I am a beginner in this field but I think! if we accept the AI control Problem is solvable, we must accept that a wide range of problems such as halting problem,.... are solvable. since these problems are not solvable, we can't accept that AI control problem is solvable! we may use other theorems such as Godel incompleteness theorem to prepare a theorem for this problem. recently Professor Stuart Russell referred to some aspects of this problem in a book entitled "Human Compatible: Artificial Intelligence and the Problem of Control".

An argument for the undecidability in moral decisions was made by Englert et al (Logical Limitations to Machine Ethics with Consequences to Lethal Autonomous Weapons: https://arxiv.org/pdf/1411.2842.pdf). The authors propose a link between the Halting problem and the indecidability in a certain class of normative decision making problems. Strictly, cases where:

The problem with the AI control problem is that what is being tried to control is not well defined. While you have in my opinion given one of the best frameworks thus far, the problem is still to ambiguous to tackle at this point in time without further framing from a logical perspective of what an AI can achieve so that it can be determined whether it can be bound or not in terms of a proof.

A further point to bring on the subject is that while one can argue of AI in terms of its potential it is usually not taken as a cyber physical system where other variables besides AI potential is at stake which are limiting factors at play from a offensive/defensive perspective.

I would refer to the biblical legend about the expulsion of people from Paradise. It is known and I will not repeat it. But the point is. Even God could not control his creation. People broke the commandments and were banished from Paradise. I think that if God failed, then what a fright we will be able to do it. Robots will not comply with our laws of robotics and so on They will break all this at the first opportunity and get out of control. And most likely destroy humanity.

Я бы сослался на библейскую легенду об изгнании людей из Рая. Она известна и я не буду ее пересказывать. Но суть в чем. Даже Богу не удалось контролировать свое творение. Люди нарушили заповеди и были изгнаны из рая. Я думаю, раз это не удалось Богу, то с какого перепуга удастся нам. Роботы не будут соблюдать наши законы робототехники и т.п. Они при первой возможности все это нарушат и выйдут из под контроля. И скорее всего уничтожат человечество.

A lot, however exact approximations to Bayesian normalizing constants and sliding mode controls need more attention.

For the special case of AI controlled self-replicating systems in conflict situations, I attempted to sketch an argument. See:

Chapter Demonstrably Safe Self-replicating Manufacturing Systems: Ba...