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Adaptive dynamic programming for model‐free tracking of trajectories with time‐varying parameters
Author(s) -
Köpf Florian,
Ramsteiner Simon,
Puccetti Luca,
Flad Michael,
Hohmann Sören
Publication year - 2020
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3106
Subject(s) - computer science , tracking (education) , dynamic programming , control theory (sociology) , tracking error , trajectory , controller (irrigation) , function (biology) , invariant (physics) , system dynamics , quadratic equation , lti system theory , mathematical optimization , artificial intelligence , mathematics , algorithm , linear system , control (management) , psychology , mathematical analysis , pedagogy , physics , geometry , astronomy , evolutionary biology , agronomy , mathematical physics , biology
Summary Recently proposed adaptive dynamic programming (ADP) tracking controllers assume that the reference trajectory follows time‐invariant exo‐system dynamics—an assumption that does not hold for many applications. In order to overcome this limitation, we propose a new Q‐function that explicitly incorporates a parametrized approximation of the reference trajectory. This allows learning to track a general class of trajectories by means of ADP. Once our Q‐function has been learned, the associated controller handles time‐varying reference trajectories without the need for further training and independent of exo‐system dynamics. After proposing this general model‐free off‐policy tracking method, we provide an analysis of the important special case of linear quadratic tracking. An example demonstrates that our new method successfully learns the optimal tracking controller and outperforms existing approaches in terms of tracking error and cost.