Objetivos e Atividades
The main objective of the TOCCATA is to bring together in one project the three different axes of optimal control (theory, applications and numerical methods) and to explore its synergies to contribute for the advances of the state of the art. At the same time, we hope to contribute to the creation of a vibrant, productive and efficient optimal control research community in Portugal, to attract young researchers, to increase awareness of the benefits of optimal control areas on different as biomedicine and economics and to deliver value to the society.
Activity: besides the scientific outcome of this project, the research team has promoted and supported the organization of the yearly conferences EPCO (encontro português de controlo ótimo), and organized the international conference NHOC2017. Two special issues in DCDS and SVA were done. Two national projects, UPWIND and TOCHAIR came up as a consequence of the research done in this project.
Resultados Esperados/Atingidos
Applications of Distributed Optimal Control Problem with Allocation of a Common Resource, new and stronger conditions for normality new optimality conditions for optimal control problems (sweeping systems, hybrid, nonregular mixed constrained and delayed), strengthened form of maximum principle condition.
New numerical methods for problems involving sweeping systems, multiobjective problems, singular optimal problems with singular arcs, new results on mesh refinement and adaptive mesh refinement, indirect method to solve Zero-sum differential game problems, method based on bilevel optimization and optimal control reformulation for solution of Zero-sum differential game problems.
A long list of applied problems were considered, formulated, studied and solved numerically. Numerical solutions validated or partially validated using numerical implementation of optimality conditions.
More work than planned was done. However, some new verifiable conditions not successful yet.
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