Nonlinear circuit model and circuit system networked control method

Abstract

The invention discloses a nonlinear circuit model and a circuit system networked control method, and belongs to the technical field of networked control. According to the networked control method for the nonlinear circuit system, a circuit model obeying Markov switching is provided, and a networked Markov jump neural network system is established based on a circuit model equation; the method comprises the following steps: establishing a closed-loop system based on a networked Markov jump neural network system, an asynchronous observation controller, a dynamic quantizer and a channel attenuation model; based on a Lyapunov function method, generating a criterion for ensuring the random stability and H-infinity performance of the closed-loop system; based on a criterion and a decoupling theorem, a design method of relevant parameters of a controller gain, an observer gain and a dynamic scaling factor is provided. According to the invention, behaviors of the circuit in actual operation can be simulated more accurately; and meanwhile, the dynamic scaling factor is designed into a piecewise function form, so that the normal operation of the dynamic quantizer can be effectively ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of networked control, and particularly relates to a non-linear circuit model and a method for networked control of a circuit system. Background Art

[0002] With the continuous improvement of the requirements for system complexity and dynamic response ability in engineering applications, non-linear circuits have gradually become a research hotspot. A non-linear circuit refers to a circuit in which the relationship between the input and output does not satisfy a linear relationship, that is, the change of the input signal cannot simply predict the output through linear superposition or proportional relationship. Such circuits are usually composed of basic circuit elements (such as resistors, capacitors, operational amplifiers, etc.) and non-linear components (such as semiconductor devices, non-linear activation function units, etc.). Among them, the non-linear activation function unit can realize non-linear mapping similar to biological neurons, enabling the circuit to have functions such as pattern recognition and adaptive regulation. Therefore, non-linear circuits have extensive application value in the fields of signal processing, neural network simulation, power electronics, and intelligent control.

[0003] However, it should be noted that in actual circuits, the value of the capacitor is not constant, but is affected by various factors, including dielectric constant fluctuations caused by temperature changes, aging phenomena after long-term use of devices, polarization effects and dielectric aging caused by compressive stress, load mutations or switching of switching modes. However, in such circuit models, researchers often ignore the influence brought by the above capacitor changes and design the value of the capacitor to remain unchanged. Specifically, such as the circuit model in Document 1: V.E. Sathishkumar, R. Vadivel, Jaehyuk Cho, Nallappan Gunasekaran, Exploring the finite-time dissipativity of Markovian jump delayed neural networks, Alex. Eng. J. 79 (2023) 427–437, which will affect the accuracy and applicable range of the circuit model.

[0004] In addition, with the increasing complexity of circuit systems, traditional modeling methods often have certain limitations in dealing with non-linear, time-varying, and multi-mode circuit behaviors. Many circuit systems, especially those with dynamic response, signal interaction, and external interference, do not have a simple linear relationship in their behaviors, but involve multiple non-linear factors. In order to effectively deal with these complex dynamic characteristics, neural networks can be used to model the circuit system for more accurate analysis.

[0005] In recent years, Markov jump neural networks have gradually become a research hotspot in the field of control. Researchers have proposed various control methods, such as state feedback control, output feedback control, robust control, etc. These methods have achieved remarkable results in different application scenarios. However, in practical engineering applications, there are real factors such as time delay, which may lead to the unmeasurability of the state of the Markov neural network system. Therefore, the control method based on the state observer is very important, which can effectively estimate the unmeasurable system state and provide necessary information for the control feedback of the Markov neural network system.

[0006] With the rapid development of computer technology, traditional control methods have gradually merged with network technology to form a networked control architecture. In this architecture, the Markov neural network system is connected to sensors, actuators, and controllers distributed in various places through a communication network, realizing efficient cooperative control. Compared with the traditional control method, the networked control architecture has stronger scalability and flexibility.

