF15]   Fernando A.C.C. Fontes, Helene Frankowska.”Normality and Nondegeneracy for Optimal Control Problems with State Constraints''.Journal of Optimization Theory and Applications (online from February 2015, DOI: 10.1007/s10957-015-0704-1).
• [FL13]  F. A. C. C. Fontes, Sofia O. Lopes. “Normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints”. Journal of Mathematical Analysis and Applications, Vol. 399, no 1, pp.27-37, 2013.
• [FRS14]  M.M.A. Ferreira, A.F. Ribeiro and G.V. Smirnov, Local Minima of Quadratic Functionals and Control of Hydro-Electric Power Stations, JOTA-Journal of Optimization Theory and Applications, DOI 10.1007/s10957-014-0610-y.
• [KOPS15]   Karamzin, D.Y., De Oliveira, V.A., Pereira, F.L., Silva, G.N., On the properness of an impulsive control extension of dynamic optimization problems, ESAIM - Control, Optimisation and Calculus of Variations, Volume 21, Issue 3, 1 July 2015, Pages 857-875.
• [KPP14]   Igor Kornienko, Luís Tiago Paiva, Maria do Rosário de Pinho, Introducing State Constraints in Optimal Control for Health Problems, Procedia Technology, Volume 17, 2014, pp 415–422.
• [LFP13]  Sofia O. Lopes, Fernando A. C. C. Fontes, Maria do Rosário de Pinho. “An Integral-type Constraint Qualification to Guarantee Nondegeneracy of the Maximum Principle for Optimal Control Problems with State Constraints”. Systems & Control Letters, Vol. 62, Issue 8, pp. 686–692, 2013. DOI: 10.1016/j.sysconle.2013.05.005
• [MFF13]  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”. Journal of Heuristics, Volume 19, Issue 1 , pp. 1-33, 2013.
• [MFF14]  Marta S.R. Monteiro, Dalila B.M.M. Fontes, Fernando A.C.C. Fontes. “Hop-constrained Minimum Spanning Tree Problems in Nonlinear Cost Network Flows: an Ant Colony Optimization Approach”. Optimization Letters (Publicado Online em Junho 2014.
  DOI:10.1007/s11590-014-0762-6.
• [MFF15]  Marta SR Monteiro, Dalila BMM Fontes, Fernando ACC Fontes. “Hop-constrained Minimum Spanning Tree Problems in Nonlinear Cost Network Flows: an Ant Colony Optimization Approach''. Optimization Letters, Volume 9, Issue 3, pp 451-464, 2015.
• [OT14]  T. Odzijewicz and D. F. M. Torres, The Generalized Fractional Calculus of Variations, Southeast Asian Bull. Math. 38 (2014), no.1, 93--117.
• [PBT14]  M. Benharrat and D. F. M. Torres, Optimal control with time delays via the penalty method, Math. Probl. Eng. 2014 (2014), Art. ID 250419, 9pp.
• [PF15]  L.T Paiva, Fernando A.C.C. Fontes. ``Adaptive Time-Mesh Refinement in Optimal Control Problems with State Constraints''. Discrete and Continuous Dynamical Systems, Volume 35, Number 9, pp. 4553-4572, September 2015.
• [PK15]   MdR de Pinho, Igor Kornienko. Differential Inclusion Approach for Mixed Constrained Problems Revisited, Set-Valued and Variational Analysis, September 2015, Volume 23, Issue 3, pp 425-441 (First online: 17 January 2015).
• [RFF14]  Luís A.C. Roque, Dalila B.M.M. Fontes, Fernando A.C.C. Fontes. “A Hybrid Biased Random Key Genetic Algorithm Approach to the Unit Commitment Problem". Journal of Combinatorial Optimization, (online from February 2014, DOI: 10.1007/s10878-014-9710-8), 2014.
• [RMT14]  H. S. Rodrigues, M. T. T. Monteiro and D. F. M. Torres, Optimal Control and Numerical Software: An Overview. In: Systems Theory: Perspectives, Applications and Developments (Editor: Francisco Miranda), Nova Science Publishers, New York, 2014, 93--110. Preprint
• [RT15a]  A. Rachah and D. F. M. Torres, Mathematical modelling, simulation, and optimal control of the 2014 Ebola outbreak in West Africa, Discrete Dyn. Nat. Soc. 2015, Art. ID 842792, 9 pp. Preprint
• [SMT15]   S. P. S. Santos, N. Martins and D. F. M. Torres, Variational problems of Herglotz type with time delay: DuBois--Reymond condition and Noether's first theorem, Discrete Contin. Dyn. Syst. 35 (2015), no.~9, 4593--4610. Preprint
• [ST13]  C. J. Silva and D. F. M. Torres, Optimal control for a tuberculosis model with reinfection and post-exposure interventions, Math. Biosci. 244 (2013), no. 2, 154--164. Preprint
• [ST14]  C. J. Silva and D. F. M. Torres, Modeling TB-HIV syndemic and treatment, J. Appl. Math. 2014 (2014), Art. ID 248407, 14pp.
• [ST15a]   C. J. Silva and D. F. M. Torres, A TB-HIV/AIDS coinfection model and optimal control treatment, Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4639--4663. Preprint
• [TAT15]   D. Tavares, R. Almeida and D. F. M. Torres, Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order, Optimization 64 (2015), no. 6, 1381--1391. Preprint

