On zero-controllability in a part of variables of nonlinear dynamic systems (Q1281013)

Certain types of nonlinear, continuous-time, finite-dimensional control systems are considered. It is generally assumed that the controls and state variables are geometrically constrained. The notion of null-controllability in a part of the state variables is defined. Using suitably defined simple linear problems of optimal control, sufficient conditions for null-controllability in finite time are formulated and proved. The relationship between null-controllability and stabilizability is also discussed. As an illustrative example, a constructive solution of the nonlinear problem of a reorientation of a rigid body is given. Moreover, several remarks and comments on relationships between controllability and optimal control problems are presented. It should be stressed, that control problems in a part of the state variables have been recently considered in the author's monograph [Stability of dynamical systems with respect to a part of the variables (Russian). Moskva: Nauka (1991; Zbl 0734.93063)].