Prescribed-Performance Control of Variable-Order Fractional-Order Nonlinear Systems Through Adaptive Dynamic...

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Fractional Calculus

Background:

• Variable-order fractional-order nonlinear systems (VOFONSs) present unique control challenges due to time-dependent and memory characteristics.
• Traditional control methods for integer-order systems are not directly applicable to VOFONSs.
• Prescribed-performance control (P²C) aims to ensure system states remain within specified bounds.

Purpose of the Study:

• To develop a control strategy for achieving prescribed-performance control (P²C) in variable-order fractional-order nonlinear systems (VOFONSs).
• To integrate safety constraints into an optimal control framework using control barrier functions (CBFs) and adaptive dynamic programming (ADP).
• To address the complexities arising from the time-varying nature of VOFONSs and CBF-embedded cost functions.

Main Methods:

• Variable-order fractional calculus and integration-by-parts formula were used to approximate VOFONSs as time-varying integer-order systems.
• A control barrier function (CBF)-embedded adaptive dynamic programming (ADP) method was developed to handle constrained optimal control.
• A neural network with a time-varying activation function approximated the time-varying discounted cost function.
• A time-varying policy iteration algorithm solved the Hamilton-Jacobi-Bellman (HJB) equation.

Main Results:

• The CBF-embedded ADP method successfully incorporated safety constraints into the optimal control framework without explicit state transformation.
• A novel control policy was derived, guaranteeing that the tracking error adheres to predefined constraints.
• The proposed method effectively addressed the challenges posed by time-varying dynamics and memory effects in VOFONSs.

Conclusions:

• The CBF-embedded ADP control scheme is effective for achieving prescribed-performance control in VOFONSs.
• The developed method provides a robust approach for handling safety-critical control problems in complex nonlinear systems.
• Simulation results validated the efficacy and practical applicability of the proposed control strategy.