An LMI adaptive-barrier function global sliding mode control of uncertain nonlinear systems with input saturation

Abstract

This paper proposes a barrier function-based adaptive control strategy with a nonlinear sliding surface for a class of uncertain dynamic systems with input saturation. Its main objectives are to ensure robustness to parametric and non-parametric uncertainties whilst eliminating the reaching phase. A global nonlinear switching surface is defined and an adaptive barrier function sliding mode control approach is derived. The barrier strategy is adopted to ensure the convergence of the states to the desired values without overestimating the control gains. System stability is analyzed using the Lyapunov stability theory. The control parameters are obtained using the linear matrix inequality (LMI) approach. The control law is designed to remove the reaching phase. The effectiveness of the proposed approach was validated using a simulation study. The proposed control approach can easily be implemented to various nonlinear uncertain systems.

Keywords

• Sliding mode control
• Adaptive control
• Uncertain system
• Input saturation
• LMI
• Exponential stability