Online neural network transformer model-free control method based on fractional order ADAM algorithm

Abstract

The application discloses an online neural network transformer model-free control method based on a fractional order ADAM algorithm, and comprises the following steps: constructing an online neural network controller; the neural network controller takes an output voltage of a transformer and an inductance current of the transformer as network input signals; a loss function based on network parameters of the neural network controller is constructed; the network parameters are based on time-varying parameters of the transformer; the transformer is controlled by using an output of the neural network controller, a value of the loss function is calculated, and it is judged whether a target precision is reached; if the target precision is not reached, the network parameters are updated based on the fractional order ADAM algorithm until the value of the loss function reaches the target precision; and if the target precision is reached, the network parameters are stopped from being updated. Compared with an integer order ADAM algorithm, the neural network controller under the fractional order ADAM algorithm has better dynamic response performance.

Description

Technical Field

[0001] The present invention relates to the fields of power electronics technology and data-driven control, and in particular to an online neural network converter model-free control method based on a fractional-order ADAM algorithm. Background Art

[0002] Model-free control, also known as data-driven control, is a method for designing system controllers that directly uses system input and output (I / O) data, without relying on a mathematical model of the controlled object. Neural network control, one of the model-free control methods, offers advantages in addressing nonlinearities and uncertainties in systems. By simply configuring the number of hidden layer neurons and activation functions, it can approximate any real-world function. Consequently, it has been widely used in the design of DC-DC converter control systems in recent years.

[0003] Fractional calculus is an extension of traditional calculus, with its roots dating back to the 18th century. While there's currently no unified definition of fractional calculus, current research is primarily based on the Grünwald-Letniko, Riemann-Liouville, and Caputo definitions. Fractional calculus is well-suited to describing the nonlinear dynamics of complex systems. Therefore, control systems based on fractional calculus can more accurately describe the dynamic response of real-world systems.

[0004] In recent years, research on the integration of fractional-order calculus theory with neural networks has continued to emerge. A series of neural network algorithms have been proposed, including fractional-order gradient descent, fractional-order momentum gradient descent, and time-scale-based fractional-order backpropagation. These studies have systematically demonstrated the effectiveness of fractional-order neural networks in accelerating convergence through both theoretical analysis and simulation experiments, providing important theoretical support for the development of fractional-order neural networks. However, all of these studies combine fractional-order calculus theory with network training algorithms with fixed learning rates. Furthermore, no research has yet explored the construction of converter control systems based on fractional-order neural networks for DC-DC converters, which exhibit strong nonlinearities and overclocking behavior. Summary of the Invention

[0005] The main purpose of the present invention is to overcome the above-mentioned defects in the prior art and propose an online neural network converter model-free control method based on the fractional-order ADAM algorithm, which has better dynamic response performance.

[0006] The present invention adopts the following technical solutions:

[0007] An online neural network converter model-free control method based on fractional-order ADAM algorithm includes:

[0008] constructing an online neural network controller; the neural network controller takes the output voltage of the converter and the inductor current of the converter as network input signals;

[0009] constructing a loss function based on the network parameters of the neural network controller; the network parameters are based on the time-varying parameters of the converter;

[0010] controlling the converter using the output of the neural network controller, calculating the value of the loss function, determining whether the target precision is reached, if not, updating the network parameters based on the fractional order ADAM algorithm until the value of the loss function reaches the target precision; if so, stopping updating the network parameters.

[0011] Preferably, the loss function is represented as follows:

[0012]

[0013] wherein v o (k) represents the output voltage of the converter at time k; v ref represents the output reference voltage; λ>0 is a weight factor used to constrain the change of network parameters; θ(k) represents the network parameters at time k; θ(k-1) represents the network parameters at time k-1.

[0014] Preferably, the network parameters at time k+1 are represented as follows:

[0015]

[0016] wherein θ(k+1) represents the network parameters at time k+1; θ(k) represents the network parameters at time k; lr is the initial learning rate; ε is a constant to prevent the denominator from being 0; represents the gradient α-order moment estimation value at time k; represents the gradient 2α-order moment estimation value at time k; α∈(0,1) represents the fractional order.

