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Volume 7 Issue 3
Apr.  2020

IEEE/CAA Journal of Automatica Sinica

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Sumit Kumar Jha and Shubhendu Bhasin, "Adaptive Linear Quadratic Regulator for Continuous-Time Systems With Uncertain Dynamics," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 833-841, May 2020. doi: 10.1109/JAS.2019.1911438
Citation: Sumit Kumar Jha and Shubhendu Bhasin, "Adaptive Linear Quadratic Regulator for Continuous-Time Systems With Uncertain Dynamics," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 833-841, May 2020. doi: 10.1109/JAS.2019.1911438

Adaptive Linear Quadratic Regulator for Continuous-Time Systems With Uncertain Dynamics

doi: 10.1109/JAS.2019.1911438
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  • In this paper, adaptive linear quadratic regulator (LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses input-output data along the system trajectory to continuously adapt and converge to the optimal controller. The result differs from previous results in that the adaptive optimal controller is designed without the knowledge of the system dynamics and an initial stabilizing policy. Further, the controller is updated continuously using input-output data, as opposed to the commonly used switched/intermittent updates which can potentially lead to stability issues. An online state derivative estimator facilitates the design of a model-free controller. Gradient-based update laws are developed for online estimation of the optimal gain. Uniform exponential stability of the closed-loop system is established using the Lyapunov-based analysis, and a simulation example is provided to validate the theoretical contribution.

     

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    Highlights

    • In this paper, adaptive linear quadratic regulator (LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses inputoutput data along the system trajectory to continuously adapt and converge to the optimal controller. The Lyapunov analysis is used to prove uniform exponential stability of the overall system.
    • The contribution of this paper is the design of a continuous-time adaptive LQR with a time-varying state-feedback gain for continuous-time LTI systems with uncertain dynamics, which is shown to exponentially converge to the optimal gain.
    • The novelty of the proposed result lies in the computational/memory efficient algorithm used to solve the optimal control problem for uncertain dynamics, without requiring an initial stabilizing control policy, unlike previous results which either use an initial stabilizing control policy and a switched policy update or past data storage. Further, the controller is updated continuously using input-output data, while ensuring exponentially converge to the optimal gain, as opposed to the commonly used switched/intermittent updates which may potentially lead to stability issues.

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