Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Electrical & Systems Engineering

First Advisor

George J. Pappas

Second Advisor

Rahul Mangharam


Electricity usage under peak load conditions can cause issues such as reduced power quality and power outages. For this reason, commercial electricity customers are often subject to demand-based pricing, which charges very high prices for peak electricity demand. Consequently, reducing peaks in electricity demand is desirable for both economic and reliability reasons. In this thesis, we investigate the peak demand reduction problem from the perspective of safe scheduling of control systems under resource constraint. To this end, we propose Green Scheduling as an approach to schedule multiple interacting control systems within a constrained peak demand envelope while ensuring that safety and operational conditions are facilitated. The peak demand envelope is formulated as a constraint on the number of binary control inputs that can be activated simultaneously. Using two different approaches, we establish a range of sufficient and necessary schedulability conditions for various classes of affine dynamical systems. The schedulability analysis methods are shown to be scalable for large-scale systems consisting of up to 1000 subsystems. We then develop several scheduling algorithms for the Green Scheduling problem. First, we develop a periodic scheduling synthesis method, which is simple and scalable in computation but does not take into account the influence of disturbances. We then improve the method to be robust to small disturbances while preserving the simplicity and scalability of periodic scheduling. However the improved algorithm usually result in fast switching of the control inputs. Therefore, event-triggered and self-triggered techniques are used to alleviate this issue. Next, using a feedback control approach based on attracting sets and robust control Lyapunov functions, we develop event-triggered and self-triggered scheduling algorithms that can handle large disturbances affecting the system. These algorithms can also exploit prediction of the disturbances to improve their performance. Finally, a scheduling method for discrete-time systems is developed based on backward reachability analysis. The effectiveness of the proposed approach is demonstrated by an application to scheduling of radiant heating and cooling systems in buildings. Green Scheduling is able to significantly reduce the peak electricity demand and the total electricity consumption of the radiant systems, while maintaining thermal comfort for occupants.