Adequate mathematical modelling by wide-sense robust control design in a thrust-vectored flight dynamics problem

Abstract

The conflict between the accuracy and the complexity of the adequate mathematical modelling approximations of physical phenomena is discussed. The need of finding certain types of topological equivalency between nonlinear mathematical models as the keystone to successful study is emphasized. We formulate the control problem when the controlling functions cannot directly act on the phase variables defining a given terminal manifold as a control aim through the right-hand sides of differential equations describing a mathematical model under study. The idea of creating a hierarchical cascade of controlling attractors–mediators is introduced. It is shown how the method of the goal-oriented formation of the local topological structure of one-codimensional foliations as the basis of Poincaré’s-strategy-based backstepping method can be successfully used for designing terminal control. One brings up the problem of developing the tools intended for the creation of the topologically equivalent and quantitative–deviation–tolerable simplifications of the complex original mathematical models suitable for the synthesis of the control laws that are supposed to be applied to the latter ones. The two-dimensional example is analytically investigated to explain the procedure of constructing the cascade of controlling one-codimensional attractor mediators. 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 core of the designed wide-sense robust and stable in the large-tracking control algorithm is a hierarchical cascade of controlling attractor–mediators consisting of the two one-codimensional manifolds. The results of the computer simulation are presented. The topicality in creating the general theory of nonlinear mathematical modelling, as the tools to construct and manipulate the sets of topologically equivalent models being qualitative–quantitative adequate to corresponding physical phenomena, is pointed up in conclusion.