On adaptive stabilization of programed motions of mechanical systems: PMM vol. 41, n≗ 5, 1977, pp. 859–869

Abstract

The problem of stabilizing programed motions of mechanical systems with holonomic and nonholonomic relationships is considered for various degrees of information about parameters of the equation of motion. First, the laws of control that stabilize programed motions in the nonadaptive case when parameters of the equation of motion are known and the initial perturbations are arbitrary, are synthesized. The adaptive control is constructed on that basis; such control ensures after the transitional process of adaption the closeness of the actual and programed motions. Solution of the adaption problem is based on the method of finite-convergent algorithms for solving systems of inequalities proposed in [1], Estimates of the time taken by the transitional process are presented for the adaptive and nonadaptive cases. Application of proposed algorithms for adaptive stabilization of programed motions of a transport robot on a caterpillar undercarriage and of a robot manipulator is discussed [2–5]