State estimation method of discrete time neural network with mixed time delay and quantization stochastic semi-Markov hopping

Abstract

The invention discloses a state estimation method of a discrete time neural network with mixed time delay and quantized random semi-Markov hopping. In the method, an estimator design problem of a random discrete time semi-Markov jump neural network (NNs) with quantization and mixed time delay is introduced. The asymptotic stability criterion of the system is established by establishing a proper Lyapunov function by using summation inequalities in a single form and a double form of the semi-Markov hopping network, and the asymptotic stability standard is obtained. And an explicit expression of the gain is provided by using a Lyapunov function technology. The method is suitable for the neural network with a random hopping mode, mixed time delay and a quantization effect, the stability of the system can be effectively improved, and the conservative property is reduced.

Description

Technical Field

[0001] The invention relates to a state estimation method of a discrete-time neural network with mixed time delay and quantized random semi-Markov jump transition, belonging to the technical field of neural network control. Background Art

[0002] For decades, neural network (NN) models have received extensive attention in theory and application in many practical fields such as automatic control, image processing, combinatorial optimization, fault diagnosis, associative memory, etc. At the same time, with the continuous development of robotics, robots have been widely used in industrial production, medical care, home services and other fields. Among them, robot control is an important part of robotics, and its core goal is to achieve precise control of robot motion so that it can complete various complex tasks. Among the networks used for robot control, discrete time networks have attracted much attention compared with traditional continuous time networks. Due to the importance of discrete time neural networks in engineering, it is found that the measured output is usually quantized to limit the bandwidth of the network in transmission. Therefore, quantization has become a key part of information exchange between networks. In addition, time delay has become a common observable fact that it can cause divergence, oscillation or instability in network systems. Therefore, it is necessary to construct a realistic neural network model for robot control that includes both discrete delay and dispersed delay. At the same time, it should be noted that although discrete time systems can be represented by difference equations of continuous time systems, and the dynamic behavior of continuous time systems is close to that of discrete time systems, the stability criteria and control of discrete time systems require different tools such as sum inequalities compared to continuous systems.

[0003] In addition to the robot control network model itself, network state estimation is also a key link in robot control. The robot motion state includes information such as position, velocity, acceleration, etc., which is crucial for the design and implementation of robot control algorithms. However, in practical applications, due to the influence of factors such as sensor noise and environmental changes, the robot motion state is often difficult to obtain accurately.

[0004] However, the existing robot motion state estimation method is difficult to deal with the above-mentioned mixed delay and random jump problems. Therefore, the present invention proposes a state estimation method for a discrete neural network with mixed delay and random semi-Markov jump and performs H ∞ Filter analysis. It is used to provide solutions to the robot motion state estimation requirements in actual robot control scenarios to improve the performance and robustness of the robot control system. Summary of the invention

[0005] The main purpose of the present invention is to fill in the field of filter design of random semi-Markov jump discrete time neural network. Under the condition of mixed time delay and quantization effect, by introducing improved summation inequality and Lyapunov function technology, the filter parameters can be designed to ensure the asymptotic stability and H ∞ The performance can be improved, thereby effectively suppressing the influence of random noise on network state estimation. This method is convenient and accurate, and can be widely used in various application scenarios of random semi-Markov jump discrete-time neural networks.

[0006] To achieve the above object, the technical solution specifically adopted by the present invention is: a state estimation method of a discrete-time neural network with mixed time delay and quantized random semi-Markov jump transition, which mainly includes the following steps:

[0007] Step 1: Establish a state estimation system of a random semi-Markov jump discrete-time neural network with mixed time delay and quantization. First, a random semi-Markov jump discrete-time neural network with mixed time delay is given:

[0008]

[0009] y(k)=g(x(k)),

[0010]

[0011] in is the neuron vector of the neural network at time k, is the neuron activation function. y(k) and u(k)∈l 2 (0, +∞) are the measured output, initial condition and input of the neural network respectively. and as well as They are the connection weight matrix, discrete time delay connection weight matrix and distributed delay connection weight matrix; τ(k) represents the distributed delay, satisfying τ m <τ(k)≤τ M , d(k) satisfies d m <τ(k)≤d M , where τ m >0,τ M >0,d m >0,d M >0 is a given integer. w(k) is a scalar Wiener process that satisfies the following conditions:

[0012]

[0013] Assume that for the given two positive constants ρ 1 and ρ 2 ,as well as

[0014]

[0015] Then, the random quantitative impact was considered in this initial model.

