Neural network control method for solving time-varying matrix based on integral enhancement

Abstract

The invention relates to a neural network control method for solving a time-varying matrix based on integral enhancement. The invention provides a novel recurrent neural network based on integral enhancement so as to solve a time-varying matrix equation. The method comprises the following steps: firstly, introducing a group of non-negative slack variables, converting a time-varying inequality group into a matrix equation form, and constructing a matrix differential equation about an error function; secondly, deriving an explicit solution of a differential equation of the matrix through pseudo-inverse transformation of the matrix, and adding an integral enhancement item on this basis to improve the anti-interference capability of a solving model; according to the method, the time-varying matrix equation is solved by adopting the advanced integral enhanced recurrent neural network method, and the method has the characteristics of high calculation efficiency, fast convergence, strong anti-noise capability and good robustness.

Description

Technical Field

[0001] The present invention relates to the fields of intelligent control and neural dynamics, and in particular to a neural network control method for solving time-varying matrices based on integral enhancement. Background Art

[0002] In many theoretical analyses and practical engineering applications, various boundary conditions often need to be considered. Solving time-varying systems, such as digital signal processing, robotic control, and energy and power system analysis, can often be transformed into solving a system of time-varying inequality equations. A typical recursive neural network model has been shown to be effective in solving time-varying problems. The idea behind this solution is to establish an error function for a specific problem and force it to converge to zero in order to solve the system of time-varying equations and inequalities.

[0003] However, classic neural network models are vulnerable to noise interference. When excessive noise is present within a time-varying system, this method struggles to guarantee convergence. In engineering applications of time-varying systems, the influence of external noise is unavoidable. Furthermore, computational errors within a time-varying system accumulate over time. For applications requiring high precision and reliability, such as medical robots and assisted driving control systems, these interference factors can reduce system reliability, making it impossible to achieve the desired goals. Summary of the Invention

[0004] The present invention addresses the shortcomings and deficiencies of existing technologies by providing a neural network control method for solving time-varying matrices based on integral enhancement. This method solves time-varying matrix equations based on the principles of neural dynamics. It offers advantages such as strong noise immunity, rapid convergence, high solution accuracy, and a wide range of applications.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A neural network control method for solving a time-varying matrix based on integral enhancement, comprising the following steps:

[0007] 1) Establish kinematic / dynamic expressions to describe the problem based on the actual context;

[0008] 2) Normalize mathematical expressions and convert them into general mathematical forms;

[0009] 3) Use matrix method to simplify the description form of expression group;

[0010] 4) Pre-solve the time-varying matrix equation based on the pseudo-inverse method;

[0011] 5) Establish an error evaluation function and apply the ZNN method to construct a neural network based on integral enhancement;

[0012] 6) Automatically adjust whether to use integral enhancement and the selection of activation function according to the type of external disturbance;

[0013] 7) The solution result is sent to the lower computer for execution.

[0014] Furthermore, the practical context described in step 1) includes, but is not limited to, robot forward / inverse kinematic planning, manipulator control, and drone and underwater robot path planning. The kinematic expressions are typically constructed by combining the corresponding Jacobian matrix with the pose and joint angles. The description layers include, but are not limited to, the position layer, velocity layer, and acceleration layer. Furthermore, the kinematic expression can also include constraints on the desired quantity. These constraints are typically introduced by device parameters, physical space, or task requirements in actual application scenarios.

[0015] Furthermore, the general mathematical form described in step 2) is to transform the kinematic description in step 1) into the following form: .in ,and , , , , is the unknown variable to be solved. The matrix equations described in the first row are the set of the aforementioned kinematic expressions, and the matrix inequalities in the second row are the set of the aforementioned related constraints.

[0016] Furthermore, non-negative slack variables can be introduced in step 3) y Expand the matrix inequality filling in step 2) into a matrix equality equation: . Thus, a new set of kinematics and constraints is obtained

[0017] If you define: Superscript. 2 Indicates that each element in the vector is squared. Define the diagonal matrix D(t) = diag{y1(t),···,y p (t)}∈R p×p , then y .2 (t) can be rewritten as: .2 (t)=D(t)y(t). Furthermore, the aforementioned kinematics and constraint conditions can be expressed in a concise form by matrix substitution: W(t)u(t)=q(t). At this time, the problem of solving the unknown variables in step 2) can be transformed into the problem of solving the transformed unknown variables u(t), where the first n elements in u(t) are the set to be solved. At this time, u(t) can also be expressed analytically is the right pseudo-inverse of W(t). This corresponds to using the pseudo-inverse method in step 4) to solve the time-varying equations.

