Nonlinear Systems with Uncertain Periodically Disturbed Control Gain Functions: Adaptive Fuzzy Control with Invariance Properties

This paper proposes a novel adaptive fuzzy dynamic surface control (DSC) method for an extended class of periodically disturbed strict-feedback nonlinear systems. The peculiarity of this extended class is that the control gain functions are not bounded a priori but simply taken to be continuous and with a known sign. In contrast with existing strategies, controllability must be guaranteed by constructing appropriate compact sets ensuring that all trajectories in the closed-loop system never leave these sets. We manage to do this by means of invariant set theory in combination with the Lyapunov theory. In other words, boundedness is achieved a posteriori as a result of stability analysis. The approximator composed of fuzzy logic systems and Fourier series expansion is constructed to deal with the unknown periodic disturbance terms.