On the Economic Control of Cyber-physical Systems

This paper presents a framework for the optimal economic control of large scale Cyber-physical systems (CPS). As an example, transportation systems are chosen to demonstrate the framework. First, it is argued that how a large scale system, such as transportation system, fits within the definition of Cyber-physical system. Next, several scenarios related to transportation system are considered and a framework for optimal economical control is provided using the theory of optimal control. For example, dynamic toll pricing problem is considered and solved using dynamic programming and principle of optimality. The problem consists of tolled lanes or routes and alternate non-tolled lanes or routes. Several control objectives are discussed and their corresponding cost functions are provided. Hamilton-Jacobi-Bellman equation is then used to derive an optimal control law that utilizes real-time traffic information. Insights are also provided on other CPS, such as power distribution networks, and the corresponding optimal economic control problem.