Systems theory can play an important in unveiling fundamental limitations of learning algorithms and architectures when used to control a dynamical system, and in suggesting strategies for overcoming these limitations. As an example, a feedforward neural network cannot stabilize a double integrator using output feedback. Similarly, a recurrent NN with differentiable activation functions that stabilizes a non-strongly stabilizable system must be itself open loop unstable, a fact that has profound implications for training with noisy, finite data. A potential solution to this problem, motivated by results on stabilization with periodic control, is the use of neural nets with periodic resets, showing that indeed systems theoretic analysis is instrumental in developing architectures capable of controlling certain classes of unstable systems. This short conference paper also argues that when the goal is to learn control oriented models, the loss function should reflect closed loop, rather than open loop model performance, a fact that can be accomplished by using gap-metric motivated loss functions. |