[0018] Furthermore, the error evaluation function e(t) described in step 5) adopts the design ideas and methods of neural network models of time-varying systems by previous scholars, and introduces an error function to achieve the design goal of returning the error level of time-varying equations and inequalities to zero. The error evaluation function is constructed as follows: e(t) = W(t)u(t)-q(t). In order to force each element e in the error function e(t) to be zero, the error evaluation function is constructed as follows: e(t) = W(t)u(t)-q(t). i (t) should converge to zero (where i=1,···,m+p). So the following neural dynamics equation can be used: in Represents the activation function in neural dynamics. Common activation functions include: linear activation function and hyperbolic sine activation function. The linear activation function has the advantage of fast calculation speed, while the hyperbolic sine activation function can make the neural network have faster convergence performance. Selecting different activation functions can obtain different error convergence effects, which corresponds to the analysis of the pre-solved results of the problem in step 4), so as to reasonably select the activation function to achieve the best performance of the entire system. In this patent, for the purpose of clear and intuitive description, the linear activation function is used: That is, the neural dynamics equation is transformed as follows:

[0019] Furthermore, step 5) derives the equation based on the error evaluation function and combines them: , ,in , , , , , , respectively , , , , , For further derivation, let: ， ， ， Where: , , , .but (Where, for right pseudo-inverse of ).

[0020] Here we get the basic framework of the neural network. In order to further obtain the integral enhanced neural network model mentioned in step 5), it is necessary to upgrade the neural dynamics model of the error evaluation function: Following a similar deduction method, we can obtain the upgraded neural network based on integral enhancement: .in The term represents external noise interference.

[0021] The neural network model based on integral enhancement constructed so far: , which can be used to solve the problem of noise interference in various time-varying matrix equations.

[0022] Furthermore, the adjustment and selection of the activation function and some parameters in step 6) should be completed under the regulation of two control channels. Control channel 1: Based on the results of the pre-solution in step 4), the complexity of the problem is judged, so as to reasonably select the activation function. Control channel 2: Based on the feedback from the lower level / end effector in step 7), the parameters in the neural dynamics model are dynamically adjusted to better adapt to the changing external environment.

[0023] Furthermore, as described in step 7), the upper-layer neural network model for solving time-varying matrices based on integral enhancement can be deployed on intelligent computing platforms such as servers, PCs, mobile embedded devices, FPGAs, and CPLDs. The solution results are input / sent in real time to devices such as robots, manipulator controllers, and drones to achieve the desired planning goals.

[0024] Compared with the existing technology, the present invention has the following advantages:

[0025] This paper provides a neural network control method for solving time-varying matrices based on integral enhancement. This method includes, but is not limited to, abstracting and modeling various practical engineering scenarios. It then uses integral enhancement to upgrade and transform neural dynamics formulas to solve the modeled time-varying matrix equations mixed with external interference. This method has the advantages of fast convergence, strong anti-interference ability, and good adaptability to external environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 The following is a flowchart of a method modeling process according to an embodiment of the present invention.

[0027] Figure 2 This is a model topology diagram of the integral enhanced neural network in an embodiment of the present invention.

[0028] Figure 3 This is the implementation framework of the system solver actually used in the embodiments of the present invention. DETAILED DESCRIPTION

[0029] The present invention will be described in further detail below with reference to the examples, but the embodiments of the present invention are not limited to these examples.

[0030] Example:

[0031] This embodiment provides a neural network control method for solving time-varying matrices based on integral enhancement. The process is as follows: Figure 1 As shown, the following steps are included:

[0032] 1) Establish kinematic / dynamic expressions to describe the problem based on the actual context;

[0033] 2) Normalize mathematical expressions and convert them into general mathematical forms;

[0034] 3) Use matrix method to simplify the description form of expression group;

[0035] 4) Pre-solve the time-varying matrix equation based on the pseudo-inverse method;

[0036] 5) Establish an error evaluation function and apply the ZNN method to construct a neural network based on integral enhancement;

[0037] 6) Automatically adjust whether to use integral enhancement and the selection of activation function according to the type of external disturbance;

[0038] 7) The solution result is sent to the lower computer for execution.

