Search

CN-121477626-B - Finite time synchronous control method for fuzzy cell neural network

CN121477626BCN 121477626 BCN121477626 BCN 121477626BCN-121477626-B

Abstract

The invention discloses a finite time synchronous control method of a fuzzy cell neural network, which relates to the technical field of new generation information, solves the technical problems that stability analysis is too conservative and difficult to accurately evaluate system stability caused by neglecting discontinuous items, and the finite time synchronous control effect is influenced due to the lack of synchronous time estimation aiming at different scenes, converts a synchronous target into 'error system finite time stable' through stability analysis, can quickly solve the gain of a controller by combining the distributed parallel computing capability of a multi-film structure, shortens synchronous convergence time, and can definitely 'maximum synchronous time boundary' through theoretical deduction, thereby being convenient for quantitatively evaluating control efficiency in engineering. For discontinuous activation functions or time-varying parameters, system stability is more accurately assessed by calculating the Lyapunov function derivative range under Filippov set value descriptions.

Inventors

  • DUAN LIAN
  • SU ZHENGHUI

Assignees

  • 安徽理工大学

Dates

Publication Date
20260512
Application Date
20251106

Claims (10)

  1. 1. The finite time synchronous control method of the fuzzy cellular neural network is characterized by comprising the following steps of: Establishing a drive-response fuzzy cell neural network FCNNs pair with a time-varying coefficient and time-lag, and setting an activation function constraint condition, including a discontinuous constraint and a generalized Lipschitz condition; constructing a stability analysis model of the multi-membrane structure controller, wherein the analysis model equates the problem of finite time synchronization of a driving-responding system with the problem of stability of an error system converged to zero in finite time, and simultaneously equates a driving system and a corresponding responding system in a management area to the same node, and calculates the relevance among all the nodes; Calculation of the decomposition of stability problems and control tasks into sub-membranes of the stability analysis model, comprising: the surface film is responsible for receiving driving system state data, responding to the system state data and time lag data and carrying out quantization pretreatment on the state data; the finite time control film is used for parallelly calculating control signals of all nodes according to the output of the surface film, the relevance among all nodes and an error system of the self-adaptive time lag feedback controller; the synchronous time analysis film is used for classifying the scenes according to the stability requirement that the error systems of different scenes converge to zero in a limited time and analyzing time synchronous estimation of different scene classifications; and the stability analysis film is used for verifying the stability of the analysis system through verifying Filippov solutions of an error system and carrying out derivative estimation on the Lyapunov function, and simultaneously verifying the limited time convergence according to the parameter constraint of the controller and the time synchronization estimation.
  2. 2. The method of claim 1, wherein establishing a drive-response fuzzy cellular neural network FCNNs pair with time-varying coefficients and time-lags comprises: A driving system: the driving system describes state evolution of n neurons, and considers time lag, fuzzy operation and discontinuous activation functions, wherein the formula is as follows: Wherein xi (t) is the state of the ith neuron at time t, i is the current neuron number, i epsilon (1, 2.,. The sum of n, n) is the sum variable, j is the sum variable, all n nodes are traversed, n is the total number of neurons of the system, ci is the passive attenuation rate of the neuron state, represents the return-to-zero rate of the state without input, aij is a feedback template parameter, bij is a feedforward template parameter, alpha ij is a fuzzy feedback MIN template parameter, beta ij is a fuzzy feedback MAX template parameter, tij is a fuzzy feedforward MIN template parameter, sij is a fuzzy feedforward MAX template parameter, lambda sum is a fuzzy AND/OR operation, vi is the neuron input, ii is the neuron bias, tau j (t) is the maximum time lag, fj ) And fj% ) Each representing a discontinuous activation function, τj (t) =e t /(1+e t ); and (3) a response system: the response system takes the driving system as a reference, introduces a synchronous controller ui (t), and the formula is as follows: Where yi (t) is the state of the ith neuron of the response system, ui (t) is the finite time synchronization controller to be designed, and the goal is to make yi (t) track xi (t) in finite time.
  3. 3. The method for finite time synchronization control of a fuzzy cellular neural network according to claim 1, wherein the setting of the activation function constraint conditions includes a discontinuity constraint and a generalized Lipschitz condition, comprising: The discontinuous constraint is that the activation function is in any tight interval, the number of discontinuous points is limited, the discontinuous points are discontinuous only at a plurality of isolated points, and each discontinuous point has a limited left limit and a limited right limit; The generalized Lipschitz condition is that the activation function has non-negative constants Lj and Qj, and for any x, y E R, if gamma E co [ fj (x) ], eta E co [ fj (y) ], gamma-eta E is equal to or less than Lj|x-y|+Qj, wherein co [ ] represents a convex hull, the convex hull co [ fj (x) ] is a single point { fj (x) } at a continuous point, and at a discontinuous point, the activation function is an interval [ min { fj (x-), fj (x+) }, max { fj (x-) } ].
  4. 4. The method for controlling finite time synchronization of a fuzzy cellular neural network according to claim 1, wherein the driving system and the corresponding response system in the management area are equivalent to the same node, and the correlation between the nodes is calculated, comprising the steps of: selecting a fixed time window [ T, t+T ], wherein T >0 is the time window length, and extracting a state sequence in the time window according to the driving system state data and the response system state data; Calculating the average value of the state sequences of all the nodes, calculating the Pearson correlation coefficient among all the nodes according to the obtained average value, and normalizing the Pearson correlation coefficient to obtain the correlation coefficient among the nodes; And setting the nodes with the inter-node relevance coefficient larger than the threshold value as relevant nodes.
