Leakage delay decomposition method for finite time complex value BAM neural network stabilization

Abstract

The invention discloses a finite time complex value BAM neural network stabilization leakage delay decomposition method, and the specific design process is as follows: proposing some new sufficient conditions of Fourier transform of a complex value bidirectional associative memory neural network with time delay based on the concept of utilizing a Lyapunov functional and an upper right Dini derivative. A complex-valued nonlinear function is successfully decomposed into a real component and an imaginary component by using a decomposition technology of a complex-valued bidirectional associative memory neural network, and a group of criteria is established. Meanwhile, under the background of a double-layer structure of the complex-valued bidirectional associative memory neural network with time delay, a feedback controller is designed and realized, and important guarantee is provided for stability and stabilization of the network. The method is of great significance to control and stability of a complex neural network system.

Description

Technical Field

[0001] The invention relates to the field of controller technology, and in particular to a leakage delay decomposition method for finite-time complex-valued BAM neural network stabilization. Background Art

[0002] As we all know, multi-valued neural networks are a special type of CVNN with multi-valued logical threshold functions. Compared with real-valued neural networks (RVNNs), CVNNs have advantages such as simple network topology, faster training time, and stronger learning skills for complex signals. Nevertheless, the fundamental issue in studying the characteristics of CVNNs is the choice of activation function. As we all know, the activation function can also be expressed by the division of the real and imaginary parts. Therefore, the emergence of CVNNs has attracted widespread attention from different perspectives and has led to the development of a large number of literatures. The study of bidirectional associative memory (BAM) neural networks has attracted many researchers due to its rich results and wide applications. Some interesting stability characteristics have been proposed. In some articles, a two-layer nonlinear feedback network model is proposed to explain the interconnection of neurons between one layer and another layer of neurons. Therefore, it is meaningful to extensively study the stability analysis of BAMNNs.

[0003] Stability is one of the most important issues for any dynamic system. However, in several practical applications, the key concern is the system behavior within a finite time interval. On the other hand, most practical neural systems function only within a finite time interval. In addition to accelerated convergence, finite-time control methodology also shows enhanced disturbance rejection properties and robustness. Finite-time stability analysis of neural networks has been proposed by many researchers. Therefore, it is very important to understand the dynamic behavior of CVNN and a lot of time has been spent studying its finite-time stability. Recently, finite-time system control has been explored on CVNN and some related findings have been proposed. In the past few decades, CVBAMNN has shown increasing competitiveness in neural networks.

[0004] So far, it is difficult to solve the above-mentioned stability and synchronization problems for UAV control systems with leakage delay and time-varying delay. Therefore, the present invention designs a finite-time complex-valued BAM neural network and its complex-valued activation function for systems with leakage delay and time-varying delay, and constructs an effective feedback controller. It provides a solution for the UAV state requirements in actual UAV control scenarios, and improves the performance and robustness of the UAV control system. Summary of the invention

[0005] The present invention considers the feedback controller field of complex-valued bidirectional associative memory neural networks, and proposes a finite-time stability criterion for CVBAMNNs under the conditions of leakage delay and time lag through decomposition methods and novel conditions. The complex-valued nonlinear function is decomposed into real and imaginary parts by using the concepts of Lyapunov function and Dini derivative, using inequality techniques such as Razumikhin conditions and Young inequality, and the corresponding controller is designed to ensure the asymptotic stability and synchronization of the system, thereby effectively suppressing the influence of delay leakage on the network state. The invention focuses on the stability analysis of CVBAMNNs, which is accurate and convenient, and can be widely used in various application scenarios of finite-time stability problems of CVBAMNNs with leakage delays.

