Linearization of the Motion Model of a Multi-Connected Dynamic Object by Pseudo-Coordinate Linearization

A method is proposed for linearizing a non-linear model of the controlled motion of a multi-connected dynamic object with attached structural elastic elements. The method is founded on the use of non-special transformations of smooth manifolds based on the well-known Lie algebra. Purpose: to apply a well-developed theory of optimal linear control based on L. S. Pontryagin’s maximum principle or R. Bellman’s principle of optimality. Methods: the general theoretical approach of pseudo-coordinate linearization is considered, and the procedure for linearizing the model of controlled angular motion of a remote-controlled aircraft is illustrated. Practical significance: a finite-dimensional mathematical model has been obtained that is applicable to solving the synthesis problems of optimal, robust and finite control of spatial angular motion of a remote-controlled aircraft. Keywords: