Related papers: Dependence of vector fields and singular controls
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
To understand the controllability of complex networks is a forefront problem relevant to different fields of science and engineering. Despite recent advances in network controllability theories, an outstanding issue is to understand the…
Interacting massive spin-1 fields have been widely used in cosmology and particle physics. We obtain a new condition on the validity of the classical limit of these theories related to the non-trivial constraints that exist for vector field…
We study the reduction of non-autonomous regular Lagrangian systems by symmetries, which are generated by vector fields associated with connections in the configuration bundle of the system $Q\times\real\to\real$. These kind of symmetries…
We prove that every trajectory of a polynomial vector field on the complex projective plane accumulates to the singular locus of the vector field. This statement represents a holomorphic version of the Poincare-Bendixson theorem and solves…
This work presents a novel framework for the formation control of multiple autonomous ground vehicles in an on-road environment. Unique challenges of this problem lie in 1) the design of collision avoidance strategies with obstacles and…
We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of…
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and…
Reference path following is a key component in the functioning of almost all engineered autonomous agents. Among several path following guidance methods in existing literature, vector-field-based guidance approach has got wide attention…
A class of quantum field theories invariant with respect to the action of an odd vector field Q on a source supermanifold $\Sigma$ is considered. We suppose that Q satisfies the conditions under which an integral of any Q-invariant function…
Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using…
We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…
A new notion of vertex independence and rank for a finite graph G is introduced. The independence of vertices is based on the boolean independence of columns of a natural boolean matrix associated to G. Rank is the cardinality of the…
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…
We show that self-interacting vector field theories exhibit unphysical behaviour even when they are not coupled to any external field. This means any theory featuring such vectors is in danger of being unphysical, an alarming prospect for…
The aim of this paper is to investigate the well-posedness of a class of boundary control and observation systems on a one dimensional spatial domain. We derive a necessary and sufficient condition characterizing the well-posedness of these…
Using monotonicity theory we investigate the continuous dependence on parameters for the discrete BVPs which can be written in a form of a nonlinear system.
In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact…