  This paper addresses the modeling and control of heterogeneous populations of
thermostatically controlled loads (TCLs) operated by model predictive control
(MPC) schemes at level of each TCL. It is shown that the dynamics of such TCLs
populations can be described by a pair of Fokker-Planck equations coupled via
the actions in the domain. The technique of input-output feedback linearization
is used in the design of aggregate power control, which leads to a nonlinear
system in closed loop. Well-posedness analysis is carried out to validate the
developed control scheme. The closed-loop stability of the system is assessed
by a rigorous analysis. A simulation study is contacted, and the obtained
results confirm the validity and the effectiveness of the proposed approach.
