  In this paper, we bridge two disciplines: systems & control and environmental
psychology. We develop second order Behavior and Personal norm (BP) based
models (which are consistent with some studies on opinion dynamics) for
describing and predicting human activities related to the final use of energy,
where psychological variables, financial incentives and social interactions are
considered. Based on these models, we develop a human-physical system (HPS)
framework consisting of three layers: (i) human behavior, (ii) personal norms
and (iii) the physical system (i.e., an AC power grid). Then, we formulate a
social-physical welfare optimization problem and solve it by designing a
primal-dual controller, which generates the optimal incentives to humans and
the control inputs to the power grid. Finally, we assess in simulation the
proposed models and approaches.
