Adaptive Optimal Control via Continuous-Time Q-Learning for Unknown Nonlinear Affine Systems

Anthony Siming Chen, Guido Herrmann

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

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This paper proposes two novel adaptive optimal control algorithms for continuous-time nonlinear affine systems based on reinforcement learning: i) generalized policy iteration (GPI) and ii) Q-learning. As a result, the a priori knowledge of the system drift f (x) is not needed via GPI, which gives us a partially model-free and online solution. We then for the first time extend the idea of Q-learning to the nonlinear continuous time optimal control problem in a noniterative manner. Thisleads to a completely model-free method where neither the system drift f (x) nor the input gain g(x) is needed. For both methods, the adaptive critic and actor are continuously and simultaneously updating each other without iterative steps, which effectively avoids the hybrid structure and the need or an initial stabilizing control policy. Moreover, finite-time convergence is guaranteed by using a sliding mode technique in the new adaptive approach, where the persistent excitation (PE) condition can be directly verified online. We also prove the overall Lyapunov stability and demonstrate the effectiveness of the proposed algorithms using numerical examples.
Original languageEnglish
Title of host publication2019 IEEE 58th Conference on Decision and Control (CDC)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages6
ISBN (Electronic)978-1-7281-1398-2
Publication statusE-pub ahead of print - 12 Mar 2020
EventIEEE Conference on Decision and Control - Nice, France
Duration: 11 Dec 201913 Dec 2019
Conference number: 58

Publication series

NameIEEE Conference on Decision and Control
ISSN (Electronic)2576-2370


ConferenceIEEE Conference on Decision and Control
Abbreviated titleCDC2019
Internet address


  • adaptive critic
  • approximate dynamic programming
  • reinforcement learning
  • nonlinear systems
  • Q-learning
  • adaptive optimal control


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