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This work focuses on the fulfillment of the Persistent Excitation (PE)condition for signals which result from transformations by means ofpolynomials. This is essential e.g. for the convergence of Adaptive DynamicProgramming algorithms due to commonly used polynomial function approximators.As theoretical statements are scarce regarding the nonlinear transformation ofPE signals, we propose conditions on the system state such that itstransformation by polynomials is PE. To validate our theoretical statements, wedevelop an exemplary excitation procedure based on our conditions using afeedforward control approach and demonstrate the effectiveness of our method ina nonzero-sum differential game. In this setting, our approach outperformscommonly used probing noise in terms of convergence time and the degree of PE,shown by a numerical example.

Excitation for Adaptive Optimal Control of Nonlinear Systems in Differential Games