Rational Continuous Neural Network Identifier for Singular Perturbed Systems With Uncertain Dynamical Models.

Area of Science:

• Control Systems Engineering
• Computational Intelligence
• Nonlinear Dynamics

Background:

• Singular Perturbed Systems (SPSs) present challenges in modeling due to their multirate nature and uncertain dynamics.
• Accurate identification of both fast and slow dynamics is crucial for effective control and analysis of SPSs.

Purpose of the Study:

• To design a robust nonparametric identifier for uncertain SPSs.
• To develop a novel identifier structure utilizing a differential neural network (DNN) with a rational form.
• To address the multirate characteristics inherent in SPSs.

Main Methods:

• A novel differential neural network (DNN) with a rational form is proposed.
• A mixed learning law incorporating rational neural network formulations is employed.
• Control Lyapunov functions and nonlinear parameter identification are used to design learning laws.
• Matrix inequality-based optimization determines the convergence invariant region.

Main Results:

• The proposed rational DNN identifier effectively captures both fast and slow dynamics of SPSs.
• The identifier demonstrates robustness in the presence of model uncertainties.
• Numerical comparisons show superior performance (lower Mean Square Error) compared to classical identifiers lacking multirate consideration.

Conclusions:

• The novel rational DNN identifier provides a robust and effective solution for modeling uncertain SPSs.
• The rational form and multirate capability are key advantages for SPS identification.
• The proposed methodology offers a practical approach for diverse SPS applications.