TY - THES
A1 - Devadze, Grigory
T1 - Analysis of control system stability under algorithmic uncertainty
N2 - Stability of control systems is one of the central subjects in control theory. The classical asymptotic stability theorem states that the norm of the residual between the state trajectory and the equilibrium is zero in limit. Unfortunately, it does not in general allow computing a concrete rate of convergence particularly due to algorithmic uncertainty which is related to numerical imperfections of floating-point arithmetic. This work proposes to revisit the asymptotic stability theory with the aim of computation of convergence rates using constructive analysis which is a mathematical tool that realizes equivalence between certain theorems and computation algorithms. Consequently, it also offers a framework which allows controlling numerical imperfections in a coherent and formal way. The overall goal of the current study also matches with the trend of introducing formal verification tools into the control theory. Besides existing approaches, constructive analysis, suggested within this work, can also be considered for formal verification of control systems. A computational example is provided that demonstrates extraction of a convergence certificate for example dynamical systems.
KW - Kontrolltheorie , Stabilität , Steuerungstheorie
Y1 - 2016
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bsz:mit1-opus4-80073
ER -