Igor Kornienko

Igor Kornienko - University of Porto

 Main host organisation: University of Porto, Portugal

• Supervisor: Maria do Rosário de Pinho
• Secondment organisation: University of Bayreuth, Germany
• Nationality: German
• Fellowship duration: April 2011 - March 2014
• Background: Igor obtained a joint degree in mathematics and economics from the University of Bayreuth in 2007. 
• Email address

SADCO project subject: First order optimality conditions under state constraints

Many practical optimal control problems involve state constraints. In some aerospace applications, for example, the requirement that a space vehicle must not overheat on re-entry into the earth’s atmosphere gives rise to a state constraint on the temperature variable. Necessary conditions for optimal control problems with state constraints are available. But they are restrictive and incomplete. Known conditions for the most part treat two special classes of problems, namely those involving pure state inequality constraints and those involving mixed control/state constraints. Our understanding of even these two classes is deficient. Numerical shooting methods for state constraint problems require a priori information about how the optimal trajectory switches onto and off the state constraint boundary, and this information is difficult to extract from the available optimality conditions. On the other hand, necessary conditions for mixed constraint problem are valid only under severe hypotheses requiring the existence of inward pointing velocities.
It is also the case that these two classes of problems are by no means exhaustive. This project area will address many of the unanswered, challenging questions in state constrained optimal control. It will aim, in particular, to provide necessary conditions for problems which fit into neither of the standard pure or mixed constraints frameworks, to relax the inward pointing hypotheses typically required for the derivation of mixed-constraint optimality conditions, and to obtain detailed information about the switching behavior of optimal arcs.

SADCO related publications