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Deterministic learning and neural control of a class of nonlinear systems toward improved performance

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Abstract

A deterministic learning theory was recently presented which states that an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of nonlinear systems in normal form. In this paper, we further investigate deterministic learning of the class of nonlinear systems with relaxed conditions, and neural control of the class of system toward improved performance. Firstly, without the assumption on the upper bound of the derivative of the unknown affine term, an adaptive neural controller is proposed to achieve stability and tracking of the plant states to that of the reference model. When output tracking is achieved, a partial PE condition is satisfied, and deterministic learning from adaptive neural control of the class of nonlinear systems is implemented without the priori knowledge on the upper bound of the derivative of the affine term. Secondly, by utilizing the obtained knowledge of system dynamics, a neural controller with constant RBF networks embedded is presented, in which the learned knowledge can be effectively exploited to achieve stability and improved control performance. Simulation studies are included to demonstrate the effectiveness of the results.

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Notes

  1. The recurrent motions comprise the most important types (though not all types) of trajectories generated from nonlinear dynamical systems, including periodic, quasi-periodic, almost-periodic and even chaotic trajectories (see [13] for a rigorous definition of recurrent trajectory).

  2. The partial parameters convergence means that the weights of the NN nodes, which are located near the trajectory \(\varphi_\varsigma(Z(t))\) after the transient process, converge to their optimal values.

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Acknowledgments

The authors would like to express their sincere appreciation to the reviewers for their helpful comments on the revision of this paper. This work was supported by the National Natural Science Foundation of China under grants 612250014, 90816028, and 60934001.

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Authors and Affiliations

  1. School of Automation and the Center for Control and Optimization, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Binhe Wen & Cong Wang

  2. Department of Electrical and Computer Engineering, Six Metrotech Center, Polytechnic Institute, New York University, Brooklyn, NY, 11201, USA

    Tengfei Liu

Authors
  1. Binhe Wen
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  2. Cong Wang
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  3. Tengfei Liu
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Correspondence to Cong Wang.

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Wen, B., Wang, C. & Liu, T. Deterministic learning and neural control of a class of nonlinear systems toward improved performance. Neural Comput & Applic 24, 637–648 (2014). https://doi.org/10.1007/s00521-012-1229-2

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  • DOI: https://doi.org/10.1007/s00521-012-1229-2

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