Consistent hierarchies of nonlinear abstractionsGeorge
نویسندگان
چکیده
In this paper, we consider the problem of constructing hierarchies of nonlinear control systems that preserve reachability properties, and, in particular, local accessibility. In this hierarchical framework, showing local accessibility of the higher level abstracted model of the nonlinear control system is equivalent to showing local accessibility of the, more detailed, lower level model. Hierachies of consistent nonlinear abstractions can therefore result in signiicant complexity reduction in determing the reachability properties of nonlinear systems.
منابع مشابه
Nonlinear Bi-Integrable Couplings of Multicomponent Guo Hierarchy with Self-Consistent Sources
Based on a well-known Lie algebra, the multicomponent Guo hierarchy with self-consistent sources is proposed. With the help of a set of non-semisimple Lie algebra, the nonlinear biintegrable couplings of the multicomponent Guo hierarchy with self-consistent sources are obtained. It enriches the content of the integrable couplings of hierarchies with self-consistent sources. Finally, the Hamilto...
متن کاملNonlinear Schrödinger Equations for Identical Particles and the Separation Property
We investigate the separation property for hierarchies of Schrödinger operators for identical particles. We show that such hierarchies of translation invariant second order differential operators are necessarily linear. A weakened form of the separation property, related to a strong form of cluster decomposition, allows for homogeneous hierarchies of nonlinear differential operators. Some conne...
متن کاملGauge Transformations and Reciprocal Links in 2 + 1
Generalized Lax equations are considered in the spirit of Sato theory. Three decompositions of an underlying algebra of pseudo-diierential operators lead, in turn, to three diierent classes of integrable nonlinear hierarchies. These are associated with Kadomtsev-Petviashvili, modiied Kadomtsev-Petviashvili and Dym hierarchies in 2+1 dimensions. Miura-and auto-BB acklund transformations are show...
متن کاملOn a class of multidimensional integrable hierarchies and their reductions
A class of multidimensional integrable hierarchies connected with commutation of general (unreduced) (N+1)-dimensional vector fields containing derivative over spectral variable is considered. They are represented in the form of generating equation, as well as in the Lax-Sato form. A dressing scheme based on nonlinear vector Riemann problem is presented for this class. The hierarchies connected...
متن کاملA Hierarchical Planner that Generates Its Own Hierarchies
PABLO’ is a nonlinear planner that reasons hierarchically by generating abstract predicates. PABLO’s abstract search spaces are generated automatically using predicate relaxation, a new technique for defining hierarchies of abstract predicates. For some domains, this mechanism generates hierarchies that are more useful than those created by previous techniques. Using abstractions can lead to su...
متن کامل