[0016] After quantization, the measured signal of the neural network yes:

[0017]

[0018] Defining a quantizer It is symmetrical That is, the mapping in the quantization process is:

[0019]

[0020] The quantizer is logarithmic type, y (j) (k) is the measured output of the jth element. Specifically, for all The quantization levels are represented in a set as:

[0021]

[0022]

[0023] in is the density of quantization. Each quantization level is associated with an interval, so that the quantizer distributes this quantization degree to the entire interval. Similarly, the description of the quantizer is as follows:

[0024]

[0025] in It is clear from the previous definition that It can be expressed as For a certain As a result, The quantized results are then transformed into sectors with bounded uncertainty. and get So that F(k)F T (k)≤I.

[0026] In the following sections, for each possible r(k)=i,iinM, the matrix G(r(k)) will be referred to as G i; The random semi-Markov jump discrete-time neural network equation with mixed time delay becomes a delayed S-MJGNN discrete-time neural network with quantization effect, which can be regarded as a collection of M delayed S-MJGNNS and can be expressed as:

[0027]

[0028]

[0029]

[0030] On this basis, the filter model is given:

[0031]

[0032] in is the state estimate of the filter; is the filter parameter matrix to be determined; is the input of the filter, ψ f (k) is the initial condition of the estimator.

[0033] Based on the neural network model and the filter model, the description of the state estimation error system can be defined:

[0034] in

[0035]

[0036] Step 2: Select an appropriate Lyapunov function to analyze the state estimation error system. The Lyapunov function is given by the following results:

[0037]

[0038] The polynomial terms are:

[0039] V 1 (k,x(k))=Θ T (k)P i Θ(k),

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] in and

[0048]

[0049] Step 3: Estimate the summation term in the derivative expectation of the determined Lyapunov function using the new summation inequality. First, define ΔV b (k) = V b (k+1)-V b (k), and taking the expectation, we get:

[0050] Using the weighted Bernoulli inequality (WBI) technique, the above equation depends on S 1 The following results can be obtained by estimating the sum of

[0051]

[0052] In addition, in order to estimate the The sum of , using the lemma:

[0053]

[0054] in

[0055]

[0056] According to the lemma, we have:

[0057]

[0058] Now we will use the previous condition to constrain the last term in the expected expression. Before doing so, please note that:

[0059]

[0060] Then, by applying the lemma and rearranging the obtained results, we obtain:

[0061]

[0062] Furthermore, according to the assumptions, there are:

[0063] 0≤2[g(W 1i x(k))-U 1 W 2i x(k)] T Λ1 [U 2 W 1i x(k)-g(W 1i x(k))],

[0064] 0≤2[g(W 1i x(kd ＊ ))-U 1 W 2i x(kd ＊ )] T Λ 2 [U 2 W 1i x(kd ＊ )-g(W 1i x(kd ＊ ))],

[0065] 0≤2[g(W 1i x(k))-g(W 1i x(kd ＊ ))-U 1 (W 2i x(k)-W 2i x(kd ＊ )] T ×Λ 3 [g(W 1i x(k))-g(W 1i x(kd ＊ ))-U 2 (W 2i x(k)-W 2i x(kd ＊ )],

[0066] Therefore, based on the above formula and combining all inequalities, we get:

[0067]

[0068] in It is easy to verify It's about ＊ ∈[d m ,d M ] is an affine function, so If and only if and This is equivalent to the linear matrix inequality:

[0069]

[0070] Therefore, if the above inequality holds, ΔV(x(k))≤-ε||x(k)|| 2For appropriately small ε>0, this shows that the state estimation error system is asymptotically stable when w(k)=0.

[0071] Next, we will consider the case where the system μ has zero initial conditions and w(k)≠0. ∞ performance.

[0072] According to the initial assumptions, we have:

[0073]

[0074] Now define ζ(k)=[Φ T (k) w T (k)] T ,but

[0075]

[0076] in and is equivalent to 2 Replace with and in

[0077]

[0078] According to Schur's complement theorem, we can get:

[0079]

[0080] Summing both sides of the above equation, and considering x(0)=0, the following conclusion holds:

[0081]

[0082] Therefore, the discrete-time semi-Markov jump state estimation error system is asymptotically stable and has H ∞ Performance indicator γ.

