A robust control method and system based on kinoform coding

Abstract

The present invention discloses a robust control method and system based on phase information pattern coding, which includes constructing a control system according to the incident light field and intensity distribution and the corresponding phase distribution; based on the control system, using a robust model predictive control algorithm and soft constraints to generate an attraction domain, and constructing a data set based on the attraction domain; based on the data set, expanding the data set based on a data density segmentation method; based on the expanded data set, training a symmetric neural network to determine a phase distribution prediction model; based on the current incident light field and intensity distribution, using the phase distribution prediction model to determine the current phase distribution; and generating a phase information pattern according to the current phase distribution. The present invention can obtain a high-precision phase hologram.

Description

Technical Field

[0001] The present invention relates to the field of robust control of optical systems, and in particular to a robust control method and system based on kinoform coding. Background Art

[0002] Computer-generated holograms can record both the amplitude and phase of a light wave field. For the object being recorded, if its own random phase mask makes the energy spread uniform, then the mode recorded by the corresponding computer-generated hologram is relatively unimportant, so only the phase needs to be extracted to generate grayscale fringes. The encoding of the phase pattern is based on an assumption: the phase distribution in the hologram plane carries the vast majority of the information, while the amplitude can be ignored. This hologram function can be expressed as: Where j is the imaginary unit, (x, y) is the coordinate of the light field sampling point, is the corresponding phase; when using the phase diagram to encode the light wave, if the object being calculated is a diffuse reflector, then the phase distribution of all object points is relatively independent and random, then the hologram function can accurately represent the object light wave field.

[0003] The kinoform kinoform calculation problem involves finding the phase distribution of the complex amplitude transmission coefficient given the intensity distribution of the incident light field and the diffraction pattern. The existence and uniqueness of this problem remain unproven, and it can only be transformed into a numerical optimization problem, seeking the optimal solution under a certain norm.

[0004] Robust model predictive control (robust MPC) is a rolling optimization technique that accounts for system uncertainty. It can solve dynamic optimization problems online and ensure closed-loop stability of uncertain systems. It is applicable to optical systems with uncertainty. During each optimization process, robust MPC primarily considers the worst-case minimum problem, which greatly increases the robustness of the problem solution. However, since obtaining an online solution to the optimization problem requires a significant amount of time, this robust optimization scheme, while providing high accuracy for calculating kinoform patterns, is mitigated by the significant computational time. Therefore, we propose a robust control method using a symmetric neural network for kinoform pattern encoding.

[0005] Therefore, how to obtain high-precision phase holograms is still a problem that needs to be solved urgently. Summary of the Invention

[0006] The object of the present invention is to provide a robust control method and system based on kinoform coding, which can obtain a high-precision phase hologram.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A robust control method based on kinoform coding, comprising:

[0009] Construct a control system based on the incident light field, intensity distribution and corresponding phase distribution;

[0010] Based on the control system, the robust model predictive control algorithm and soft constraints are used to generate the attraction domain, and a data set is constructed based on the attraction domain;

[0011] According to the data set, the segmentation method based on data density is used to expand the data set;

[0012] Based on the expanded data set, a symmetric neural network is trained to determine the phase distribution prediction model;

[0013] According to the current incident light field and intensity distribution, a phase distribution prediction model is used to determine the current phase distribution; and a kinoform diagram is generated according to the current phase distribution.

[0014] Optionally, the control system is constructed according to the incident light field, intensity distribution and corresponding phase distribution, specifically including the following formula:

[0015]

[0016] y(k)=[0 1]x(k)+0.1;

[0017] Among them, x(k) represents the incident light field at sampling time k, which is the control system state, x(k+1) represents the incident light field at sampling time k+1, u(k) represents the phase distribution, which is the control system input, ω is a random number, ω∈(0,1), A(k) and B(k) are system models at different sampling times.

[0018] Optionally, the control system uses a robust model predictive control algorithm and soft constraints to generate an attraction domain, and constructs a data set based on the attraction domain, specifically including the following formula:

[0019] F(k)=YQ -1 ;

[0020] Where F(k) is the attraction domain Q = γP(k) -1 , P(k) is a positive definite weight matrix, and γ is a number greater than 0.

[0021] Optionally, the step of expanding the data set by using a segmentation method based on data density according to the data set specifically includes:

[0022] Define data density as the number of samples per unit area;

[0023] Determine the data density based on the sampling step size;

[0024] The dataset is sampled according to the data density to obtain the expanded dataset.