  5. 5. The method for finite time synchronization control of a fuzzy cellular neural network according to claim 1, wherein the step of calculating control signals of nodes in parallel according to the correlation between the output of the surface layer membrane and each node and the error system of the adaptive time-lag feedback controller comprises the steps of: defining a state error ei (t) =yi (t) -xi (t), combining the driving system and the response system, and eliminating common terms (such as vj, ii and fuzzy feedforward terms) to obtain an error system: wherein, ci is the passive attenuation rate of the neuron state, ei (t) is the system state error, aij is the feedback template parameter, bij is the feedforward template parameter, αij is the fuzzy feedback MIN template parameter, βij is the fuzzy feedback MAX template parameter, τj (t) is the maximum time lag, ηj (t) and γj (t) are the activation functions, and ηj (t) e [ fj (yj (t)) ] is satisfied, γj (t) e [ co [ fj (xj (t)) ]; Acquiring a real-time error signal ́ ei (t) of an associated node, and analyzing a finite time synchronization controller, namely a control signal ui (t) of the node according to an error instant term, a time lag term and a finite time convergence term: wherein ρi is the error instant compensation coefficient, For the node-node relevance coefficient of the relevant node, λi is a bias compensation coefficient, ωi is a time lag compensation coefficient, k is an adjustable gain, μ is a finite time convergence index, sign (ei (t)) is a sign function, and nonlinear feedback is realized.
  6. 6. The method for finite time synchronization control of a fuzzy cellular neural network according to claim 1, wherein the classification of the scene according to the stability requirement that the error system of different scenes converges to zero in a finite time comprises the steps of: respectively calculating corresponding coefficients according to the number of integral links, open loop gain, error coefficients and convergence speed requirements of the acquisition system; Calculating the number coefficient of integration links = the number of integration links/the maximum number of integration links of the type II system history, the open loop gain coefficient = the system open loop gain/the reference gain, the error coefficient = 1/(1+ess/eref), wherein ess is a steady-state error, eref is a maximum steady-state error allowed, and the convergence speed requirement coefficient = 1/the system requirement convergence time; The obtained integral link quantity coefficient, open loop gain coefficient, error coefficient and convergence speed requirement coefficient are weighted and averaged to obtain scene classification coefficient; and classifying the scenes with the scene classification coefficients larger than the preset threshold value as high-dimensional or strong-stability scenes, or classifying the scenes with the scene classification coefficients smaller than the preset threshold value as low-dimensional or common-stability scenes.
  7. 7. The method for finite time synchronization control of a fuzzy cellular neural network of claim 5, wherein analyzing time synchronization estimates for different scene classifications comprises the steps of: according to the scene classification, performing time synchronization estimation on the scene classification as a scene with high dimension or strong stability or a scene with low dimension or common stability; Selecting a 1-order Lyapunov function for a scene with low dimension or common stability, and performing time synchronization estimation; and selecting a p-order Lyapunov function for synchronous time estimation aiming at a scene with high dimension or strong stability.
  8. 8. The method of claim 7, wherein selecting a Lyapunov function of order 1 for time synchronization estimation and selecting a Lyapunov function of order p for synchronization time estimation comprises: Selecting a1 st order Lyapunov function According to the finite time stability theory, the calculated synchronization time is as follows: Wherein T1 is the scene system synchronization time of low dimension or common stability, lj is the non-negative constant of the activation function meeting the generalized Lipschitz condition, vt1 (0) = Lyapunov value for initial error; selecting a Lyapunov function Vt2 (t) = P is more than or equal to 2, and the synchronization time is as follows: wherein T2 is Gao Weihuo strong-stability scene system synchronization time, vt2 (0) = 。
  9. 9. The method of claim 8, wherein the finite time convergence is verified by verifying Filippov solutions of the error system and performing derivative estimation on the Lyapunov function, and simultaneously based on the controller parameter constraints and the time synchronization estimation, comprising the steps of: According to the constraint condition of the activation function, if the error system state e (T) is continuous on [ -tau, T) and is absolutely continuous on [0, T ], a measurable function delta j (T) =eta j (T) -gamma j (T) exists, and delta j (T) ∈co [ fj (yj (T)) ] -co [ fj (xj (T)) ] ], the existence verification of Filippov solutions is completed, otherwise the error system does not meet the finite time convergence; After the existence verification of Filippov solutions is completed, deriving the corresponding Lyapunov function Vt (t) of the system, substituting an error system and a controller, and calculating Filippov the derived range by using a triangle inequality and an activation function constraint condition: Wherein λ= >0; According to the finite time criterion, under the range constraint of Filippov after derivation, whether the error e (t) is converged to zero in the preset time or not and whether the system synchronization time corresponding to the scene meets the design requirement or not are verified through numerical simulation or experiments.
  10. 10. The method for finite time synchronization control of a fuzzy cellular neural network of claim 9, wherein the system stability is analyzed by finite time convergence verification, comprising the steps of: If the error e (T) converges to zero in the time T and the convergence time T meets the design requirement, the error system meets the limited time convergence, and the system stability meets the requirement, otherwise, the error system does not meet the limited time convergence, and the system stability does not meet the requirement.