Papers accepted in International Journals with Reviewing

• [BFRS14]  V.A. Bushenkov, M.M.A. Ferreira, A.F. Ribeiro and G.V. Smirnov, Problem of Hydroelectric Resources Management: Numerical Approach, AMIS-Applied Mathematics & Information Sciences.
• [MP16]  Helmut Maurer, Maria do Rosario de Pinho, Optimal Control of Epidemiological SEIR Models with L1Objectives and Control -State Constraints, Pacific Journal of Optimization

Papers Submitted to International Journals with Reviewing

• [dP13]   M. H. A. Biswas and MdR de Pinho. A Nonsmooth Maximum Principle for Optimal Control Problems with State and Mixed Constraints (submitted 2013).
• [PK14]   MdR de Pinho, Igor Kornienko. Differential Inclusion Approach for Mixed Constrained Problems Revisited (submitted 2013).

Proceedings of International Conferences with Reviewing

• [AFR14]  Ana Filipa Ribeiro. Optimal Control for a Cascade of Hydroelectric Power Stations: Case Study. CONTROLO’2014- Proc. of the 11th Port. Conf. on Autom. Control, Lecture Notes in Electrical Engineering 321, pp.135--145; DOI: 10.1007/978-3-319-10380-8_15.
• [BFRS13]  V.A. Bushenkov, M.M.A. Ferreira, A.F. Ribeiro and G.V. Smirnov, Numerical approach to a problem of hydroelectric resources management, Proc. of ICNAAM 2013-11th International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Greece, p. 630-633, 21-27 september 2013.
• [D49]  Ionela Prodan, Sorin Olaru, Fernando A. C. C. Fontes, Cristina Nicoleta Stoica, Silviu-Iulian Niculescu. “A predictive control-based algorithm for path following for autonomous aerial vehicles”, 2013 IEEE Multi-conference on Systems and Control, Hyderabad, India, August 28th – 30th, 2013.
• [D50]  L.T. Paiva, F.A.C.C. Fontes. “Mesh refinement strategy for optimal control problems”. AIP Conference Proceedings ICNAAM 2013, 21–27 September 2013, Rhodes, Greece. AIP vol 1558, 2013, pp. 590-593 DOI : 10.1063/1.4825560
• [D51]  S.O. Lopes, F.A.C.C. Fontes, R.M.S. Pereira, A.M. Gonçalves, G.J. Machado. “Irrigation planning: An optimal control approach”. AIP Conference Proceedings ICNAAM 2013, 21–27 September 2013, Rhodes, Greece. AIP vol 1558, 2013, pp. 622-625 DOI : 10.1063/1.4825568
• [D52]  S.O. Lopes, F.A.C.C. Fontes, M.F.P Costa, R.M.S Pereira, A.M. Gonçalves, G.J. Machado. “Irrigation planning: Replanning and numerical solution”. AIP Conference Proceedings ICNAAM 2013, 21–27 September 2013, Rhodes, Greece. AIP vol 1558, 2013, pp. 626-629. http://dx.doi.org/10.1063/1.4825569
• [D53]  S.O. Lopes, F.A.C.C. Fontes, M.R. de Pinho, R. Pereira, A.M. Gonçalves, G.J. Machado. “An optimal control approach to the irrigation planning problem”. Proc. of Conferência Brasileira de Dinâmica, Controle e Aplicações (DINCON 2013), Fortaleza, Brasil, 13-17 Outubro 2013.
• [D54]  L.A.C. Roque, D.B.M.M. Fontes, F.A.C.C. Fontes. “Recent Results on Approximate Optimization Methods for the Unit Commitment Problem”. Proc. of EPESE’13-7th International Conference on Energy Planning, Energy Saving, Environmental Education, Paris, France, November 2013.
• [D55]  L.T. Paiva and F. A. C. C. Fontes. “Time-mesh refinement in optimal control problems for nonholomic vehicles”. Proc. of Conference on Electronics, Telecommunications and Computers, December 5-6, 2013. Lisbon, Portugal.
• [D56]  S. O. Lopes, F. A. C. C. Fontes, G. Machado, R. Pereira, and M. d. R. de Pinho. “Optimal control of the irrigation problem: characterization of the solution”. Proc. of Conference on Electronics, Telecommunications and Computers, December 5-6, 2013. Lisbon, Portugal.
• [D57]  Sofia O. Lopes, Fernando A.C.C. Fontes and M. Rosário De Pinho. “Optimal Control for an Irrigation Planning Problem: characterisation of solution and validation of the numerical results”. Proc. of CONTROLO 2014. Porto, Portugal, Julho 2014.
• [FRS13]  M.M.A. Ferreira, A.F. Ribeiro and G.V. Smirnov, Suficient Conditions of Optimality for Control of Hydro-Electric Power Stations, Proc. of ICNAAM 2013-11th International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Greece, p. 586-589, 21-27 september 2013.
• [KC14]  Igor Kornienko and MdR de Pinho. On First Order State Constrained Optimal Control Problems, Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), July 7-11, 2014, University of Groningen, Groningen, Netherlands, 2014.
• [KPD13]  Igor Kornienko, L. T. Paiva and MdR de Pinho. Introducing State Constraints in Optimal Control for Health Problems. Accepted for publication in Procedia Technology, Proceedings of CETC2013, Conference of Electronics, Telecommunications and Computer (to appear).
• [PKM14]  MdR de Pinho, Igor Kornienko, Helmut Maurer. Optimal Controlo f a SEIR Model with Mixed Constraints and L1 Cost. CONTROLO’2014- Proc. of the 11th Port. Conf. on Autom. Control, Lecture Notes in Electrical Engineering 321, pp.135--145; DOI: 10.1007/978-3-319-10380-8_14.
• [PMB04]  T. Pinho, A.P. Moreira and J. Boaventura-Cunha, Framework using ROS and SimTwo Simulator for Realistic Test of Mobile Robot Controllers, 11th Portuguese Conference on Automatic Control, Porto, July 2014.
• [RT15b]  A. Rachah and D. F. M. Torres, Modelling and Numerical Simulation of the Recent Outbreak of Ebola. In: Proceedings of the 2nd International Conference on Numerical and Symbolic Computation: Developments and Applications (SYMCOMP 2015), Universidade do Algarve, Faro, March 26-27, 2015. Edited by APMTAC (Editors: A. Loja, J. I. Barbosa and J. A. Rodrigues), pp. 179--190. ISBN 978-989-96264-7-8.

