Adaptive Tracking Control of Uncertain Nonlinear Systems With Saturated Input Quantization

The problem of controlling an uncertain nonlinear system with a saturated input quantization has not yet been addressed until now due to the difficulty of handling saturation and quantization simultaneously, although this problem is recognized as being of both theoretical and practical importance in the field of quantized control. In this note, we fill in the gap by presenting a new tuning function control scheme that is developed from a backstepping recursive design with n+1 steps. Moreover, a series of smooth functions are incorporated in our design to circumvent the possible chattering arising from the quantization error and saturation approximate error. It is proved that the steady-state tracking error is controlled into a prescribed bound with our scheme, and the global boundedness of all the closed-loop signals is ensured. Besides asymptotic performance, an explicit transient tracking performance in terms of L2-norm is also established.