February 10, 2012, Webb 1100

In decentralized control problems, multiple decision-makers collaborate to achieve a common global objective despite not having access to the same information about the system. Such architectures are inevitable as large systems such as the power grid continue to become more complex. In this talk, we consider a fundamental decentralized optimal control problem: two interconnected linear subsystems with a partially nested information pattern and output feedback. Our main contribution is an explicit minimal state-space realization of the optimal controller, which was previously not known. The solution we present provides much more than just a formula; it gives us the state dimension of the optimal controller, and reveals precisely what sort of estimation and control structure is optimal. This structure is different from the Kalman Filter/LQR separation one would expect in a classical LQG scenario, yet there is no increase in computational complexity for finding the optimal controller. This work provides a first step toward a state-space theory for decentralized control.

Laurent Lessard is a post doctoral researcher at Lund University, Sweden. His research interests include decentralized control, optimization, and finding computationally tractable approaches for complex engineering applications. Prior to coming to Lund, he received a BASc degree in Engineering Science at the University of Toronto in 2003, and a PhD degree in Aeronautics and Astronautics from Stanford University in 2011.