Dimensionality reduction in optimal control and estimation problems for systems of solid bodies with low dissipation

Abstract

We use the method of integral manifolds to reduce optimal control and filtering problems in application to mechanical systems with low friction.

Reduction of flexible joint manipulator mathematical model

“…This makes it possible to use the slow subsystem, which describes the motion on the manifold, as the simplified model of the manipulator. Similar questions for other classes of quasi-oscillating systems are studied in [10][11][12][13].…”

“…One of the approaches, which allows to reduce the complex multirate dynamic systems, is based on the theory of integral manifolds [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The conditions of the existence of an attractive slow integral manifold are investigated.…”