| Summary: |
This project aims to contribute to the development of Optimal Control methods and applications. It focuses on building
bridges between theory, applications and numerical treatment of optimal control problems by solving a selected
number of problems from different areas.
This project is launched as a continuation of the work initialized with the FCT project PTDC/EEI-AUT/1450/2012|
FCOMP-01-0124-FEDER-028894. It brings together a renewed researcher team with a multidisciplinary background
including Optimal Control Theory, Control Engineering, Optimization and Numerical Analysis to work on theoretical
developments in conjunction with interesting and relevant applications of optimal control.
We seek to bring together major Portuguese research centers in Optimal Control to promote the exchange of
experience and knowledge based on on-going research activities, the training of young researchers and to deliver
value to the society. The proposed Research Team will collaborate closely with EU and American research groups
to explore new research methods and to promote the introduction of optimal control methods on different areas. We
aim to contribute to the creation of a vibrant, productive and efficient optimal control research community, to attract
young researchers, to increase awareness of the benefits of optimal control areas as different as biomedicine and
economics and to deliver value to the society.
While the driving force behind the choice of applications to be studied will be the need to test and illustrate recent
theoretical advances, we expect the applications themselves to trigger new theoretical development. Many results
leading to a characterization of solution to optimal control problems may be used to validate numerical solutions (i.e.,
to verify that a certain solution is possibly an optimal solution). However, the numerical verification of optimality is
in general a hard task. We hope to remedy some of these situations by proposing num  |
Summary
This project aims to contribute to the development of Optimal Control methods and applications. It focuses on building
bridges between theory, applications and numerical treatment of optimal control problems by solving a selected
number of problems from different areas.
This project is launched as a continuation of the work initialized with the FCT project PTDC/EEI-AUT/1450/2012|
FCOMP-01-0124-FEDER-028894. It brings together a renewed researcher team with a multidisciplinary background
including Optimal Control Theory, Control Engineering, Optimization and Numerical Analysis to work on theoretical
developments in conjunction with interesting and relevant applications of optimal control.
We seek to bring together major Portuguese research centers in Optimal Control to promote the exchange of
experience and knowledge based on on-going research activities, the training of young researchers and to deliver
value to the society. The proposed Research Team will collaborate closely with EU and American research groups
to explore new research methods and to promote the introduction of optimal control methods on different areas. We
aim to contribute to the creation of a vibrant, productive and efficient optimal control research community, to attract
young researchers, to increase awareness of the benefits of optimal control areas as different as biomedicine and
economics and to deliver value to the society.
While the driving force behind the choice of applications to be studied will be the need to test and illustrate recent
theoretical advances, we expect the applications themselves to trigger new theoretical development. Many results
leading to a characterization of solution to optimal control problems may be used to validate numerical solutions (i.e.,
to verify that a certain solution is possibly an optimal solution). However, the numerical verification of optimality is
in general a hard task. We hope to remedy some of these situations by proposing numerically verifiable optimality
conditions and such conditions on regularity and normality. Special attention will be paid to problems with state
constraints, mixed constraints, bang-bang controls, singular controls, bang-singular junctions. We shall also be
concerned with the synthesis of controlled trajectories, sensitivity analysis of the solutions to parameters and Model
Predictive Control techniques.
Selected problems from biomedicine, such as epidemiology, power systems; economics and also more classical areas
such as the planning of trajectories of unmanned vehicles will be considered. The challenges related to applied
problems that will be addressed can be divided into four classes
a) formulation of the problems for some applications;
b) solving the problems numerically via optimization methods;
c) establishing the optimality of the numerical solution;
d) connections between the types of solutions and concepts of the application under study.
While b) and c) fall within the expertise of the research team, their collaborators and the project advisory board, items
a) and d) above will be conducted in close consultation with experts on the specific area of the applied problems.
The choice of problems is based primarily on their societal interest but it is done to ascertain that their
analytical treatment will trigger the need for improvements of theoretical results. We do not intend to address modeling
issues. Rather we shall work with known models. However, we will seek to break new ground and to obtain new
insight on the problems with innovative choices of objective functions, reformulatio |