Memristive neural network state estimation method with random sensor time-delay driving

Abstract

The invention discloses a memristive neural network state estimation method with random sensor time delay driving. The method comprises the following steps: 1, establishing a memristive neural network dynamic model with random sensor time delay and H infinity performance constraint under variance constraint; 2, performing state estimation on the memristor neural network dynamic model under variance constraint; 3, calculating an error covariance matrix upper bound and an H infinity performance constraint condition of the memristor neural network; 4, solving the value of an estimator gain matrix, and achieving the state estimation of the memristor neural network under the time-delay driving of the random sensor. The method solves the problems that the existing state estimation method cannot simultaneously process the multi-index state estimation of the memristor neural network with variance constraint and H infinity performance constraint under the random sensor time delay, so that the estimation accuracy is low, and the estimation accuracy is low under the condition that information exists under the random sensor time delay and information at other moments cannot be received. And the accuracy of the estimation performance is low.

Description

Technical Field

[0001] This invention belongs to the field of memristor neural network state estimation, and relates to a variance-constrained state estimation method for memristor neural networks, specifically a multi-index variance-constrained state estimation method for memristor neural networks with random sensor time delays. Background Technology

[0002] In today's era of rapid development in information technology, the traditional von Neumann computing architecture, constrained by core bottlenecks such as the "memory wall" and "power wall," is struggling to meet the stringent requirements of emerging application scenarios such as artificial intelligence and big data processing for computing speed and energy efficiency.

[0003] Memristors, as nonlinear resistive elements with memory function, are the fourth type of fundamental circuit component, distinct from resistors, capacitors, and inductors. They possess the core characteristics of high-speed response, low-power operation, high integration density, and "integrated information storage and computing," providing a key technological path to overcome the bottlenecks of traditional architectures. Since the concept of memristors was first proposed by Chinese-American scientist Shao-Tang Tsai in 1971, and its physical existence was confirmed by a research team at Hewlett-Packard in 2008, memristor-related technologies have gradually become a hot topic in interdisciplinary research.

[0004] Memristor-based neural networks, leveraging the variable resistance and non-volatility of memristors—advantages that closely match the core characteristics of biological synapses—can accurately simulate the plasticity of biological synapses, enabling continuous adjustment of synaptic weights and thus supporting the construction of artificial neural network hardware circuits. Compared to artificial neural networks implemented through software programs in traditional von Neumann architecture computers, memristor neural network hardware circuits possess significant technical advantages such as high computing speed and low power consumption, demonstrating broad application prospects in key areas such as pattern recognition and neuromorphic computing. In recent years, researchers both domestically and internationally have conducted extensive pioneering research in the field of memristor neural networks, achieving basic pattern recognition functions such as letter recognition, handwritten character recognition, and facial image recognition. However, this technology still faces multiple technical challenges in practical engineering applications, including optimizing memristor device performance, further reducing operating power consumption, increasing integration density, and ensuring compatibility between memristor synaptic devices and traditional electrical components. These technical pain points urgently require breakthroughs through further in-depth research. In practical engineering applications, especially in complex network environments, information transmission is prone to problems such as random time delays and bandwidth limitations due to uncertainties such as equipment failures and communication channel congestion, directly affecting system stability and data processing accuracy. Therefore, for applications with random sensor time delays that simultaneously satisfy H... ∞ The design of a state estimation method with strong adaptability and high reliability for memristor neural networks under performance constraints and variance limitations has important engineering application value and practical significance.

[0005] Currently, although some research results related to memristor neural network state estimation have been disclosed in existing technologies, such methods are difficult to simultaneously satisfy H in application scenarios with random sensor time delays. ∞ The dual technical requirements of performance constraints and variance limitations result in insufficient accuracy of state estimation results, which cannot meet the needs of high-precision state estimation in practical engineering applications. Therefore, an optimization scheme that can solve the above-mentioned technical defects is urgently needed. Summary of the Invention

[0006] This invention provides a memristor neural network state estimation method driven by random sensor time delay. This method solves the problem that existing state estimation methods cannot simultaneously handle variance constraints and H-values ​​under random sensor time delay. ∞ The performance-constrained multi-index state estimation problem of memristor neural networks, which leads to low estimation accuracy and low estimation performance accuracy under random sensor time delays where information cannot be received at other times, can be applied to the field of memristor neural network state estimation.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A memristor neural network state estimation method driven by random sensor time delay includes the following steps:

[0009] Step 1: Establish a system with random sensor time delay and H under variance constraints. ∞ The state-space form of the performance-constrained memristor neural network dynamic model is as follows:

[0010]

[0011]

[0012]

[0013] In the formula, , , These are the memristor neural networks at the 1st... , , The state variables of the time-delay memristor neural network at time t. It is the Euclidean space of the states of the time-delay memristor neural network and its spatial dimension is . ; In the first The controlled measurement output at any given time. Let Euclidean space be the controlled output state of a time-delay memristor neural network, and let its dimension be . ; , In the first The initial value at time , The time delay exists in a discrete-time delay memristor neural network; In the first The self-feedback diagonal matrix of the memristor neural network at time step. In the first The weight matrix of the connection activation function at known time. In the first A system matrix with known dimensions at time points and dependent on time delays; In the first The nonlinear excitation function at time t; In the first The adjustment matrix for measurements at known times; In the first The adjustment matrix of the controlled output is known at all times; In the first The mean at time step is zero and the covariance is Gaussian white noise sequence;