[0007] In a networked control environment, due to bandwidth and throughput limitations, it is usually necessary to quantize the signal before transmission to reduce the burden on the communication network. Quantization reduces the amount of data to be transmitted by mapping continuous signals to discrete signals, thereby optimizing the utilization efficiency of the bandwidth. Quantizers are mainly divided into static quantizers and dynamic quantizers. Compared with static quantizers, dynamic quantizers have greater potential in preventing saturation and maintaining key performance. This is because dynamic quantizers introduce a dynamic scaling factor that can adjust the quantization threshold in real time to more flexibly handle signal changes. However, when the quantized signal is zero, it will cause the quantizer to malfunction, thus unable to effectively ensure the stability and reliability of the networked control of the nonlinear circuit system. Summary of the Invention

[0008] The first object of the present invention is to provide a nonlinear circuit model, so as to solve the technical problem that the existing nonlinear circuit model usually ignores the influence brought by the actual change of the capacitance, thus affecting the accuracy and applicable range of the circuit model;

[0009] The second object of the present invention is to provide a networked control method for a nonlinear circuit system, so as to solve the influence of the abnormal operation of the dynamic quantizer on the circuit safety control in the prior art, and can effectively ensure the stochastic stability and H ∞ performance.

[0010] To achieve the above object, the technical solution provided by the present invention is as follows:

[0011] The first aspect of the present invention provides a non - linear circuit model, which includes: the circuit model is composed of two symmetric loops, and each loop includes an activation function unit, a controller, an operational amplifier, a capacitor, a resistor, a bias current source, and a time - delay unit, where:

[0012] The operational amplifier, together with two capacitors and a resistor, forms an integrator for the dynamic evolution of state variables x1(t) and x2(t), and the switching of the capacitors is controlled by a Markov chain;

[0013] The controller is connected in parallel to the input and output ends of the integration circuit, used to generate control input signals u1(t) and u2(t), and adjust the input through a feedback mechanism;

[0014] The activation function unit constructs two different feedback channels for the system state. The first channel is directly connected in parallel to the input and output ends of the integration - summation circuit, used for non - linear transformation of the integrated state variables x1(t) and x2(t). The second channel is connected in series with the time - delay unit and then connected in parallel to the input and output ends of the integration - summation circuit; the time - delay unit introduces a time - delay α(t), so that the current state of the neuron is affected not only by the current input but also by the past state, and can be used to simulate the short - term memory ability of the neuron;

[0015] R 11 b 11 ,R 12 b 12 ,R 21 b 21 ,R 22 b 22 and R α11 v 11 ,R α12 v 12 ,R α21 υ 21 ,R α22 v 22 constitute a resistor network to achieve weighted connection between neurons;

[0016] The bias current source represents the external stimulus received by the neural network.

[0017] Based on the existing circuit model, the present invention fully considers the influence brought by the capacitance change. By introducing the Markov jump characteristic, a circuit model subject to Markov switching is proposed, so that the behavior of the circuit in actual operation and the capacitance change under different operation modes can be more accurately simulated, and thus the accuracy and application range of the circuit system model can be improved.

[0018] The second aspect of the present invention also provides a networked control method for a non-linear circuit system. Based on the circuit model described in the first aspect of the present invention, the specific control method includes:

[0019] Based on the circuit model equation, establish a networked Markov jump neural network system;

[0020] Establish an asynchronous controller based on an observer;

[0021] Establish a dynamic quantizer;

[0022] Establish a channel attenuation model;

[0023] Based on the networked Markov jump neural network system, asynchronous observer controller, dynamic quantizer, and channel attenuation model, establish a closed-loop system;

[0024] Based on the Lyapunov function method, generate criteria to ensure the stochastic stability and H ∞ performance of the closed-loop system;

[0025] Based on the criteria and decoupling theorem, propose a design method for the controller gain, observer gain, and related parameters of the dynamic scaling factor.

[0026] Specifically, the circuit model equation of the present invention is:

[0027]

[0028] where m ∈ {1, 2}, n ∈ {1, 2}, R m , R mn , R αmn represent resistors, b mn and v mn are used to describe the current direction between different electric potentials. If m = n, then b mn = v mn = -1; otherwise, b mn = v mn = 1; α(t) represents a time-varying time delay, C m represents the capacitance related to the mode, is the activation function; θ(t) is a Markov chain process, θ(t) = {1,..., a}.

