|Learning a Neural-Network Controller for a Multiplicative Observation Noise System
|Vignesh Subramanian, Moses Won, Gireeja Ranade, UC Berkeley, United States
|T.2: Information and Control
|Topics in Information Theory
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|We consider the stabilization of a linear control system with multiplicative observation noise. Linear strategies have been proven to be ineffective in this system, and non-linear strategies can unboundedly outperform the best linear strategies. The current best-known control strategy is hand-crafted and far from optimal. In this paper, we use neural-network-based controllers to narrow the gap between the achievability and the converse for this problem. We propose a periodic controller structure and a greedy training procedure. This enables us to train our controller on a finite horizon problem but learn strategies that outperform the best-known hand crafted strategy and also generalize, i.e. provide stabilizing control at times beyond the training horizon. Further, we show that for our periodic approach, the learned strategies display a piecewise linear structure and are well approximated by interpretable functions.