Presentations in Conferences

• [AIMS14:DT]  M. Dryl and D. F. M. Torres, Necessary condition for a dynamic Euler-Lagrange integro-differential equation, Special Session SS20: Dynamics with fractional and time scale derivatives, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 07 -- July 11, 2014 Madrid, Spain.
• [AIMS14:ST]  C. J. Silva and D. F. M. Torres, Application of Optimal Control to the Reduction of Co-Infected Tuberculosis-HIV/AIDS Individuals, Special Session: Optimal control and its applications, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications July 07 -- July 11, 2014 Madrid, Spain.
• [BCP15]   Diogo Bastos, Amélia Cladeira and Maria do Rosário de Pinho, Going on a Diet with a little help from Optimal Control, Workshop on Nonlinear Analysis and Optimization (inspired on Francis Clarke’s and Richard Vinter’s 65 birthday). The Royal Society, London, 7- 8 September, 2015.
• [BCP152]   Diogo Bastos, Amélia Cladeira and Maria do Rosário de Pinho, Application of model predictive control in dieting control, EPCO 2015 - Portuguese Meeting on Optimal Control, September 15th, University of Minho, Guimarães, Portugal.
• [BVP14]  Andrea Boccia, Richard Vinter and MdR de Pinho. On Optimal Control Problems with Mixed and Pathwise State Constraints. The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 7- 11, 2014, Madrid, Spain.
• [DGS14]  M. Dryl and D. F. M. Torres, Direct and Inverse Problems of the Calculus of Variations on Time Scales, International Conference Dynamics, Games and Science III, 17-21 of February, 2014, University of Porto, Portugal.
• [dPB14]  MdR de Pinho and M. H. A. Biswas. On Nonsmooth Maximum Principle for Problems with State and Mixed Constraints. The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 7- 11, 2014, Madrid, Spain.
• [E52]  Mário Amorim Lopes, Fernando A. C. C. Fontes, Dalila A. C. C. Fontes. “Optimal Control of Infinite-Horizon Growth Models - a direct approach". OMPC 2013 - SADCO Summer School and Workshop on Optimal and Model Predictive Control, University of Bayreuth, Germany, September 2013.
• [E53]  F.A.C.C. Fontes. “MPC for nonholonomic vehicles and vehicle formations”. Workshop on optimization-based Control and Estimation, Supelec, Paris, France, November 21-22, 2013.
• [E54]  L.T. Paiva, F.A.C.C. Fontes. Industrial Workshop on "Safety Systems, Driver Assistance and Optimal Control- DAOC, 27-28 January 2014, Wolfsburg, Germany.
• [E55]  Dalila B.M.M. Fontes, Fernando A.C.C. Fontes. “Project scheduling with alternative tasks subject to technical failure via dynamic programming”. INFORMS Optimization Society Conference Theory and Practice: Dealing with Big Data and other challenges, Houston, USA March 2014.
• [E56]  Sofia O. Lopes, Fernando A. C. C. Fontes, M.d.R. de Pinho. “An Overview of Stronger forms of Necessary Conditions for Dynamic Optimization Problems” Workshop Applied Variational Analysis. Braga, Portugal, Abril 2014.
• [E57]  F.A.C.C. Fontes, L.T. Paiva. “A dynamically adaptive mesh-grid algorithm for continuous-time model predictive control”. Conference on Optimization Control and Applications in the Information Age, Chalkidiki, Greece, June 15-20, 2014.
• [E58]  Sofia Lopes, Fernando A.C.C. Fontes“Normal Forms of Necessar Conditions of Optimality: Calculus of Variations and Optimal Control Problem”. Optimization 2014, Guimarães, Portugal, 28-30 julho 2014.
• [E59]  Luís Roque, Dalila Fontes, Fernando Fontes. “The Unit Commitment Problem with Periodicity Constraints”. Optimization 2014, Guimarães, Portugal, 28-30 julho 2014.