[0083] Step 4: After verifying the stability of the state estimation error system and H ∞ After the performance, we proceed to solve the gain matrix in the filter model defined above, that is, the filter parameters

[0084] For a given 0 <d m <d M , and u(k)≠0 if there exists a symmetric matrix Diagonal Matrix And any matrix If the following conditions hold, the constructed neural network is asymptotically stable and γ>0:

[0085]

[0086] in

[0087]

[0088]

[0089]

[0090] In addition, the filter parameters are given by 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, the state estimation method of the discrete-time neural network with mixed time delay and quantized random semi-Markov jump transition is implemented.

[0091] A computer-readable storage medium stores computer instructions, which, when executed by a processor, implement the state estimation method of a discrete-time neural network with mixed time delay and quantized random semi-Markov jump transition.

[0092] Compared with the prior art, the present invention has the following advantages:

[0093] 1. This invention takes into account the characteristics of mixed delay and quantized random jump in robot control in actual scenarios, which is more in line with actual engineering application scenarios. At the same time, targeted optimization of these characteristics can effectively improve the accuracy and robustness of robot motion state estimation, thereby improving the performance and reliability of the robot control system and achieving precise control of robot motion.

[0094] 2. The present invention uses a new summation inequality for the stability analysis of discrete-time networks for robot control, and adopts single and double summation inequalities, which can more effectively handle mixed delays. The proposed stability criterion is more accurate and can more effectively ensure the asymptotic stability of the system, thereby improving the accuracy of robot motion state estimation and further optimizing the implementation of robot control strategies.

[0095] 3. The present invention adopts the form of LMI to give the stability criterion, which is easy to solve and verify, and is more convenient and feasible in practical engineering applications. For actual robot control systems, the LMI toolbox can be used to quickly design suitable and effective state estimation filters and verify their performance, thereby reducing development costs and shortening development cycles. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 is the state response of the system in the numerical example 1 under the state estimation method of the present invention;

[0097] Figure 2 It is the state response of the system in numerical example 2 under the state estimation method described in the present invention. DETAILED DESCRIPTION

[0098] In order to deepen the knowledge and understanding of the inventors, the embodiments of the present invention are described below in conjunction with the accompanying drawings of the specification, and the present invention is verified by Matlab simulation experiments.

[0099] Example: See Figure 1 , Figure 2 , a state estimation method with a hybrid time delay and quantized random semi-Markov jump discrete-time neural network mainly includes the following steps:

[0100] Step 1: Establish a state estimation system of a random semi-Markov jump discrete-time neural network with mixed time delay and quantization. First, a random semi-Markov jump discrete-time neural network with mixed time delay is given:

[0101]

[0102] y(k)=g(x(k)),

[0103]

[0104] in is the neuron vector of the neural network at time k, is the neuron activation function. y(k) and are the measured output, initial conditions and input of the neural network respectively. and as well as They are the connection weight matrix, discrete time delay connection weight matrix and distributed delay connection weight matrix; τ(k) represents the distributed delay, satisfying τ m <τ(k)≤τ M , d(k) satisfies d m <τ(k)≤d M , where τ m >0,τ M >0,d m >0,d M >0 is a given integer. w(k) is a scalar Wiener process that satisfies the following conditions:

[0105]

[0106] Assume that for the given two positive constants ρ 1 and ρ 2 ,as well as

[0107]

[0108] Then, the random quantitative impact was considered in this initial model.

[0109] After quantization, the measured signal of the neural network yes:

[0110]

[0111] Defining a quantizer It is symmetrical That is, the mapping in the quantization process is:

[0112]

[0113] The quantizer is logarithmic type, y (j) (k) is the measured output of the jth element. Specifically, for all The quantization levels are represented in a set as:

[0114]

[0115] in is the density of quantization. Each quantization level is associated with an interval, so that the quantizer distributes this quantization degree to the entire interval. Similarly, the description of the quantizer is as follows:

[0116]

[0117] in It is clear from the previous definition that It can be expressed as For a certain As a result, The quantized results are then transformed into sectors with bounded uncertainty. and get So that F(k)F T (k)≤I.

[0118] In the following sections, for each possible r(k)=i,iinM, the matrix G(r(k)) will be referred to as G i ; The random semi-Markov jump discrete-time neural network equation with mixed time delay becomes a delayed S-MJGNN discrete-time neural network with quantization effect, which can be regarded as a collection of M delayed S-MJGNNS and can be expressed as:

[0119]

[0120]

[0121]

[0122] On this basis, the filter model is given:

[0123]

[0124] in is the state estimate of the filter; is the filter parameter matrix to be determined; is the input of the filter, ψ f (k) is the initial condition of the estimator.

