ABSTRACT
The goal of tracking is the achievement of the desired plant behavior under simultaneous actions of the external disturbances and of all initial conditions on the plant, while none of the stability concepts aims at such a goal. The tracking goal is the primary control goal. Tracking is the crucial control issue. Stability is the essential dynamic systems topic in general and the control systems topic in particular. Various types of the plant controllability and of the disturbance compen-
sation do not clarify whether the plant has a property to enable the existence of a control that can force the plant output to track (su¢ ciently accurately, precisely, with a good quality) any of its desired output behaviors Yd (:) from a given functional family Yd under the simultaneous action of an arbitrary disturbance D (:) from a functional family Di and under the in‡uence of arbitrary initial conditions. The plant property that does enable the existence of such control is the plant trackability . Among various concepts of the plant trackability presented herein the particular importance for tracking control synthesis is the plant natural trackability. It discovers the plant ability to enable the existence, synthesis and implementation of the tracking control without knowing the real form and instantaneous vector value of the disturbance vector D (t), without using information about the plant internal dynamics, hence about the whole plant mathematical model. The book presents de…nitions of perfect and imperfect trackability and of
natural trackability. The relationships among them are discovered herein. The book resolves completely the problems of the necessary and su¢ cient
conditions for the trackability and for the natural trackability properties. The conditions have simple algebraic forms in the complex domain. The book provides the fundamentals of the tracking theory and of the tracka-
bility theory. It presents the tracking concept in Lyapunov sense, i.e., Lyapunov tracking concept, and the concept of tracking with …nite, either scalar or vector, reachability time. It discovers the great richness of di¤erent tracking types that re‡ect various tracking qualities. They show essential di¤erences between stability and tracking, which are mutually independent properties in general.