[0029] Based on the above circuit model, the present invention further constructs a networked Markov jump neural network system. The Markov jump neural network is a type of neural network model that depends on the Markov random process. By introducing the state switching mechanism in the Markov process, it can accurately simulate the dynamic behavior of the system in multiple different states, and is particularly suitable for describing systems with complex dynamic characteristics and random changes. According to the control method described in the second aspect of the present invention, the constructed networked Markov jump neural network system is specifically as follows:

[0030]

[0031] Wherein, respectively represent the state variable, control input, disturbance input, measurement output, and control output; A θ(t) , B θ(t) , C θ(t) , B α,θ(t) , D 1,θ(t) , E 1,θ(t) , E 2,θ(t) , D 2,θ(t) are all system parameter matrices; α(t) represents the time-varying time delay.

[0032] Furthermore, the transition probability of θ(t) is:

[0033]

[0034] Furthermore, the obtained observer-based asynchronous controller is established as follows:

[0035]

[0036] Wherein, represents the observed state, represents the output reaching the observer, and respectively represent the observer gain and the controller gain. represents the observed measurement output, r(t) is a random process, r(t) = {1,..., b}, and its conditional transition probability is:

[0037]

[0038] Furthermore, the dynamic quantizer Q d (y(t)) is used to quantize the measurement output y(t), and its mathematical expression is as follows:

[0039]

[0040] Wherein, Let \(q(\cdot)\) denote a static quantizer with \(q(0) = 0\) and satisfying the following conditions:

[0041] \(\vert q(\zeta)-\zeta\vert\leq\omega\) q , \(\vert\zeta\vert\leq\omega\) s ,

[0042] \(\vert q(\zeta)-\zeta\vert>\omega\) q , \(\vert\zeta\vert>\omega\) s ,

[0043] \(\omega\) q \(\in\mathbb{R}\) + and \(\omega\) S \(\in\mathbb{R}\) + represent the quantization error bound and the quantization saturation threshold respectively.

[0044] In a networked control environment, due to bandwidth and throughput limitations, signals usually need to be quantized before transmission to reduce the burden on the communication network. Quantization maps a continuous signal to a discrete signal, thereby reducing the amount of data to be transmitted and optimizing the bandwidth utilization efficiency. Quantizers are mainly divided into static quantizers and dynamic quantizers. Since dynamic quantizers introduce a dynamic scaling factor and can adjust the quantization threshold in real time to more flexibly handle signal variations, dynamic quantizers have greater potential in preventing saturation and maintaining key performance compared to static quantizers.

[0045] However, since is in the denominator position, if is 0, then \(Q\) d (y(t)) cannot operate properly. The influence of this point is usually ignored in the prior art. Therefore, to overcome the above defects, the present invention further improves and designs it as the following piecewise function:

[0046]

[0047] where is a parameter related to the dynamic scaling factor.

[0048] By optimizing the design of the dynamic scaling factor, that is, designing it as a piecewise function, the normal operation of the dynamic quantizer can be effectively guaranteed, preventing adverse effects on the circuit safety control caused by its abnormal operation, and thus being beneficial to ensuring the stochastic stability and \(H\) ∞ performance.

[0049] Furthermore, the measured output quantized by the dynamic quantizer is affected by channel attenuation, and its mathematical model is:

[0050]

[0051] Among them, φ(t) represents an additional perturbation input, and β(t) ∈ [0, 1] represents a decay coefficient, and its expected value is:

[0052] Furthermore, the observer-based asynchronous controller is introduced into the established Markov jump neural network, and the following closed-loop system is obtained:

[0053]

[0054] Among them, the respective system parameter matrices are:

[0055]

[0056] Furthermore, the criteria for ensuring the stochastic stability and H ∞ performance are:

[0057] Given scalars γ > 0, β > 0, if there exist scalars ∈ > 0, matrices Q > 0, Λ1 > 0, Λ2 > 0 such that holds, then the closed-loop system has stochastic stability and H ∞ performance index; where:

[0058]

