STABILIZATION OF CONTROLLED SYSTEMS WITH A GUARANTEED ESTIMATE OF THECONTROL QUALITY

The problem of stabilizing motion in controlled systems with a guarant eed estimate of the control quality is considered. It arises from the optimal stabilization problem when the conditions on the cost function al are relaxed: no minimization of this functional is required, it is only necessary for it not to exceed a certain limit. This enables the class of solvable problems to be extended compared to the class of opt imal stabilization problems. The solution of the problem is based on L yapunov's direct method using Lyapunov functions with derivatives of c onstant sign. Some of the results are new even in the case of the opti mal stabilization problem. The following examples are considered: a ho lonomic mechanical system with time-dependent Lagrangian, a controlled linear mechanical system and the problem of using the gravitational m oment to stabilize the controlled plane rotational motion of a satelli te in an elliptic orbit. (C) 1997 Elsevier Science Ltd. All rights res erved.