The Decomposition of Controlled Dynamic Systems

摘要

Nonlinear dynamic systems are considered that are described by the Lagrangian equations and subjected to uncertain disturbances and bounded control forces. Under certain assumptions, feedback control laws are obtained that satisfy the imposed constraints and drive the systems to the prescribed terminal states in finite time. The approaches developed in the paper are based on the decomposition of the given system into subsystems with one degree of freedom each. Methods of optimal control and differential games are then applied to the subsystems. As a result, explicit formulae for the closed-loop control forces and for the time of motion are derived. The obtained feedback controls are time-suboptimal and robust, they can cope with small disturbances and parameter variations. Applications to control of robots are discussed.