Identifiability and Detectability of Lyapunov Exponents in Robotics

Abstract

Lyapunov exponents (LE) are one of the most effective tools for analyzing the quality of systems in robotics. They are used to optimize the robot work, evaluate the quality of their work, and solve various tasks in control systems with robots. Calculating the full spectrum of LE is a complex problem. It relates to the identifiability recoverability and detectability of LE. The identifiability recoverability and detectability issues of Lyapunov exponents were not considered. This problem is relevant. The authors propose an approach to verify these characteristics for the linear dynamical system. It bases on the analysis of geometric frameworks (GF) that depends on the structural properties coefficient (SPC). The SPC reflects the change in Lyapunov exponents, and GF guarantees decision-making on the LE type. They obtain (1) conditions of fully detectable LE (these conditions correspond to the determination of an indicators complete set in the robot control system) and (2) s-detectability conditions with level v-no recoverability if the system contains no recoverable lineals.

Structural Identification of Control Objects—A Review

“…This problem has not been raised or discussed. For the first time, the problem formulation and methods of its solution were proposed for linear and non-stationary systems in [57, 116,117].…”