Adaptive discrete-time neural prescribed performance control: A safe control approach

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Discrete-Time Systems

Background:

• Existing prescribed performance control (PPC) primarily addresses continuous-time systems.
• Challenges include input saturation and initial condition limitations in discrete-time nonlinear systems.
• Singular problems arise in PPC when input saturation is present.

Purpose of the Study:

• To develop a novel adaptive switching control strategy for discrete-time nonlinear systems.
• To address input saturation and initial condition limitations within the PPC framework.
• To release initial condition constraints under PPC.

Main Methods:

• Devised a new discrete-time global finite-time performance function (DTGFTPF) to ensure performance boundaries are insensitive to initial values.
• Constructed a discrete-time adaptive finite-time prescribed performance controller (DTAFPPC) for finite-time tracking error convergence.
• Developed a discrete-time adaptive backstepping controller (DTABC) to handle input saturation and prevent instability.
• Integrated current error values into controllers and adaptive update laws to overcome non-causal issues in backstepping.

Main Results:

• The DTGFTPF ensures performance boundaries are independent of arbitrary initial system values.
• The DTAFPPC guarantees tracking errors converge within finite time and predefined bounds.
• The DTABC maintains system stability during input saturation, allowing temporary excursions beyond performance bounds.
• Lyapunov analysis and simulations confirm the closed-loop system's stability.

Conclusions:

• The proposed adaptive switching control strategy effectively handles discrete-time nonlinear systems with input saturation and initial condition variations.
• The controller ensures finite-time prescribed performance and overall system stability.
• The approach relaxes limitations of existing PPC methods for discrete-time systems.