[0125] Based on the neural network model and the filter model, the description of the state estimation error system can be defined:

[0126] in

[0127]

[0128] Step 2: Select an appropriate Lyapunov function to analyze the state estimation error system. The Lyapunov function is given by the following results:

[0129]

[0130] The polynomial terms are:

[0131] V 1 (k,x(k))=Θ T (k)P i Θ(k),

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] in and

[0140]

[0141] Step 3: Estimate the summation term in the derivative expectation of the determined Lyapunov function using the new summation inequality. First, define ΔV b (k) = V b (k+1)-V b (k), and taking the expectation, we get:

[0142] Using the weighted Bernoulli inequality (WBI) technique, the above equation depends on S 1 The following results can be obtained by estimating the sum of

[0143]

[0144] In addition, in order to estimate the The sum of , using the lemma:

[0145]

[0146] in

[0147]

[0148] According to the lemma, we have:

[0149]

[0150] Now we will use the previous condition to constrain the last term in the expected expression. Before doing so, please note that:

[0151]

[0152] Then, by applying the lemma and rearranging the obtained results, we obtain:

[0153]

[0154] Furthermore, according to the assumptions, there are:

[0155] 0≤2[g(W 1i x(k))-U 1 W 2i x(k)] T Λ 1 [U 2 W 1i x(k)-g(W 1i x(k))],

[0156] 0≤2[g(W 1ix(kd ＊ ))-U 1 W 2i x(kd ＊ )] T Λ 2 [U 2 W 1i x(kd ＊ )-g(W 1i x(kd ＊ ))],

[0157] 0≤2[g(W 1i x(k))-g(W 1i x(kd ＊ ))-U 1 (W 2i x(k)-W 2i x(kd ＊ )] T ×Λ 3 [g(W 1i x(k))-g(W 1i x(kd ＊ ))-U 2 (W 2i x(k)-W 2i x(kd ＊ )],

[0158] Therefore, based on the above formula and combining all inequalities, we get:

[0159]

[0160] in It is easy to verify It's about ＊ ∈[d m ,d M ] is an affine function, so If and only if and This is equivalent to the linear matrix inequality:

[0161]

[0162] Therefore, if the above inequality holds, ΔV(x(k))≤-ε||x(k)|| 2 For appropriately small ε>0, this shows that the state estimation error system is asymptotically stable when w(k)=0.

[0163] Next, we will consider the case where the system μ has zero initial conditions and w(k)≠0. ∞ performance.

[0164] According to the initial assumptions, we have:

[0165]

[0166] Now define ζ(k)=[Φ T (k) w T (k)] T ,but

[0167]

[0168] in and is equivalent to 2 Replace with and in

[0169]

[0170] According to Schur's complement theorem, we can get:

[0171]

[0172] Summing both sides of the above equation, and considering x(0)=0, the following conclusion holds:

[0173]

[0174] Therefore, the discrete-time semi-Markov jump state estimation error system is asymptotically stable and has H ∞ Performance indicator γ.

[0175] Step 4: After verifying the stability of the state estimation error system and H ∞ After the performance, we proceed to solve the gain matrix in the filter model defined above, that is, the filter parameters

[0176] For a given 0 <d m <d M , and u(k)≠0 if there exists a symmetric matrix

[0177] Diagonal Matrix And any matrix If the following conditions hold, the constructed neural network is asymptotically stable and γ>0:

[0178]

[0179] in

[0180]

[0181]

[0182]

[0183] In addition, the filter parameters are given by

[0184] Some numerical examples are provided below to demonstrate the practicality of the generated conclusions.

[0185] Example 1. The system parameters of the neural network for a given point are set as follows:

[0186]

[0187]

[0188]

[0189] The activation function is:

[0190]

[0191] When 1 =0.13 and ρ 2 =0.04, the quantized density is: The probability of the random variable δ(k) is δ=0.87

[0192] First, consider the quantitative impact and then use the following neural network model mentioned in the previous steps

[0193]

[0194]

[0195]

[0196] Build examples of discrete-time neural networks with mixed time delays and quantized random semi-Markov jumps. And the state estimation filter of the neural network.

