Adaptive stabilization for a class of non-affine non-minimum phase systems using neural networks

For a class of single-input single-output non-affine non-minimum phase nonlinear systems, a neural control synthesis method based on backstepping combined with inverting design is considered. The method reduces the number of steps in designing a backstepping controller compared to previous approaches by seeking a state that stabilizes the unstable internal dynamics. The method does not need a fixed-point assumption nor the boundedness assumption on the time derivative of a control effectiveness term. Using Lyapunov's direct method, it is shown that all the signals of the closed-loop system are uniformly ultimately bounded. Simulation results illustrate the approach.