[0017] Preferably, the gradient α-order moment estimation value at time k is and the gradient 2α-order moment estimation value at time k is Based on the fractional order ADAM algorithm, it is represented as follows:

[0018]

[0019] wherein β1, β2∈(0,1) are the attenuation coefficients of the gradient α-order moment estimation value and the 2α-order moment estimation value, respectively; represents the gradient α-order moment estimation value at time k-1; represents the fractional order gradient at time k; represents the gradient 2α-order moment estimation value at time k-1.

[0020] Preferably, the fractional gradient at time k It is obtained based on the fractional-order ADAM algorithm and is expressed as follows:

[0021]

[0022] Where Δθ(k) represents the change in the network parameter θ between adjacent moments, Δθ(k) = θ(k) - θ(k-1); Γ(2-α) represents the Γ function that only retains the first term of the series; e(k) represents the output tracking error, e(k) = v ref -v o (k); represents the estimated value of the time-varying parameters of the converter; d(k) represents the output of the neural network; λ>0 is the weight factor used to constrain the change of network parameters.

[0023] Preferably, the estimated value of the time-varying parameter at time k is It is expressed as follows:

[0024]

[0025] in, represents the estimated value of the time-varying parameter at time k-1; μ>0 represents the weight factor in the penalty term; 0<η≤1 represents the introduced step size factor; Δd(k) represents the change in the output of the neural network at adjacent moments, Δd(k)=d(k)-d(k-1); Δv o (k) represents the change in the converter output voltage between adjacent moments, Δv o (k)=v o (k)-v o (k-1).

[0026] Preferably, the output voltage of the converter at time k is expressed as follows

[0027]

[0028] Among them, v o (k-1) represents the output voltage of the converter at time k-1.

[0029] Preferably, determining whether the value of the loss function reaches the target accuracy specifically includes:

[0030] Set a target accuracy value Tol and a counter count. When the loss function value L is less than the target accuracy, the counter increases by one. Once the loss function value L is greater than the target accuracy at a certain moment, the counter returns to zero and counts again. The target accuracy is achieved if and only if L < Tol for n consecutive times.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] Compared with the integer-order ADAM algorithm, the online neural network model-free control method constructed based on the fractional-order ADAM algorithm of the present invention has better dynamic response performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Flowchart of the online neural network converter model-free control method based on the fractional-order ADAM algorithm of the present invention;

[0034] Figure 2 Comparison of the network training iteration error curve and output voltage simulation waveform of the model-free control method for high-gain boost DC-DC converter based on the online neural network of integer-order and fractional-order ADAM algorithms; (a) shows the network iteration error curve; (b) shows the output voltage simulation waveform;

[0035] Figure 3 The graphs are a comparison of the network training iteration error curve and the output voltage simulation waveform of the online neural network converter model-free control system based on the fractional-order ADAM algorithm at different orders of the present invention; wherein (a) represents the network iteration error curve; (b) represents the output voltage simulation waveform;

[0036] Figure 4 The figure shows a comparison of the network steady-state training error curve and the steady-state output voltage simulation waveform of the online neural network converter model-free control system based on the fractional-order ADAM algorithm at different orders of the present invention; wherein (a) shows the network iteration error curve when the converter is in steady state; (b) shows the output voltage simulation waveform when the converter is in steady state;

[0037] Figure 5 The transient response output waveform of the model-free control method for the high-gain boost DC-DC converter based on the online neural network with integer-order and fractional-order ADAM algorithms; (a) represents the reference voltage v ref Jump output voltage transient response simulation waveform; (b) represents the input voltage v in (c) shows the simulation waveform of the transient response of the output voltage when the load R jumps. DETAILED DESCRIPTION

[0038] Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiments are only used to illustrate the present invention and are not used in limiting the scope of the present invention.In addition, should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall equally within the scope limited by the appended claims of the application.

[0039] The overall idea of ​​the online neural network converter model-free control method based on the fractional-order ADAM algorithm of the present invention is described below.

