Decomposition-based continuous control of mechanical systems

For Lagrangian dynamical systems with inexactly known parameters, a continuous feedback control is constructed using ideas of the decomposition method on the major segment of the trajectory and linear feedbacks with the coefficients depending on the phase variables in the vicinity of the terminal state. It is supposed that the matrix of kinetic energy of the system is close to a constant matrix in the motion domain and that the system is affected by uncontrollable bounded disturbances. The proposed controls make it possible to steer the system from an arbitrary initial state into a given terminal state in a finite amount of time using generalized forces that are bounded by magnitude. An upper estimate on the total time of system motion is given and techniques for its reduction are described. The efficiency of the proposed algorithms is demonstrated by the numerical simulation of the dynamics of some simple mechanical systems.