Dynamic Learning from Adaptive Neural Control of Nonlinear Non-Minimum Phase Systems

This study proposes a dynamic learning control scheme for a class of nonlinear non-minimum phase systems with unknown nonlinear terms. To deal with the unstable internal dynamics, the system is transformed into a serial-connected form. After the transformation, the internal dynamics are directly driven by control input signals, while the output dynamics are driven by the internal dynamics. Adaptive neural control is initially proposed for nonlinear non-minimum phase systems based on neural function approximation. This approach ensures that the system output and internal dynamics converge to a small neighborhood of the reference signal and the expected stable response, respectively. Moreover, the neural estimated weights converge to a small neighborhood of the ideal weights based on the dynamic learning theory. The converged constant weights are used to develop a learning controller that enhances the control performance. A cart with an inverted pendulum is simulated to demonstrate the effectiveness of the developed scheme.