Group theory and controllability of partial differential control systems

2008 ◽  
pp. 271-278
Author(s):  
J. F. Pommaret
Keyword(s):  
Group Theory ◽  
Control Systems ◽  
Partial Differential ◽  
Differential Control

scholarly journals The Boundary Proportion Differential Control Method of Micro-Deformable Manipulator with Compensator Based on Partial Differential Equation Dynamic Model

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 799
Author(s):  
Xiangli Pei ◽  
Ying Tian ◽  
Minglu Zhang ◽  
Ruizhuo Shi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamic Model ◽  
Control Method ◽  
System Modeling ◽  
Working Environment ◽  
Partial Differential ◽  
External Interference ◽  
Differential Control ◽  
Differential Control Method

It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in the micro-deformable manipulator system modeling. Furthermore, an infinite-dimensional radial basis function neural network compensator suitable for the dynamic model was proposed to compensate for boundary and uncertain external interference. Based on this compensation method, a distributed boundary proportional differential control method was designed to improve control accuracy and speed. The effectiveness of the proposed model and method was verified by theoretical analysis, numerical simulation, and experimental verification. The results show that the proposed method can effectively improve the response speed while ensuring accuracy.

Nonlinear Quasi-differential Control Systems

1992 ◽  
Vol 21 (1-2) ◽  
pp. 65-82
Author(s):  
W. N. Everitt ◽  
L. Markus
Keyword(s):  
Control Systems ◽  
Differential Control

scholarly journals Global Structure of Determining Matrices for a Class of Differential Control Systems

2021 ◽  
Vol 2 (1) ◽  
pp. 88-101
Author(s):  
Chukwunenye Ukwu ◽  
Onyekachukwu Henry Ikeh Ikeh
Keyword(s):  
Control Systems ◽  
Problem Instance ◽  
Computational Process ◽  
Rank Condition ◽  
Small Problem ◽  
Controllability Matrix ◽  
Computing Complexity ◽  
Double Time ◽  
Functional Differential ◽  
Differential Control

This paper developed and established unprecedented global results on the structure of determining matrices of generic double time-delay linear autonomous functional differential control systems, with a view to obtaining the controllability matrix associated with the rank condition for the Euclidean controllability of the system. The computational process and implementation of the controllability matrix were demonstrated on the MATLAB platform to determine the controllability disposition of a small-problem instance. Finally, the work examined the computing complexity of the determining matrices.

SET-VALUED DYNAMICS IN PROBLEMS OF MATHEMATICAL THEORY OF CONTROL PROCESSES

2012 ◽  
Vol 26 (25) ◽  
pp. 1246010 ◽  
Author(s):  
TATIANA FILIPPOVA
Keyword(s):  
Control System ◽  
Differential Equations ◽  
Nonlinear Control ◽  
Control Systems ◽  
Mathematical Theory ◽  
Quadratic System ◽  
Nonlinear Control System ◽  
Reachable Sets ◽  
The Right ◽  
Differential Control

The dynamics and properties of set-valued states of differential control systems with uncertainties in initial data are studied. It is assumed that the dynamical system has a special structure, in which nonlinear terms in the right-hand sides of related differential equations are quadratic in state coordinates. We construct external and internal ellipsoidal estimates of reachable sets of nonlinear control system and find differential equations of proposed ellipsoidal estimates of reachable sets of nonlinear control system. The results obtained for quadratic system nonlinearities are extended to other types of control systems under uncertainty.

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