• [E60]  Sofia O. Lopes, Fernando A. C. C. Fontes. “Optimal Control Problems with Higher Index State Constraints”, EPCO 2014– Portuguese Meeting on Optimal Control, June 6, 2014.
• [E61]  Luís Tiago Paiva And Fernando A.C.C. Fontes. “Multi–Level Adaptive Time–Mesh Refinement in Optimal Control Problems” EPCO 2014– Portuguese Meeting on Optimal Control, June 6, 2014.
• [EPCO14]  M. Dryl and D. F. M. Torres, A General Delta-Nabla Calculus of Variations on Time Scales with Application to Economics, EPCO 2014 --- Portuguese Meeting on Optimal Control, June 6, 2014.
• [EPSCICON14]  D. F. M. Torres, The Fractional Calculus of Variations and The Fractional Optimal Control, International Conference on Power, Control, Signals and Computations (EPSCICON'14), Thrissur, Kerala, India, January 8-10, 2014.
• [EURO14:DT]  M. Dryl and D. F. M. Torres, Necessary condition for an Euler-Lagrange equation on time scales, EURO mini conference "Optimization in Natural Sciences", University of Aveiro, 5th-9th February, 2014.
• [EURO14:ST]  C. J. Silva and D. F. M. Torres, A Tuberculosis -HIV/AIDS model and optimal treatments for the reduction of co-infected individuals, EURO mini conference "Optimization in Natural Sciences", University of Aveiro, 5th-9th February, 2014.
• [FNB15]   Filipa Nogueira, Helmut Maurer, Maria do Rosário de Pinho, Optimal Control for Infectious Diseases, Micro and Macro Systems in Life Sciences (MMSLS 2015), June 8-13, 2015, Bedlewo, Poland.
• [FNER15]   Filipa Nogueira, Maria do Rosário de Pinho, Optimal control for Epidemiology: choice of cost and introduction of constraints, Erice MathCompEpi 2015, August 30 to September 4, 2015, Erice, Siciliy, Italy.
• [FNER215]   Filipa Nogueira, Maria do Rosário de Pinho, Optimal Control for the NIV Virus, Erice MathCompEpi 2015, August 30 to September 4, 2015, Erice, Siciliy, Italy.
• [FNP15]   Filipa Nogueira, Maria do Rosário de Pinho, Optimal Control for Epidemiology using SEIR models: the role of state and mixed constraints, 2015 AMS,EMS, SPM International Meeting, June 10-13, 2015, Porto, Portugal.
• [FP15]   F.A.C.C. Fontes, L.T. Paiva. An Adaptive Mesh Refinement Algorithm for Optimal Control Problems, SIAM Conference on Control and Its Applications, Paris, Julho 2015.
• [FP15_2]   F.A.C.C. Fontes, L.T. Paiva. Optimal control and model predictive control of kite power systems, 2015 Portuguese Meeting on Optimal Control, Guimarães, Setembro 2015.
• [FRS14_2]  M.M.A.Ferreira, A.F.Ribeiro and G.V.Smirnov, Optimal control for a system of hydroelectric power stations, EPCO- Encontro Português de Controlo Óptimo 2014. 6 June 2014, Aveiro. Portugal
• [FRS14_34]  M.M.A.Ferreira, A.F.Ribeiro and G.V.Smirnov, Optimality in the management of two hydroelectric power stations in cascade, VARIANT- 2nd Workshop on Variational Analysis and Applications, Braga, April 04, 2014.
• [FRS14_4]  M.M.A.Ferreira, A.F.Ribeiro and G.V.Smirnov, Optimality in the management of hydroelectric power stations in cascade, NetCo2014-Conference on new trends on optimal control. 23-27 June 2014. Tours, France.
• [FRS14_4b]  M.M.A.Ferreira, A.F.Ribeiro and G.V.Smirnov, Optimal control to analyze a hydroelectric power station, NetCo2014-Conference on new trends on optimal control. 23-27 June 2014. Tours, France.
• [FRS15]   M.M.A.Ferreira, A. F. Ribeiro and G.V.Smirnov, Optimal control for a hydroelectric power stations problem, Workshop on Nonlinear Analysis and Optimization (inspired on Francis Clarke’s and Richard Vinter’s 65 birthday). The Royal Society, London, 7- 8 September, 2015.
