Differential Neural Network Identifier for Dynamical Systems With Time-Varying State Constraints

This study presents a state nonparametric identifier based on neural networks with continuous dynamics, also known as differential neural networks (DNNs). The 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 continuous-time functions. The obtained learning laws require solving differential continuous-time Riccati equations and nonlinear differential equations 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 for a robotic arm intended to reproduce a nonstandard flight simulator. This evaluation confirmed that the identification results were improved using the proposed learning laws and considering that the state limits were not transgressed. The quality indicators based on the mean square error were more minor by 4.2 times.