Excitation for Adaptive Optimal Control of Nonlinear Systems in Differential Games

This article focuses on the fulfillment of the persistent excitation (PE) condition for signals which result from transformations by means of polynomials. This is essential, e.g., for the convergence of adaptive dynamic programming algorithms due to commonly used polynomial function approximators. A...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2023-01, Vol.68 (1), p.596-603
Main Authors: Karg, Philipp, Kopf, Florian, Braun, Christian A., Hohmann, Soren
Format: Article
Language:English
Subjects:
Adaptive algorithms
Adaptive control
Adaptive dynamic programming (ADP)
adaptive optimal control
Convergence
Differential games
Dynamic programming
Excitation
Feedforward control
Indexes
Nonlinear control
Nonlinear systems
Optimal control
persistent excitation (PE)
Polynomials
Trajectory
Transformations
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Summary:This article focuses on the fulfillment of the persistent excitation (PE) condition for signals which result from transformations by means of polynomials. This is essential, e.g., for the convergence of adaptive dynamic programming algorithms due to commonly used polynomial function approximators. As theoretical statements are scarce regarding the nonlinear transformation of PE signals, we propose conditions on the system state such that its transformation by polynomials is PE. To validate our theoretical statements, we develop an exemplary excitation procedure based on our conditions using a feed-forward control approach and demonstrate the effectiveness of our method in a nonzero-sum differential game. In this setting, our approach outperforms commonly used probing noise in terms of convergence time and the degree of PE, shown by a numerical example.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3145651