Adaptive Projection and Fuzzy Tracking Design for Unknown Control Coefficients and References

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Fuzzy Logic Systems

Background:

• Nonlinear pure-feedback systems present significant control challenges due to unknown parameters.
• Existing methods often rely on assumptions like Nussbaum functions, which can be restrictive.

Purpose of the Study:

• To develop a robust tracking control strategy for nonlinear pure-feedback systems with unknown control coefficients and reference dynamics.
• To overcome limitations of existing methods by avoiding the need for Nussbaum functions.

Main Methods:

• Utilizing fuzzy-logic systems (FLSs) to approximate unknown control coefficients.
• Designing an adaptive projection law to permit fuzzy approximations to cross zero, circumventing Nussbaum function requirements.
• Developing an adaptive law to estimate unknown reference dynamics.
• Integrating adaptive laws into a saturated tracking control law.

Main Results:

• The proposed method successfully handles unknown control coefficients and reference dynamics.
• The adaptive projection law avoids the need for Nussbaum functions, allowing coefficients to cross zero.
• The control scheme achieves uniformly ultimately bounded (UUB) performance for the closed-loop system.
• Simulation results validate the feasibility and effectiveness of the developed control strategy.

Conclusions:

• The novel fuzzy-logic-based adaptive control scheme provides a robust solution for tracking control in nonlinear pure-feedback systems.
• The method offers improved performance and broader applicability by eliminating the reliance on Nussbaum functions.