A Leakage Delay Decomposition Method Stabilized by Finite-Time Complex-Valued BAM Neural Network

Abstract

This invention discloses a leakage delay decomposition method for stabilizing finite-time complex-valued BAM neural networks. The specific design process is as follows: Based on the concepts of Lyapunov functionals and the upper right Dini derivative, some new sufficient conditions for the Fourier transform of complex-valued bidirectional associative memory neural networks with time delay are proposed. Using the decomposition technique of complex-valued bidirectional associative memory neural networks, the complex-valued nonlinear function is successfully decomposed into real and imaginary components, and a set of criteria is established. Simultaneously, under the two-layer structure of the complex-valued bidirectional associative memory neural network with time delay, a feedback controller is designed and implemented, providing important guarantees for the stability and stabilization of the network. This invention is of great significance for the control and stability of complex neural network systems.

Description

Technical Field

[0001] This invention relates to the field of controller technology, and in particular to a leakage delay decomposition method stabilized by a finite-time complex-valued BAM neural network. Background Technology

[0002] As is well known, multivalued neural networks (CVNNs) are a special type of CVNN with multivalued logistic threshold functions. Compared to real-valued neural networks (RVNNs), CVNNs have advantages such as simpler network topology, faster training time, and stronger ability to learn complex signals. Nevertheless, a fundamental problem in studying the characteristics of CVNNs is the choice of activation function. It is known that activation functions can also be represented by dividing the real and imaginary parts. Therefore, the emergence of CVNNs has attracted widespread attention from different perspectives, leading to a large number of subsequent publications. Research on bidirectional associative memory (BAM) neural networks has attracted many researchers due to its rich results and wide applications. Some interesting stability features have been proposed. Some articles have proposed a two-layer nonlinear feedback network model to explain the neuronal connections between neurons in one layer and another. Therefore, extensive research on the stability analysis of BAMNNs is meaningful.

[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 finite time intervals. On the other hand, most real-world neural systems operate only within finite time intervals. Besides accelerating convergence, finite-time control methodologies have shown enhanced interference suppression properties and robustness. Many researchers have proposed finite-time stability analyses for neural networks. Therefore, understanding the dynamic behavior of CVNNs is crucial, requiring significant time to study their finite-time stability. Recently, finite-time system control has been explored in CVNNs, leading to several related findings. Over the past few decades, CVBAMNN has demonstrated increasing competitiveness in neural networks.

[0004] To date, it has been difficult to solve the stability and synchronization problems mentioned above for UAV control systems with leakage delay and time-varying delay. Therefore, this 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, constructing an effective feedback controller. It provides a solution for the UAV state requirements in practical UAV control scenarios, improving the performance and robustness of the UAV control system. Summary of the Invention

[0005] This invention addresses the issue of finite-time stability in CVBAMNNs under conditions of leakage delay and time lag. Through decomposition and novel conditions, it proposes a finite-time stability criterion. Utilizing the concepts of Lyapunov functions and Dini derivatives, and employing inequality techniques such as the Razumikhin condition and Young's inequality, the complex-valued nonlinear function is decomposed into real and imaginary parts. A corresponding controller is designed to ensure the asymptotic stability and synchronization of the system, effectively suppressing the impact of delay leakage on the network state. This invention focuses on the stability analysis of CVBAMNNs, offering accuracy and convenience, and can be widely applied to various scenarios involving the finite-time stability of CVBAMNNs with leakage delay.

[0006] To achieve the above objectives, the specific technical solution adopted by this invention is: a leakage delay decomposition method stabilized by a finite-time complex-valued BAM neural network. It mainly includes the following steps:

[0007] Step 1: For conditions with leakage delay, establish a complex-valued BAM neural network, and design its mathematical expression as follows:

[0008]

[0009] Where l = 1, 2, ..., k = 1, 2, ..., r; φ 1l , φ 2k It is a positive constant u l (t), v k (t) represents 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; 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) represents the external input. The uncertainty lies in the time-varying parameters;

[0010] The following are the initial conditions related to the above equation: in and It is continuous on [-τ,0].