[0014] Step 2: Perform state estimation on the memristor neural network dynamic model established in Step 1 under variance constraints. The specific steps are as follows:

[0015] Step 2.1: The measurement output format of the memristor neural network is as follows:

[0016]

[0017] In the formula, It is the first The measurement output of the time-delay memristor neural network. It is the real number field of the output of the time-delay memristor neural network dynamic model. It is the dimension; It is a Gaussian white noise sequence with zero mean and covariance of . ; In the first The time-known measurement outputs the right adjustment matrix; Represents the random variable i.e. Random sensor time delay phenomena that occur at any given moment In the first The noise distribution matrix of the system is known at any given time.

[0018] The random sensor time delay phenomenon is described by a Bernoulli distributed random variable, which follows the statistical properties as follows:

[0019]

[0020] In the formula, Indicates the probability of an event occurring. This represents the probability of random sensor time delay occurring, and It is a known scalar;

[0021] Step 22: Nonlinear Excitation Function satisfy Bounded conditions for sectors:

[0022]

[0023] In the formula, and Represent the first and second known matrices of appropriate dimension. This represents the difference between two matrices. It is a positive definite symmetric matrix;

[0024] Steps 2 and 3: State Dependency Matrix Parameters of Memristor Neural Networks , and satisfy:

[0025]

[0026] in, , Represents absolute value. express arrive Summation, , , Indicates capacitance. Indicates parallel resistance. and Let these represent the weight matrix and the connection weight matrix, respectively, representing the connection time delay. , , and These are the known first, second, third, and fourth constants. Represents a symbolic function;

[0027] Step Two Four, Definition:

[0028]

[0029] In the formula, , , , , , , , , , , , These are the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, and twelfth stored variables, respectively. , , , This indicates taking the minimum value. This indicates taking the maximum value;

[0030] make , and Then we can get:

[0031]

[0032] in

[0033]

[0034] Furthermore, the aforementioned uncertainty matrix satisfies norm-bounded uncertainty:

[0035]

[0036] In the formula, This represents the first uncertain matrix. This represents the second uncertainty matrix. This represents the third uncertainty matrix. and Both are known first and second real-valued matrices. This represents the first unknown matrix. This represents the second unknown matrix. Let the third unknown matrix satisfy... ;

[0037] , , satisfy:

[0038]

[0039] Then we have:

[0040]

[0041] definition , and ,in Indicates the first A column vector with 1 element and 0 elements. , and They are unknown scalar number one, unknown scalar number two, and unknown scalar number three, respectively, satisfying , and and , and ;

[0042] Step 25: Based on the known information, design the following time-varying state estimator:

[0043]

[0044] In the formula, It is the memristor neural network in the first... State estimation at time 10:00 For the real number field of the state in the dynamic model of the neural network, It is the memristor neural network in the first... State estimation at time 10:00 It is the memristor neural network in the first... State estimation at time 10:00 Let be the real number field of the state of the neural network dynamic model, and let its dimension be . ; In the first State estimation of the controlled output at any given time. Let be the first matrix in the left and right intervals. This is the second matrix in the left and right intervals. Let be the third matrix in the left and right intervals. In the first State estimation of the nonlinear excitation function at time t. It is the first The measurement output of the time decoder, It is the first known constant matrix. The estimator gain matrix is ​​the unknown. This represents the probability of random sensor time delay occurring, and It is a known scalar;

[0045] Step 3, given H ∞ Performance indicators positive semidefinite matrix No. 1 positive semidefinite matrix No. 2 The third positive semidefinite matrix and initial conditions and Calculate the upper bound of the error covariance matrix and H of the memristor neural network. ∞ The performance constraints are defined in the following steps:

[0046] Step 3: Prove H according to the following formula. ∞ The performance analysis problem is presented, along with corresponding sufficient conditions that are easy to solve:

[0047]

[0048] In the formula:

[0049]

[0050] In the formula, For a given positive scalar; , , , , , , , , , , , , , They are respectively , , , , , , , , , , , , , transpose; In the first The positive semi-definite matrix at time 1; In the first The positive semi-definite matrix at time 2; In the first The known matrix at time; In the first The matrix at a given time; In the first The known matrix at time; This represents the probability of random sensor time delay occurring, and It is a known scalar; yes The block matrix in the first row and first column, yes The block matrix in the first row and second column, yes The block matrix in the second row and second column, yes The block matrix in the 3rd row and 3rd column, yes The block matrix in the 4th row and 4th column, yes The block matrix in the 5th row and 5th column, yes The 6th row and 6th column of the matrix is ​​a block matrix, where 0 represents that all elements in the block are 0; An identity matrix of appropriate dimension;

[0051] Step 3.2: Exploring the covariance matrix The problem involves upper bound constraints, and the following sufficient conditions are given:

[0052]

[0053] In the formula,

[0054]

