SOLSP a New Algorithm to Reduce The Complexity Time of Controllability Matrix

2020 ◽  
Author(s):  
Abeer Mahmood Hassan ◽  
Saad Talib Hasson
Keyword(s):  
Controllability Matrix

scholarly journals A New Solution to the Matrix EquationX−AX¯B=C

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Caiqin Song
Keyword(s):  
Unique Solution ◽  
Canonical Form ◽  
Matrix Equation ◽  
Explicit Solution ◽  
Symmetric Operator ◽  
Operator Matrix ◽  
Numerical Example ◽  
Controllability Matrix ◽  
The Matrix

We investigate the matrix equationX−AX¯B=C. For convenience, the matrix equationX−AX¯B=Cis named as Kalman-Yakubovich-conjugate matrix equation. The explicit solution is constructed when the above matrix equation has unique solution. And this solution is stated as a polynomial of coefficient matrices of the matrix equation. Moreover, the explicit solution is also expressed by the symmetric operator matrix, controllability matrix, and observability matrix. The proposed approach does not require the coefficient matrices to be in arbitrary canonical form. At the end of this paper, the numerical example is shown to illustrate the effectiveness of the proposed method.

scholarly journals Controllability, Reachability, and Stabilizability of Finite Automata: A Controllability Matrix Method

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Yalu Li ◽  
Wenhui Dou ◽  
Haitao Li ◽  
Xin Liu
Keyword(s):  
Matrix Method ◽  
Finite Automata ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Form ◽  
Controllability Matrix ◽  
Necessary And Sufficient ◽  
Semitensor Product Of Matrices ◽  
Product Of Matrices ◽  
Inputs And Outputs

This paper investigates the controllability, reachability, and stabilizability of finite automata by using the semitensor product of matrices. Firstly, by expressing the states, inputs, and outputs as vector forms, an algebraic form is obtained for finite automata. Secondly, based on the algebraic form, a controllability matrix is constructed for finite automata. Thirdly, some necessary and sufficient conditions are presented for the controllability, reachability, and stabilizability of finite automata by using the controllability matrix. Finally, an illustrative example is given to support the obtained new results.

Modeling and Analyses of the N-Link Bent-Arm PenduBot

2010 ◽  
Vol 171-172 ◽  
pp. 644-647
Author(s):  
Shao Qiang Yuan ◽  
Xin Xin Li
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Nonlinear Model ◽  
Condition Number ◽  
Kinematics And Dynamics ◽  
Controllability Matrix ◽  
Human Arm ◽  
The World ◽  
The Mathematical Model ◽  
Natural Characteristics

Bent-arm PenduBot is more similar to human arm, which attaches more and more robot experts’ attention around the world. As the foundation of the multi-link PenduBot control, the mathematical model should be established first. Based on the method of kinematics and dynamics, the N-link bent-arm PenduBot mathematical models are established in this paper, including the nonlinear model and the linear model. The natural characteristics of different pendulum are analyzed. By using the condition number of the controllability matrix, the control difficulty for higher order systems is compared.

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.

Procedure of System Control Using Distributed Parameters through Discrete Finitisation

2014 ◽  
Vol 657 ◽  
pp. 864-868
Author(s):  
Sever Şerban ◽  
Doina Corina Şerban
Keyword(s):  
Dimensional Space ◽  
Original Method ◽  
System Control ◽  
Finite Dimensional Space ◽  
Controllability Matrix ◽  
Finite Dimensional ◽  
Distributed Parameters ◽  
Systems With Distributed Parameters

This paper presents an original method for the synthesis command involving a controllability matrix, which is used for systems with distributed parameters, and further more for systems reduced to a finite dimensional space.

Properties of the mode-controllability matrix†

1970 ◽  
Vol 12 (2) ◽  
pp. 289-295 ◽  
Author(s):  
T. R. CROSSLEY ◽  
B. PORTER
Keyword(s):  
Controllability Matrix

The Controllability of the Point Reactor Neutron Kinetics Equations

2014 ◽  
Author(s):  
Dong Liu ◽  
Xiuchun Luan ◽  
Tao Yu ◽  
Weining Zhao ◽  
Lei Liu
Keyword(s):  
Nuclear Reactor ◽  
Radioactive Decay ◽  
Pole Placement ◽  
Reactor Neutron ◽  
Final Conclusion ◽  
Delayed Neutron ◽  
Neutron Kinetics ◽  
Controllability Matrix ◽  
The Matrix ◽  
Point Kinetics

In this paper, the conditions to ensure the controllability of the point reactor neutron kinetics equations are studied. In a nuclear reactor, due to the delayed neutron precursor concentration and the internal reactivity, the kinetics equations of the nuclear reactor are nonlinear. To solve the problem of the pole placement, the controllability of the point kinetics equations must be guaranteed. Then, a new method to analysis of the controllability conditions of the point kinetics equations of a reactor is carried out here. The method is based on the controllability matrix directly denoted by relevant symbols, and a formula used for controllability analysis is showed with symbols by calculating the determinant of the matrix. First, with using the linearization technique, the equations are linearized with respect to any possible equilibrium point. Subsequently, an analysis of the controllability of the general linear model that includes only one group delayed neutron precursor is performed, obtaining the interesting result that the controllability of the equations are controllable except when the effective precursor radioactive decay constant and the reciprocal of the fuel-to-coolant heat transfer mean time have the same value, which does not occur in practice. Thus, with the same method, the other analysis obtained the conditions to guarantee the controllability of the point kinetics equations with different groups delayed neutron precursor, which includes two-group, three-group and six-group models. Then, the results are compared with that of the numerical controllability matrix, obtaining the final conclusion that the results of the new analysis method give the closer results to the actual situation and list the restrictions that guarantee the controllability of the point reactor neutron kinetics equations.

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