Fractional order neural network sliding mode control buffeting analysis method

Abstract

The invention provides a fractional order neural network sliding mode control buffeting analysis method, and belongs to the technical field of artificial intelligence. The technical problem of buffeting control of a fractional order neural network sliding mode is solved. According to the technical scheme, the method comprises the following steps that 1, a neural network control error system is constructed, and a sliding mode controller is designed according to the error system; 2, according to a sliding mode controller and a feedback learning period, separating a transient term and a steady term, and carrying out a neural network buffeting analysis method; and step 3, intercepting historical information with a certain length according to memory attenuation characteristics of the neural network, and carrying out optimal estimation on buffeting of the neural network. The fractional order neural network sliding mode control buffeting analysis method has the advantages that the sliding mode control output transient term and the steady state term are separated from each other from the neural network memory characteristics, historical information with a certain length is intercepted by combining the memory attenuation characteristics, and the fractional order neural network sliding mode control buffeting analysis method is established.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a chattering analysis method for a fractional-order neural network sliding mode control. Background Art

[0002] Neural network is an abstraction of human neural network, which establishes a simple model and simulates human intelligence by forming a network with different connection methods. It has successfully solved many practical problems that are difficult to solve with modern computers in the fields of pattern recognition, intelligent robots, automatic control, prediction and estimation, biology, medicine, and economy, and has demonstrated good intelligent characteristics.

[0003] The nervous system is a memory learning system, which continuously learns new knowledge and updates memory. The neural network is a memory network, not a memoryless network. The learning process of the neural network is a memory update process, which is a process of updating old knowledge with new knowledge. The memory update process of human knowledge is a gradual update process. There is a process for new knowledge to replace old knowledge, that is, there is a transition period.

[0004] Neural network is an artificial system that simulates human intelligence, and the human nervous system itself is a memory system with memory function. Integer-order differentials defined by local limits do not have memory function, while fractional-order differentials defined by convolution contain all historical information, and the weight of historical information decays over time, which can well reflect the characteristics of human memory and the characteristics of memory decay over time. In recent years, fractional-order neural network research on artificial intelligence has become a hot topic in the field of artificial intelligence.

[0005] The learning process is the process of updating old knowledge with new knowledge, that is, the process of providing feedback to the output through the output. The learning process is often a discontinuous feedback control process. Sliding mode control is favored because it is independent of the model and has good robustness to noise and parameter disturbances. However, sliding mode control will inevitably bring about system chattering, and the same is true for fractional order neural network sliding mode control.

[0006] Studying the chattering characteristics of sliding mode control of fractional-order neural networks is of great significance for the application of fractional-order neural networks, machine learning characteristics, and improving learning convergence speed.

[0007] The technical problem of chattering controlled by sliding mode of fractional order neural network is the subject faced by the present invention. Summary of the invention

[0008] The purpose of the present invention is to provide a method for analyzing chattering of a fractional-order neural network sliding mode control. Aiming at the technical problem of chattering of a fractional-order neural network sliding mode control, the present invention separates the transient term and the steady-state term of the sliding mode control output based on the memory characteristics of the neural network, and combines the memory decay characteristics to intercept a certain length of historical information to establish a method for analyzing chattering of a fractional-order neural network sliding mode control.

[0009] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is specifically: a chattering analysis method of a fractional-order neural network sliding mode control, comprising the following steps:

[0010] Step 1: Construct a neural network control error system and design a sliding mode controller based on the error system;

[0011] Step 2: Separate the transient term and the steady-state term according to the sliding mode controller and the feedback learning cycle, and perform the neural network chattering analysis method;

[0012] Step 3: According to the memory decay characteristics of the neural network, a certain length of historical information is intercepted to make the optimal estimate of the neural network jitter.

[0013] As a chattering analysis method for fractional-order neural network sliding mode control provided by the present invention, the step 1: constructing a neural network control error system, and designing a sliding mode controller according to the error system, specifically includes the following steps:

[0014] Step 1.1 Construct the driving neural network model:

[0015]

[0016] Among them, x j (t) represents the state variable of the jth node, g(x j (t)) represents the nonlinear state function that satisfies the Lipschitz condition, and the Lipschitz constant is l c , C is the connection gain constant, Π is the inline matrix, It represents the coupling relationship between the jth node and the kth node of the neural network, and N represents the total number of nodes in the network.

