Learning Trajectories of Dynamical Systems

Abstract

The aim of the present paper is to describe the method that is capable of adjusting the parameters of a dynamical system so that the trajectories gain certain specified properties. Three problems are considered: (i) learning fixed points, (ii) learning to periodic trajectories, (iii) restrictions on the trajectories. An error function, which measures the discrepancy between the actual and desired trajectories is introduced. Numerical results of several examples, which illustrate the efficiency of the method, are presented.

Keywords:

• dynamical systems
• learning trajectories
• gradient descent method
• sensitivity analysis

AMS Subject Classification:

• 93C15
• 68T05
• 68Q32