[0039] Figure 2 The following is a diagram showing the network topology of the neural network control method based on integral enhancement to solve the time-varying matrix. According to the differential equation of the error function, by substituting the coefficient matrix in different practical problems, the network topology of the neural network control method based on integral enhancement to solve the time-varying matrix can be obtained. Figure 2 As shown. It is worth noting that ⊕ represents the summator, Denotes an integrator. Considering the hardware feasibility of neural networks, when constructing neural network topologies, it is important to minimize the use of different-function arithmetic units and reuse simpler units as much as possible. This facilitates subsequent deployment of neural networks on embedded hardware platforms or other parallel computing circuits. Youcheng denotes matrix multiplication operations.

[0040] Figure 3The following is an implementation framework of the system solver used in the embodiment of the present invention, which includes the following modules: a problem description module, which covers various practical control problems that can be solved by the neural network solver based on integral enhancement; a formula abstraction module, which describes complex practical problems with unified mathematical equations and inequalities, which is conducive to improving the versatility of the solution method; a processing calculation part, which first matches the data structure according to the requirements of different computing platforms to meet the requirements of different computing platforms, and then sends the data to the neural network model pre-built on the platform for solution; a lower-level computer request execution part, where the solution output of the upper-level network is sent to the lower-level computer or a node in the multi-agent to achieve the expected effect. For applications with higher effect requirements, this part will also assume the evaluation and feedback functions of the execution effect (as shown by the dotted arrows in the figure). The upper-level control network can adjust the important parameters of the neural network in a timely manner based on the feedback from the execution end.

[0041] According to the relevant steps described in the flowchart, the present invention is analyzed in detail:

[0042] In step 1), the kinematic expression described is usually a Jacobian matrix or a kinematic equation of the manipulator related to the Jacobian matrix, and a set of unequal limits on the variables to be solved.

[0043] In step 2), the normalization process is usually to classify and integrate the inequality group containing the Jacobian matrix and the variable change limit range in step 1) into a form such as: The matrix equations and inequalities shown are: Represents the vector of variables to be solved. usually contains the Jacobian matrix described in step 1). Contains the constraints of various variables described in step 1).

[0044] Step 3), add a set of non-negative relaxation variables on both sides of the matrix inequality in step 2) , expanding the inequality to an equality . Also define , , , then the simplified expression group can be simplified as; .

[0045] Step 4), based on step 3), use the pseudo-inverse method to Perform a presolve: .in represent The pseudo-inverse of . The pre-solved result has a regulatory effect on the selection of some neural network parameters in the subsequent steps.

[0046] Step 5), in order to reasonably zero the simplified matrix equation, an error function is introduced here , in order to achieve the design goal of returning the equation group to zero at the error level.

[0047] Among them, each element e in the error function e(t) i (t) should all converge to zero (where i = 1, ···, m + p), so the following neural dynamics equation based on integral enhancement is adopted: in, is the time derivative of e(t), α>0∈R is an adjustable parameter that can be appropriately selected for different time-varying systems to achieve the best solution. Therefore, if each element e in the error function e(t) i (t) converges to zero, which means that u(t) can converge to the theoretical solution u * (t). In order to further study the error function e(t), the following lemma is given in It is y .2 (t) is the time derivative. After combining the derivatives of the equations, we can get are the time derivatives of A(t), C(t), b(t), d(t), x(t), and y(t). Further, let where M(t)∈R (m +p)×(n+p) , N(t)∈R (m+p)×(n+p) , Then the neural network formula can be simplified as: in is the right pseudo-inverse of M(t), which is the formal description of the neural network control method for solving time-varying matrices based on integral enhancement proposed in this patent.

[0048] In step 6), the common external disturbance is represented by δ(t). When the problem to be solved involves a large disturbance, the integral enhanced neural network can be selected as follows When the problem to be solved is relatively ideal or does not contain complex disturbances, the neural network dynamics equation is simplified to The corresponding neural network model also becomes The solution method and key parameter selection can be adjusted based on the results of the pre-solution in step 4). Generally speaking, appropriately increasing the values ​​of α and β is beneficial to improving the overall noise resistance of the solution method.

