This paper addresses the design of an active cyberattack detection architecture based on multiplicative watermarking, allowing for detection of covert attacks. We propose an optimal design problem, relying on the so-called output-to-output ℓ 2 -gain, which characterizes the maximum gain between the residual output of a detection scheme and some performance output. Although optimal, this control problem is non-convex. Hence, we propose an algorithm to design the watermarking filters by solving the problem suboptimally via LMIs. We show that, against covert attacks, the output-to-output ℓ 2 -gain is unbounded without watermarking, and we provide a sufficient condition for boundedness in the presence of watermarks.

Demand side energy management (DSEM) promises to regulate ensembles of loads to track desired power levels, in response to grid events (demand peaks, emergencies, variable renewable power generation, etc). A large fraction of such loads are Thermostatically Controlled Loads (TCLs) such as refrigerators, electric water heaters, and air conditioners. Such loads exhibit parametric uncertainty and heterogeneity which make power tracking difficult. Adaptive control strategies are explored in this work as a way to achieve power tracking. Effectiveness of such strategies are studied via numerical simulations.