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Geometry and flatness of m-crane systems

Nowicki M., Respondek W., Piasek J., Kozłowski K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 5

893--903

We propose a class of m-crane control systems that generalizes two- and three-dimensional crane systems. We prove that each representant of the described class is feedback equivalent to the second order chained form with drift. In consequence, we prove that it is differentially flat. Then we investigate its control properties and derive a control law for tracking control problem.

Phase portraits of planar control-affine systems

Jakubczyk B., Respondek W.

Control and Cybernetics

2005

Vol. 34, no 3

819-847

We study nonlinear control systems in the plane, affine with respect to control. We introduce two sets of feedback equivariants forming a phase portrait PP and a parameterized phase portrait PPP of the system. The phase portrait PP consists of an equilibrium set E, a critical set C (parameterized, for PPP), an optimality index, a canonical foliation and a drift direction. We show that under weak generic assumptions the phase portraits determine, locally, the feedback and orbital feedback equivalence class of a system. The basic role is played by the critical set C and the critical vector field on C. We also study local classification problems for systems and their families.