[0040] First, the gradient solution process is replaced by the original integer order calculation to the fractional order calculation, and a fractional order ADAM algorithm is constructed. Assume that the fractional order is α∈(0,1), m α is the gradient α-order moment estimate, v α is the estimated value of the gradient 2α moment, and the update formula of the two can be expressed as:

[0041]

[0042] In the formula, the subscript represents the iterative calculation value at time k, g α is the fractional gradient of any network parameter, β1,β2∈(0,1) are the attenuation coefficients of the gradient α-order moment estimate and 2α-order moment estimate respectively. The learning rate in the algorithm is mainly controlled by the 2α-order moment of the gradient. To ensure its convergence, the 2α-order moment of the gradient v α The update formula is modified as follows:

[0043]

[0044] In addition to the above adjustments, the algorithm omits the traditional bias correction step, improves the computational efficiency of online training, and sets a lower limit for the learning rate to enhance the convergence of the network in the later stages of training.

[0045] Introducing a fractional differential operator t0 D α t , taking a differentiable function f(t) as an example, the fractional differential expression under Caputo's definition is described, which can be expressed as:

[0046]

[0047] In the formula, n-1<α≤n, the value of n is rounded up to the value of α, and the value is recorded as Furthermore, by performing countless partial integration operations and summing up the fractional differentials defined by Caputo, we can obtain the series form of the fractional differentials defined by Caputo as follows:

[0048]

[0049] In order to ensure the convergence of the subsequent algorithm, the memory length of the fractional differential is limited to include only the current time t k With the previous moment t k-1 The historical data of the fractional differential can be further expressed in the form of the fractional order differential under Caputo's definition as follows:

[0050]

[0051] The infinite series form of fractional derivative cannot be directly applied to practical systems for calculation. Here, the high-order terms in the above equation are truncated, and an approximate expression of fractional derivative under Caputo definition is obtained as follows:

[0052]

[0053] Based on the above fractional order ADAM algorithm and the expression of fractional derivative under Caputo definition, see Figure 1 The online neural network transformer model-free control process based on the fractional order ADAM algorithm of the present application is disclosed as follows. First, an online neural network controller is constructed. First, a single hidden layer neural network structure is used as a model, and the output voltage v o and the transformer inductor current i L are taken as the network input signals, and the Sigmoid function is selected as the hidden layer activation function. The number of neurons in the hidden layer and the output layer is set to 1, and the linear mapping between layers is set. Second, a mean square error function with a network parameter θ regularization term is constructed as the system loss function. According to the actual network structure and control conditions, the predicted value of the loss function is the output voltage v o of the high-gain boost DC-DC converter system, and the true value is the output reference voltage v ref . The loss function can be expressed as:

[0054]

[0055] In the formula, λ>0 is a weight factor used to constrain the change of network parameters. Finally, the input of the online neural network controller is normalized to improve its training efficiency and performance.

[0056] At the same time, a dynamic linearization data-driven model of the high-gain boost DC-DC converter is constructed to provide online updates for the parameters of the online neural network controller. The mapping relationship between the output voltage v o of the converter and the duty cycle signal d of the neural network controller output is regarded as a SISO nonlinear discrete-time system. When |Δd(k)|≠0, there is a time-varying parameter φ c (k)∈R, so that the system can be converted into the following dynamic linearization data model:

[0057] v o (k)=v o (k-1)+φ c (k)·(d(k)-d(k-1))

[0058] Further, the value of the time-varying parameter φ c (k) is estimated, and the estimated value The expression is

[0059]

[0060] Among them, μ>0 is the weight factor in the algorithm penalty term, and 0<η≤1 is the introduced estimation algorithm step size factor.

[0061] Finally, the online gradient is obtained based on the fractional-order ADAM algorithm, and the fractional-order gradient g of the network parameter θ at time k with an order of α is α k It can be expressed as

[0062]

[0063] According to the given fractional-order differential approximation algorithm and chain rule, the above formula can be further described as

[0064]

[0065] In the formula, bracket k represents the iterative sampling value or calculated value at time k, and the output tracking error is defined as e(k) = v ref -v o (k), the change of network parameter θ at adjacent moments Δθ(k)=θ(k)-θ(k-1). According to the constructed data-driven model and forward Euler approximation theory, it can be obtained by φ c (k) For the high gain boost DC-DC converter output voltage v o Relationship with network output d(k) Describe:

[0066]

[0067] Final fractional gradient g α k Expressed as:

[0068]

[0069] Finally, the network parameter θ at the k+1th iteration under the fractional-order ADAM algorithm can be expressed as:

[0070]

[0071] Where lr is the initial learning rate, and a sufficiently small constant ε is set to prevent the denominator from being zero.

