Title :
Physics, control, and Kolmogorov complexity
Author_Institution :
Dept. of Mech. Eng., Houston Univ., TX, USA
Abstract :
The paper addresses a new possible approach to interrelations between physics, control, and mathematics. The approach is based on a principally new mathematical theory: Kolmogorov complexity that rejects infinite precision in numbers and algorithms. In the paper this principle is taken as a necessary condition for physically meaningful interrelations between indicated above sciences. To satisfy this condition the paper starts with (physical) definitions of K-numbers and K-observables. On this basis the corresponding notions of Kontrol, Kaos, K-systems, and K-gauge are introduced. This permits to establish a bridge between control and dynamical systems that traditionally are considered as different objects. One of results of this approach: K-equivalence of optimal control and optimal gauge (interrelation: control-gauge). Algorithmic efficiency of the approach is demonstrated by examples.
Keywords :
chaos; modelling; nonlinear control systems; nonlinear dynamical systems; optimal control; physics; K-gauge notion; K-number definition; K-observables definition; K-system notion; Kaos notion; Kolmogorov complexity; Kontrol notion; chaos; dynamical systems; gauge field theory; mathematical theory; optimal control; Bridges; Chaos; Control systems; Differential equations; Hilbert space; Mathematics; Mechanical engineering; Optimal control; Physics; Quantum mechanics;
Conference_Titel :
Physics and Control, 2003. Proceedings. 2003 International Conference
Print_ISBN :
0-7803-7939-X
DOI :
10.1109/PHYCON.2003.1236781