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Nerve computing model for solving matrix equation set

A technology for computing models and matrix equations, applied in the field of neural computing models, can solve problems such as violation of real-time computing, time-consuming, time-varying matrix solution errors, etc.

Inactive Publication Date: 2017-11-24
QUFU NORMAL UNIV
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Problems solved by technology

Therefore, the time-varying matrix solution obtained by ZNN without considering the influence of noise has a large error with the actual situation, and even leads to the failure of the solution in some cases
In addition, any noise reduction processing may consume additional time, violating the requirement of real-time calculation

Method used

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  • Nerve computing model for solving matrix equation set
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Embodiment Construction

[0017] The present invention will be further described below.

[0018] A method for constructing a neural computing model for solving matrix equations, comprising the steps of:

[0019] a) Define the error function E(t) of the matrix value according to the design method of Zhang Neural Network, where E(t)=A(t)X(t)-B(t), where A(t), B(t ) is a known stable time-varying coefficient matrix, X(t) is an unknown time-varying coefficient matrix to be solved, and t is time;

[0020] b) According to Zhang neural network design formula get deformed

[0021] c) definition Find the derivative of e according to the mathematical derivation formula make get

[0022] d) will bring in get in

[0023] e) the formula Shift to get where k 1 =k 2 = 1, F(E(t)) and are activation functions;

[0024] f) Obtain the derivative of the error function E(t) according to the mathematical derivation formula Will substitute The model formula is obtained in: ,in It i...

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Abstract

A method for constructing a neural computing model for solving matrix equations, the formula of which is: A ( t ) X ( t ) · = - A · ( t ) X ( t ) + B · ( t ) - F ( A ( t ) X ( t ) - B ( t ) ) - G ( A ( t ) X ( t ) - B ( t ) + ∫ 0 t F ( A ( t ) X ( t ) - B ( t ) ) d t ) + W ( t ) Calculate the solved X(t) through this final formula, starting from any initial state X(0)∈Rn×m, which is equivalent to the state matrix of the time-varying theoretical solution, and each of their elements is a monotonically increasing odd activation function . The neural computing model for solving matrix equations of the present invention has the characteristics of converging to the theoretical solution of matrix equations in a limited time even under the pollution of noise (constant noise, random noise), and no matter what activation function is used, the present invention The invention can converge to the theoretical solution of matrix equations.

Description

technical field [0001] The invention relates to the fields of matrix equations and neural networks, in particular to a neural calculation model for solving matrix equations. Background technique [0002] The problem of systems of linear matrix equations has been extensively studied in academia and industry in recent years, and has found applications in mathematics, system control, robotics, and other fields. Due to its huge potential academic value and practical value, finding a fast and effective solution to linear matrix engineering has become one of the directions that many researchers are striving to achieve. Therefore, many related algorithms have been proposed and discussed, and good research results have been obtained. However, it is a pity that these proposed algorithms for serial processing are not suitable for time-varying linear matrices due to the shortcoming of requiring related iterative algorithms to be completed within a single sampling period. [0003] Rec...

Claims

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Application Information

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IPC IPC(8): G06F17/16G06N3/04
CPCG06F17/16G06N3/04
Inventor 禹继国李晓晓李帅
Owner QUFU NORMAL UNIV
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