[0055] In the formula, In the first The upper bound of the error covariance matrix at time t. In the first The upper bound matrix obtained at each time step; In the first The upper bound of the error covariance matrix at time t; In the first The upper bound of the error at time, In the first The trace of the upper bound matrix of the error covariance matrix at time t; In the first Error matrix at time step; The normal constant is known. The trace of the matrix; It is the first known variance matrix. It is the known second variance matrix;

[0056] Analysis of the two results above shows that the system that guarantees the estimation error satisfies the given H. ∞ Sufficient conditions for performance requirements and the boundedness of error covariance;

[0057] Step 4: Using stochastic analysis, the estimator gain matrix is ​​obtained by solving the following recursive linear matrix inequality. The value of is used to perform state estimation on a memristor neural network driven by random sensor time delays:

[0058]

[0059]

[0060]

[0061] The updated matrix is:

[0062]

[0063]

[0064]

[0065] In the formula, , , , , and In the first The normal values ​​of the first, second, third, fourth, fifth, and sixth adjustments at each moment; It is the first component in The first real matrix of appropriate dimension known at time t. It is the second component. The second real matrix of appropriate dimension known at time t; , , They are , , transpose; They are The inverse matrix; , , , and These are the measurement matrices numbered 1, 2, 3, 4, and 5, respectively. For unknown normal values, It is the first component in The first measure matrix of known appropriate dimension at time; It is the second component. The second metric matrix of known appropriate dimension at time; It is the third component. The third metric matrix of known appropriate dimension at time; It is the 4th component. The fourth metric matrix of known appropriate dimension at time; It is the 5th component. The fifth metric matrix of known appropriate dimension at time; It is a block matrix in the first row and first column. It is the block matrix in the 1st row and 2nd column. It is the block matrix in the 1st row and 3rd column. It is the block matrix in the 2nd row and 2nd column. It is the block matrix in the 2nd row and 3rd column. It is the block matrix in the 3rd row and 3rd column. It is the block matrix in the 1st row and 4th column. It is the block matrix in the 2nd row and 5th column. It is the block matrix in the 2nd row and 6th column. It is the block matrix in the 2nd row and 7th column. It is the block matrix in the 3rd row and 8th column. It is the block matrix in the 3rd row and 9th column. It is the block matrix in the 4th row and 4th column. It is the block matrix in the 5th row and 5th column. It is the block matrix in the 6th row and 6th column. It is the block matrix in the 7th row and 7th column. It is the block matrix in the 8th row and 8th column. It is a block matrix in the 9th row and 9th column. It is a block matrix in the first row and first column. It is the block matrix in the 1st row and 2nd column. It is the block matrix in the 1st row and 3rd column. It is the block matrix in the 1st row and 4th column. It is the block matrix in the 1st row and 5th column. It is the block matrix in the 2nd row and 2nd column. It is the block matrix in the 3rd row and 3rd column. It is the block matrix in the 4th row and 4th column. It is the block matrix in the 5th row and 5th column; and These are the known first matrix and the known second matrix, respectively;

[0066] judge Has the total duration N been reached? If yes, proceed to step two; otherwise, end the process.

[0067] Compared with the prior art, the present invention has the following advantages:

[0068] 1. This invention designs a multi-index state estimation method for memristor neural networks suitable for stochastic sensor time-delay driven environments. In its design, this method fully incorporates the influence of stochastic sensor time delay on the state estimation performance of memristor neural networks, and efficiently utilizes the effective information of the estimation error covariance matrix by employing stochastic analysis methods and inequality handling techniques. Compared to traditional neural network state estimation methods, this invention focuses on the key problem of "multi-index state estimation of memristor neural networks under stochastic sensor time-delay driven environments," and the derived estimation method allows the error system to simultaneously satisfy the upper bound constraint of the estimation error covariance and the predetermined H... ∞ Performance constraints effectively achieve the dual technical effects of disturbance suppression and improved estimation accuracy.

[0069] 2. This invention utilizes stochastic analysis to construct a research framework. The specific implementation path is as follows: First, construct estimation error systems that satisfy H... ∞ The sufficiency criteria for performance constraints and the existence of an upper bound on the error covariance are then established. Subsequently, by integrating these two types of conditions, a sufficiency criterion for the estimation error system to simultaneously satisfy H is derived. ∞ A unified criterion for performance constraints and upper bounds on error covariance is established; finally, the optimal value of the estimator gain matrix is ​​determined by solving multiple sets of linear matrix inequalities. This approach fully considers H in the case of stochastic sensor time delay. ∞ The two performance metrics of performance constraints and variance limitation effectively suppress the interference of disturbances on the estimation process, ultimately improving the estimation accuracy.

[0070] 3. This invention addresses the difficulty of existing state estimation methods in simultaneously handling random sensor time-delay driven conditions, while also possessing H... ∞ The performance constraints and variance limitations of memristor neural networks (MNNs) in state estimation have led to poor estimation accuracy. This invention proposes a novel state estimation method that significantly improves the estimation accuracy. Simulation results clearly show that as the probability of hybrid attacks increases, the performance of the MNN state estimation gradually declines, and the estimation error increases accordingly. This result not only verifies that the proposed state estimation method can effectively handle complex application scenarios with random sensor time delays, but also further confirms the feasibility and effectiveness of the proposed method.

