Title :
The contact problem for linear continuous-time dynamical systems: a geometric approach
Author :
ten Dam, A.A. ; Dwarshuis, K.F. ; Willems, Jan C.
Author_Institution :
Nat. Aerosp. Lab., Chofu, Japan
fDate :
4/1/1997 12:00:00 AM
Abstract :
In this paper linear time-invariant dynamical systems described by a combination of differential equalities and static inequalities in state-space formulation are investigated. Of special interest is the contact problem: the effect of the boundary of the constraint set on the behavior of the system. This effect is studied by dividing the state-space in a number of disjunct subsets. It is shown that these subsets are invariant under linear state feedback. In our framework, a specific place is reserved for modeling the laws of collision, i.e., physical modeling, which are regarded as external factors. Our main results are a system theoretical framework in which we describe what happens upon contact and a definition of the constrained state-space system in terms of its restricted behavior. The results presented here can be considered as an extension for restricted linear systems of the classic positive invariance theory for linear systems
Keywords :
computational geometry; continuous time systems; invariance; linear systems; set theory; state feedback; state-space methods; constrained mechanical systems; contact problem; continuous-time dynamical systems; differential equality; inequality constraints; linear state feedback; linear systems; positive invariance theory; state-space systems; static inequality; Constraint theory; Control systems; Differential algebraic equations; Helium; Lagrangian functions; Linear systems; Manipulators; Mechanical systems; Robots; State feedback;
Journal_Title :
Automatic Control, IEEE Transactions on