[0011] Step 2: Considering the complex-valued activation function of the neural network, we make more reasonable assumptions and use decomposition methods to decompose the complex-valued nonlinear activation function into its real and imaginary parts:

[0012] First, we introduce the following assumptions:

[0013] Assumption 1: For u l =μ l +iη l and It is a virtual unit, with a real part and an imaginary part h. k (·) and f l (·) often becomes:

[0014]

[0015] For any

[0016] Both have positive scalars So that for θ = R, I,

[0017]

[0018] Therefore, for complex-valued BAM neural networks, we can decompose their activation function as follows:

[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 transform as follows:

[0022]

[0023]

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

[0025]

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

[0027] Assumption 2: Deviation

[0028] Both are bounded, meaning they have positive constants. Make

[0029]

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

[0031]

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

[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] Apply the Razumikhin condition to the above equation:

[0040] Also consider this inequality:

[0041]

[0042] Where γ>0, 0<η<1 and 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 Ξ min If > 0 and 0 < ∈ < 1, then Settling time

[0048] It can be proven that if there exists a dependency on the initial value... and constant but and when (in (This is called the steady-state time).

[0049] As can be seen from the above, the equilibrium point of CVBAMNNs is within a finite time. The internal situation is stable.

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

[0051]

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

[0053] Therefore, if (Γ min +Φ min -Λ max If )>0 holds true, the complex-valued neural network can achieve asymptotic stability under the controller in the above equation, 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 includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the aforementioned finite-time complex-valued BAM neural network-stabilized leakage delay decomposition method.

[0059] A computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the aforementioned finite-time complex-valued BAM neural network-stabilized leak delay decomposition method.

[0060] Compared with existing technologies, this invention has the following advantages:

[0061] 1. This invention takes into account the leakage delay and time lag characteristics of UAV control in real-world scenarios, making it more consistent with actual engineering applications. Furthermore, targeted optimization of these characteristics effectively improves the accuracy and robustness of UAV state estimation, thereby enhancing the performance and stability of the UAV control system and achieving precise control of the UAV system.

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

[0063] 3. This invention proposes some novel sufficient conditions and stability criteria to achieve the stability of CVBAMNNs in finite time. The stability of CVBAMNNs in finite time is proved by using the concepts of Lyapunov functions and Dini derivatives. Further optimization is carried out using inequality techniques such as Razumikhin conditions and Young's inequality, contributing new theoretical results to the stability analysis in this field.

[0064] 4. This invention not only proposes new methods and criteria at the theoretical level, but also demonstrates the feasibility of these methods through actual numerical examples. This shows that the invention has good versatility and scalability, and can be modified and adjusted in real time according to specific application scenarios, thus having high practicality and guiding significance. Attached Figure Description

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

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

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

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

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

[0070] Figure 6 The diagram shows the state trajectory of the controller nns with the imaginary part when δ(t) = 5 in Example 6.

[0071] Figure 7 This is a flowchart of the present invention. Detailed Implementation

[0072] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. It should be noted that the terms "front," "rear," "left," "right," "up," and "down" used in the following description refer to directions in the accompanying drawings, and the terms "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0073] This invention is verified using Matlab simulations, demonstrating its effectiveness and feasibility. For example, considering the signal delay and parameter mismatch problem, a complex-valued BAM neural network with leakage is considered, its form being as follows:

[0074]

[0075] When l,k=1,2,3:

[0076] φ 11 =7,φ 21 =11,φ 31 =15,φ 12 =18,φ 22 =17,φ 32 =19,

[0077] φ 13 =3,φ 23 =21,φ 33 =23, δ(t)=2, λ(t)=1.5

[0078] And we have:

[0079]

[0080]

[0081] Meanwhile, we choose the activation function as follows:

[0082]

[0083] have Therefore, the following equation is satisfied:

[0084]

[0085] The uncertainty of time-varying parameters is defined as follows:

[0086]

[0087] Therefore, satisfying l,k=1,2,3,θ=R,I

[0088] To ensure the above equation holds true, select the following control parameters:

[0089] ∈ 11 =2.3,∈ 12 =3.4,∈ 13 =2.9,∈ 21 =3.3,∈ 22 =2.4,∈ 23 =3.9,∈ 31 =4.3,∈ 32

[0090] =2.7,

[0091]

[0092] ∈=0.5

[0093] The initial value of the replicated BAM neural network is It is continuous on [-τ,0].