[0059] Furthermore, the design methods of the controller gain, observer gain, and related parameters of the dynamic scaling factor are as follows:

[0060] Given scalars γ > 0, β > 0, if there exist matrices Q > 0, Λ1 > 0, Λ1 > 0, X kj ,X lj ,Y ki ,Y lj such that holds, then the asynchronous controller gain and observer gain are respectively: The range of the related parameters of the dynamic scaling factor is Among them,

[0061]

[0062] Adopting the technical solution provided by the present invention, compared with the prior art, it has the following beneficial effects:

[0063] (1) The present invention proposes a circuit model subject to Markov switching. Since the influence brought by the capacitance change in the actual circuit is fully considered, it can more accurately simulate the behavior of the circuit in actual operation, thereby improving the accuracy and application scope of the circuit system model.

[0064] (2) Based on the above new circuit model, the present invention also provides a networked control method for a non-linear circuit system. By introducing a dynamic quantizer and designing the dynamic scaling factor in the form of a piecewise function, it can not only effectively save communication channel resources, but also overcome the defect that the dynamic quantizer cannot operate normally when the dynamic scaling factor is zero, ensuring the stability and reliability of the circuit safety control.

[0065] (3) The present invention fully considers the influence of channel fading on data transmission. By establishing a channel attenuation model, it is beneficial to further improve the stability of the control system. At the same time, by designing reasonable controller gain, observer gain and related parameters of the dynamic scaling factor, the closed-loop system is stochastically stable and has H ∞ performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 is a flowchart of the networked control method for the circuit system according to an embodiment of the present invention;

[0067] Figure 2 is a framework diagram of the networked Markov jump neural network system according to an embodiment of the present invention;

[0068] Figure 3 is a circuit model structure diagram according to an embodiment of the present invention;

[0069] Figure 4 is an open-loop Markov jump neural network state trajectory diagram according to an embodiment of the present invention;

[0070] Figure 5 is a closed-loop Markov jump neural network state trajectory diagram according to an embodiment of the present invention;

[0071] Figure 6 is a measurement output quantization error and error upper bound diagram according to an embodiment of the present invention;

[0072] Figure 7 is the H ∞ performance index function trajectory diagram according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0073] Combined with Figure 3As shown, the neural network simulation circuit of the present invention is used to study the dynamic behavior of the neural network. It consists of two symmetric loops. For the sake of simplicity in introduction, a single loop will be introduced here. Taking the loop where x1(t) is located as an example, the main body of this loop is a capacitive-resistive integration and summation circuit, which is composed of four parallel resistors R 11 , R 21 , R α11 , R α12 , capacitor C 11 , capacitor C 12 , an activation function unit, a controller, and a time-delay unit. Among them:

[0074] Capacitor C 11 , capacitor C 12 , resistor R1, and an operational amplifier are connected in parallel to form an integration circuit to realize the dynamic evolution of the state variable x1(t), and the switching of the capacitor is controlled by a Markov chain;

[0075] The controller is connected in parallel to the input end and the output end of the integration circuit, used to generate the control input signal u1(t), and correct the error between the output signal and the input signal through an internal feedback adjustment mechanism to realize functions such as system stability adjustment;

[0076] The activation function unit constructs two different feedback channels for the system state. The first channel is directly connected in parallel to the input end and the output end of the integration and summation circuit, used to perform non-linear transformation on the state variables x1(t) and x2(t) to simulate the activation characteristics of neurons; the second channel is connected in series with the time-delay unit and then connected in parallel to the input end and the output end of the integration and summation circuit; the time-delay unit introduces a time delay α(t), so that the current state of the neuron is affected not only by the current input but also by the past state, which can be used to simulate the short-term memory ability of neurons;

[0077] R 11 b 11 , R 21 b 21 , and R α11 υ 11 , R α12 υ 12 constitute a resistor network to realize the weighted connection between neurons;

[0078] The bias current source represents the external stimulus received by the neural network, thus used to study the influence of the external environment on the dynamics of the neural network.