[0071] 4. Within the technical framework of this invention, memristor neural networks can be applied in multiple fields, including digital circuits, chaotic systems, image processing, color digital image restoration, and associative memory. Compared to artificial neural networks implemented by software programs on traditional computer architectures, memristor neural network circuits offer the core advantages of "high speed and low power consumption," providing strong support for technological breakthroughs in fields such as pattern recognition and neuromorphic computing, and demonstrating broad application prospects. Attached Figure Description

[0072] Figure 1 This is a flowchart of the multi-index state estimation method of memristor neural network driven by random sensor time delay according to the present invention;

[0073] Figure 2 This is the actual state of the memristor neural network. and state estimation The trajectory diagram, For memristor neural networks in the first... The state variables at time t, where: "It is the system state trajectory," "State estimation trajectory;"

[0074] Figure 3 This is a graph showing the output estimation error of a memristor neural network, where: "This is the control output estimation error trajectory;"

[0075] Figure 4 This is a trajectory diagram of the actual state error covariance and the upper bound of the error covariance of a memristor neural network, where " "It is the locus of the upper bound of the error covariance." "This is the upper bound of the actual error covariance locus;

[0076] Figure 5 This is a trajectory diagram showing the influence of different sensor time delay probabilities on the upper bound when the memristor neural network controls the output, where: "This is the control output trajectory under the following circumstances," "This is the control output trajectory under scenario two." Detailed Implementation

[0077] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0078] This invention provides a state estimation method for a memristor neural network driven by random sensor time delay, such as... Figure 1 As shown, the method includes the following steps:

[0079] Step 1: Establish H under random sensor time delay drive ∞ Dynamic model of memristor neural network with performance constraints and variance constraints.

[0080] In this step, the state-space form of the memristor neural network dynamic model is as follows:

[0081] (1)

[0082] (2)

[0083] (3)

[0084] In the formula, , , These are the memristor neural networks at the 1st... , , The state variables of the time-delay memristor neural network at time t. It is the Euclidean space of the states of the time-delay memristor neural network and its spatial dimension is . ; In the first The controlled measurement output at any given time. Let Euclidean space be the controlled output state of a time-delay memristor neural network, and let its dimension be . ; , In the first The initial value at time , The time delay exists in a discrete-time delay memristor neural network; In the first The self-feedback diagonal matrix of the memristor neural network at time step. Let be the dimension. It is a diagonal matrix. In the first time The One portion, It is the dimension; In the first The weight matrix of the connection activation function at known time. In the first time The One portion, In the first A system matrix with known dimensions at time points and dependent on time delays. In the first time The One component; In the first The nonlinear excitation function at time t; In the first The adjustment matrix for measurements at known times; In the first The mean at time step is zero and the covariance is A Gaussian white noise sequence.

[0085] Step 2: Perform state estimation on the memristor neural network dynamic model established in Step 1 under variance constraints. The specific steps are as follows:

[0086] Step 2.1: The measurement output format of the memristor neural network is as follows:

[0087] (4)

[0088] In the formula, It is the first The measurement output of the time-delay memristor neural network. It is the real number field of the output of the time-delay memristor neural network dynamic model. It is the dimension; It is a Gaussian white noise sequence with zero mean and covariance of . ; In the first The noise distribution matrix of the system is known at any given time.

[0089] The random sensor time delay phenomenon is described by a Bernoulli distributed random variable, which follows the statistical properties as follows:

[0090]

[0091] In the formula, Indicates the probability of an event occurring. Represents the random variable i.e. Random sensor time delay phenomena that occur at any given moment This represents the probability of random sensor time delay occurring, and It is a known scalar.

[0092] Step 22: Nonlinear Excitation Function satisfy Bounded conditions for sectors:

[0093]

[0094] In the formula, and Represent the first and second known matrices of appropriate dimension. Represents the difference between two matrices It is a positive definite symmetric matrix.

[0095] Steps 2 and 3: State Dependency Matrix Parameters of Memristor Neural Networks , and satisfy:

[0096]

[0097] in, , Represents absolute value. express arrive Summation, , , Indicates capacitance. Indicates parallel resistance. and These represent the weight matrix for the connection delay and the connection weight matrix, respectively. , , and These are the known first, second, third, and fourth constants. The symbolic function is defined as follows:

[0098] .

[0099] Step Two Four, Definition:

[0100]

[0101] It is not difficult to conclude , and In the formula, , , and These are the known first, second, third, and fourth constants. This indicates taking the minimum value. This indicates taking the maximum value.

[0102] make , and Then we can get:

[0103]

[0104] in

[0105]

[0106] Furthermore, the aforementioned uncertainty matrix satisfies norm-bounded uncertainty:

[0107]

[0108] In the formula, This represents the first uncertain matrix. This represents the second uncertainty matrix. This represents the third uncertainty matrix. and Both are known first and second real-valued matrices. This represents the first unknown matrix. This represents the second unknown matrix. Let the third unknown matrix satisfy... .

