Nilpotent bases of distributions
نویسندگان
چکیده
When modelling controlled dynamical systems one commonly chooses individual control variables u1, . . . um which appear natural from a physical, or practical point of view. In the case of nonlinear models evolving on R (or more generally, an analytic manifold M) that are affine in the control, such a choice corresponds to selecting vector fields f0, f1, . . . fm:M 7→ TM , and the system takes the form
منابع مشابه
Nilpotent Bases for Nonholonomic Distributions
This paper develops a constructive method for nding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior di erential systems. The results are applied to the problem of nding a set of nilpotent input vector elds for a nonholonomic control system, which can then used to constru...
متن کاملOn Grr Obner Bases for Two-sided Ideals in Nilpotent Group Rings
An algorithm for constructing Grr obner bases for right and for two-sided ideals in nilpotent group rings is presented.
متن کاملNilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems
This paper develops a constructive method for finding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then used to ...
متن کاملBases for Coordinate Rings of Conjugacy Classes of Nilpotent Matrices
A general conjecture is given for an explicit basis of the coordinate ring of the closure of the conjugacy class of a nilpotent matrix. This conjecture is proven when the partition given by the transpose Jordan type of the nilpotent matrix is a hook or has two parts.
متن کاملOn nilpotent and solvable polygroups
Applications of hypergroups have mainly appeared in special subclasses. One of the important subclasses is the class of polygroups. In this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. In particular, we give a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.
متن کامل