[0072] During training, a target accuracy value, Tol, and a counter, count, are set. When the loss function value, L, is less than the target accuracy, the counter increments by one. Once the loss function value, L, exceeds the target accuracy at a certain moment, the counter resets to zero and restarts. Network training is considered converged and system control is achieved if and only if L < Tol for n consecutive times.

[0073] In order to verify the actual control effect of the present invention, a simulation model with an initial input voltage of 48V, a reference voltage of 380V, a rated power of 400W, an excitation inductance L of 51uH, a primary-secondary turns ratio of 1, and a switching capacitor C was built on Matlab / Simlink. f1 / C f2 The simulation circuit of a high-gain boost DC-DC converter with a clamping capacitor of 17.6uF, an output capacitor of 470uF, and a switching frequency of 50kHz is shown. In the control design, a single hidden layer neural network model with two inputs and a single output is built and trained based on the fractional-order ADAM algorithm. The network output is used to generate a PWM modulation signal. The initial learning rate of the network is set to 5e -4 , and the lower limit is 1e -6 . In the case that the learning rate and the network structure do not change, the fractional order is kept at 0 <a<1的范围内调整。设仿真步长为2e -5 , the simulation time is 0.2s, and the network training accuracy is not restricted here to observe the impact of different orders on the final convergence accuracy of the network.

[0074] See also Figure 2 Figure 2 shows a comparison of the network training iteration error curve and output voltage simulation waveform for an online neural network model-free control method for a high-gain boost DC-DC converter based on integer-order and fractional-order ADAM algorithms, where α = 1 represents integer order, and a = 0.6 and a = 0.8 represent fractional order. It is clear that incorporating fractional-order calculations into network algorithm training effectively accelerates network convergence, reduces the number of iterations, and improves the dynamic performance of the control method. However, it should be noted that the choice of fractional order has limitations. When a = 0.6, the network saturates at the beginning of training, causing the loss function to remain at a large value and no longer adjust, resulting in control system divergence.

[0075] See also Figure 3 Figure 2 shows a comparison of the network training iteration error curves and output voltage simulation waveforms for an online neural network converter model-free control method based on the fractional-order ADAM algorithm at different orders. As the fractional order decreases, the output voltage overshoot generated during the control process gradually decreases. However, its dynamic performance is correspondingly weakened.

[0076] See also Figure 4Figure 2 shows a comparison of the steady-state training error curve and steady-state output voltage simulation waveform for an online neural network converter model-free control method based on the fractional-order ADAM algorithm at different orders. As the fractional order approaches 1, the convergence accuracy increases, and the output voltage under control is closer to the reference voltage.

[0077] right Figures 2 to 4 Analysis of the simulation results shows that the network's convergence accuracy requirements should be ensured first, and then the fractional order should be selected based on dynamic performance. Here, balancing network iteration speed and convergence accuracy, the fractional-order ADAM algorithm order of 0.85 was selected and compared with the control performance of the integer-order optimized ADAM algorithm. Simulations of the system's transient process were conducted under both control strategies, and the corresponding output voltage transient response waveforms were obtained. To ensure consistency in the analysis, the simulation duration was set to 0.3 seconds, and the two consecutive step changes were set at 0.1 seconds and 0.2 seconds, respectively.

[0078] See also Figure 5 As shown in FIG, the transient response output waveform of the model-free control method of the online neural network high-gain boost DC-DC converter based on integer-order and fractional-order ADAM algorithms. Figure 5 (a), (b), and (c) show the transient response waveforms of the reference voltage, input voltage, and output voltage during load transitions, respectively. Overall, the online neural network model-free control method based on the fractional-order ADAM algorithm significantly improves its dynamic response performance compared to the integer-order ADAM algorithm.

