The principle of uniform boundedness for topological measures

1982 ◽  
Vol 31 (2) ◽  
pp. 135-137
Author(s):  
A. N. Sazhenkov
Keyword(s):  
Uniform Boundedness ◽  
Topological Measures

scholarly journals Topological measures for identifying and predicting the spread of complex contagions

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Douglas Guilbeault ◽  
Damon Centola
Keyword(s):  
Social Networks ◽  
Shortest Path ◽  
Empirical Data ◽  
Path Length ◽  
Centrality Measures ◽  
Social Phenomena ◽  
Node Centrality ◽  
Network Connectedness ◽  
Topological Measures ◽  
Definition Of

AbstractThe standard measure of distance in social networks – average shortest path length – assumes a model of “simple” contagion, in which people only need exposure to influence from one peer to adopt the contagion. However, many social phenomena are “complex” contagions, for which people need exposure to multiple peers before they adopt. Here, we show that the classical measure of path length fails to define network connectedness and node centrality for complex contagions. Centrality measures and seeding strategies based on the classical definition of path length frequently misidentify the network features that are most effective for spreading complex contagions. To address these issues, we derive measures of complex path length and complex centrality, which significantly improve the capacity to identify the network structures and central individuals best suited for spreading complex contagions. We validate our theory using empirical data on the spread of a microfinance program in 43 rural Indian villages.

Trajectory following control of lower limb exoskeleton robot based on Udwadia–Kalaba theory

2021 ◽  
pp. 107754632110317
Author(s):  
Jin Tian ◽  
Liang Yuan ◽  
Wendong Xiao ◽  
Teng Ran ◽  
Li He
Keyword(s):  
Lower Limb ◽  
Control Method ◽  
Uniform Boundedness ◽  
Adaptive Robust Control ◽  
Structural Vibration ◽  
Control Approach ◽  
Lower Limb Exoskeleton ◽  
Exoskeleton Robot ◽  
Constraint Problem ◽  
Trajectory Following

The main objective of this article is to solve the trajectory following problem for lower limb exoskeleton robot by using a novel adaptive robust control method. The uncertainties are considered in lower limb exoskeleton robot system which include initial condition offset, joint resistance, structural vibration, and environmental interferences. They are time-varying and have unknown boundaries. We express the trajectory following problem as a servo constraint problem. In contrast to conventional control methods, Udwadia–Kalaba theory does not make any linearization or approximations. Udwadia–Kalaba theory is adopted to derive the closed-form constrained equation of motion and design the proposed control. We also put forward an adaptive law as a performance index whose type is leakage. The proposed control approach ensures the uniform boundedness and uniform ultimate boundedness of the lower limb exoskeleton robot which are demonstrated via the Lyapunov method. Finally, simulation results have shown the tracking effect of the approach presented in this article.

Constraint-oriented integrated longitudinal and lateral robust control for connected and automated vehicle platoons

2021 ◽  
pp. 107754632110026
Author(s):  
Zeyu Yang ◽  
Jin Huang ◽  
Zhanyi Hu ◽  
Diange Yang ◽  
Zhihua Zhong
Keyword(s):  
Robust Control ◽  
Estimation Error ◽  
Uniform Boundedness ◽  
Path Tracking ◽  
Adaptive Robust Control ◽  
Connected Vehicle ◽  
Vehicle Platoon ◽  
Tracking Model ◽  
Vehicle Platoons ◽  
Following Error

The coupling, nonlinearity, and uncertainty characteristics of vehicle dynamics make the accurate longitudinal and lateral control of an automated and connected vehicle platoon a tough task. Little research has been conducted to fully address the characteristics. By using the ideology of constraint-following control this article proposes an integrated longitudinal and lateral adaptive robust control methodology for a vehicle platoon with a bidirectional communication topology. The platoon control objectives contain the path tracking stability, the platoon internal stability, and the string stability. First, we establish the nonlinear kinematics path tracking model and the coupled vehicle longitudinal and lateral dynamical model that contains time-varying uncertainties. Second, we design a series of nonlinear equality constraints that directly guarantee the control objectives based on the kinematic relations. On this basis, an adaptive robust constraint-following control is proposed. It is shown that the control guarantees the uniform boundedness and the uniform ultimate boundedness of the constraint-following error and the uncertainty estimation error. Finally, simulation results are provided to validate the effectiveness of the proposed methodology.

scholarly journals Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness

2021 ◽  
Author(s):  
Ulrich Kohlenbach
Keyword(s):  
Uniform Boundedness ◽  
Metric Structures

AbstractIn this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use of countable Heine–Borel compactness.

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

Bifurcation Analysis and Optimal Harvesting of a Delayed Predator–Prey Model

2015 ◽  
Vol 25 (01) ◽  
pp. 1550012 ◽  
Author(s):  
P. Tchinda Mouofo ◽  
R. Djidjou Demasse ◽  
J. J. Tewa ◽  
M. A. Aziz-Alaoui
Keyword(s):  
Natural Resource Management ◽  
Optimal Control Theory ◽  
Uniform Boundedness ◽  
Optimal Harvesting ◽  
Global Dynamics ◽  
Saddle Node Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Local Bifurcations ◽  
Prey Model

A delay predator–prey model is formulated with continuous threshold prey harvesting and Holling response function of type III. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The positive invariance of the non-negative orthant is proved and the uniform boundedness of the trajectories. Stability of equilibria is investigated and the existence of some local bifurcations is established: saddle-node bifurcation, Hopf bifurcation. We use optimal control theory to provide the correct approach to natural resource management. Results are also obtained for optimal harvesting. Numerical simulations are given to illustrate the results.

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