[0006] To achieve the above purpose, the technical solution specifically adopted by the present invention is: a leakage delay decomposition method for finite-time complex-valued BAM neural network stabilization. It mainly includes the following steps:

[0007] Step 1: Under the condition of leakage delay, a complex-valued BAM neural network is established, and its mathematical expression is designed as:

[0008]

[0009] where l = 1, 2, ..., k = 1, 2, ..., r; φ 1l ,φ 2k is a normal constant u l (t), v k (t) is the state variable h k (v k (t)), f l (u l (t)),h k (v k (t-λ 2k (t))) and f l (u l (t-λ 1l (t))) is a complex-valued activation function; the time-varying delay λ 1l (t), λ 2k (t), leakage delay δ 1l , δ 2k λ(t)=max{λ 1l ,λ 2k}, δ(t) = max{δ 1l , δ 2k}, τ(t) = max{δ, λ}I 1l (t), I 2k (t) is the external input, is the time-varying parameter uncertainty;

[0010] The following are the initial conditions associated with the above equation: in and Continuous on [-τ,0];

[0011] Step 2: Consider the complex-valued activation function of the neural network, give a more reasonable assumption, and use the decomposition method to decompose the complex-valued nonlinear activation function into real and imaginary parts:

[0012] First, the following assumptions are introduced:

[0013] Assumption 1: For u l =μ l +iη l and is an imaginary unit, the real and imaginary parts h k (·) and f l (·) often becomes:

[0014]

[0015] For any

[0016] There are positive scalars So that for θ=R,I,

[0017]

[0018] Therefore, for the complex-valued BAM neural network, we can decompose its activation function into:

[0019]

[0020]

[0021] The system has an equilibrium point (u*,v*), let u k =uu*,v σ =vv*, then the above formula can be transformed by Fourier as follows:

[0022]

[0023]

[0024] where u k (t) = u(t) - u * (t)=(μ-μ * )+i(η-η * )=μ k +iη k ,

[0025]

[0026] Through this transformation, a dynamic model is successfully established, which can effectively process finite-time complex-valued BAM neural networks. Step 3: For systems with leakage delay and time-varying delay, design a suitable Lyapunov function to show that the real and imaginary parts of the deviation and angular velocity in the system are bounded, considering the following assumptions:

[0027] Assumption 2: Bias

[0028] are all bounded, that is, there exists a positive constant Make

[0029]

[0030] By choosing the Lyapunov function, we can get:

[0031]

[0032] The upper derivative of V1(t) is calculated as:

[0033]

[0034] Based on the assumptions, it can be deduced that:

[0035]

[0036] Based on the above assumptions, we can also conclude that:

[0037]

[0038]

[0039] Applying Razumikhin conditions to the above formula:

[0040] Also consider this inequality:

[0041]

[0042] Where γ>0,0<η<1 and they are two constants. Then V(t) satisfies:

[0043] V 1-η (t)≤V 1-η (t0)-γ(1-η)(t-t0),t0≤t≤T

[0044]

[0045] Therefore, we can have:

[0046]

[0047] If min >0, 0<∈<1 satisfies, then Settling time

[0048] It can be shown that if there is a dependence on the initial value and The constant but and when (in is called stabilization time).

[0049] From the above, we can see that the equilibrium point of CVBAMNNs is in a finite time The inside is stable.

[0050] Step 4: To achieve asymptotic stability of the finite-time complex-valued BAM neural network, we can design the controller as:

[0051]

[0052] Among them, ε 1l >0,ε 2l >0,ε 3k >0,ε 4k >0.

[0053] Therefore, if (Γ min +Φ min -Λ max )>0 holds, the complex-valued neural network can achieve asymptotic stability under the above controller, where:

[0054] Γ min =min{Γ1,Γ2,Γ3,Γ4},

[0055] Φ min =min{φ 11 ,φ 2m},

[0056] Λ max =max{Λ1,Λ2,Λ3,Λ4}

[0057]

[0058] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, a leakage delay decomposition method for finite-time complex-valued BAM neural network stabilization is implemented.

[0059] A computer-readable storage medium stores computer instructions, which, when executed by a processor, implement a leakage delay decomposition method for finite-time complex-valued BAM neural network stabilization.

[0060] Compared with the prior art, the present invention has the following advantages:

[0061] 1. The present invention takes into account the leakage delay and time lag of drone control in actual scenarios, which is more in line with the application scenarios in actual engineering. At the same time, the targeted optimization of these characteristics can effectively improve the accuracy and robustness of drone state estimation, thereby improving the performance and stability of the drone control system and achieving precise control of the drone system.