[0079] In summary, the present invention proposes an online neural network converter model-free control method based on the fractional-order ADAM algorithm. Integrating fractional-order theory into neural networks can better describe the actual DC-DC converter system, thereby improving the control performance of the converter. On the basis of the ADAM algorithm, the integer-order gradient is replaced by the fractional-order gradient, and a set of online neural network converter model-free control methods based on the fractional-order ADAM algorithm is designed, and the control process of the method is elaborated in detail. Finally, through simulation analysis and comparison, it is verified that the control system under the fractional-order ADAM algorithm is significantly better than the integer-order ADAM algorithm in dynamic performance.

[0080] The above is only a specific implementation of the present invention, but the design concept of the present invention is not limited to this. Any non-substantial changes to the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention.

Claims

1. A model-free control method for an online neural network converter based on a fractional-order ADAM algorithm, characterized in that: include: An online neural network controller is constructed; the neural network controller uses the output voltage of the converter and the inductor current of the converter as network input signals; Constructing a loss function based on network parameters of a neural network controller; wherein the network parameters are based on time-varying parameters of the converter; Use the output of the neural network controller to control the converter, calculate the value of the loss function, and determine whether the target accuracy has been achieved. If not, update the network parameters based on the fractional-order ADAM algorithm until the loss function value reaches the target accuracy; if so, stop updating the network parameters. The loss function is expressed as follows: Among them, v o (k) represents the output voltage of the converter at time k; v ref represents the output reference voltage; λ>0 is the weight factor used to constrain the change of network parameters; θ(k) represents the network parameters at time k; θ(k-1) represents the network parameters at time k-1; The network parameters at time k+1 are expressed as follows: Among them, θ(k+1) represents the network parameters at time k+1; θ(k) represents the network parameters at time k; lr is the initial learning rate; ε is a constant to prevent the denominator from being zero; Represents the estimated value of the gradient α-order moment at time k; represents the estimated value of the 2α-order moment of the gradient at time k; α∈(0,1) represents the fractional order; Gradient α-order moment estimate at time k and the k-time gradient 2α-order moment estimate It is obtained based on the fractional-order ADAM algorithm and is expressed as follows: Among them, β1,β2∈(0,1) are the attenuation coefficients of the gradient α-order moment estimate and the 2α-order moment estimate respectively; Represents the estimated value of the gradient α-order moment at time k-1; represents the fractional gradient at time k; Represents the estimated value of the 2α-order moment of the gradient at time k-1; Fractional gradient at time k It is obtained based on the fractional-order ADAM algorithm and is expressed as follows: Where Δθ(k) represents the change in the network parameter θ between adjacent moments, Δθ(k) = θ(k) - θ(k-1); Γ(2-α) represents the Γ function that only retains the first term of the series; e(k) represents the output tracking error, e(k) = v ref -v o (k); represents the estimated value of the time-varying parameters of the converter; d(k) represents the output of the neural network; λ>0 is the weight factor used to constrain the change of network parameters; The estimated value of the time-varying parameter at time k It is expressed as follows: in, represents the estimated value of the time-varying parameter at time k-1; μ>0 represents the weight factor in the penalty term; 0<η≤1 represents the introduced step size factor; Δd(k) represents the change in the output of the neural network at adjacent moments, Δd(k)=d(k)-d(k-1); Δv o (k) represents the change in the converter output voltage between adjacent moments, Δv o (k)=v o (k)-v o (k-1); The output voltage of the converter at time k is expressed as follows Among them, v o (k-1) represents the output voltage of the converter at time k-1.

2. The online neural network converter model-free control method based on the fractional-order ADAM algorithm according to claim 1 is characterized in that: Determine whether the value of the loss function reaches the target accuracy, specifically including: Set a target accuracy value Tol and a counter count. When the loss function value L is less than the target accuracy, the counter increases by one. Once the loss function value L is greater than the target accuracy at a certain moment, the counter returns to zero and counts again. The target accuracy is achieved if and only if L < Tol for n consecutive times.

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