Adaptive Control of Piecewise Linear Systems: the State Tracking Case

Nonlinear controlled systems at multiple operating points are modeled as piecewise linear systems, where changes in operating points are modeled as switches between constituent linearized systems. This note studies the adaptive state feedback for state tracking control problem for such systems. Piecewise linear reference model systems are used for generating desired state trajectories and their stability properties are studied. Adaptive state feedback control schemes are developed, and their stability and tracking performance are analyzed and evaluated by simulation examples. It is shown that exponential tracking performance can be achieved if the reference input is sufficiently rich and the switches are sufficiently slow.