[0197]

[0198] The random semi-Markov process is controlled by the following parameters: the transition rate matrix is ​​0.1≤θ 12 ≤2.0,0.8≤θ 21 ≤1.7. Get θ 12,1 =0.1,θ 12,2 =2.0,θ 21.1 =0.8,θ 21.2 =1.7, transfer rate θ 12 (h) and θ21 (h) Without loss of generality.

[0199] Then the filter gain, i.e., the filter parameter, is calculated. The filter gain can be obtained by setting w(k) = (0, 1) and solving the linear matrix inequality in the theorem using the Matlab toolbox, thereby obtaining the asymptotic stability of the semi-Markov neural network. Table 1 lists the different d m γ under the value min value, and the maximum allowed upper bound value.

[0200] Table 1 Different d m The optimal γ under min Performance Level

[0201] Table 1

[0202]

[0203] Finally, the designed filter estimator gain is given by:

[0204]

[0205] The designed filter is used to estimate the state of the neural network in this example. The results are as follows Figure 1 As shown, it is revealed that The state changes of the neural network under .

[0206] Example 2. The experimental process is the same as Example 1. Here, some of the explanations are simplified. The system parameters of the semi-Markov neural network (4-2) are set as:

[0207]

[0208]

[0209]

[0210] The activation function is

[0211]

[0212] By choosing the values ​​of the noise diffusion coefficient vector, the probability of the random variable δ(k), the quantization density, and the transfer matrix to be the same as in Example 1, the initial conditions are By using the Matlab LMI toolbox, it can be easily checked that LMI is feasible. Therefore, the model is globally asymptotically stable. Figure 2 The dynamic convergence of the system is depicted.

[0213] It should be noted that the above embodiments are not intended to limit the protection scope of the present invention, and equivalent changes or substitutions made on the basis of the above technical solutions all fall within the protection scope of the claims of the present invention.

Claims

1. A state estimation method with a hybrid time-delay and quantized random semi-Markov jump discrete-time neural network, suitable for robot motion state estimation in robot control applications, characterized in that: The method comprises the following steps: S1: Define and construct the state estimation error system between the actual motion state of the robot and the filter output, which is composed of the actual motion state vector of the robot and the state estimation vector of the filter; S2: Construct a suitable Lyapunov function V(k,x(k)) for the robot's motion state, which contains multiple sub-functions V b (k, x(k)), corresponding to different state parameters in robot motion such as velocity, acceleration, position, etc., which are used for subsequent analysis of the stability of the state estimation error system; S3: Using the improved summation inequality to estimate the derivative summation term of the Lyapunov function, a delay-dependency criterion including a single summation term and a double summation term is established. This criterion is used to judge the stability of the state estimation error system to improve the accuracy of the robot motion state estimation and thus better implement the robot control strategy. S4: Determine the parameters of the robot state estimator to effectively design a filter for estimating the robot motion state. Construct a linear matrix matrix inequality (LMI) based on the upper bound of the derivative of the estimated Lyapunov function and other quantities. Solve the LMI to obtain the gain matrix of the filter. and S5: Use the designed state estimation filter to estimate the state of the robot motion, and output the network state estimation value x through the filter. f (k), calculate the state estimation error vector with the actual state vector of the robot motion, analyze the state estimation error system, and verify its H ∞ Performance is improved to ensure that the filter can effectively estimate the robot's motion state, guide and adjust the implementation of the robot's control strategy, and achieve more precise control of the robot.

