Complete controllability criteria for classes of mechanical systems with bounded controlst

✍ Scribed by Ye.S. Pyatnitskii

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 676 KB
• Volume: 60
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(96)00089-5

✦ Synopsis

A collection (class) of controllable dynamical systems, each described by Lagrange equations of the second kind, is considered. The class is defined by specifying the bounded domains in which the controls and generalized forces may take their respective values. The systems differ from one another both in the expression for the kinetic energy, which may be chosen at will from a set of positive-definite quadratic forms in the velocities (with coefficients, which depend on the coordinates), and in the generalized forces, which may vary within the same domain. Necessary and sufficient conditions are established for any such class to be completely controllable (i.e. for any system belonging to the class to be completely controllable). These conditions have an obvious physical meaning. In the ease, for example, of robot manipulators, the conditions imply that a system is completely controllable if and only if the maximum values of the control torques exceed the corresponding torques of the other forces (weight, resistance, etc.) in absolute value.