Hot Topic zaproszenie na wykład prof. Heinza Schaettlera

abstrakt:

Synthesis in Optimal Control Problems:
Applications to Physics, Flight Control, and Medicine
Heinz Sch¨attler
Preston M. Green Dept. of Electrical and Systems Engineering
Washington University in St. Louis, USA
Explicit constructions of solutions to optimal control problems based on the method of
characteristics will be discussed. The emphasis will be on illustrating how such constructions
can be utilized to prove (global and/or local) optimality in difcult, but realistic practical settings
in the context of three examples:
1. (physics) Frictionless atom cooling in a harmonic trap is relevant in quantum computing
as quantum computers can only operate at extremely low temperatures in the range of
fractions of a degree above absolute zero. A global solution to the corresponding minimum
time optimal control problem modelled by Ermakov’s equation will be given.
2. (flight control) Ground collision avoidance system (GCAS) aim to safely return an airplane
in nose dive to level flight. Mathematically, this requires to derive perturbation feedback
control laws for non-singular extremals with free terminal time. A local feld of extremals
will be constructed.
3. (medicine) The forced asynchronous selective spiking of “integrate and fre” neurons leads
to optimal control problems with loss of small-time local controllability. For such problems
the corresponding value function is not continuous and such problems are not amenable to
methods of analysis such as viscosity solutions to the associated Hamilton-Jacobi-Bellman
equation while the method of characteristics works.