[0109] Step 25: Based on the known information, design the following time-varying state estimator:

[0110] (5)

[0111] In the formula, It is the memristor neural network in the first... State estimation at time 10:00 For the real number field of the state in the dynamic model of the neural network, It is the memristor neural network in the first... State estimation at time 10:00 It is the memristor neural network in the first... State estimation at time 10:00 Let be the real number field of the state of the neural network dynamic model, and let its dimension be . ; The time delay exists in discrete fixed neural networks. In the first State estimation of the controlled output at any given time. Let be the first matrix in the left and right intervals. This is the second matrix in the left and right intervals. Let be the third matrix in the left and right intervals. In the first State estimation of the nonlinear excitation function at time t. It is the first The measurement output of the time decoder, It is the first known constant matrix. The estimator gain matrix is ​​the unknown. This represents the probability of random sensor time delay occurring, and It is a known scalar.

[0112] The main purpose of this step is to design a time-varying state estimator (5) driven by a random sensor time delay, so that the proposed state estimation algorithm can simultaneously meet the following two performance constraints:

[0113] 1) Set the disturbance attenuation level positive semidefinite matrix number one positive semidefinite matrix No. 2 The third positive semidefinite matrix For the initial state Control output estimation error H satisfies the following ∞ Performance constraints:

[0114] (6)

[0115] In the formula, For a finite number of nodes, This represents the mathematical expectation. , ,and These are positive semi-definite matrices number one, positive semi-definite matrix number two, and positive semi-definite matrix number three, respectively. It is in the The time estimation error, It is a given disturbance attenuation level. It's noise. and augmented vector, It is in the time transpose, It represents the norm form. It represents the form of the norm squared.

[0116] 2) The estimation error covariance satisfies the following upper bound constraint:

[0117] (7)

[0118] In the formula, It is in the time transpose, It is in the A series of pre-given, acceptable estimation accuracy matrices for each time step.

[0119] Step 3, given H ∞ Performance indicators positive semidefinite matrix No. 1 positive semidefinite matrix No. 2 The third positive semidefinite matrix and initial conditions and Calculate the upper bound of the error covariance matrix and H of the memristor neural network. ∞ The performance constraints are defined in the following steps:

[0120] Step 3: Prove H according to the following formula. ∞ The performance analysis problem is presented, along with corresponding sufficient conditions that are easy to solve:

[0121] (8)

[0122] In the formula:

[0123]

[0124] In the formula, For a given positive scalar; , , , , , , , , , , , , , They are respectively , , , , , , , , , , , , , transpose; In the first The positive semi-definite matrix at time 1; In the first The positive semi-definite matrix at time 2; In the first The known matrix at time; In the first The matrix at a given time; In the first The known matrix at time; This represents the probability of random sensor time delay occurring, and It is a known scalar; yes The block matrix in the first row and first column, yes The block matrix in the first row and second column, yes The block matrix in the second row and second column, yes The block matrix in the 3rd row and 3rd column, yes The block matrix in the 4th row and 4th column, yes The block matrix in the 5th row and 5th column, yes The 6th row and 6th column of the matrix is ​​a block matrix, where 0 represents that all elements in the block are 0; An identity matrix of appropriate dimension;

[0125] Step 3.2: Exploring the covariance matrix The problem involves upper bound constraints, and the following sufficient conditions are given:

[0126] (9)

[0127] In the formula,

[0128] In the formula, In the first The upper bound of the error covariance matrix at time t. In the first The upper bound matrix obtained at each time step; In the first The upper bound of the error covariance matrix at time t; In the first The upper bound of the error at time, In the first The trace of the upper bound matrix of the error covariance matrix at time t; In the first Error matrix at time step; The normal constant is known. The trace of the matrix, It is the first known variance matrix. It is the first known variance matrix. It is the known second variance matrix. , , , , , , , , , , , , , They are respectively , , , , , , , , , , , , , transpose; In the first The positive semi-definite matrix at time 1; In the first The positive semi-definite matrix at time 2; In the first The known matrix at time; In the first The matrix at a given time; In the first The matrix at time known, This represents the probability of random sensor time delay occurring, and It is a known scalar;

[0129] Analysis of the two results above shows that the system that guarantees the estimation error satisfies the given H. ∞ Sufficient conditions for performance requirements and the boundedness of error covariance;

[0130] Step 4: Using stochastic analysis methods, and by solving a series of recursive linear matrix inequalities, the estimator gain matrix is ​​obtained. The value of is used to perform state estimation on a memristor neural network with random sensor time delay; the value of is determined. Has the total duration N been reached? If yes, proceed to step two; otherwise, end the process.