• [FRS15_2]   M.M.A.Ferreira, A. F. Ribeiro and G.V.Smirnov, Optimal control for a hydroelectric power stations problem, EPCO 2015 - Portuguese Meeting on Optimal Control, September 15th, University of Minho, Guimarães, Portugal.
• [FS15]   M.M.A.Ferreira and G.V.Smirnov, On sufficient conditions for a class of constrained problems with indefinite quadratic functionals, SIAM conference on Control & its Applications, July 8 − 10, 2015, Paris, France.
• [HM15]   Maria d Rosario de Pinho, Helmut Maurer, Optimal Control of Epidemiological Seir Models with L1-Objectives and Control-State Constraints, SIAM conference on Control & its Applications, July 8 – 10, Paris, France.
• [HMP15]   Maria d Rosario de Pinho, Helmut Maurer, Optimal Control of Epidemiological Seir Models with L1-Objectives and Control-State Constraints, 15th British-French-German Conference on Optimization, London, Imperial College, June 15--17, 2015.
• [IK15]   Maria do Rosário de Pinho, Igor Kornienko, A Maximum Principle for Implicit and DAE Systems, SIAM conference on Control & its Applications, July 8 – 10, Paris, France.
• [KL14]   N. Khalil and S. O. Lopes “Necessary conditions in normal form for Calculus of Variations Problems”, RICAM, France, November 17-21, 2014.
• [LF14]  S. O. Lopes, F. A. C. C. Fontes “Optimal Control Problems with Higher Index State Constraints”, Portuguese Meeting on Optimal Control 2014 - EPCO 2014, Aveiro, Portugal, 2014.
• [LF14a]   S. O. Lopes, F. A. C. C. Fontes “Nondegeneracy of the maximum principle for higher index constrained problems”, NHCO, Cascais, Portugal, September 8-10, 2014.
• [LFPGM13]  S. O. Lopes, F. A. C. C. Fontes, R. M. Pereira, A. Manuela Gonçalves and G. J. Machado “Preditive Control in an Irrigation Planning Problem", Summer school and workshop on optimal and model predictive control - OMPC 2013, Bayreuth, Germany, September 2013.
• [MEME14]  C. J. Silva and D. F. M. Torres, Optimal Control Interventions in Tuberculosis-HIV/AIDS, The International Conference "Mathematics and Engineering in Marine and Earth Problems" (MEME'2014), University of Aveiro, Portugal, July 22-25, 2014.
• [NHOC14]  D. F. M. Torres, Computational Methods in the Fractional Calculus of Variations, New Horizons on Optimal Control 2014 (NHOC2014), September 8-10, 2014, Cascais, Portugal.
• [Opt14]  C. J. Silva and D. F. M. Torres, Optimal Control Interventions in Tuberculosis-HIV/AIDS co-infection, Optimization 2014, University of Minho, Guimarães, Portugal, July 28-30, 2014.
• [PF15]   L.T. Paiva, F.A.C.C. Fontes. An adaptive mesh refinement method for state constrained optimal control problem, 2015 Portuguese Meeting on Optimal Control, Guimarães, Setembro 2015.
• [PFLGM13]   R. M. Pereira, F. A. C. C. Fontes, S. O. Lopes, A. Manuela Gonçalves and G. J. Machado ``Irrigation Planning Problem as an Optimal Control Problem´´, Mathematical Modelling and Numerical Simulation for Engineering Applications – MMNSEA 2013, Braga, Portugal, 2013.
• [RBFS13]   A.F.Ribeiro, V. A. Bushenkov, M. M. A. Ferreira and G. V. Smirnov, Numerical approaches in a problem of management of hydroelectric resources, ICCOPT 2013, The Fourth International Conference on Continuous Optimization, Costa da Caparica, Portugal, July 27 to August 1, 2013.
• [SDEDE14]  M. Dryl and D. F. M. Torres, Direct and Inverse Problems of the Calculus of Variations on Time Scales, Symposium on Differential and Difference Equations (SDEDE 2014), Homburg, Germany, 5th--8th September 2014.