[0025] A robust control system based on kinoform coding, comprising:

[0026] A control system building module, used to build a control system according to the incident light field and intensity distribution and the corresponding phase distribution;

[0027] A data set construction module is used to generate an attraction domain based on a control system using a robust model predictive control algorithm and soft constraints, and to construct a data set based on the attraction domain;

[0028] The data set expansion module is used to expand the data set according to the data set and the data density-based segmentation method;

[0029] A phase distribution prediction model determination module is used to train a symmetric neural network based on the expanded data set to determine the phase distribution prediction model;

[0030] The kinoform diagram generation module is used to determine the current phase distribution according to the current incident light field and intensity distribution using a phase distribution prediction model; and generate the kinoform diagram according to the current phase distribution.

[0031] A robust control system based on kinoform coding comprises: at least one processor, at least one memory and computer program instructions stored in the memory, wherein the method described is implemented when the computer program instructions are executed by the processor.

[0032] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0033] The present invention provides a robust control method and system based on kinoform coding. Based on a control system, this method employs a robust model predictive control algorithm and soft constraints to generate an attraction domain. This domain then constructs a data set, achieving environmental interference mitigation. The introduction of soft constraints improves the feasibility of the optimization problem. A data density segmentation method ensures consistent distribution of data samples across different datasets. A symmetric neural network is trained based on the expanded dataset to determine a phase distribution prediction model, thereby accurately determining the phase distribution and ensuring high precision of the phase hologram. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 A schematic flow chart of a robust control method based on kinoform coding provided by the present invention;

[0036] Figure 2 Schematic diagram of the attraction domain;

[0037] Figure 3 Schematic diagram of symmetric neural network structure;

[0038] Figure 4 It is a schematic diagram of the symmetric neural network control principle;

[0039] Figure 5 Schematic diagram of the symmetric neural network training process. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0041] The object of the present invention is to provide a robust control method and system based on kinoform coding, which can obtain a high-precision phase hologram.

[0042] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] like Figure 1 As shown, the present invention provides a robust control method based on kinoform coding, comprising:

[0044] S101, constructing a control system according to the incident light field, intensity distribution and corresponding phase distribution;

[0045] S101 specifically includes the following formula:

[0046] The process of converting the incident light field into the kinoform diagram is regarded as a control system to be controlled, the current light field and intensity distribution are the system state, and the phase distribution is the system input;

[0047]

[0048] y(k)=

[01] x(k)+0.1(1.2)

[0049]

[0050]

[0051]

[0052] Among them, x(k) represents the incident light field at sampling time k, which is the control system state, x(k+1) represents the incident light field at sampling time k+1, u(k) represents the phase distribution, which is the control system input, and A(k) and B(k) are system models at different sampling times.

[0053] S102, based on the control system, a robust model predictive control algorithm and soft constraints are used to generate an attraction domain, and a data set is constructed based on the attraction domain; Figure 2 As shown in Figure 3, the original attraction domain is extended to the regular region. If the mapping relationship between the state and the control action in the attraction domain can be learned, an explicit control rate can be obtained, thus avoiding the online solution of the optimization problem.

[0054] Considering model uncertainty, at each sampling time, the optimization problem that should be considered is as follows:

[0055]

[0056] Consider that the closed-loop system is stable, that is:

[0057]

[0058] in, and Represent the control action and the constraints of the system state respectively; Ψ is a transition matrix; x(k+i)=x(k+i|k+i), x(k+i|k) represents the predicted state at the kth sampling moment for the k+i moment; Ω=Co{[A1 B1],[A2B2],…,[A G B G ]} is a multipacket, G is the number of multipacket vertices. γ>0 represents the robust performance indicator function. Define Q=γP(k) -1 and F(k)=YQ -1 , according to the Lyapunov stability criterion, for the above formula, the following linear matrix inequality can be obtained:

[0059]

[0060]

[0061]

[0062]

[0063] s∈{1,…,q},g∈{1,…,G}

[0064] Where Q = γP(k) -1 , F(k)=YQ -1 ; I is the identity matrix; [A g Bg ] represents the vertex of the multi-packet system. If and only if there exists Q>0, Y=FQ and γ, the j(s)th diagonal element of Z(Γ) is represented by Z jj (Γ ss );β j and β s is the correlation factor. Therefore, Equation (1.3) can be transformed into the following constrained optimization problem:

[0065]

