Modified neural dynamic surface approach to output feedback of MIMO nonlinear systems

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Artificial Intelligence

Background:

• Traditional state feedback control struggles with immeasurable states and unknown system functions.
• Dynamic Surface Control (DSC) methods often face limitations due to filter performance impacting closed-loop stability.
• Output feedback control is crucial for systems where all states are not directly measurable.

Purpose of the Study:

• To develop an adaptive output feedback dynamic surface control (DSC) strategy for uncertain multi-input, multi-output nonlinear systems.
• To maintain prescribed performance and ensure system stability under uncertainties.
• To overcome limitations of traditional state feedback and standard DSC by integrating advanced estimation and differentiation techniques.

Main Methods:

• Design of a finite-time Echo State Network (ESN) observer for online state estimation and approximation of unknown system functions.
• Modification of the DSC approach by incorporating a high-order sliding mode differentiator to replace first-order filters.
• Application of input-to-state stability (ISS) principles to guarantee semiglobal uniform ultimate boundedness of all closed-loop system signals.

Main Results:

• The proposed ESN observer successfully estimates immeasurable states and approximates unknown nonlinear functions in finite time.
• The modified DSC approach with a high-order sliding mode differentiator reduces the impact of filter performance on stability.
• The control scheme ensures that tracking errors converge to a predefined compact set around the equilibrium, demonstrating prescribed performance.

Conclusions:

• The developed adaptive output feedback DSC strategy effectively controls uncertain nonlinear systems while maintaining prescribed performance.
• The integration of ESN observers and high-order sliding mode differentiators provides a robust and stable control solution.
• Numerical examples validate the efficacy and satisfactory performance of the proposed control scheme.