Fixed-Time Neural Adaptive Control for Nonlinear Asymmetric Constrained Systems Subject to Time-Varying Input Delay

Area of Science:

• Control Systems Engineering
• Nonlinear Systems Theory
• Adaptive Control

Background:

• Addressing fixed-time (FxT) control challenges in nonlinear systems (NS) with time-varying input delays (TVID) and error/state constraints.
• Existing FxT control methods may be conservative or require stringent feasibility conditions.

Purpose of the Study:

• Develop a novel fixed-time adaptive tracking control strategy for nonlinear systems subject to TVID and error/state constraints.
• Improve the accuracy of stability analysis and remove feasibility conditions for constrained systems.

Main Methods:

• Introduction of two new FxT stability lemmas for less conservative upper-bound estimates (UBEs) of settling time (ST).
• Reconstruction of asymmetric constrained systems into unconstrained systems using nonlinear transformation functions (NTFs).
• Development of a novel FxT adaptive tracking control strategy (FxTAS-nps) to handle unknown input delays.
• Utilization of FxT stability criteria and Lyapunov-Krasovskii functional approach for stability proofs.

Main Results:

• The proposed FxTAS-nps ensures practical fixed-time stability (PFxTS) for the controlled systems.
• Error and state constraints are satisfied throughout the operation.
• The control algorithm effectively handles unknown time-varying input delays.
• The approach uniformly addresses both constrained and unconstrained systems without framework modification.

Conclusions:

• The research successfully presents a robust fixed-time adaptive control solution for complex nonlinear systems.
• The developed method offers improved stability analysis and constraint handling capabilities.
• Simulation results validate the effectiveness and applicability of the proposed control strategy.