System Analysis and Optimization of Human-Actuated Dynamical Systems

This paper investigates dynamical systems where system inputs are induced by human behavior. In particular, we consider linear time-invariant systems with a stochastic discrete choice actuation model. We are motivated by increasingly important cyber-physical-social systems (CPSS), such as smart mobility, smart energy, and smart cities. Existing literature regarding random dynamical systems (RDS) predominantly considers additive noise models with well-defined probability distributions. Furthermore, the role of human interactions is usually considered a disturbance. The closed-loop system must not be designed explicitly for this disturbance, but must be robust to it instead. This paper adds two original contributions to the existing literature. First, we integrate Discrete Choice Models (DCM) from behavioral economics into dynamical systems to incorporate human decision making, yielding a Dynamical System with Discrete Choice Models (DSDCM). System inputs are triggered by human actuators, who act selfishly by taking actions that maximize their own utility functions. Second, we formulate a convex optimization problem for DSDCM that seeks to incentivize human decision making to achieve a system-wide objective. Finally, we apply DSDCM in the context of demand response and provide potential directions for future work.