Roshanak Partoazar - dept. of computer engineering,Shiraz University, Shiraz, Iran,
Abolfazl Shabani - dept. of computer engineering,Shiraz University, Shiraz, Iran,

Operator theoretic methods for learning, controland optimization of data driven dynamical systems based onKoopman operators have shown great advances in recentyears. In this paper we review these methods in diagnosis andcontrol of nonlinear and chaotic dynamical systems. The keyidea is that the Koopman operator provides an infinitedimensional linear global dynamic on function spaces which aredefined on the phase space. The dynamic mode decompositionalgorithm will provide a dimensionality reduction to have afinite dimensional approximation of this operator. Theapproximation and control problems are represented as(convex) optimization problems. A great advantage of thesemethods is that they provide tools for modeling and control ofhighly complex systems from data without knowing thesystem. As an application of this approach we present twoproblems in controlling the performance of robots. The firstapplication deals with optimal control of a soft robot arm andthe second one is a framework for path planning optimization ofmoving robots based on harmonic functions. In addition, we givedirections and novel ideas for future research.

data driven dynamical systems, Koopmanoperator, dynamic mode decomposition, robot control,harmonic functions.