[0017] Step 1.2 Construct a response neural network model:

[0018]

[0019] Among them, y j (t) represents the state variable of the jth node of the response system, and the meanings of other parameters are the same as those in step 1.1.

[0020] Step 1.3: Define the control error and establish the control error expression.

[0021] Definition error e j (t) = y j (t)-x j (t), we get the error system:

[0022]

[0023] in,

[0024] Step 1.4 Construct the sliding surface.

[0025] Construct sliding surface for j nodes

[0026]

[0027] Where k is a constant to be determined, s j (e j (t)) is the sliding surface constructed by the control error.

[0028] Step 1.5 Design a sliding mode controller.

[0029] According to the sliding surface stability condition s j (e j (t)) = 0 and Designing a sliding mode controller

[0030]

[0031] As a chattering analysis method for fractional-order neural network sliding mode control provided by the present invention, the step 2: separating transient terms and steady-state terms according to the sliding mode controller and the feedback learning cycle, and performing a neural network chattering analysis method, specifically includes the following steps:

[0032] Step 2.1: Establish a neural network cycle feedback learning model

[0033] The principle of neural network sliding mode control is as follows Figure 2 , sample the error cycle, and provide feedback based on the sampling, and feedback learning to the neural network based on the sampling results:

[0034]

[0035] Among them, represents the sampling period, l represents the duty cycle, and l represents the lth sampling.

[0036] Step 2.2: Construct the Lyapunov function and study the characteristics of the Lyapunov function:

[0037] Construct the Lyapunov function:

[0038]

[0039] According to the properties of fractional differentials:

[0040]

[0041] V 1 (t) is a positive definite Lyapunov function.

[0042] 2.3: Introduce the unit step function s(t) to transform the intermittent sampling feedback learning equation into a piecewise continuous function:

[0043]

[0044] Step 2.4: Using the fractional integral property, we can get the output expression:

[0045]

[0046] Step 2.5 splits the output at any switching time mT (m represents the mth switching) into the output generated by the input before this time and the output generated by the input after this time:

[0047]

[0048] Step 2.6 divides the output generated by the historical input into steady state and transient state:

[0049]

[0050] in the formula It represents the output of historical input before time mT, which affects the initial state of mT.

[0051]

[0052] It means the output generated by the input before time mT after time mT. The output is not 0 and decays with time, which is called transient.

[0053] Step 2.7 Neural Network Sliding Mode Control Chattering Analysis:

[0054] In formula (11)

[0055]

[0056] It is a transient term. When the historical input changes alternately, the transient output formed by the historical input will also change alternately, forming chattering. The chattering frequency is related to the switching frequency of the sliding surface. The higher the switching frequency, the higher the chattering frequency. The chattering amplitude is related to the input change amplitude. The greater the input change, the greater the chattering amplitude.

[0057] The present invention provides a chattering analysis method for a fractional-order neural network sliding mode control, wherein step 3: based on the memory decay characteristics of the neural network, intercepting a certain length of historical information, and performing optimal estimation on the neural network chattering, specifically comprises the following steps:

[0058] Step 3.1: According to formula (3), study the system memory decay characteristics.

[0059] According to the definition of fractional differential, a system with a differential order of α is equivalent to having an impulse response of systems such as Figure 3 , memory decays over time. According to the decay characteristics, we can choose an appropriate L. When the historical information exceeds L, the impact on the transient state is small and can be ignored.