[0062] 2. In this invention, the activation function of UAV control is further optimized. By decomposing the complex-valued nonlinear function into real and imaginary parts, the stability criterion of CVBAMNNs is established using the decomposition method. This method is innovative in the stability analysis of neural networks.

[0063] 3. This paper proposes some novel sufficient conditions and stability criteria to realize the stability of CVBAMNNs in finite time. The finite time stability of CVBAMNNs is proved by using the concepts of Lyapunov function and Dini derivative. It is further optimized by using inequality techniques such as Razumikhin condition and Young inequality, which contributes new theoretical results to the stability analysis in this field.

[0064] 4. The present invention not only proposes new methods and criteria at the theoretical level, but also demonstrates the feasibility of these methods through actual numerical examples, which shows that the invention has good versatility and scalability, can be modified and adjusted in real time according to specific application scenarios, and has high practicality and guiding significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is the state trajectory diagram of the nns real part of the controller in Example 1 when δ(t)=2;

[0066] Figure 2 is the state trajectory diagram of the nns imaginary part of the controller in Example 2 when δ(t) = 2;

[0067] Figure 3 is the state trajectory diagram of the nns real part of the controller in Example 3 when δ(t)=4;

[0068] Figure 4 is the state trajectory diagram of the nns imaginary part of the controller in Example 4 when δ(t)=4;

[0069] Figure 5 is the state trajectory diagram of the nns real part of the controller in Example 5 when δ(t) = 5;

[0070] Figure 6 is the state trajectory diagram of the nns imaginary part of the controller in Example 6 when δ(t)=5. Figure 7 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0071] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the accompanying drawings, and the words "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0072] The present invention is verified by Matlab simulation, which shows the effectiveness and feasibility of the invention. For example, under the problem of signal delay and parameter mismatch, a complex-valued BAM neural network with leakage is considered, and its form is as follows:

[0073]

[0074] When l,k=1,2,3:

[0075] φ 11 =7,φ 21 =11,φ 31 =15,φ 12 =18,φ 22 =17,φ 32 =19,

[0076] φ 13 =3,φ 23 =21,φ 33 =23,δ(t)=2,λ(t)=1.5

[0077] And we have:

[0078]

[0079]

[0080] At the same time, we take the activation function as follows:

[0081]

[0082] have Therefore, the following equation is satisfied:

[0083]

[0084] The time-varying parameter uncertainty is defined as follows:

[0085]

[0086] Therefore, satisfying l,k=1,2,3,θ=R,I

[0087] To ensure the above equation holds, select the control parameters:

[0088] ∈ 11 =2.3,∈ 12 =3.4,∈ 13 =2.9,∈ 21 =3.3,∈ 22 =2.4,∈ 23 =3.9,∈ 31 =4.3,∈ 32

[0089] =2.7,

[0090]

[0091] ∈=0.5

[0092] Copy the initial value of the BAM neural network to Continuous on [-τ,0].

[0093] It can be seen from the content of claim S1:

[0094]

[0095] Therefore, the condition Satisfied. Then the complex-valued BAM neural network with the above parameters can achieve stabilization in a finite time. Further, the estimated settling time is:

[0096]

[0097] Under the initial conditions, u1(s)=0.3-0.2i,u2(s)=-0.6-0.2i,u3(s)=0.7+0.9i,

[0098] v1(s)=-0.4-0.6i, ν2(s)=0.7+0.5i, v3(s)=-0.9-0.7i,

[0099] The real and imaginary parts of the complex-valued BAM neural network system and the state response of the controller are as follows: Figure 1 and Figure 2 As shown in the figure, the equilibrium point of the system and the controller is finite time stable. It is well known that leakage delay is the main cause of poor system performance, oscillation and instability. For example, when the leakage delay increases to A, Figure 3 and Figure 4 It is shown that the state responses of the real and imaginary parts of the neural network system are oscillatory under the same initial conditions. When B increases continuously, it can also be verified that there is no feasible solution. Figure 5 and Figure 6 It shows that under the same initial conditions, the state responses of the real and imaginary parts of the system are unstable, such as Figure 7 Flowchart of the invention shown.

[0100] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above technical features.

