An adaptive design for quantized feedback control of uncertain switched linear systems

Abstract

This paper addresses the problem of asymptotic tracking for switched linear systems with parametric uncertainties and dwell-time switching, when input measurements are quantized due to the presence of a communication network closing the control loop. The problem is solved via a dynamic quantizer with dynamic offset that, embedded in a model reference adaptive control framework, allows the design of the adaptive adjustments for the control parameters and for the dynamic range and dynamic offset of the quantizer. The overall design is carried out via a Lyapunov-based zooming procedure, whose main feature is overcoming the need for zooming out at every switching instant, in order to compensate for the possible increment of the Lyapunov function at the switching instants. It is proven analytically that the resulting adjustments guarantee asymptotic state tracking. The proposed quantized adaptive control is applied to the piecewise linear model of the NASA Generic Transport Model aircraft linearized at multiple operating points.