Abstract:
We present a model which consists of a control system coupled with a generalized equation, which we call Differential Generalized Equation (DGE). This model covers a large territory in control and optimization, such as differential variational inequalities, control systems with constraints, as well as necessary optimality conditions in optimal control. We study metric regularity and strong metric regularity of mappings associated with DGE by focusing in particular on the interplay between the pointwise versions of these properties and their infinite-dimensional counterparts.
Metric regularity of a control system subject to inequality state-control constraints is characterized. A sufficient condition for local controllability of a nonlinear system is obtained via metric regularity. Sufficient conditions for strong metric regularity in function spaces are presented in terms of uniform pointwise strong metric regularity. A characterization of the Lipschitz continuity of the control part of the solution mapping as a function of time is established. Finally, a path-following procedure for a discretized DGE is proposed for which an error estimate is derived.
About the speaker:
Asen Dontchev received successively M.Sc. (in 1971) and Ph.D. (in 1974) in Control Sciences from the Warsaw University of Technology. He became Doctor of Mathematical Sciences in 1987 and soon after that – full Professor. Currently he is Associate Editor at Mathematical Reviews, a division of the American Mathematical Society (since 1990) and Adjunct Professor at the University of Michigan (since 2000). From 2007 till 2009 Asen Dontchev served as a Program Director of the Analysis Program, DMS of the US National Science Foundation. Since 2009 Dontchev’s research has been funded by the National Science Foundation (USA). He has supervised 8 Ph.D. students.
Asen Dontchev has about 130 publications, including three books published by Springer, one of which was translated into Russian, and three textbooks. According to Google Scholar, his works have been cited more than 3700 times, and according to MathSciNet more than 1200 times by more than 500 authors (since 2000). He has served on editorial boards of SIAM Journal on Control and Optimization, SIAM Journal on Optimization (till 2009), Journal of Mathematical Analysis and Applications, Journal of Optimization Theory and Applications and many others.
Venue:
ACE room T121, T Building, Mt Helen Campus, Federation University Australia
How to participate in this seminar:
1. Book your nearest ACE facility;
2. Notify the seminar convenor at Federation University (Helen Wade) to notify you will be participating.
No access to an ACE facility? Contact Maaike Wienk to arrange a temporary Visimeet licence for remote access (limited number of licences available – first come first serve)