Description

Finite time synchronous control method for fuzzy cell neural network Technical Field The invention belongs to the technical field of new generation information, and particularly relates to a finite time synchronous control method of a fuzzy cell neural network. Background The fuzzy cellular neural network is a fusion model of fuzzy logic and a Cellular Neural Network (CNNs), combines the advantages of the fuzzy logic and the cellular neural network, processes inaccurate and fuzzy information through membership functions and fuzzy rules (such as air conditioning refrigeration enhancement if the temperature is high and the humidity is high), and is suitable for complex systems (such as industrial reaction kettles and unmanned systems) which are difficult to establish mathematical models. Each neuron is only connected with neurons in the neighborhood, supports rapid parallel calculation, and is suitable for scenes with high real-time requirements such as image processing, pattern recognition and the like. The synchronicity of dynamic characteristics and synchronization requirements FCNNs means that a plurality of subsystems reach a consistent state in a limited time, which is important for applications such as multi-robot collaboration, distributed sensor networks, smart grids and the like, so that a fuzzy cell neural network limited time synchronization control method is needed. The fuzzy cellular neural network often comprises discontinuous activation functions or time-varying parameters, stability analysis is too conservative due to the fact that discontinuous items are ignored in the traditional method, the existence or uniqueness of solutions cannot be guaranteed, system stability is difficult to evaluate accurately, meanwhile, control signals of nodes are difficult to analyze by combining comprehensive data among the nodes, synchronous time estimation is not carried out for different scenes, and limited time synchronous control effect is affected. Disclosure of Invention The invention aims to at least solve one of the technical problems in the prior art, and therefore, the invention provides a finite time synchronous control method of a fuzzy cell neural network, which is used for solving the technical problems that stability analysis is too conservative and difficult to accurately evaluate system stability due to neglecting discontinuous items, and synchronous time estimation is carried out for different scenes and the finite time synchronous control effect is influenced. In order to solve the above problems, a first aspect of the present invention provides a finite time synchronization control method for a fuzzy cellular neural network, including the steps of: Establishing a drive-response fuzzy cell neural network FCNNs pair with a time-varying coefficient and time-lag, and setting an activation function constraint condition, including a discontinuous constraint and a generalized Lipschitz condition; constructing a stability analysis model of the multi-membrane structure controller, wherein the analysis model equates the problem of finite time synchronization of a driving-responding system with the problem of stability of an error system converged to zero in finite time, and simultaneously equates a driving system and a corresponding responding system in a management area to the same node, and calculates the relevance among all the nodes; Calculation of the decomposition of stability problems and control tasks into sub-membranes of the stability analysis model, comprising: the surface film is responsible for receiving driving system state data, responding to the system state data and time lag data and carrying out quantization pretreatment on the state data; the finite time control film is used for parallelly calculating control signals of all nodes according to the output of the surface film, the relevance among all nodes and an error system of the self-adaptive time lag feedback controller; the synchronous time analysis film is used for classifying the scenes according to the stability requirement that the error systems of different scenes converge to zero in a limited time and analyzing time synchronous estimation of different scene classifications; and the stability analysis film is used for verifying the stability of the analysis system through verifying Filippov solutions of an error system and carrying out derivative estimation on the Lyapunov function, and simultaneously verifying the limited time convergence according to the parameter constraint of the controller and the time synchronization estimation. Optionally, in one example of the above aspect, establishing a drive-response fuzzy cellular neural network FCNNs pair having a time-varying coefficient and a time-lag includes: A drive system and a response system; The driving system describes state evolution of n neurons, and considers time lag, fuzzy operation and discontinuous activation functions; The response system is referenced to the