Canonical Form of Lyapunov Second Method in Mathematical Modelling and Control Design

TL;DR

This paper introduces a canonical form of Lyapunov functions and related concepts, demonstrating their application to control design for a nonlinear aircraft model with improved stability and robustness.

Contribution

It generalizes the Lyapunov second method through canonical forms and diffeomorphisms, applying these to nonlinear aircraft control modeling.

Findings

Successful design of a wide-sense robust tracking control law

Application of canonical Lyapunov functions to a 5D aircraft model

Hierarchical control structure with attractors for stability

Abstract

The objective of the paper is to put canonical Lyapunov function(CLF), canonizing diffeomorphism (CD) and canonical form of dynamical systems (CFDS), which have led to the generalization of the Lyapunov second method, in perspective of their high efficiency for Mathematical Modelling and Control Design. We show how the symbiosis of the ideas of Henri Poincare and Nikolay Chetaev leads us to CD, CFDS and CLF. Our approach successfully translates into mathematical modelling and control design for special two-angles synchronized longitudinal maneuvering of a thrust-vectored aircraft. The essentially nonlinear five-dimensional mathematical model of the longitudinal flight dynamics of a thrust-vectored aircraft in a wing-body coordinate system with two controls, namely the angular deflections of a movable horizontal stabilizer and a turbojet engine nozzle, is investigated. The wide-sense robust and stable in the large tracking control law is designed. Its core is the hierarchical cascade of two controlling attractor-mediators and two controlling terminal attractors embedded in the extended phase space of the mathematical model of the aircraft longitudinal motion. The detailed demonstration of the elaborated technique of designing wide-sense robust tracking control for the nonlinear multidimensional mathematical model constitutes the quintessence of the paper.