All solutions to the ℋ/sub ∞/ control synthesis problem with unstable weights

2002 ◽  
Author(s):  
K.-Z. Liu ◽  
M. Hirata ◽  
T. Sato
Keyword(s):  
Synthesis Problem ◽  
Control Synthesis ◽  
All Solutions

Robust Control Synthesis Techniques for Multirate and Multisensing Track-Following Servo Systems in Hard Disk Drives

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Ryozo Nagamune ◽  
Xinghui Huang ◽  
Roberto Horowitz
Keyword(s):  
Controller Design ◽  
Linear Time ◽  
Hard Disk Drives ◽  
General System ◽  
Hard Disk ◽  
Disk Drive ◽  
Synthesis Problem ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Advantages And Disadvantages

This paper proposes controller design methods, specially for track-following control of the magnetic read/write head in a hard disk drive (HDD). The servo system to be considered is a general dual-stage multisensing system, which encompasses most of the track-following configurations encountered in the HDD industry, including the traditional single-stage system. For the general system, a robust track-following problem is formulated as a time-varying version of the robust H2 synthesis problem. Both dynamic and real parametric uncertainties, which are typical model uncertainties in track-following control, are taken into account in the formulation. Three optimal robust controller design techniques with different robustness guarantees are applied to solve the synthesis problem. These are mixed H2/H∞, mixed H2/μ, and robust H2 syntheses. Advantages and disadvantages of each method are presented. Multirate control, which is inherent to control problems in HDDs, is obtained by reducing multirate problems into linear time-invariant ones, for which there are many useful theories and algorithms available. Most of the techniques proposed in this paper heavily rely on efficient numerical tools for solving linear matrix inequalities.

Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages

1992 ◽  
Vol 114 (1) ◽  
pp. 153-159 ◽  
Author(s):  
C. W. Wampler ◽  
A. P. Morgan ◽  
A. J. Sommese
Keyword(s):  
Unsolved Problem ◽  
Complete Solution ◽  
Synthesis Problem ◽  
Computer Algorithm ◽  
All Solutions ◽  
Path Synthesis

The problem of finding all four-bar linkages whose coupler curve passes through nine prescribed points has been a longstanding unsolved problem in kinematics. Using a combination of classical elimination, multihomogeneous variables, and numerical polynomial continuation, we show that there are generically 1442 nondegenerate solution along with their Roberts cognates, for a total of 4326 distinct solutions. Moreover, a computer algorithm that computes all solutions for any given nine points has been developed.

scholarly journals Synthesis of a mobile robot spatial stabilization system based on machine learning control by symbolic regression

2021 ◽  
Vol 22 (2) ◽  
pp. 129-138
Author(s):  
Askhat I. Diveev ◽  
Neder Jair Mendez Florez
Keyword(s):  
Machine Learning ◽  
Mobile Robot ◽  
Initial Conditions ◽  
Symbolic Regression ◽  
Synthesis Problem ◽  
Terminal Point ◽  
Control Synthesis ◽  
Stabilization System ◽  
Nonlinear Feedback ◽  
Regression Methods

The spatial stabilization system synthesis problem of the robot is considered. The historical overview of methods and approaches for solving the problem of control synthesis is given. It is shown that the control synthesis problem is the most important task in the field of control, for which there are no universal numerical methods for solving it. As one of the ways to solve this problem, it is proposed to use the method of machine learning based on the application of modern symbolic regression methods. This allows you to build universal algorithms for solving control synthesis problems. Several most promising symbolic regression methods are considered for application in control tasks. The formal statement of the control synthesis problem for its numerical solution is given. Examples of solving problems of synthesis of system of spatial stabilization of mobile robot by method of network operator and variation Cartesian genetic programming are given. The problem required finding one nonlinear feedback function to move the robot from thirty initial conditions to one terminal point. Mathematical records of the obtained control functions are given. Results of simulation of control systems obtained by symbolic regression methods are given.

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