${\cal L}_{1}$ Adaptive Controller for Uncertain Nonlinear Multi-Input Multi-Output Systems With Input Quantization

We study the merits of the
${\cal L}_{1}$
adaptive controller for nonlinear uncertain Multi-Input Multi-Output (MIMO) systems in the presence of significant unmodeled dynamics and input quantization. We show that with both logarithmic quantization and uniform quantization, if the quantization is sufficiently dense, the
${\cal L}_{1}$
adaptive controller ensures that the output of the MIMO system follows a desired reference signal with uniform transient and steady-state performance bounds. Compared with the same feedback architecture without quantization, the uniform performance bounds have an additional positive additive term, linear in the quantization constant, which can be reduced by increasing the quantization density. Simulations illustrate the performance of the
${\cal L}_{1}$
adaptive controller in the presence of quantization.