Related papers: Topological Necessary Conditions for Control Dynam…

In this article we prove a necessary and a sufficient condition for a finite subset of the special linear group to be dominated. These conditions are purely geometric in nature, as they only involve the trace and the eigenvectors of the…

In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…

We introduce High-Relative Degree Stochastic Control Lyapunov functions and Barrier Functions as a means to ensure asymptotic stability of the system and incorporate state dependent high relative degree safety constraints on a non-linear…

The Fast Lyapunov Indicators are functions defined on the tangent fiber of the phase-space of a discrete (or continuous) dynamical system, by using a finite number of iterations of the dynamics. In the last decade, they have been largely…

In this paper, we examine the controllability of Laplacian dynamic networks on cographs. Cographs appear in modeling a wide range of networks and include as special instances, the threshold graphs. In this work, we present necessary and…

In the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…

In this paper we consider an optimal control problem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with matrix- valued non-smooth controls in coefficients and a nonlinear equation of Ham- merstein type. Since…

This paper deals with asymptotic stability of a class of dynamical systems in terms of smooth Lyapunov pairs. We point out that well known converse Lyapunov results for differential inclusions cannot be applied to this class of dynamical…

Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such…

This paper develops sharp Hautus-type criteria, stochastic counterparts of the classical Popov-Belevitch-Hautus test, for exact controllability and stabilizability of backwardstructured stochastic linear systems. The main finding is that…

Topological characteristics reveal important physical properties of plasma structures and astrophysical processes. Physical parameters and constraints are linked with topological invariants, which are important for describing magnetic…

This paper is concerned with providing the maximum principle for a control problem governed by a stochastic evolution system on a separable Hilbert space. In particular, necessary conditions for optimality for this stochastic optimal…

We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.

We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically…

We prove that if a smooth vector field $F$ of $S^3$ generates a sufficiently complicated heteroclinic knot, the flow also generates infinitely many periodic orbits, which persist under smooth perturbations which preserve the heteroclinic…

D. K. Biss (Topology and its Applications 124 (2002) 355-371) introduced the topological fundamental group and presented some interesting basic properties of the notion. In this article we intend to extend the above notion to homotopy…

Classical turnpikes correspond to optimal steady states which are attractors of optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the…

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…

In this paper we study the Lyapunov stability and Hopf bifurcation in a system coupling a Watt-centrifugal-governor with a steam-engine. Sufficient conditions for the stability of the equilibrium state in terms of the physical parameters…