2. The state estimation method of the discrete-time neural network with mixed time delay and quantized random semi-Markov jump transition according to claim 1 is characterized in that: In step S1, for the state error estimation system, the random semi-Markov jump discrete time neural network with mixed time delay is first given as: y(k)=g(x(k)), in is the neuron vector of the neural network at time k, is the neuron activation function, y(k) and are the measured output, initial conditions and input of the neural network respectively. and as well as They are the connection weight matrix, discrete time delay connection weight matrix and distributed delay connection weight matrix; τ(k) represents the distributed delay, satisfying τ m <τ(k)≤τ M , d(k) satisfies d m <τ(k)≤d M , where τ m >0,τ M >0,d m >0,d M >0 is a given integer, w(k) is a scalar Wiener process that satisfies the following conditions: Assume that for two given positive constants ρ1 and ρ2, and Established, Considering the random quantization effect, after quantization, the measurement signal of the neural network yes: Defining a quantizer It is symmetrical That is, the mapping in the quantization process is: The quantizer is logarithmic type, y (j) (k) is the measurement output of the jth element, as follows, for all The quantization levels are represented in a set as: in is the density of quantization. Each quantization level is associated with an interval, so that the quantizer distributes this quantization degree to the entire interval. Similarly, the description of the quantizer is as follows: in It is clear from the previous definition that Expressed as For a certain As a result, Then, the quantized results are transformed into sectors with bounded uncertainty, defined as and get So that F(k)F T (k)≤I, In the following sections, for each possible r(k)=i,iinM, the matrix G(r(k)) will be referred to as G i ; The random semi-Markov jump discrete-time neural network equation with mixed time delay becomes a delayed S-MJGNN discrete-time neural network with quantization effect, which can be regarded as a collection of M delayed S-MJGNNS and can be expressed as: The mathematical expression of the filter is given below: in is the state estimate of the filter; is the filter parameter matrix to be determined; is the input of the filter, ψ f (k) is the initial condition of the estimator, and finally creates the variable is the state estimation error vector, and the estimation error system is: in 3. The state estimation method with hybrid time delay and quantized random semi-Markov jump discrete time neural network according to claim 1 is characterized in that: In step S2, the Lyapunov function is: The polynomial terms are: V1(k,x(k))=Θ T (k)P i Θ(k), in and Let ΔV b (k) = V b (k+1)-V b (k), and taking the expectation, we get:

4. The state estimation method of the discrete-time neural network with mixed time delay and quantized random semi-Markov jump transition according to claim 1 is characterized in that: In step S3, the derivative sum of the Lyapunov function is estimated, and the sum dependent on S1 is estimated using the weighted Bernoulli inequality (WBI) technique, and the following results are obtained: In order to estimate the dependence The sum of , using the lemma: in According to the lemma, we have: Now we will use the previous condition to constrain the last term in the expected expression. Before that, Then, by applying the lemma and rearranging the obtained results, we obtain: Furthermore, according to the assumptions, there are: 0≤2[g(W 1i x(k))-U1W 2i x(k)] T Λ1[U2W 1i x(k)-g(W 1i x(k))], 0≤2[g(W 1i x(k-d ★ ))-U1W 2i x(k-d ★ )] T Λ2[U2W 1i x(k-d ★ )-g(W 1i x(k-d ★ ))], 0≤2[g(W 1i x(k))-g(W 1i x(k-d ★ ))-U1(W 2i x(k)-W 2i x(k-d ★ )] T ×Λ3[g(W 1i x(k))-g(W 1i x(k-d ★ ))-U2(W 2i x(k)-W 2i x(k-d ★ )], Therefore, based on the above formula and combining all inequalities, we get: in It is easy to verify It's about ★ ∈[d m ,d M ] is an affine function, so If and only if and This is equivalent to the linear matrix inequality: Therefore, if the above inequality holds, ΔV(x(k))≤-ε||x(k)|| 2 For appropriately small ε>0, this shows that the state estimation error system is asymptotically stable when w(k) = 0. Next, we will consider the case where the system μ has zero initial conditions and w(k)≠0. ∞ performance, According to the initial assumptions, we have: Now define ζ(k)=[Φ T (k) w T (k)] T ,but in and is equivalent to, except that Σ2 is replaced by and in According to Schur's complement theorem, we can get: Summing both sides of the above equation, and considering x(0)=0, the following conclusion holds: Therefore, the discrete-time semi-Markov jump state estimation error system is asymptotically stable and has a performance index γ.

5. The state estimation method with hybrid time delay and quantized random semi-Markov jump discrete time neural network according to claim 1 is characterized in that: In step S4, the gain matrix, i.e., the parameters of the filter, is calculated. The filter parameters of the filter model given above are calculated using the criterion based on the linear matrix inequality (LMI). For a given 0 <d m <d M , and u(k)≠0 if there exists a symmetric matrix Diagonal Matrix And any matrix If the following conditions hold, the constructed neural network is asymptotically stable and γ>0: in In addition, the filter parameters are given by Given, Next, after successfully building the state estimation error system, the filter is designed using the obtained gain matrix. The output y(k) of the neural network is then used as the input of the estimator system, and the state estimation x of the neural network is obtained. f (k), and then complete the stability analysis, performance evaluation, control and optimization of the neural network system.

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 state estimation method with a hybrid delay and quantized random semi-Markov jump discrete-time neural network as described in any one of claims 1 to 5 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, a state estimation method with a hybrid time delay and quantized random semi-Markov jump discrete-time neural network as described in any one of claims 1 to 5 is implemented.

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