[0060] Step 3.2: intercept a certain length of historical information for chattering analysis:

[0061] According to [L / T], appropriate historical information is selected for chattering analysis. [L / T] represents the rounding of L / T, and the chattering estimation of the fractional-order neural network sliding mode control is obtained:

[0062]

[0063]

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] 1. The present invention proposes a method for analyzing the chattering of a fractional-order neural network sliding mode control. The method establishes the relationship between the chattering of a fractional-order neural network sliding mode control and the system response characteristics and historical inputs, provides a basis for chattering analysis, and provides a new analysis method for the convergence analysis of neural network learning. The chattering analysis shows that there must be transient behavior in the discontinuous feedback or learning of a neural network, which will cause system oscillations and even cause learning to not converge. This provides a new idea for the convergence analysis of neural network mechanical learning.

[0066] 2. The present invention uses memory characteristics to separate the steady state and transient state of the neural network output, treats discontinuous feedback as a piecewise continuous function, establishes the relationship between the neural network output and all historical feedback inputs, and establishes the relationship between the system output and historical inputs. The model better reflects the system memory characteristics, and the memory characteristics do not change with external inputs. The present invention provides a new method for neural network memory analysis.

[0067] 3. The present invention reasonably forgets historical information exceeding a certain length based on the system attenuation characteristics, which not only conforms to the cognitive laws, but also reflects the attenuation characteristics of the memory system, taking into account both the accuracy of analysis and the simplicity of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0069] Figure 1 This is a schematic diagram of the fractional-order neural network sliding mode control principle in the present invention.

[0070] Figure 2 This is a graph showing the attenuation of the impulse response over time in the present invention.

[0071] Figure 3 This is a flow chart of chattering analysis of the fractional order neural network sliding mode control in the present invention.

[0072] Figure 4 The flow chart of the sliding mode controller designed in the present invention.

[0073] Figure 5 This is a flow chart of chattering analysis of the fractional order neural network sliding mode control in the present invention.

[0074] Figure 6 This is a flow chart of chattering analysis and estimation of the fractional order neural network sliding mode control in the present invention.

[0075] Figure 7 This is a transient analysis diagram of the fractional order neural network sliding mode control when α=0.5 in the present invention.

[0076] Figure 8 This is a transient analysis diagram of the fractional-order neural network sliding mode control when α=0.8 in the present invention.

[0077] Fig. 9 This is a transient analysis diagram of the fractional order neural network sliding mode control when α=1 in the present invention.

[0078] Fig.10 This is the chattering diagram of the sliding mode control when α=0.5 and the control gain k=1 in the present invention.

[0079] Fig.11 This is the chattering diagram of the sliding mode control when α=0.5 and the control gain k=3 in the present invention.

[0080] Fig.12 This is the chattering diagram of the sliding mode control when α=0.8 and the control gain k=1 in the present invention.

[0081] Fig.13 This is the chattering diagram of the sliding mode control when α=0.8 and the control gain k=3 in the present invention.

[0082] Fig.14 This is the chattering diagram of the sliding mode control when α=1 and the control gain k=1 in the present invention.

[0083] Fig.15This is the chattering diagram of the sliding mode control when α=1 and the control gain k=3 in the present invention. DETAILED DESCRIPTION

[0084] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0085] Example 1

[0086] See also Figures 1 to 9 This embodiment provides a chattering analysis method for a fractional order neural network sliding mode control, comprising the following steps:

[0087] Step 1: Construct a neural network control error system and design a sliding mode controller based on the error system;

[0088] Step 2: Separate the transient term and the steady-state term according to the sliding mode controller and the feedback learning cycle, and perform the neural network chattering analysis method;

[0089] Step 3: According to the memory decay characteristics of the neural network, a certain length of historical information is intercepted to make the optimal estimate of the neural network jitter.

[0090] Furthermore, the step 1: constructing a neural network control error system and designing a sliding mode controller according to the error system specifically includes the following steps:

[0091] Step 1.1 Construct the driving neural network model:

[0092]

[0093] where x j (t) represents the state variable of the jth node, g(x j (t)) represents the nonlinear state function that satisfies the Lipschitz condition, and the Lipschitz constant is l c , C is the connection gain constant, Π is the inline matrix, It represents the coupling relationship between the jth node and the kth node of the neural network, and N represents the total number of nodes in the network.

