Information flows for universal control in systems
This talk explores ideas in universal control as a parallel to universal communication and compression. For such control systems with uncertain parameters, we explore the value of side-information in control as a parallel to the value of information in portfolio theory à la Cover.
Estimation is the natural bridge between information theory and control. While control and estimation are traditionally thought of as dual problems, we will see that systems with parameter uncertainty can break this duality, and hence provide an alternate perspective.
We first discuss the estimation and control of a system observed over a non-coherent channel, i.e. a channel with unknown and varying channel state. The system behaves differently than we might expect given existing results on non-coherent communication and the MMSE dimension: we show that the system cannot be meaningfully observed at all. Surprisingly, if the uncertainty is small enough the system can be controlled. The control action can shape the channel input and thus extract state information.
In the second example, we consider uncertainty on the control channel instead of on the observation channel. In contrast to the first example, here the control problem is harder than the observation problem. In both these examples, carry-free bit-level models adapted from wireless communication illustrate the information flows in the system.
Gireeja Ranade is a PhD candidate in the EECS department at UC Berkeley working with Prof. Anant Sahai. She received a S.B. in EECS from MIT in 2007 and an M.S. in EECS from UC Berkeley in 2009.