[0079] Based on the existing circuit model, the embodiment of the present invention considers the influence of capacitance change on the circuit, and thus proposes a new circuit model subject to Markov switching, which can accurately simulate the behavior of the circuit in actual operation.

[0080] The present invention further provides a method for networked control of a circuit system. Based on the above circuit model subject to Markov switching, as Figure 1 shown, the control method includes:

[0081] Establish a networked Markov jump neural network system based on the circuit model equation;

[0082] Establish an asynchronous controller based on an observer;

[0083] Establish a dynamic quantizer;

[0084] Establish a channel attenuation model;

[0085] Based on the networked Markov jump neural network system, asynchronous observer controller, dynamic quantizer, and channel attenuation model, establish a closed-loop system;

[0086] Based on the Lyapunov function method, generate criteria for ensuring the stochastic stability and H ∞ performance of the closed-loop system;

[0087] Based on the criteria and decoupling theorem, propose a design method for the parameters related to the controller gain, observer gain, and dynamic scaling factor.

[0088] Among them, the specific process of establishing the networked Markov jump neural network system is as follows:

[0089] First, based on the circuit model, establish the Markov switching circuit model equation as follows:

[0090]

[0091] where m ∈ {1, 2}, n ∈ {1, 2}, R m , R mn , R αmn represents resistance, b mn and v mn are used to describe the current direction between different electric potentials. If m = n, then b mn = v mn = -1, otherwise b mn = v mn = 1; α(t) represents the time-varying time delay, C m represents the capacitance related to the mode, is the activation function; θ(t) is the Markov chain process.

[0092] Then, perform mathematical operations on the Markov switching circuit model equation to obtain the following networked Markov jump neural network system:

[0093]

[0094] Among them, represent the state variable, control input, disturbance input, measurement output, and control output respectively, is the derivative of x(t).

[0095] A θ(t) , B θ(t) , C θ(t) , B α,θ(t) , D 1,θ(t) , E 1,θ(t) , E 2,θ(t) , D 2,θ(t) are all known system parameter matrices, specifically as follows:

[0096]

[0097] Furthermore, θ(t) is a Markov chain, and its transition probability is:

[0098]

[0099] α(t) represents a time-varying time delay, is an activation function, and they respectively satisfy Assumption 1 and Assumption 2.

[0100] Assumption 1: α(t) is a continuous function and satisfies the condition:

[0101]

[0102] where α and are all known constants.

[0103] Assumption 2: There exists a matrix such that

[0104]

[0105] holds, where k ∈ {1, …, n x} and μ1, μ2 are constants and μ1 ≠ μ2.

[0106] Furthermore, in the embodiment of the present invention, an observer-based asynchronous controller is established, and the specific process is as follows:

[0107]

[0108] Among them, represents the observed state, is the derivative of; represents the output reaching the observer, and represent the observer gain and the controller gain respectively. Denote the observed measurement output. r(t) is a random process with conditional transition probability as follows:

[0109]

[0110] Furthermore, the specific process of establishing the dynamic quantizer in the present invention is as follows:

[0111] After the measurement output y(t) is quantized, its mathematical expression is:

[0112]

[0113] where Q d (y(t)) represents the dynamic quantizer, and its mathematical expression is as follows:

[0114]

[0115] Here q(·) represents the static quantizer, q(0) = 0, and satisfies the following conditions:

[0116] |q(ζ) - ζ| ≤ ω q , |ζ| ≤ ω s , (4)

[0117] |q(ζ) - ζ| > ω q , |ζ| > ω s , (5)

[0118] ω q ∈R + and ω s ∈R + represent the quantization error bound and the quantization saturation threshold respectively.

[0119] As can be seen from equation (3), is in the denominator position. If is 0, then Q d (y(t)) cannot operate properly. This point is usually not considered in the prior art, thus affecting the normal operation of the quantizer. To improve this defect, the present invention further improves as follows:

[0120] is the dynamic scaling factor, and the present invention further designs it as the following piecewise function:

[0121]

[0122] where is a parameter related to the dynamic scaling factor.