[0131] In this step, by solving a series of recursive linear matrix inequalities (10) to (13), the estimation error system is given to simultaneously satisfy H ∞ The value of the estimator gain matrix can be calculated based on the sufficient conditions of performance requirements and variance constraints:

[0132] (10)

[0133] (11)

[0134] (12)

[0135] The updated matrix is:

[0136] (13)

[0137] in

[0138]

[0139]

[0140]

[0141] In the formula, , , , , and In the first The normal values ​​of the first, second, third, fourth, fifth, and sixth adjustments at each moment; It is the first component in The first real matrix of appropriate dimension known at time t. It is the second component. The second real matrix of appropriate dimension known at time t; , , They are , , transpose; They are The inverse matrix; , , , and These are the measurement matrices numbered 1, 2, 3, 4, and 5, respectively. For unknown normal values, It is the first component in The first measure matrix of known appropriate dimension at time; It is the second component. The second metric matrix of known appropriate dimension at time; It is the third component. The third metric matrix of known appropriate dimension at time; It is the 4th component. The fourth metric matrix of known appropriate dimension at time; It is the 5th component. The fifth metric matrix of known appropriate dimension at time; It is a block matrix in the first row and first column. It is the block matrix in the 1st row and 2nd column. It is the block matrix in the 1st row and 3rd column. It is the block matrix in the 2nd row and 2nd column. It is the block matrix in the 2nd row and 3rd column. It is the block matrix in the 3rd row and 3rd column. It is the block matrix in the 1st row and 4th column. It is the block matrix in the 2nd row and 5th column. It is the block matrix in the 2nd row and 6th column. It is the block matrix in the 2nd row and 7th column. It is the block matrix in the 3rd row and 8th column. It is the block matrix in the 3rd row and 9th column. It is the block matrix in the 4th row and 4th column. It is the block matrix in the 5th row and 5th column. It is the block matrix in the 6th row and 6th column. It is the block matrix in the 7th row and 7th column. It is the block matrix in the 8th row and 8th column. It is a block matrix in the 9th row and 9th column. It is a block matrix in the first row and first column. It is the block matrix in the 1st row and 2nd column. It is the block matrix in the 1st row and 3rd column. It is the block matrix in the 1st row and 4th column. It is the block matrix in the 1st row and 5th column. It is the block matrix in the 2nd row and 2nd column. It is the block matrix in the 3rd row and 3rd column. It is the block matrix in the 4th row and 4th column. It is the block matrix in the 5th row and 5th column. In the first The upper bound of the error covariance matrix at time t. In the first The upper bound matrix obtained at each time step; In the first The upper bound of the error covariance matrix at time t; In the first The upper bound of the error at time, In the first The trace of the upper bound matrix of the error covariance matrix at time t; In the first Error matrix at time step; The normal constant is known. The trace of the matrix, It is the first known variance matrix. It is the first known variance matrix. It is the known second variance matrix. , , , , , , , , , , , , , They are respectively , , , , , , , , , , , , , transpose; In the first The positive semi-definite matrix at time 1; In the first The positive semi-definite matrix at time 2; In the first The known matrix at time; In the first The matrix at a given time; In the first The matrix at time known, This represents the probability of random sensor time delay occurring, and It is a known scalar. and These are the known first matrix and the known second matrix, respectively. It is in the The matrix at time unknown and satisfies , yes The transpose of , where 0 represents all elements in the matrix block being 0.

[0142] In this invention, the theory described in steps three and four is as follows:

[0143] First, prove that H ∞ The paper first analyzes performance problems and provides corresponding easily solvable discrimination criteria; secondly, it discusses the covariance matrix. The upper bound constraint problem is solved, and sufficient conditions are given. Through the analysis of the above two results, it is found that the proposed estimation algorithm simultaneously satisfies the given H. ∞ The performance requirements and the sufficient condition for the boundedness of the error covariance are solved by solving a series of recursive linear matrix inequalities to obtain the estimator gain matrix. The value of .

[0144] Example:

[0145] This embodiment uses a memristor neural network with random sensor time delay and multiple indicators as an example. Besides this, the technology can also be applied to digital circuit design, chaotic system control, image processing optimization, color digital image restoration, and associative memory construction. The breakthrough from theoretical proposal to physical implementation of memristors has provided a new direction for artificial neural networks to overcome existing development bottlenecks. Neural networks built based on memristors possess characteristics similar to those of biological brain neural networks, enabling multi-task parallel processing. Crucially, they do not require repeated data migration when processing massive amounts of data, a core performance that makes them particularly suitable for machine learning systems. Therefore, the method described in this invention was used to conduct simulation verification for relevant digital circuit applications in practical situations.

[0146] First, to demonstrate the feasibility of the proposed memristor neural network state estimation algorithm under multiple indices, a practical example is selected to verify the key theoretical results. In the circuit implementation of the neural network connection part, replacing the resistor with a memristor allows the construction of a memristor-based neural network; under this premise, according to Kirchhoff's circuit laws, the first... Subsystem equations of a circuit:

[0147]

[0148] In the formula, This refers to the actual measured capacitance value. and For actual parallel weighted resistors, This represents the actual measured value of the parallel resistance. and These represent the magnitudes of the actual delay connection weight resistors and the connection weight matrix weight resistors, respectively. for The state of the subsystem at any given moment. Let be the excitation function of the subsystem. The weight component matrix of the subsystem. Let be the noise component matrix of the subsystem, and let the sign function satisfy the following condition:

[0149]

[0150] In the formula, This represents a symbolic function. This indicates an inequality sign.

[0151] Furthermore, the actual model of the memristor neural network constructed according to the algorithm proposed in this invention is as follows:

[0152]

[0153] In the formula, , and They are respectively , and In the The first moment One portion, for The state of the subsystem at any given moment. Let be the excitation function of the subsystem. The weight component matrix of the subsystem. Let be the noise component matrix of the subsystem.

