Teams of coordinating vehicles, wireless communication networks, and power grids all consist of collections of locally controlled, interacting components. Despite technological advances in sensing, actuation, and communication, effectively controlling these complex systems is still largely an unsolved problem. The fact that decision making must be performed in a distributed manner introduces problems not addressed by conventional control theory. One of the key challenges in the development of tools for controlling these systems is devising effective algorithms which avoid the inherent computational complexity of synthesizing optimal decentralized control laws.
In this talk, I will discuss the challenges associated with decision making in complex systems and present my recent research addressing these issues. The methods discussed have connections with recent and highly effective optimization techniques such as sum of squares programming and approximate dynamic programming. The concepts presented will be illustrated by several numerical examples, including distributed detection by multiple sensors and power control in wireless data networks.