[0123] Let ey Q(t)=Q d Let the quantization error be denoted as (y(t)) - y(t). Then, according to formulas (3), (4), and (5), it can be deduced that:

[0124]

[0125] According to the control method described in any technical solution of the present invention, the specific process of establishing the channel attenuation model is as follows:

[0126] The measured output after quantization is affected by channel attenuation, and its mathematical model is:

[0127]

[0128] where φ(t) represents an additional disturbance input, β ∈ [1, 0] represents the attenuation coefficient, and its expected value is:

[0129]

[0130] Furthermore, the specific process of establishing the closed-loop system is as follows:

[0131] Bring the asynchronous controller into the Markov jump neural network to obtain the closed-loop system:

[0132]

[0133] where, to simplify the mathematical process, θ(t) is denoted as i 1, θ(t + Δ) is denoted as i2, and r(t) is denoted as j. Then:

[0134]

[0135]

[0136] Furthermore, the specific process of generating the performance criterion to ensure the stochastic stability and H ∞ performance of the closed-loop system is as follows: When If:

[0137]

[0138] holds, then the closed-loop system (7) is said to be stochastically stable.

[0139] Under zero initial conditions, if there exists a scalar γ > 0 such that:

[0140]

[0141] holds, then the closed-loop system is said to have H ∞ performance, where Denote the expected value.

[0142] The selected Lyapunov function is where:

[0143]

[0144] Denote as the infinitesimal generator of the stochastic process, and its specific expression is:

[0145]

[0146] For any θ(t) = i, using (8) we can obtain:

[0147]

[0148] When the closed-loop system (7) is:

[0149]

[0150] where Substitute (11) into (10) and find its expected value:

[0151]

[0152] Find the infinitesimal operator for (9), and we can obtain:

[0153]

[0154] According to Assumption 2, (13) can be written as:

[0155]

[0156] According to Assumption 1, it can be concluded that:

[0157]

[0158]

[0159] where, Λ1 and Λ2 are unknown positive definite diagonal matrices, and Λ f is a known positive definite diagonal matrix.

[0160] Introduce the constraint condition of the quantization dynamic scaling factor:

[0161]

[0162] where,

[0163] From formulas (12), (14), (15), (16) and (17), we can obtain:

[0164]

[0165] where

[0166] When holds, then we have

[0167]

[0168] where λ min (·) represents the minimum eigenvalue.

[0169] The Dynkin formula is:

[0170]

[0171] Based on (18) and the Dynkin formula, we can deduce:

[0172]

[0173] From (19), we can deduce:

[0174]

[0175] When t → ∞, we can obtain: Then the closed-loop system (7) is stochastically stable. Under zero initial conditions,

[0176]

[0177] where

[0178] If holds, then we can obtain:

[0179]

[0180] Thus, it can be known that the closed-loop system (7) has stochastic stability and H ∞ performance index.

[0181] Therefore, the criteria for ensuring the stochastic stability and H ∞ performance of the closed-loop system (7) are summarized as follows:

[0182] Given scalars γ > 0, β > 0, if there exist scalars ∈ > 0, matrices Q > 0, Λ1 > 0, Λ2 > 0 such that is established, the closed-loop system has stochastic stability and H ∞ performance index.

[0183] Furthermore, based on the criterion and the decoupling theorem, the specific process of the design method for the parameters related to the controller gain, observer gain, and dynamic scaling factor is as follows:

[0184] The dynamic scaling factor is designed as:

[0185]

[0186] And the parameter satisfies the following conditions:

[0187]

[0188] Based on the above conditions, it can be concluded that:

[0189]

[0190] Therefore, it can be obtained that

[0191] The controller gain and observer gain are respectively designed as

[0192] The decoupling theorem is used here as follows:

[0193] For any scalar ρ ι > 0, matrices W, U ι , V ι and X ι (ι = 1,..., m), if and only if

[0194]

[0195] is established, the following inequality holds:

[0196]

[0197] Where:

[0198] W1 = [U1 + ρ1V1…U m + ρ m V m

[0199] W2 = diag{-ρ1He(X1),…,-ρ m He(X m )}

[0200] The matrix can be written as:

