Kolmogorov complexity: how a paradigm motivated by foundations of physics can be applied in robust control

摘要

Born about three decades ago, Kolmogorov Complexity Theory (KC) led to important discoveries that, in particular, give a new understanding of the fundamental problem: interrelations between classical continuum mathematics and reality (physics, biology, engineering sciences, ...). Crudely speaking, it enables us to better distinguish between mathematical possible (possible abnormal) and physically possible situations. We show that this formalization is not only in good accordance with theoretical physics, but it can also be applied to robust control: instead of requiring that the control work for all mathematically possible situations, we only require that the control works for all "non-abnormal" situations.