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.

METHODS AND ALGORITHMS FOR THE COMPLETE PROCESSING OF A POSTDETECTOR LOW-CONTRAST OPTICAL IMAGE

2018 ◽  
pp. 99-107
Author(s):  
V. V. Lavrov ◽  
R. S. Luchkin ◽  
O. I. Nemykin ◽  
M. E. Prokhorov ◽  
Yu. G. Ryndin ◽  
...  
Keyword(s):  
Optical Image ◽  
Structural Elements ◽  
Filtration Process ◽  
Low Contrast ◽  
Information Object ◽  
Detection Stage ◽  
Metric Structures ◽  
Spot 5 ◽  
Integrated Indicators ◽  
Complete Processing

Methods and algorithms for the complete processing of a post-detector low-contrast optical image (OI) of an unknown remote object obtained by ground-based optical means of observation under conditions of a complex background situation are considered. The purpose of processing is to separate and interpret at least with the help of the analyst, of the main constructive elements using the integrated indicators introduced in [6] and the characteristics of the analyzed OI, which are connected by the information, topological and metric structures of the OI. The stages of processing the OI include extracting the image-containing information object of the image portion (detection) and filtration of the OI, using recursive rank filtering. The final stages of processing include the segmentation of the OI and the allocation on it constructive elements using the apparatus of graph theory. An example of image processing of a Spot-5 spacecraft obtained in real conditions is given. It is shown that in this case at the detection stage it is possible to reduce the volume of information processed at subsequent stages by 8 times, in the filtration process to increase the compactness of the OI and to increase its connectivity in comparison with the post-detection OI. As a result of segmentation and allocation of constructive elements, three structural elements that can be interpreted as a spacecraft case and two remote panels can be identified with the analyst’s participation.

ON THE PRINCIPLE OF UNIFORM BOUNDEDNESS FOR LSC CONVEX PROCESSES IN A STRICTLY N LOCALLY CONVEX SPACES

2008 ◽  
Vol 41 (1) ◽  
Author(s):  
S. Lahrech ◽  
A. Jaddar ◽  
J. Hlal ◽  
A. Ouahab ◽  
A. Mbarki
Keyword(s):  
Uniform Boundedness ◽  
Locally Convex Spaces ◽  
Convex Processes ◽  
Locally Convex ◽  
Convex Spaces

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 A new solution to the problem of finding all numerical solutions to ordered metric structures

Psychometrika ◽  
1980 ◽  
Vol 45 (1) ◽  
pp. 135-137 ◽  
Author(s):  
Paul E. Lehner ◽  
Elliot Noma
Keyword(s):  
Numerical Solutions ◽  
Metric Structures

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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