Second Variations and Sufficiency Conditions

1984 ◽  
pp. 90-109
Author(s):  
Pierre Ninh Van Tu
Keyword(s):  
Sufficiency Conditions

scholarly journals Utilizing Shelve Slots: Sufficiency Conditions for Some Easy Instances of Hard Problems

1994 ◽  
Vol 10 (2) ◽  
pp. 216-229 ◽  
Author(s):  
Moshe Dror ◽  
Benjamin T. Smith ◽  
Martin Trudeau
Keyword(s):  
Hard Problems ◽  
Sufficiency Conditions

Some Sufficiency Conditions for Pareto-Optimal Control

1973 ◽  
Vol 95 (4) ◽  
pp. 356-361 ◽  
Author(s):  
G. Leitmann ◽  
W. Schmitendorf
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pareto Optimality ◽  
Optimal Control Theory ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Vector Valued ◽  
Sufficiency Conditions

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

On the Sufficiency of the Principle of Virtual Work for Mechanical Equilibrium: A Critical Reexamination

1989 ◽  
Vol 56 (3) ◽  
pp. 704-707 ◽  
Author(s):  
John G. Papastavridis
Keyword(s):  
Virtual Work ◽  
Mechanical Equilibrium ◽  
Principle Of Virtual Work ◽  
Holonomic Constraints ◽  
Kinetic Principle ◽  
Sufficiency Conditions

Starting from the general kinetic principle of d’Alembert/Lagrange, an energetic proof of the sufficiency conditions for equilibrium (known as Principle of Virtual Work) is presented. It is clearly demonstrated why to maintain equilibrium requires that, in addition to the familiar vanishing of the virtual work of the impressed forces on the originally motionless system, its geometrical (holonomic) constraints be explicitly time independent (stationary) and its nonintegrable kinematical (nonholonomic) ones be linear and homogeneous in the generalized velocities (catastatic).

scholarly journals Convergence of the New Iterative Method

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Sachin Bhalekar ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Iterative Method ◽  
Functional Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Efficient Technique ◽  
Nonlinear Functional ◽  
Adomian Decomposition ◽  
New Iterative Method ◽  
Sufficiency Conditions

A new iterative method introduced by Daftardar-Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. Further equivalence of DJM and Adomian decomposition method is established.

scholarly journals CONDITIONS FOR SOLVABILITY OF THE HARTMAN–WINTNER PROBLEM IN TERMS OF COEFFICIENTS

2003 ◽  
Vol 46 (3) ◽  
pp. 687-702
Author(s):  
N. A. Chernyavskaya ◽  
L. Shuster
Keyword(s):  
Asymptotic Integration ◽  
Subject Classification ◽  
Continuous Complex ◽  
Complex Valued ◽  
Sufficiency Conditions

AbstractThe Equation (1) $(r(x)y')'=q(x)y(x)$ is regarded as a perturbation of (2) $(r(x)z'(x))'=q_1(x)z(x)$. The functions $r(x)$, $q_1(x)$ are assumed to be continuous real valued, $r(x)>0$, $q_1(x)\ge0$, whereas $q(x)$ is continuous complex valued. A problem of Hartman and Wintner regarding the asymptotic integration of (1) for large $x$ by means of solutions of (2) is studied. Sufficiency conditions for solvability of this problem expressed by means of coefficients $r(x)$, $q(x)$, $q_1(x)$ of Equations (1) and (2) are obtained.AMS 2000 Mathematics subject classification: Primary 34E20

scholarly journals Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed Graphs

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Shuai Liu ◽  
Zhijian Ji ◽  
Huizi Ma
Keyword(s):  
Model Simulation ◽  
Directed Graphs ◽  
Jordan Form ◽  
System Matrix ◽  
Information Communication ◽  
Input Disturbance ◽  
Practical Engineering ◽  
Modernization Process ◽  
Sufficiency Conditions ◽  
Selection Of

Based on the Jordan form of system matrix, this paper discusses algebraic conditions for the controllability of the multiagent network system with directed graph from two aspects: leader-follower network attribute and coupling input disturbance. Leader-follower network attribute refers to the topology structure and information communication among agents. Coupling input disturbance includes the number of external coupling inputs and the selection of leader nodes. When the leader-follower network attribute is fixed, the selection method of coupling input disturbance is studied for the controllability, and when the coupling input disturbance is known, we derive necessity and sufficiency conditions to determine the controllability. The reliability of theoretical results is verified by numerical examples and model simulation. Besides, the generally perfect controllability is introduced, that is, the system is always controllable regardless of the number and the locations of leaders. In practical engineering applications, the perfectly controllable topology can improve the system fault tolerance and accelerate the commercialization process, which has a profound significance for promoting the modernization process.

The Robust Control Research for Non-Linear Inverted Pendulum System in Mechanical Industry

2013 ◽  
Vol 675 ◽  
pp. 31-34
Author(s):  
Hong Xing Li ◽  
Yong Xin Zhang
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Uncertain System ◽  
Paper Analysis ◽  
Pendulum System ◽  
Numerical Examples ◽  
Inverted Pendulum System ◽  
Non Linear ◽  
Control Research ◽  
Sufficiency Conditions

Inverted pendulum system is a non-linear，natural instability and uncertain system. As a controlled objects of control system in mechanical industry, it can be analysis and verification by different control theory and methods. The paper analysis the non-linear inverted pendulum system, then deduces sufficiency conditions of the existence of controller with state feedback. It utilizes standard digital software to get the answer. The feasibility and robustness is demonstrated by numerical examples.

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