Undergrad Research Project - Optimization of Neural Signal Path Following using Brain-Machine Interfaces

Fall 2014

Chidimma Onwuegbule
Pulkit Grover
Project description

The objective of this research is to apply the ideas of implicit communication from the Witsenhausen counterexample to find an optimal way of following a neural signal path using a brain-machine interface. The control problem that this aims to solve has a scalar state which evolves in discrete time according to linear dynamics. This problem attempts to bring the state close to zero within two time steps using two controllers -- one "weak" controller whose observations are noise-free but whose control signals cost is high, and one "blurry" controller whose observations are noisy but whose control signal is free. Witsenhausen's counterexample provides a nonlinear strategy for minimizing the expected quadratic cost associated with this problem that outperforms all linear strategies, which had previously been thought to be optimal. Witsenhausen's work also introduces the idea of implicit communication, wherein the weak controller can communicate with the blurry controller using the implicit channel of the modifiable system state, allowing the controllers to use as little power as possible. Using these ideas, we will be following-up on the work of center faculty Todd Coleman on following a path using a brain-machine interface. However, instead of using pure estimation techniques of continuous variables, we hope to divide the space into discrete variables (using intuition from Witsenhausen's counterexample) and detect them, simplifying the problem of inference through noise.

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