  This paper presents a new aggregate power tracking control scheme for
populations of thermostatically controlled loads (TCLs). The control design is
carried out in the framework of partial differential equations (PDEs) based on
a late-lumping procedure without truncating the infinite-dimensional model
describing the dynamics of the TCL population. An input-output linearization
control scheme, which is independent of the system parameters and uses only
partial state measurement, is derived, and a sliding model control is applied,
which allows achieving a finite-time input-to-state stability for the tracking
error dynamics. Such a control strategy can ensure a robust performance in the
presence of modeling uncertainties while considerably reducing the
communication burden in large scale distributed systems as the one considered
in the present work. To guarantee the validity of the developed control scheme,
a rigourous analysis on the solutions to the underlying PDE is conducted. Two
implementations of the proposed control strategy, based on discrete-time
approximation and fuzzy logic control, respectively, are validated through
simulation studies.
