Control Theory in the Modern Era. Is it dead?

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Does control theory have an association with machine learning?

I’ll start with the basic building block of the modern machine learning paradigm: the perceptron. This was a hardware structure built in the ’50s by Rosenblatt [3]to mimic the real neural network in our brains. It came out of control theory literature when people tried to identify highly complex and nonlinear dynamical systems.

The classic sigmoid nonlinear activation function often used in machine/deep learning as a nonlinear optimizer, came out of control theory literature. Neural networks, artificial neural networks were first used in a supervised learning scenario to control theory. Kurt Hornik[4] was the first to identify that neural networks were universal approximators. Without classical control theory, we could say there would be no back-propagation (invented by Rumelhart & Hinton[5] in the ’80s based on inspiration from control theory); there would probably not be the LSTM (invented by Horchreiter in 1996) which are used in modeling tapped delay lines in memory-based neural networks. These have found massive use in speech recognition, language models, or time-series sequences.

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The antagonism between exploration and exploitation in reinforcement learning is known in control engineering as the conflict between identification (or estimation) and control. You could arguably say massive reinforcement learning problems arose out of Control Engineering research. I am attaching a link to Andrew Ng’s Thesis [6]for a perspective.

If you read the works of modern machine learning theorists, you’ll find control jargon camouflaged into new diction to make their ideas sound new or sexy. What they call back-propagation, for example, is nothing more than old-fashioned calculus-based differential chain rule. Variants of recurrent neural networks are simply NARX models that you would encounter in any system identification literature. So to answer the question, modern machine learning is a derived class of classical control theory.

Machine learning is basically functional learning and is prone to errors. I.e., no matter how large your training set is and how good your algorithm is, it’s not 100% guaranteed that the outcome it predicts is correct. It’s based on probability. Control theory, on the other hand, is based on rigorous mathematical proofs. Provided you model a system right; you can rely on control theory.

The best approach would be to use both in autonomous systems building.

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