Claims

1. A leakage delay decomposition method for finite-time complex-valued BAM neural network stabilization, suitable for UAV state control with leakage delay in UAV control applications, characterized by: The method comprises the following steps: S1: For the UAV control system with leakage delay and time-varying delay, a finite-time complex-valued BAM neural network is designed, the mathematical expression is given, and a dynamic model including leakage delay is established through Fourier transform; S2: For the neural network model of the system under consideration, design its complex-valued activation function, use the decomposition method to decompose the complex-valued nonlinear activation function into real and imaginary parts, and show that the real and imaginary parts of the deviation and angular velocity in the system are bounded; S3: Design a suitable Lyapunov function for the motion state control of the UAV, use inequality techniques such as Razumikhin conditions and Young's inequality to analyze the derivatives of the Lyapunov function, and derive sufficient conditions to ensure the finite-time stability of the UAV system; S4: Based on the constructed neural network model, the mathematical expression of the feedback controller of the UAV state is effectively designed to achieve the asymptotic stability of the complex-valued BAM neural network.

2. The leakage delay decomposition method for finite-time complex-valued BAM neural network stabilization according to claim 1, characterized in that: In S1, each finite-time complex-valued BAM neural network is expressed as: where l = 1, 2, ..., k = 1, 2, ..., r; φ 1l ,φ 2k is a normal constant u l (t), v k (t) is the state variable h k (v k (t)),f l (u l (t)),h k (v k (t-λ 2k (t))) and f l (u l (t-λ 1l (t))) is a complex-valued activation function; the time-varying delay λ 1l (t),λ 2k (t), leakage delay δ 1l ,δ 2k λ(t)=max{λ 1l ,λ 2k },δ(t)=max{δ 1l ,δ 2k },τ(t)=max{δ,λ}I 1l (t),I 2k (t) is external input, is the time-varying parameter uncertainty; The following are the initial conditions associated with the above equation: s∈[-τ,0], where and Continuous on [-τ,0]; Consider that the system has an equilibrium point (u*,v*), let u k =uu*,v σ =vv*, then the finite-time complex-valued BAM neural network is transformed into the following form through Fourier transform: This representation allows for a more accurate analysis of the complex-valued activation function of the neural network under consideration.

3. The leakage delay decomposition method for finite-time complex-valued BAM neural network stabilization according to claim 1, characterized in that: The S2 gives a more reasonable assumption for the complex-valued activation function of the neural network under consideration, and uses a decomposition method to decompose the complex-valued nonlinear activation function into real and imaginary parts: Assumption 1: For and is an imaginary unit, the real and imaginary parts h k (·) and f l (·) often becomes: For any There are positive scalars and Make for Assumption 2: Bias are all bounded, that is, there exists a positive constant Make Where θ = R, I. The neural network of step S2 is divided into real and imaginary parts and expressed as follows:

4. The method for decomposing leakage delays stabilized by a finite-time complex-valued BAM neural network according to claim 1, characterized in that: For the system with leakage delay and time-varying delay in S3, a suitable Lyapunov function is designed: By choosing the Lyapunov function, we get: The upper derivative of V1(t) is calculated as: With the above assumptions, using the Razumikhin conditions we have: From this we can get (Γ min +Φ min -Λ max >0) is established. At this time, if Ξ min >0, 0<∈<1, then We can estimate the settling time t * :

5. The method for leakage delay decomposition of finite-time complex-valued BAM neural network stabilization according to claim 1, characterized in that: Step S4 is to achieve asymptotic stability of the finite-time complex-valued BAM neural network, and the controller is designed as: Consider the following parameter conditions: C min =min{Γ1,Γ2,Γ3,Γ4}, F min =min{φ 11 ,f 2k }, L max =max{Λ1,Λ2,Λ3,Λ4}, Therefore, when the above inequality holds, and from step S3, we know that (Γ min +φ min -Λ max )>0 holds, so the complex-valued BAM neural network considered in this system reaches asymptotic stability under the above controller.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the leakage delay decomposition method for finite-time complex-valued BAM neural network stabilization as described in any one of claims 1 to 5 above is implemented.

7. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed by a processor, the leakage delay decomposition method for finite-time complex-valued BAM neural network stabilization as described in any one of claims 1-5 is implemented.

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