EPCO 2014, Portuguese Meeting on Optimal Control, June 6, 2014, University of Aveiro, Aveiro, Portugal.

Delfim Torres, General Chair, Organizing Committee and Scientific Committee

Maria do Rosário de Pinho, Scientific Committee

Controlo 2014-11th Conference on Automatic Control, July 21-23, 2014, Porto Portugal.

António Paulo Moreira, General Chair, Organizing Committee and Scientific Committee

Maria do Rosário de Pinho, Organizing Committee and Scientific Committee

Fernando Fontes, Scientific Committee

Paulo Costa, Scientific Committee

NHOC, Wokshop New Horizonts on Optimal Control, September 8-10, 2014, Cascais, Portugal.

Steering Committee:

Maurizio Falcone, Città Universitaria, Roma, Italy

Hasnaa Zidani, INRIA Saclay - Ile de France, UMA

Organizing Committee:

Maria do Rosário de Pinho, FEUP, Universidade do Porto

Maria Margarida A. Ferreira, FEUP, Universidade do Porto

Igor Kornienko, FEUP, Universidade do Porto

Ana Filipa Ribeiro, FEUP, Universidade do Porto

EPCO 2015, Portuguese Meeting on Optimal Control, September 15, 2015, University of Minho, Guimarães, Portugal.

Sofia Lopes, General Chair, Organizing Committee

Amélia Caldeira, Organizing Committee

Tiago Paiva, Organizing Committee

Margarida Ferreira, Scientific Committee

Maria do Rosário de Pinho, Scientific Committee

Fernando Fontes, Scientific Committee

Delfim Torres, Scientific Committee

Matemática Fora de Horas

Although not organized under this project, the activity Matemática Fora de Horas had in its organization a researcher of this project. Such activity was directed to secondary students and it was intended to heighten interest in mathematics. For that, some common real life problems (including, in human health context, the problem of alcohol ingestion) were analysed in the context of mathematics.

Researcher: Amélia Caldeira

[1] RTP- Jornal da Tarde, 20-03-2014,

[2] Jornal Público, 10-01-2015,

[3] TVI – Jornal das 8, 24-01-2015,

Contact information

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