[0154] Furthermore, based on the state of digital circuits in physics, a corresponding adjustment matrix is ​​given. Consider the following relevant parameter matrix for the neural network system:

[0155]

[0156] The measurement adjustment matrix is ​​as follows:

[0157]

[0158] The controlled output adjustment matrix is:

[0159]

[0160] The state weight matrix is:

[0161]

[0162]

[0163] The weight matrix and adjustment parameters of the nonlinear function are as follows:

[0164]

[0165] The activation function is taken as:

[0166]

[0167] In the formula, It is the state vector of the memristor neuron. In the first Moment State The first component weight matrix, In the first Moment State The second component weight matrix.

[0168] Other initial values ​​for the simulation are selected as follows:

[0169] Disturbance attenuation level The positive semi-definite matrix number one, positive semi-definite matrix number two, and positive semi-definite matrix number three are respectively , and Upper bound matrix The sum and covariance are respectively and initial state , .

[0170] The values ​​of the correlated estimator gain matrix are solved using recursive linear matrix inequalities, and some of the values ​​are shown below:

[0171] Case 1: ;

[0172]

[0173] Case II: ;

[0174]

[0175] State estimator effect:

[0176] Depend on Figure 2 As can be seen, for variance-constrained memristor neural networks with random sensor time delays, the state estimator design method of the present invention can effectively estimate the target state.

[0177] Depend on Figure 3 , Figure 4 , Figure 5 It can be seen that, for each moment, the estimation error deteriorates as the probability of sensor time delay increases.

Claims

1. A method for state estimation of a memristor neural network driven by random sensor time delay, characterized in that... The method includes the following steps: Step 1: Establish a system with random sensor time delay and H under variance constraints. ∞ A performance-constrained dynamic model of a memristor neural network; Step 2: Perform state estimation on the memristor neural network dynamic model established in Step 1 under variance constraints; Step 3: Given H ∞ Performance indicators positive semidefinite matrix No. 1 positive semidefinite matrix No. 2 The third positive semidefinite matrix and initial conditions and Calculate the upper bound of the error covariance matrix and H of the memristor neural network. ∞ The performance constraints are defined in the following steps: Step 3: Prove H according to the following formula. ∞ The performance analysis problem is presented, along with corresponding sufficient conditions that are easy to solve: In the formula: In the formula, For a given positive scalar; , , , , , , , , , , , , , They are respectively , , , , , , , , , , , , , Transpose of; In the first The positive semi-definite matrix at time 1; In the first The positive semi-definite matrix at time t; In the first The known matrix at time; In the first The matrix at a given time; In the first The known matrix at time; This represents the probability of random sensor time delay occurring, and It is a known scalar; yes The block matrix in the first row and first column, yes The block matrix in the first row and second column, yes The block matrix in the second row and second column, yes The block matrix in the 3rd row and 3rd column, yes The block matrix in the 4th row and 4th column, yes The block matrix in the 5th row and 5th column, yes The 6th row and 6th column of the matrix is ​​a block matrix, where 0 represents that all elements in the block are 0; It is the identity matrix; Step 3.2: Exploring the covariance matrix The problem involves upper bound constraints, and the following sufficient conditions are given: In the formula, In the formula, In the first The upper bound of the error covariance matrix at time t. In the first The upper bound matrix obtained at each step; In the first The upper bound of the error covariance matrix at time step; In the first The upper bound of the time error, In the first The trace of the upper bound matrix of the error covariance matrix at time t; In the first Error matrix at time step; The normal constant is known; The trace of the matrix, It is the first known variance matrix. It is the known second variance matrix; Analysis of the two results above shows that the system that guarantees the estimation error satisfies the given H. ∞ Sufficient conditions for performance requirements and the boundedness of error covariance; Step 4: Using stochastic analysis, the estimator gain matrix is ​​obtained by solving the following recursive linear matrix inequality. The value of is used to perform state estimation on a memristor neural network driven by random sensor time delays: The updated matrix is: In the formula, , , , , and In the first The normal values ​​of the first, second, third, fourth, fifth, and sixth adjustments at each moment; It is the first component in The first real matrix of appropriate dimension known at time t. It is the second component. The second real matrix of appropriate dimension known at time t; , , They are , , Transpose of; They are The inverse matrix; , , , and These are the measurement matrices numbered 1, 2, 3, 4, and 5, respectively. For unknown normal values, It is the first component in The first measure matrix of known appropriate dimension at time; It is the second component. The second metric matrix of known appropriate dimension at time; It is the third component. The third metric matrix of known appropriate dimension at time; It is the 4th component. The fourth metric matrix of known appropriate dimension at time; It is the 5th component. The fifth metric matrix of known appropriate dimension at time; It is a block matrix in the first row and first column. It is the block matrix in the 1st row and 2nd column. It is the block matrix in the 1st row and 3rd column. It is the block matrix in the 2nd row and 2nd column. It is the block matrix in the 2nd row and 3rd column. It is the block matrix in the 3rd row and 3rd column. It is the block matrix in the 1st row and 4th column. It is the block matrix in the 2nd row and 5th column. It is the block matrix in the 2nd row and 6th column. It is the block matrix in the 2nd row and 7th column. It is the block matrix in the 3rd row and 8th column. It is the block matrix in the 3rd row and 9th column. It is the block matrix in the 4th row and 4th column. It is the block matrix in the 5th row and 5th column. It is the block matrix in the 6th row and 6th column. It is the block matrix in the 7th row and 7th column. It is the block matrix in the 8th row and 8th column. It is a block matrix in the 9th row and 9th column. It is a block matrix in the first row and first column. It is the block matrix in the 1st row and 2nd column. It is the block matrix in the 1st row and 3rd column. It is the block matrix in the 1st row and 4th column. It is the block matrix in the 1st row and 5th column. It is the block matrix in the 2nd row and 2nd column. It is the block matrix in the 3rd row and 3rd column. It is the block matrix in the 4th row and 4th column. It is the block matrix in the 5th row and 5th column; and These are the known first matrix and the known second matrix, respectively. ; judge Has the total duration N been reached? If yes, proceed to step two; otherwise, end the process.

