Excitation for Adaptive Optimal Control of Nonlinear Systems in Differential Games

This article focuses on the fulfillment of persistent excitation (PE) condition for signals which result from transformations by means polynomials. is essential, e.g., convergence adaptive dynamic programming algorithms due to commonly used polynomial function approximators. As theoretical statements are scarce regarding nonlinear transformation PE signals, we propose conditions system state such that its polynomials PE. To validate our statements, develop an exemplary procedure based using a feed-forward control approach and demonstrate effectiveness method in nonzero-sum differential game. In this setting, outperforms probing noise terms time degree PE, shown numerical example.