Local Stability and Convergence Analysis of Neural Network Controllers With Error Integral Inputs.

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear Dynamics

Background:

• Neural network (NN) controllers are increasingly used in control systems.
• Traditional NN controllers with only error inputs can exhibit steady-state errors.
• Achieving stability and convergence in NN control systems is crucial for reliable performance.

Purpose of the Study:

• To investigate the local stability and convergence of NN controllers with error integral inputs.
• To demonstrate that error integrals eliminate steady-state errors for constant references.
• To establish conditions for local asymptotic stability and exponential convergence in NN control systems.

Main Methods:

• Formal mathematical proofs were used to analyze stability and convergence properties.
• Nonlinear NN control systems were linearized around equilibrium points.
• Simulations of single-layer and multi-layer NN controllers were conducted for verification.

Main Results:

• NN controllers using only error terms result in non-zero steady-state errors.
• Incorporating error integrals into NN controller inputs eliminates steady-state errors for any constant reference.
• Local asymptotic stability and exponential convergence are guaranteed if linearized system eigenvalues have negative real parts.

Conclusions:

• Error integral inputs are sufficient to remove steady-state errors in NN controllers.
• The stability analysis provides a clear condition for guaranteeing system convergence.
• Simulations confirm that NN controllers with error integrals perform comparably to generalized PI controllers under specific conditions.