About “learning by being told” applied to multivariable systems-stability, precision and rapidity of convergence

The “learning by being told”, allows a system to improve its task performance by repetition of this task, like an athlete who trains himself by the execution of the same movement several times. During these repetitions, the system gains know-how which is progressively improved. We propose a mathematical model of this learning process, applied to multivariable systems. This model is based on the usual representations of continuous systems. It allows us to determine the stability, precision and rapidity of convergence criteria of this learning process. We apply these theoretical results and show the efficiency of the approach, in the example of a 2 axes robot control, realizing very quickly a large movement. The learning process allows us to compensate in 4 or 5 iterations the interactions between two actuators, without any dynamic law equation calculus