[0201]

[0202] Among them:

[0203]

[0204] According to the decoupling theorem and (20), it can be written as:

[0205]

[0206] Among them:

[0207]

[0208]

[0209] Therefore, the design methods for the controller gain, observer gain, and the parameters related to the dynamic scaling factor are as follows:

[0210] Given γ>0, β>0, if there exist matrices Q>0, Λ1>0, Λ2>0, X kj , X lj , Y kj , Y lj such that (21) holds, then the asynchronous controller gain and observer gain are respectively The range of the parameters related to the dynamic scaling factor is

[0211] To further understand the content of the present invention, the present invention will now be described in detail in conjunction with specific embodiments.

[0212] First, the circuit model equations established in the embodiments of the present invention are as follows:

[0213]

[0214] Among them, m∈{1,2}, n∈{1,2}, R m , R mn , R αmn represents resistance, C mi represents the capacitance related to the mode, b mn and v mn are used to describe the current direction between different electric potentials. If m = N, then b mn = v mn = -1, otherwise b mn = v mn = 1; in this embodiment, θ(t) = {1,2}, r(t) = {1,2}.

[0215] The parameter values of each component in the circuit are given as follows:

[0216] C 11 = 1, C 12 = 0.8, C 21 = 0.9, C 22 = 1, R 11 = 0.5, R 12 = 0.4, R 21 = 1.25,

[0217] R 22 = 5, R α11 = 2, R α12 = 2.5, R α21 = 10, R α22 = 0.4, R1 = 1, R2 = 1.

[0218] Then, performing mathematical operations on the circuit model equations, the following networked Markov jump neural network system can be obtained:

[0219]

[0220] Among them,

[0221]

[0222] Other parameters related to the mode are given as:

[0223]

[0224] E 2,1 = [0.1 -0.1], E 2,2 = [0.11 -0.11],

[0225] D 2,1 = [0.2 -0.2], D 2,2 = [0.1 -0.1].

[0226] The transition probability matrix and the conditional probability matrix are respectively set as

[0227]

[0228] The expected value of the channel attenuation coefficient β(t) is given as The quantization saturation threshold and the quantization error bound are respectively ω s = 0.3, ω q = 30, the decoupling parameter is ρ k = ρ l = 0.1.

[0229] Given γ = 0.3986, using MATLAB and the MOSEK toolbox to solve the linear matrix inequality, the controller gain and the observer gain can be obtained respectively as:

[0230]

[0231] Parameters related to the dynamic scaling factor In the simulation, the initial state is given as The activation function is given as The disturbances ω(t) and φ(t) are given respectively as:

[0232] ω(t) = [2.5e -0.15t sin(0.1πt) 2.5e -0.25t sin(0.3πt)] T

[0233] φ(t) = [5.5e -0.1t sin(0.5πt) 1.5e -0.7t sin(0.6πt)] T

[0234] As Figure 4 shown, the state trajectory of the open-loop circuit system is oscillatory, indicating that the circuit system is unstable without the action of a controller. According to Equation (6), define:

[0235]

[0236] Then, under the proposed dynamic quantization controller, the trajectories of Q e1 (t) and Q e2 (t) are as Figure 5 shown. Obviously, the values of these two functions are non-negative, thus indicating that the dynamic quantizer designed in the embodiment of the present invention is effective. Under the action of the controller, the state trajectory of the closed-loop system is as Figure 6 shown. It can be seen that when t → ∞, the state trajectory tends to zero. In order to characterize the H ∞ performance level, let:

[0237]

[0238] Figure 7 depicts the evolution curve of γ(t) under zero initial conditions. It can be observed that the maximum value of γ(t) is 1.957 (<γ = 0.3986). Therefore, it can be shown that the controller designed in the present invention can ensure the stochastic stability and H ∞ performance of the closed-loop system.

