Deterministic Learning-Based Adaptive Neural Control for Nonlinear Full-State Constrained Systems

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Abstract
In this article, an adaptive neural learning method is introduced for a category of nonlinear strict-feedback systems with time-varying full-state constraints. The two challenging problems of state constraints and learning capability are investigated and solved in a unified framework. To obtain the learning of unknown functions and satisfy full-state constraints, three main steps are considered. First, an adaptive dynamic surface controller (DSC) based on barrier Lyapunov functions (BLFs) is structured to implement that the closed-loop systems signals are bounded and full-state variables remain within the prescribed time-varying intervals. Moreover, the radial basis function neural networks (RBF NNs) are used to identify unknown functions. The output of the first-order filter, instead of virtual control derivatives, is used to simplify the complexity of the RBF NN input variables. Second, the state transformation is used to obtain a class of linear time-varying subsystems with small perturbations such that the recurrence of the RBF NN input variables and the partial persistent excitation condition are actualized. Therefore, the unknown functions can be accurately approximated, and the learned knowledge is kept as constant NN weights. Third, the obtained constant weights are borrowed into an adaptive learning scheme to achieve the batter control performance. Finally, simulation studies illustrate the advantage of the reported adaptive learning method on higher tracking accuracy, faster convergence rate, and lower computational expense by reusing learned knowledge.
Funding Information
  • National Key Research and Development Project (2018YFC1900800-5)
  • National Science Foundation of China (61803189, 62021003, 61890930-5, 61903010)
  • Beijing Outstanding Young Scientist Program (BJJWZYJH01201910005020)
  • Beijing Natural Science Foundation (KZ202110005009)
  • Fundamental Research Funds for the Universities of Liaoning Province (JJL202015406)

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