Adaptive Neural PD Control With Semiglobal Asymptotic Stabilization Guarantee

This paper proves that adaptive neural plus proportional-derivative (PD) control can lead to semiglobal asymptotic stabilization rather than uniform ultimate boundedness for a class of uncertain affine nonlinear systems. An integral Lyapunov function-based ideal control law is introduced to avoid the control singularity problem. A variable-gain PD control term without the knowledge of plant bounds is presented to semiglobally stabilize the closed-loop system. Based on a linearly parameterized raised-cosine radial basis function neural network, a key property of optimal approximation is exploited to facilitate stability analysis. It is proved that the closed-loop system achieves semiglobal asymptotic stability by the appropriate choice of control parameters. Compared with previous adaptive approximation-based semiglobal or asymptotic stabilization approaches, our approach not only significantly simplifies control design, but also relaxes constraint conditions on the plant. Two illustrative examples have been provided to verify the theoretical results.