[0094] Step 1.2 Construct a response neural network model:

[0095]

[0096] where y j (t) represents the state variable of the j-th node of the response system, and the meanings of other parameters are the same as those in step 1.1.

[0097] Step 1.3: Define the control error and establish the control error expression.

[0098] Definition error e j (t) = y j (t)-x j (t), we get the error system:

[0099]

[0100] in

[0101] Step 1.4 Construct the sliding surface.

[0102] Construct sliding surface for j nodes

[0103]

[0104] Among them, k is a constant to be determined, s j (e j (t)) is the sliding surface constructed by the control error.

[0105] Step 1.5 Design a sliding mode controller.

[0106] According to the sliding surface stability condition s j (e j (t)) = 0 and Designing a sliding mode controller

[0107]

[0108] Furthermore, the step 2: separating the transient term and the steady-state term according to the sliding mode controller and the feedback learning cycle, and performing a neural network chattering analysis method specifically includes the following steps:

[0109] Step 2.1: Establish a neural network cycle feedback learning model

[0110] The principle of neural network sliding mode control is as follows Figure 2 , sample the error cycle, and provide feedback based on the sampling, and feedback learning to the neural network based on the sampling results:

[0111]

[0112] Wherein, represents the sampling period, ι represents the duty cycle, and l represents the lth sampling.

[0113] Step 2.2: Construct the Lyapunov function and study the characteristics of the Lyapunov function:

[0114] Construct the Lyapunov function:

[0115]

[0116] According to the properties of fractional differentials:

[0117]

[0118] 2.3: Introduce the unit step function s(t) to transform the intermittent sampling feedback learning equation into a piecewise continuous function:

[0119]

[0120] Step 2.4: Using the fractional integral property, we can get the output expression:

[0121]

[0122]

[0123] Step 2.5 splits the output at any switching time mT (m represents the mth switching) into the output generated by the input before this time and the output generated by the input after this time:

[0124]

[0125] Step 2.6 divides the output generated by the historical input into steady state and transient state:

[0126]

[0127] in the formula It represents the output of historical input before time mT, which affects the initial state of mT.

[0128]

[0129] It means the output generated by the input before time mT after time mT. The output is not 0 and decays with time, which is called transient.

[0130] Step 2.7 Neural Network Sliding Mode Control Chattering Analysis:

[0131] In formula (11)

[0132]

[0133] It is a transient term. When the historical input changes alternately, the transient output formed by the historical input will also change alternately, forming jitter. The jitter frequency is related to the switching frequency of the sliding surface. The higher the switching frequency, the higher the jitter frequency. The jitter amplitude is related to the input change amplitude. The greater the input change, the greater the jitter amplitude.

[0134] Furthermore, the step 3: according to the memory decay characteristics of the neural network, intercepting a certain length of historical information and performing optimal estimation on the neural network jitter specifically includes the following steps:

[0135] Step 3.1: According to formula (3), study the system memory decay characteristics.

[0136] According to the definition of fractional differential, a system with a differential order of α is equivalent to having an impulse response of systems such as Figure 3 , memory decays over time. According to the decay characteristics, we can choose an appropriate L. When the historical information exceeds L, the impact on the transient state is small and can be ignored.

[0137] Step 3.2: intercept a certain length of historical information for chattering analysis:

[0138] According to [L / T], appropriate historical information is selected for chattering analysis, where [L / T] represents the rounding of L / T. The chattering estimation of the fractional order neural network sliding mode control is obtained:

[0139]

[0140] The transient analysis of fractional-order system switching control is as follows:

[0141] Assume that the system satisfies the following equation:

[0142]

[0143] The simulation diagrams are as follows when k is 1 and -1 respectively and α is different. The simulation shows that the transient process is related to the historical process and the memory decay characteristics of the system. When α=1, it is an integer-order system with no memory characteristics and no transient process.

[0144] Example 2

[0145] Based on Example 1, see Figures 10 to 15 , assuming that the neural network has 5 nodes, each node is 2-dimensional, in formula (1)

[0146]

[0147] Simulation of sliding mode control error chattering simulation process when α and control gain k take different values.

