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.

scholarly journals Fundamental Results on Determining Matrices for a Certain Class of Hereditary Systems

2021 ◽  
Vol 2 (1) ◽  
pp. 62-87
Author(s):  
Onyekachukwu Henry Ikeh Ikeh ◽  
Chukwunenye Ukwu
Keyword(s):  
Time Delay ◽  
Control Systems ◽  
Rank Condition ◽  
Integer Multiple ◽  
Delay Control ◽  
Double Time ◽  
Functional Differential ◽  
Differential Control ◽  
Controllability Grammian ◽  
Delay Control Systems

Three major tools are required to investigate the controllability of control systems, namely, determining matrices, index of control systems and controllability Grammian. Determining matrices are the preferred choice for autonomous control systems due to the fact that they are devoid of integral operators in their computations. This article developed the structure of certain parameter-ordered 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 Euclidean controllability of the system. Expressions for the relevant determining matrices were formulated and it was established that the determining matrices for double time-delay linear autonomous functional differential control systems do not exist if one of the time-delays is not an integer multiple of the other paving the way for the investigation of the Euclidean controllability of generic double time-delay control systems.

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 Approximate controllability of neutral functional differential system with unbounded delay

2001 ◽  
Vol 26 (12) ◽  
pp. 737-744 ◽  
Author(s):  
Jong Yeoul Park ◽  
Sang Nam Kang
Keyword(s):  
Differential Equation ◽  
Control Systems ◽  
Functional Differential Equation ◽  
Differential System ◽  
Approximate Controllability ◽  
Neutral Functional Differential Equation ◽  
Unbounded Delay ◽  
Functional Differential ◽  
Functional Differential System

We consider a class of control systems governed by the neutral functional differential equation with unbounded delay and study the approximate controllability of the system. An example is given to illustrate the result.

scholarly journals Control sets for bilinear and affine systems

2021 ◽  
Author(s):  
Fritz Colonius ◽  
Alexandre J. Santana ◽  
Juliana Setti
Keyword(s):  
Projective Space ◽  
Control Systems ◽  
Lie Algebra ◽  
Diophantine Approximation ◽  
Rank Condition ◽  
Approximation Result ◽  
Bilinear Control ◽  
Control Sets ◽  
Bilinear Control Systems ◽  
Affine Control Systems

AbstractFor homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control systems, the control sets around the equilibria for constant controls are characterized with particular attention to the question when the control sets are unbounded.

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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