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Koopman Approximator based Adaptive Model Predictive Control of Continuous Nonlinear Systems
  • +2
  • Yi Zheng,
  • Yueyan Zhang,
  • Qiangyu Li,
  • Shaoyuan Li,
  • Min Luo
Yi Zheng

Corresponding Author:[email protected]

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Yueyan Zhang
Shanghai Jiao Tong University
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Qiangyu Li
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Shaoyuan Li
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This paper considers the real-time control of a class of complex continuous nonlinear systems with an increasing requirement on control accuracy and unknown dynamics at the start time due to their complex dynamics and uncertainties. A Koopman approximate model-based adaptive MPC design using the Lyapunov technique is explored. Specifically, the nonlinear system is modeled/transformed into a linear model in a lifting space with the Koopman operator. A recursive update of the approximator is provided by which the parameters set of the approximator is in a nested form and a shrinking of the boundary of the approximator’s mismatch from the real system is obtained. Also, based on the Koopman model and its mismatch boundary, a sufficient condition that ensures the states of the nonlinear system eventually converge to a small neighborhood of the origin is deduced. An FCCU example is employed to show the effectiveness of the proposed control law.