[0049] In order to demonstrate the actual time-varying system design process, a practical example is used to illustrate the problem. Assume that the time-varying parameter matrix of the system has been obtained, and consider a real domain time-varying equation with the following time-varying matrix, where A(t) = [3+sin(t), 4+cos(t), 5-sin(t)], b(t) = [sin(3t)+cos(3t)], δ b (t)=[sin(t), 1.2*cos(t), 1.1*sin(t)+1.4*cos(t)] T , α=30,β=100, computer simulation experiments can verify the effectiveness of the solution obtained by this method.

[0050] In step 7), the solution of the upper neural network is sent to a specific lower computer for execution (or the solved posture and trajectory are deployed to the nodes on the network in advance. When the system is running, the various parts of the node can be smoothly moved to the corresponding position to achieve the expected effect).

[0051] In application areas where control effects are more demanding, step 7) will also assume the function of judging and transmitting the execution effect. In this way, the method described in this patent can not only direct the actions of the lower computer to achieve the expected effect, but also judge the execution effect to timely adjust the neural network solution algorithm and the values ​​of important parameters. This link can significantly improve the robustness of the solution of this method (such as Figure 3 dotted arrow).

[0052] The above are only embodiments with better effects of the present invention, but the scope of protection of the present invention is not limited to them. Any technician familiar with the technical field can make equivalent replacements or changes based on the technical solution and invention concept of the present invention within the scope disclosed by the present invention, which falls within the scope of protection of the present invention.

Claims

1. A neural network control method for solving time-varying matrices based on integral enhancement, the method mainly includes the following steps: 1) Establish a mathematical expression to describe the problem based on the actual context; 2) Normalize mathematical expressions and convert them into general forms; 3) Use matrix method to simplify the description form of expression group; 4) Pre-solve the time-varying matrix equation based on the pseudo-inverse method; 5) Establish an error evaluation function and apply the ZNN method to construct a neural network based on integral enhancement; 6) Automatically adjust whether to use integral enhancement and the selection of activation function according to the type of external disturbance; 7) The solution result is sent to the lower computer for execution.

2. A neural network control method for solving time-varying matrices based on integral enhancement according to claim 1, characterized in that The practical background of step 1) is usually robot kinematic planning, manipulator control, drone, underwater robot path planning and other problems. The mathematical expression is usually based on the position and angle of the object and joints to establish the kinematic equations (sets) of the position layer, velocity layer, and acceleration layer.

3. The neural network control method for solving time-varying matrices based on integral enhancement according to claim 1, characterized in that: The mathematical expression in step 2) should use a matrix-based description form, combining the equal relationships in step 1) into a matrix equation and the unequal relationships in step 1) into a matrix inequality. This allows various complex operating scenarios to be abstracted into a unified description form.

4. The neural network control method for solving time-varying matrices based on integral enhancement according to claim 1, characterized in that: In step 3), the matrix inequality is expanded into an equation by adding a set of relaxation variables. The equation is then combined with the equation constructed in claim 2 by substitution, facilitating subsequent analysis.

5. The neural network control method for solving time-varying matrices based on integral enhancement according to claim 1, characterized in that: In the step 4), the above equation is pre-solved using the inverse transformation method and the pre-solved result is analyzed to provide a basis for the selection of the activation function in the subsequent step 6).

6. The neural network control method for solving time-varying matrices based on integral enhancement according to claim 1, characterized by: In step 5), the difference between the production result and the expected result is made to generate the error evaluation function e(t) in the neural network solution process. According to the design concept of recursive neural network dynamics, the differential convergence equation of the error function is constructed to force the error e(t) in the solution process to converge to zero quickly.

7. The neural network control method for solving time-varying matrices based on integral enhancement according to claim 1, characterized by: In step 6), the external interference encountered in the actual production process is classified into four types: constant, linear time-varying, bounded time-varying, and bounded random. The pre-solved analysis results as described in claim 5 are then used to determine whether to use an integral-enhanced neural network to optimize the solution process. At the same time, different activation functions are appropriately selected to improve the speed of solution convergence.

8. The neural network control method for solving time-varying matrices based on integral enhancement according to claim 1, characterized by: The solution generated in step 7) is sent to the lower computer or terminal mechanism in real time for execution via appropriate means. Furthermore, the lower computer or terminal mechanism should have a real-time monitoring module to provide real-time feedback of the execution results to the upper neural network. This expands the adaptability of the neural network based on integral enhancement to complex environments.

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