[0094] As can be seen from the content of claim S1:

[0095]

[0096] Therefore, conditions If the above parameters are satisfied, then the complex-valued BAM neural network with the above parameters can achieve stabilization within a finite time. Furthermore, the estimated settling time is:

[0097]

[0098] Under the initial conditions, u1(s) = 0.3 - 0.2i, u2(s) = -0.6 - 0.2i, u3(s) = 0.7 + 0.9i.

[0099] v1(s)=-0.4-0.6i, ν2(s)=0.7+0.5i, v3(s)=-0.9-0.7i,

[0100] In the example, the real and imaginary parts of the complex-valued BAM neural network system are related to the state response of the controller as follows: Figure 1 and Figure 2 As shown in the figure, the equilibrium point between the system and the controller is finite-time stabilization. It is well known that leakage delay is a major cause of poor system performance, oscillations, and instability. For example, when the leakage delay increases to A, Figure 3 and Figure 4 This shows that the state responses of the real and imaginary parts of the neural network system are oscillating under the same initial conditions. It can also be verified that there is no feasible solution when B increases continuously. Figure 5 and Figure 6 This demonstrates that under the same initial conditions, the state responses of the real and imaginary parts of the system are unstable, such as... Figure 7 The flowchart of the invention shown is shown.

[0101] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features.

Claims

1. A leakage delay decomposition method stabilized by a finite-time complex-valued BAM neural network, applicable to UAV state control applications with leakage delays, characterized in that: The method includes the following steps: S1: For UAV control systems with leakage delay and time-varying delay, a finite-time complex-valued BAM neural network is designed, a 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 explain that the real and imaginary parts of the deviation and angular velocity in the system are bounded. S3: For the motion state control of UAVs, design a suitable Lyapunov function, analyze the derivative of the Lyapunov function using the Razumikhin condition and Young's inequality, and derive sufficient conditions to ensure the stability of the UAV system in finite time. S4: Based on the constructed neural network model, effectively design the mathematical expression of the feedback controller for the UAV state to achieve asymptotic stability of the complex-valued BAM neural network; Step S4, to achieve asymptotic stability of the finite-time complex-valued BAM neural network, designs the controller as follows: 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 as can be seen from step S3, (Γ) min +Φ min -Λ max The condition )>0 holds true, therefore the complex-valued BAM neural network considered by the system reaches asymptotic stability under the above controller; where l=1,2,…,k=1,2,…,r; φ 1l , φ 2k It is a positive constant u l (t), v k (t) represents 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.

2. The leakage delay decomposition method stabilized by a finite-time complex-valued BAM neural network according to claim 1, characterized in that: In S1, each finite-time complex-valued BAM neural network is expressed as follows: Where l = 1, 2, ..., k = 1, 2, ..., r; φ 1l , φ 2k It is a positive constant u l (t), v k (t) represents 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; 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) represents the external input. The uncertainty lies in the time-varying parameters; The following are the initial conditions related to the above equation: in and It is 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 can be transformed into the following form through Fourier transform: This representation method allows for a more accurate analysis of the complex-valued activation function of the neural network under consideration.

3. The leakage delay decomposition method stabilized by a finite-time complex-valued BAM neural network according to claim 1, characterized in that: S2 makes a more reasonable assumption about 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 u l =μ l +iη l and It is a virtual unit, with a real part and an imaginary part h. k (·) and f l (·) often becomes: For any μ l ,η l ,μ l′ ,η l′ , Both have positive scalars and So that for θ = R, I, Assumption 2: Deviation Both are bounded, meaning they have positive constants. Make Where θ = R, I. The neural network in step S2 is divided into real and imaginary parts as follows:

4. The leakage delay decomposition method stabilized by a finite-time complex-valued BAM neural network according to claim 1, characterized in that: For the system in S3 with leakage delay and time-varying delay, design a suitable Lyapunov function: By selecting the Lyapunov function, we obtain: The upper derivative of V1(t) is calculated as follows: The conditions for using Razumikhin are: Therefore, we can obtain (Γ) min +Φ min -Λ max >0) is true; If Ξ is satisfied at this time min >0, 0<∈<1, then Estimated settlement time t * :

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements the finite-time complex-valued BAM neural network-stabilized leakage delay decomposition method as described in any one of claims 1 to 4.

6. A computer-readable storage medium storing computer instructions thereon, characterized in that: When executed by the processor, the computer instructions implement the leak delay decomposition method stabilized by the finite-time complex-valued BAM neural network as described in any one of claims 1-4.

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