[0148] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A chattering analysis method for fractional order neural network sliding mode control, characterized in that: The following steps are involved: Step 1: Construct a neural network control error system and design a sliding mode controller based on the error system; Step 2: Separate the transient term and the steady-state term according to the sliding mode controller and the feedback learning cycle, and perform the neural network chattering analysis method; Step 3: According to the memory decay characteristics of the neural network, a certain length of historical information is intercepted to make the optimal estimate of the neural network jitter.

2. The chattering analysis method of fractional order neural network sliding mode control according to claim 1 is characterized in that: The step 1: constructing a neural network control error system, and designing a sliding mode controller according to the error system, includes the following steps: Step 1.1 Construct the driving neural network model: Among them, x j (t) represents the state variable of the jth node, Represents the state variable x j Caputo fractional derivative of (t), α represents the differential order, g(x j (t)) represents the nonlinear state function that satisfies the Lipschitz condition, and the Lipschitz constant is l c , C is the connection gain constant, Π is the inline matrix, represents the coupling relationship between the jth node and the kth node of the neural network, and N represents the total number of nodes in the network; Step 1.2 Construct a response neural network model: Among them, y j (t) represents the state variable of the jth node of the response system, and the meanings of other parameters are the same as those in step 1.1; Step 1.3: Define the control error and establish the control error expression; Definition error e j (t) = y j (t)-x j (t), we get the error system: in, Step 1.4: Construct the sliding surface: Construct sliding surface for j nodes Among them, k is a constant to be determined, s j (e j (t)) is the sliding surface constructed by the control error; Step 1.5 Design the sliding mode controller: According to the sliding surface stability condition s j (e j (t)) = 0 and Designing a sliding mode controller 3. The chattering analysis method of fractional order neural network sliding mode control according to claim 1 is characterized in that: The step 2: separating the transient term and the steady-state term according to the sliding mode controller and the feedback learning cycle, and performing a neural network chattering analysis method includes the following steps: Step 2.1: Establish a neural network cycle feedback learning model; Sample the error cycle and provide feedback based on the sampling, and feedback learning to the neural network based on the sampling results: Wherein, represents the sampling period, k is the control parameter to be determined, T is the control period, ι represents the duty cycle, and l represents the lth sampling; Step 2.2: Construct the Lyapunov function and study the characteristics of the Lyapunov function: Construct the Lyapunov function: According to the properties of fractional differentials: 2.3: Introduce the unit step function s(t) to transform the intermittent sampling feedback learning equation into a piecewise continuous function: Step 2.4: Using the fractional integral property, we can get the output expression: Step 2.5: Split the output at any switching time mT into the output generated by the input before this time and the output generated by the input after this time, where m represents the mth switching; Step 2.6 divides the output generated by the historical input into steady state and transient state: (10) in the formula Represents the output of historical input before time mT, affecting the initial state of mT; It means the output generated by the input before time mT after time mT. This output is not 0 and decays with time, which is called transient state. Step 2.7 Neural Network Sliding Mode Control Chattering Analysis: In formula (11) It is a transient term. When the historical input changes alternately, the transient output formed by the historical input will also change alternately, forming jitter. The jitter frequency is related to the switching frequency of the sliding surface. The higher the switching frequency, the higher the jitter frequency. The jitter amplitude is related to the input change amplitude. The greater the input change, the greater the jitter amplitude.

4. The chattering analysis method of fractional order neural network sliding mode control according to claim 1, characterized in that: The step 3: based on the memory decay characteristics of the neural network, intercepting a certain length of historical information, and performing optimal estimation on the neural network jitter, includes the following steps: Step 3.1: According to formula (3), study the system memory decay characteristics; According to the definition of fractional differential, a system with a differential order of α is equivalent to having an impulse response of For a system, memory decays over time. According to the decay characteristics, select an appropriate L. Step 3.2: Intercept a certain length of historical information for chattering analysis: According to [L / T], appropriate historical information is selected for chattering analysis. [L / T] represents the rounding of L / T, and the chattering estimation of the fractional-order neural network sliding mode control is obtained:

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