A Second Order Sufficient Condition for Optimality in Nonlinear Control — the Conjugate Point Approach

1998 ◽  
pp. 69-78
Author(s):  
Andrzej Nowakowski
Keyword(s):  
Nonlinear Control ◽  
Conjugate Point ◽  
Second Order ◽  
Sufficient Condition

scholarly journals On the Global Asymptotic Stability of a Second-Order System of Difference Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Ibrahim Yalcinkaya
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
System Of Difference Equations ◽  
Initial Values

A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations where the parameter and the initial values (for .

scholarly journals On the Oscillation of Second Order Nonlinear Neutral Delay Dynamic Equations

2007 ◽  
Vol 14 (4) ◽  
pp. 597-606
Author(s):  
Hassan A. Agwo
Keyword(s):  
Dynamic Equation ◽  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Sufficient Condition ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Delay Dynamic Equation ◽  
Neutral Delay Dynamic Equation ◽  
Delay Dynamic Equations

Abstract In this paper we obtain some new oscillation criteria for the second order nonlinear neutral delay dynamic equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))ΔΔ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, on a time scale 𝕋. Moreover, a new sufficient condition for the oscillation sublinear equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))″ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, is presented, which improves other conditions and an example is given to illustrate our result.

scholarly journals On controllability for a class of second-order differential inclusions

2011 ◽  
Vol 27 (1) ◽  
pp. 34-40
Author(s):  
AURELIAN CERNEA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inclusion ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Second Order ◽  
Sufficient Condition ◽  
Liouville Type ◽  
Sturm Liouville ◽  
The Right

By using a suitable fixed point theorem a sufficient condition for controllability is obtained for a Sturm-Liouville type differential inclusion in the case when the right hand side has convex values.

Second-Order Conditions

2018 ◽  
Author(s):  
John E. Prussing
Keyword(s):  
Optimal Control ◽  
Optimization Problems ◽  
Conjugate Point ◽  
Test Procedure ◽  
Second Order ◽  
Order Conditions ◽  
Second Order Conditions ◽  
The First Variation ◽  
The Cost ◽  
The Second Variation

Second-order conditions for both parameter optimization problems and optimal control problems are analysed. A new conjugate point test procedure is discussed and illustrated. For an optimal control problem we will examine the second variation of the cost. The first variation subject to constraints provides first-order NC for a minimum of J. Second-order conditions provide SC a minimum.

scholarly journals Optimizing the Kelvin force in a moving target subdomain

2017 ◽  
Vol 28 (01) ◽  
pp. 95-130 ◽  
Author(s):  
Harbir Antil ◽  
Ricardo H. Nochetto ◽  
Pablo Venegas
Keyword(s):  
Magnetic Field ◽  
Time Discretization ◽  
Dipole Approximation ◽  
Second Order ◽  
Sufficient Condition ◽  
Final Time ◽  
Magnetic Drug Delivery ◽  
Backward Euler ◽  
Pointwise Constraints ◽  
The Magnetic Field

In order to generate a desired Kelvin (magnetic) force in a target subdomain moving along a prescribed trajectory, we propose a minimization problem with a tracking type cost functional. We use the so-called dipole approximation to realize the magnetic field, where the location and the direction of the magnetic sources are assumed to be fixed. The magnetic field intensity acts as the control and exhibits limiting pointwise constraints. We address two specific problems: the first one corresponds to a fixed final time whereas the second one deals with an unknown force to minimize the final time. We prove existence of solutions and deduce local uniqueness provided that a second-order sufficient condition is valid. We use the classical backward Euler scheme for time discretization. For both problems we prove the [Formula: see text]-weak convergence of this semi-discrete numerical scheme. This result is motivated by [Formula: see text]-convergence and does not require second-order sufficient condition. If the latter holds then we prove [Formula: see text]-strong local convergence. We report computational results to assess the performance of the numerical methods. As an application, we study the control of magnetic nanoparticles as those used in magnetic drug delivery, where the optimized Kelvin force is used to transport the drug to a desired location.

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