Neural Network-Based Adaptive Control for Uncertain Nonlinear Systems with Input Quantization

This paper addresses the asymptotic stabilization problem for a class of uncertain nonlinear systems with logarithmic quantization at the control input. Different from the existing results and approaches, a Lyapunov function candidate and a neural network-based adaptive control law are developed to adaptively estimate the unknown nonlinear functions and to asymptotically stabilize the uncertain nonlinear system, in which the control input also involves uncertain parameters, possibly in the nonlinear form. We demonstrate that asymptotic stabilization can be achieved under mild conditions, even when the adaptive estimates do not converge to the true system functions. A sufficient condition for asymptotic stabilizability is derived in terms of quantization density and multiplicative parameter error bounds at the control input. Notably, the proposed neural-network-based adaptive controller guarantees the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{H}_{\infty}$</tex>-norm strictly less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\gamma$</tex> (for any <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\gamma&gt;1$</tex>) for the uncertain linearized closed-loop system, effectively suppressing bounded network reconstruction errors. Simulation results validate the method's effectiveness.