Approximate solution of the boundary value problem for control systems satisfying the rank condition. (Russian. English summary) Zbl 1340.93131

Grushkovskaya, V. V.; Zuyev, A. L.

Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 4, 86-101 (2014).

Summary: The paper is devoted to studying the motion planning problem that consists in steering control-linear system from a given initial point to a target point for a fixed time. There is supposed that the vector fields of a system satisfy the rank condition with the first-order Lie brackets. The approach considered makes it possible to reduce the point-to-point control problem to a system of second-order algebraic equations. The solvability of such a system is proved, and the error of the method is estimated. Kinematic equations of an underwater vehicle and a rigid body with flywheels are considered as examples.

MSC:

93C85

Automated systems (robots, etc.) in control theory

Keywords:

control system; boundary value problem; first-order Lie brackets