Claims

1. A nonlinear circuit model, characterized in that: The circuit model consists of two symmetrical loops, each of which includes an activation function unit, a controller, an operational amplifier, a capacitor, a resistor, a bias current source, and a time-delay unit, where: The operational amplifier, two capacitors and a resistor together form an integrator for the dynamic evolution of state variables x1(t) and x2(t), and the switching of the capacitors is controlled by the Markov chain; The controller is connected in parallel to the input and output of the integration circuit, and is used to generate control input signals u1(t) and u2(t), and adjust the input through a feedback mechanism; The activation function unit constructs two different feedback channels for the system state. The first channel is directly connected in parallel to the input and output of the integral summation circuit to perform nonlinear transformation on the integrated state variables x1(t) and x2(t). The second channel is connected in series with the time-delay unit and then connected in parallel to the input and output of the integral summation circuit. R 11 b 11 ,R 12 b 12 ,R 21 b 21 ,R 22 b 22 and R α11 υ 11 ,R α12 υ 12 ,R α21 υ 21 ,R α22 v 22 Form a resistor network to achieve weighted connections between neurons; The bias current source represents the external stimulus received by the neural network.

2. A circuit system network control method, characterized in that: Based on the circuit model described in claim 1, the control method specifically includes: Based on the circuit model equation, a networked Markov jump neural network system is established; Building observer-based asynchronous controllers; Building a dynamic quantizer; Establish channel attenuation model; A closed-loop system is established based on a networked Markov jump neural network system, an asynchronous observation controller, a dynamic quantizer, and a channel attenuation model; Based on the Lyapunov function method, the generated closed-loop system is guaranteed to be stochastically stable and H ∞ Performance criteria; Based on the criterion and decoupling theorem, a design method for controller gain, observer gain and dynamic scaling factor related parameters is proposed.

3. The control method according to claim 2, characterized in that: The resulting networked Markov jump neural network system is established as follows: in, Respectively represent state variables, control input, disturbance input, measurement output and control output; A θ(t) ,B θ(t) ,C θ(t) ,B α,θ(t) ,D 1,θ(t) ,E 1,θ(t) ,E 2,θ(t) ,D 2,θ(t) are all system parameter matrices; α(t) represents the time-varying delay, is the activation function; θ(t) is the Markov chain process.

4. The control method according to claim 3, wherein the observer-based asynchronous controller is established as follows: in, represents the observed state, represents the output reaching the observer, and represent the observer gain and controller gain respectively; represents the observed measurement output; r(t) is a random process with the conditional transition probability:

5. The control method according to claim 4, characterized in that: The dynamic quantizer Q d (y(t)) is used to quantify the measured output y(t), and its mathematical expression is as follows: in, q(·) represents a static quantizer, q(0) = 0, and satisfies the following conditions: |q(ζ)-ζ|≤ω q ,|ζ|≤ω s , |q(ζ)-ζ|>ω q ,|ζ|>ω s , ω q ∈R + and ω s ∈R + Represent the quantization error limit and quantization saturation threshold respectively, is the dynamic scaling factor, which is expressed as follows: in, is a parameter related to the dynamic scaling factor.

6. The control method according to any one of claim 5, characterized in that: The measured output after quantization by the dynamic quantizer Affected by channel attenuation, its mathematical model is: Among them, φ(t) represents the additional disturbance input, β(t)∈[0,1] represents the attenuation coefficient, and its expected value is:

7. The control method according to claim 6, characterized in that: By introducing the observer-based asynchronous controller into the established Markov jump neural network, the following closed-loop system is obtained: Among them, the system parameter matrices are:

8. The control method according to claim 7, characterized in that: Ensure the closed-loop system is stochastically stable and H ∞ The performance criteria are: Given scalars γ>0, β>0, if there exists a scalar ∈>0, the matrix Q>0, Λ1>0, Λ2>0 makes If holds, the closed-loop system has stochastic stability and H ∞ Performance indicators; in:

9. The control method according to claim 8, characterized in that: The design method of the controller gain, observer gain and dynamic scaling factor related parameters is as follows: Given scalars γ>0, β>0, if there exists a matrix Q>0, Λ1>0, Λ1>0, X kj , X lj , Y kj , Y lj Make If holds, the asynchronous controller gain and observer gain are: The dynamic scaling factor related parameters range is in:

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