Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 15: Statistical Physics far from equilibrium

DY 15.6: Talk

Wednesday, March 28, 2012, 11:00–11:15, MA 004

Experimentally realizable control functions: optimal control with arbitrary basis functions — •Selina Rohrer, Joachim Ankerhold, and Jürgen Stockburger — Institut für Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany

Optimal control theory aims at driving a dynamical system towards a final state that minimizes a figure of merit and at finding the required time-dependent controls. Using the Moore-Penrose Pseudoinverse [1] we are able to find optimal control functions, not in the whole control space, but in a subspace, which is spanned by arbitrary, not necessarily orthogonal basis functions. This optimization technique allows us to take into account limitations of experimental set-ups, such as, eg., a finite rise time of the control pulses. To illustrate this optimization technique with different sets of basis functions, we study a harmonic oscillator as model system, which is coupled to a thermal environment. For all presented sets of basis functions, we are able to cool the system below the temperature of the coupled bath.

[1] R. Penrose, A generalized inverse for matrices. Proceedings of the Cambridge Philosophical Society 51, S. 406-413, 1955