2. The memristor neural network state estimation method with random sensor time delay driven according to claim 1, characterized in that... In step one, the state-space form of the memristor neural network dynamic model is as follows: In the formula, , , These are the memristor neural networks at the 1st... , , The state variables of the time-delay memristor neural network at each time step; In the first The controlled measurement output at any given time; , In the first The initial value at time , The time delay exists in a discrete-time delay memristor neural network; In the first The self-feedback diagonal matrix of the memristor neural network at time step. In the first The weight matrix of the connection activation function at known time. In the first A system matrix with known dimensions at time points and dependent on time delays; In the first The nonlinear excitation function at time t; In the first The adjustment matrix for measurements at known times; In the first The adjustment matrix of the controlled output is known at all times; In the first The mean at time step is zero and the covariance is A Gaussian white noise sequence.

3. The memristor neural network state estimation method with random sensor time delay driven according to claim 2, characterized in that... The specific steps of step two are as follows: Step 2.1: The measurement output format of the memristor neural network is as follows: In the formula, It is the first The measurement output of the time-delay memristor neural network; It is a Gaussian white noise sequence with zero mean and covariance of . , In the first The time-known measurement outputs the right adjustment matrix; Represents the random variable i.e. Random sensor time delay phenomena that occur at any given moment In the first The noise distribution matrix of the system is known at any given time. Step 22: Nonlinear Excitation Function satisfy Bounded conditions for sectors: In the formula, and Represent the first and second known matrices of appropriate dimension. This represents the difference between two matrices. It is a positive definite symmetric matrix; Steps 2 and 3: State Dependency Matrix Parameters of Memristor Neural Networks , and satisfy: in, , Represents absolute value. express arrive Summation, , , Indicates capacitance. Indicates parallel resistance. and Let these represent the weight matrix and the connection weight matrix, respectively, representing the connection time delay. , , and These are the known first, second, third, and fourth constants. Represents a symbolic function; Step Two Four, Definition: In the formula, , , , , , , , , , , , These are the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, and twelfth stored variables, respectively. , , , This indicates taking the minimum value. This indicates taking the maximum value; make , and Then we can get: in In the formula, This represents the first uncertain matrix. This represents the second uncertainty matrix. This represents the third uncertainty matrix; Step 25: Based on the known information, design the following time-varying state estimator: In the formula, It is the memristor neural network in the first... State estimation at time 10:00 It is the memristor neural network in the first... State estimation at time 10:00 It is the memristor neural network in the first... State estimation at time; In the first State estimation of the controlled output at any given time. Let be the first matrix in the left and right intervals. This is the second matrix in the left and right intervals. Let be the third matrix in the left and right intervals. In the first State estimation of the nonlinear excitation function at time t. The estimator gain matrix is ​​the unknown. This indicates the probability of random sensor time delay phenomena occurring.

4. The memristor neural network state estimation method with random sensor time delay driven according to claim 3, characterized in that... In step two, the random sensor time delay phenomenon is described by a Bernoulli distributed random variable, which follows the statistical characteristics as follows: In the formula, Indicates the probability of an event occurring. This represents the probability of random sensor time delay occurring, and It is a known scalar.

5. The memristor neural network state estimation method with random sensor time delay driven according to claim 3, characterized in that... In steps two and three, the function The following conditions must be met: 。 6. The memristor neural network state estimation method with random sensor time delay driven according to claim 3, characterized in that... In step two or four, , and Satisfying norm-bounded uncertainty: In the formula, This represents the first uncertain matrix. This represents the second uncertainty matrix. This represents the third uncertainty matrix. and Both are known first and second real-valued matrices. This represents the first unknown matrix. This represents the second unknown matrix. Let the third unknown matrix satisfy... , .

7. The memristor neural network state estimation method with random sensor time delay driven according to claim 3, characterized in that... In step two or four, , , satisfy: , and ,in Indicates the first A column vector with 1 element and 0 elements. , and These are the unknown first scalar, the unknown second scalar, and the unknown third scalar, respectively.

Images