Log-approximable minimization problems on random inputs

1995 ◽  
pp. 217-227
Author(s):  
Anders Malmström
Keyword(s):  
Random Inputs ◽  
Minimization Problems

The Condition for Absolute Stability of an Electroelastic Actuator Control System for Nanomechatronics

2020 ◽  
Vol 10 (10) ◽  
pp. 52-58
Author(s):  
Sergey M. AFONIN ◽  
Keyword(s):  
Control System ◽  
Adaptive Optics ◽  
Absolute Stability ◽  
Deformation Characteristic ◽  
Straight Line Segment ◽  
Control Mechanisms ◽  
Relative Width ◽  
Random Inputs ◽  
Deformation Control ◽  
Actuator Control

An electroelastic actuator for nanomechatronics is used in nanotechnology, adaptive optics, microsurgery, microelectronics, and biomedicine to actuate or control mechanisms, systems based on the electroelastic effect, and to convert electrical signals into mechanical displacements and forces. In nanomechatronic systems, a piezoactuator is used in scanning microscopy, laser systems, in astronomy for precision alignment, for compensation of temperature, gravitational deformations and atmospheric turbulence, focusing, and stabilizing the image. In this study, a condition for absolute stability of an electroelastic actuator control system for nanomechatronics under deterministic and random inputs is obtained. A number of equilibrium positions in an electroelastic actuator mechatronic control system are found, the totality of which is represented by a straight line segment. The electroelastic actuator’s deformation control system dead band relative width is determined for the actuator’s symmetric and asymmetric hysteresis characteristics. Under deterministic inputs and with fulfilling the condition for the derivative of the nonlinear hysteresis actuator deformation characteristic, the set of equilibrium positions of the electroelastic actuator control system for nanomechatronics is absolutely stable. Under random inputs, the system absolute stability with respect to the mathematical expectations of the electroelastic actuator mechatronic control system equilibrium positions has been determined subject to fulfilling the condition on the derivative of the actuator hysteresis characteristic.

Equivalent gain of an instantaneous quantiser with two independent random inputs

1968 ◽  
Vol 4 (13) ◽  
pp. 269
Author(s):  
L. Giacomelli ◽  
M. Dècina
Keyword(s):  
Random Inputs

scholarly journals An Efficient Method for Convex Constrained Rank Minimization Problems Based on DC Programming

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wanping Yang ◽  
Jinkai Zhao ◽  
Fengmin Xu
Keyword(s):  
Objective Function ◽  
Minimization Problem ◽  
Dc Programming ◽  
Rank Minimization ◽  
Closed Form Solutions ◽  
Minimization Problems ◽  
Difference Of Convex Functions ◽  
Convex Objective Function ◽  
Difference Of Convex ◽  
Cut Problems

The constrained rank minimization problem has various applications in many fields including machine learning, control, and signal processing. In this paper, we consider the convex constrained rank minimization problem. By introducing a new variable and penalizing an equality constraint to objective function, we reformulate the convex objective function with a rank constraint as a difference of convex functions based on the closed-form solutions, which can be reformulated as DC programming. A stepwise linear approximative algorithm is provided for solving the reformulated model. The performance of our method is tested by applying it to affine rank minimization problems and max-cut problems. Numerical results demonstrate that the method is effective and of high recoverability and results on max-cut show that the method is feasible, which provides better lower bounds and lower rank solutions compared with improved approximation algorithm using semidefinite programming, and they are close to the results of the latest researches.

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