Dichotomic Structure of DAEs Solutions for the Aircraft Control

Abstract

The paper has its roots in earlier studies focused on DAEs solutions, for the aircraft flight control and intends to be a synthesis of them. The main goal is to structure the solution for the control laws so as to derive its components, which control any significant mechanical phenomenon for the controlled flight. The basic method used becomes from a unified manner of finding the solution of DAEs using a rigorous guideline stated as “necessary and sufficient condition” in an algebraic equation form that is used in an algorithmic procedure and for statement of the equations, which emphasises the dichotomic structure. The viewpoint considers an extended DAE system, including the differential equations of control variables, that allows to formulate this question as an inverse problem and to regard the algebraic equation, for constraints, as a singular implicit solution of the differential subsystem. Stating the necessary and sufficient condition for an implicit equation be a singular implicit solution of the extended differential system, we use it to approach the solution for flight control and for its dichotomic structure with additive components.