Superlinear Convergence Using Controls Based on Second-Order Needle Variations

2018 ◽  
Author(s):  
Giorgos Mamakoukas ◽  
Malcolm A. MacIver ◽  
Todd D. Murphey
Keyword(s):  
Superlinear Convergence ◽  
Second Order ◽  
Needle Variations

scholarly journals Feedback synthesis for underactuated systems using sequential second-order needle variations

2018 ◽  
Vol 37 (13-14) ◽  
pp. 1826-1853 ◽  
Author(s):  
Giorgos Mamakoukas ◽  
Malcolm A. MacIver ◽  
Todd D. Murphey
Keyword(s):  
Vector Fields ◽  
Underwater Vehicle ◽  
Second Order ◽  
Three Dimensions ◽  
Control Synthesis ◽  
Nonlinear Feedback ◽  
First Order ◽  
Lie Bracket ◽  
Control Response ◽  
Needle Variations

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions, the second-order needle variations of optimal control, as the basis for choosing each control response to the current state. A second result of this paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Finally, the underactuated dynamic underwater vehicle model demonstrates convergence even in the presence of a velocity field.

An SQP-type Method with Superlinear Convergence for Nonlinear Semidefinite Programming

2018 ◽  
Vol 35 (03) ◽  
pp. 1850009 ◽  
Author(s):  
Qi Zhao ◽  
Zhongwen Chen
Keyword(s):  
Semidefinite Programming ◽  
Superlinear Convergence ◽  
Second Order ◽  
Nonlinear Semidefinite Programming ◽  
Sqp Method ◽  
Type Method ◽  
Sigma Term ◽  
Semidefinite Programming Problem ◽  
Quadratic Semidefinite Programming ◽  
Correction Step

A sequentially semidefinite programming method is proposed for solving nonlinear semidefinite programming problem (NLSDP). Inspired by the sequentially quadratic programming (SQP) method, the algorithm generates a search direction by solving a quadratic semidefinite programming subproblem at each iteration. The [Formula: see text] exact penalty function and a line search strategy are used to determine whether the trial step can be accepted or not. Under mild assumptions, the proposed algorithm is globally convergent. In order to avoid the Maratos effect, we present a modified SQP-type algorithm with the second-order correction step and prove that the fast local superlinear convergence can be obtained under the strict complementarity and the second-order sufficient condition with the sigma term. Finally, some numerical experiments are given to show the effectiveness of the algorithm.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Second order interference in two photon absorption

1996 ◽  
Vol 43 (9) ◽  
pp. 1765-1771 ◽  
Author(s):  
M. W. HAMILTON and D. S. ELLIOTT
Keyword(s):  
Second Order ◽  
Photon Absorption ◽  
Two Photon Absorption ◽  
Two Photon
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