However, I will state that using e.g. Lyapunov functions to prove the stability of the system requires a model of the system. And even if you need a guarantee for your system, that guarantee is only as good as the fidelity of your model. For an inexpensive RC car, with slippage and saturation, without torque control or inertial sensing, you're going to have a hard time doing something that sounds as principled as what you suggest.
In any case I think I understand your comment, that in addition to the control problem, there's a perception problem.
This is an unbelievably wrong comment. All the Lyapunov and traditional Process control theory in the world won't help you solve autonomous driving. Also regarding "Guarantees and Safety" they don't magically appear out of thin air when you use traditional process control especially in noisy domains like autonomous driving. This comment is equivalent of "I can write code to solve Atari Pong in any programming language deterministicly so any post showing Deep Reinforcement Learning is stupid"...
Guarantees of safety (more accurately stability) is the entire point of lyaponov analysis, and it's used on noisy systems all of the time (https://www.mathematik.hu-berlin.de/~imkeller/research/paper...). Can you point to a specific noisy system that control theory is ill suited for?
The whole Lyapunov and control theory assumes perfect knowledge of sensors. Even though the signal itself might be error prone you have a signal. In case of autonomous driving even in simple cases as those described in the blogposts knowing the exact position of the markers and then using them to tune the contoller is not as easy as you might think.
The end-to-end system shown here solves three problems it processes the images to derive the signal, it then represents it optimally to the controller and then tunes the controller using provided training labels.
But classical control theory hasn't been able to extract, from camera pixels, the open path in a road with cars, bicycles, and pedestrians. Camera inputs are million-dimensional, and there aren't accurate theoretical models for them.
But in this case though, any kind of state space control also requires rather precise knowledge of the physical laws that govern the dynamics of the vehicles. When such information is not available, can neural nets do a decent job at mimicking an analytical control algorithm? I think that's an interesting problem worth exploring.
I think Rockets are straightforward too just a bottle with expanding gasse through a series of nozzles, pointed at different angles at correct time but since I know I am not a rocket scientist I dont go around claiming moon-landing was not a "great intellectual" effort.
A tree falls in an intersection because some carpenter ants chewed through trunk. Cars swerve to miss the tree and collide in an inelastic ball of nonlinearity, showering debris everywhere. You approach this at 65 mph and have 23 ft to decide what to do. Fear not, you have a list, a perfect list with coordinates, velocities, and material properties of every solid body in the area. Furthermore, without great intellectual effort, you can solve the millions of coupled differential equations that govern the dynamics of the entire system in near real time. Oh, and your list also has a measure of importance of each bit of mass, whether it is human, animal, or inert. And your list also accounts for the degrees of freedom introduced by every other car approaching the intersection, also using their own respective lists and perfect knowledge of the world to miss each other?