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Differential Neural Network Identifier for Dynamical Systems with Time-Varying State Constraints
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  • Ilya Nachevsky ,
  • Olga Andrianova ,
  • Ernest Sleptsov ,
  • Isaac Chairez ,
  • Alexander Poznyak
Ilya Nachevsky
Russian Academy of Sciences

Corresponding Author:[email protected]

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Olga Andrianova
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Ernest Sleptsov
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Isaac Chairez
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Alexander Poznyak
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Abstract

This study presents a state non-parametric identifier based on neural networks with continuous dynamics, also known as differential (namely DNNs) whose laws for adjusting their parameters are developed using a control Barrier Lyapunov Functions (BLFs). The motivation for using the BLF comes from the preliminary information of the system states, which remain in a predefined time-depending set characterized by state or purely time-dependent functions. In this study, time-dependent state constraints are supposed to be known in advance of continuous-time functions. The obtained learning laws require solving differential continuous-time Riccati equations and nonlinear differentialequations for the learning laws that depend on the identification error and the state restrictions. The developed identifier was evaluated concerning the identifier that does not consider the state restrictions. This comparison included the numerical evaluation of the identifier considering its application on a robotic arm that is intended to reproduce a non-standard flight simulator. This evaluation confirmed that the identification results were improved using the proposed learning laws considering that the state limits were not transgressed, and the quality indicators based on the mean square error were more minor by 4.2 times.