Adaptive Prescribed Performance Asymptotic Tracking for High-Order Odd-Rational-Power Nonlinear Systems

Practical tracking results have been reported in the literature for high-order odd-rational-power nonlinear dynamics (a chain of integrators whose power is the ratio of odd integers). Asymptotic tracking remains an open problem for such dynamics. This note gives a positive answer to this problem in the framework of prescribed performance control, without approximation structures (neural networks, fuzzy logic, etc.) being involved in the control design. The unknown system uncertainties are first transformed to unknown but bounded terms using barrier Lyapunov functions, and then these terms are compensated by appropriate adaptation laws. A method is also proposed to extract the control terms in a linear-like fashion during the control design, which overcomes the difficulty that virtual or actual control signals appear in a nonaffine manner. A practical poppet valve system is used to validate the effectiveness of the theoretical findings.