Method of decomposition and its applications to uncertain dynamical systems

Authors:	Chernousko Felix, Institute for Problems in Mechanics of the Russian Academy of Sciences, Russian Federation Reshmin Sergey, Institute for Problems in Mechanics of the Russian Academy of Sciences, Russian Federation
Topic:	2.1 Control Design
Session:	Control and Estimation Under Set-Membership Uncertainty - II
Keywords:	Decomposition methods, Nonlinear control systems, Feedback control,Bang-bang control

Abstract

A nonlinear dynamical system described by Lagrange's equations isconsidered. The system is subjected to uncertain external forces and controlsbounded by geometric constraints. A feedback control that satisfies the imposedconditions and brings the system to a prescribed terminal state in a finite timeis proposed. The control is based on the decomposition of the system and usesideas of optimal control and differential games. Explicit formulas for the feedbackcontrol are presented. Applications to control of robots and underactuated systemsare discussed. Computer simulation of motions of a double pendulum controlledby one torque is presented.