Optimal Control of Mechanical Descriptor Systems

In recent years the analysis and synthesis of linear control systems in descriptor form has been established. One class of descriptor systems are mechanical descriptor systems, i.e. mechanical systems with explicit holonomic and/or nonholonomic constraints. This special form of description of mechanical systems according to Lagrange’s equations of the first kind is important for many applications such as vehicle dynamics, machine dynamics, dynamics of robots etc. Although well-known methods of analytical mechanics exist to eliminate the constraints and form a regular set of differential equations, aspects of physical transparency and subsystem techniques are reasons to deal with the original descriptor system.