Will machine learning outrun traditional control theory ?

No! Still Machine learning has to learn a lot to challenge traditional control theory ( branch of applied mathematics). Nothing in mathematics can be replaced by machine learning.

But, people may do this in future, so far it seems to be only in lab environments. Andrew Ng used reinforcement learning methods to make an unmanned helicopter fly upside down. Raffalleo D’andrea uses ML to improve the performance of his quadrotors. Steve Brunto has utilized dynamical system analysis using ML.

Control engineering is a rigorous discipline and has nice theories of stability, robustness, optimality. It is true that some CS researchers applied ML techniques to some control problems, which were already solved by classical control algorithms. But, one cannot prove any stability, robustness properties of the closed-loop system when there is a ML algorithm with hundreds of parameters in the loop.

In general, ML can be handy when there is no model for the problem we are trying to solve, e.g., perception problems. For control applications, we know how cars drive, helicopters fly, robotic arms move; and industry prefers a PID control algorithm with a handful parameters instead of a deep learning algorithm with billions of parameters. One important task, that is usually ignored by CS academics in their academic environment, is verification and validation of control algorithms. When there is a PID control algorithm in the loop, it is easy to check if the closed-loop system is stable. However, such basic property cannot be checked for any known ML algorithm. Whenever a traditional control method can be applied, it usually comes with a decent set of guarantees about what will happen. This is perhaps why ML will not make PID controllers obsolete.

People show things like good asymptotic learning rate behaviour in ML, but these are academic results which amount to sanity checks, not practical guarantees. Another problem is that ML methods require a ridiculous amount of training data. In contrast, control methods only require a good enough system model. Adaptive control is somewhat combination of control and learning.