[0066] S103, based on the data set, a data density-based segmentation method is used to expand the data set; the training samples consist of system states and control inputs, and are obtained by sampling within the attraction domain. In principle, as long as the sampling step is small enough, a complete set of system states can be generated from the attraction domain. However, regular sampling will result in a relatively uniform data set. The result of dividing it into training and test sets is that the data distribution between different data sets is inconsistent. In addition, shuffling the data set and destroying the original data distribution pattern makes it more challenging to accurately approximate the training model. Specifically, in some cases, taking too small a sampling step within a fixed range will lead to a lack of diversity in the data. This results in limited changes between the training set and the test set. This increases the risk of model overfitting during training. In order to solve the problems encountered in data set construction, a data density-based segmentation method (DDSD) is proposed.

[0067] S103 specifically includes:

[0068] Define data density as the number of samples per unit area;

[0069] Determine the data density based on the sampling step size;

[0070] The dataset is sampled according to the data density to obtain the expanded dataset.

[0071] Assuming the sampling steps are s1 and s2, the data density is:

[0072] Set a benchmark data density as ρ o =10 8 , and use this as a reference to define the sample set For ease of presentation and description, the data density of a dataset is expressed as a relative value relative to a predetermined benchmark. This allows the subsequent discussion of data density to be understood relative to this benchmark.

[0073] The expanded dataset consists of three subsets: training set Validation set and test set Furthermore, it is sufficient to choose a data density that is consistent with the numerical precision of the state and that produces a dataset that is relatively small compared to the total number of samples.

[0074] S104, training a symmetric neural network based on the expanded data set to determine a phase distribution prediction model;

[0075] like Figure 3 and Figure 4 As shown, use N = [n 1 ,…,n l ,…,n L ] to represent a symmetric neural network, where n l represents the number of neurons in layer l; W = [W 1 ,…,W l ,…,W L ] is the weight matrix sequence of the network, W l is the weight matrix connecting layer l and layer l-1, and its form is as follows:

[0076]

[0077] Where, is the weight connecting the cth neuron in layer l and the rth neuron in layer l-1; the network bias is B = [b 1 ,...,b l ,...,b L ],in is the bias of layer l. W and B constitute the network parameters θ, so the objective function of the network can be expressed as:

[0078]

[0079] In the formula, p represents the sample number, m s is the total number of samples in the dataset; is the network’s predicted value for the pth sample, y (p) is the label value of the pth sample. In this method, the sampling momentum gradient descent algorithm updates the network parameters, and the specific update method is as follows:

[0080]

[0081]

[0082] W l :=W l -αv dWl

[0083] bl:=bl-αv dbl

[0084] Where β is a hyperparameter that controls the weighted average, α represents the learning law; parameter and Represents the first layer and momentum.

[0085] A deep neural network with 10 hidden layers ([3, 10, 25, 80, 400, 400, 80, 25, 10, 3]) was constructed. The network input is the system state and the network output is the control action.

[0086] To obtain high-performance network parameters, we used three stages to train the neural network. In the first stage, we used a ten-fold cross-validation experiment and obtained the penalty factor for the regularization term during the second stage of training. In the second stage, we proposed a measurement function to evaluate the network performance:

[0087]

[0088] In the formula, x(p) represents the sample to be evaluated, F DNN (x(p)) is the predicted value of DNN, F(x(p)) is the calculated value of the robust algorithm; η is the allowable input disturbance of robust MPC. If Then it means that the sample being evaluated meets the robust constraint requirements. The specific algorithm effect is as follows Figure 5 As shown, the specific algorithm is as follows:

[0089]

[0090]

[0091] S105 , determining the current phase distribution using a phase distribution prediction model according to the current incident light field and intensity distribution; and generating a kinoform diagram according to the current phase distribution.

[0092] As another specific embodiment, the present invention further provides a robust control system based on kinoform coding, comprising:

[0093] A control system building module, used to build a control system according to the incident light field and intensity distribution and the corresponding phase distribution;

[0094] A data set construction module is used to generate an attraction domain based on a control system using a robust model predictive control algorithm and soft constraints, and to construct a data set based on the attraction domain;

[0095] The data set expansion module is used to expand the data set according to the data set and the data density-based segmentation method;

[0096] A phase distribution prediction model determination module is used to train a symmetric neural network based on the expanded data set to determine the phase distribution prediction model;

[0097] The kinoform diagram generation module is used to determine the current phase distribution according to the current incident light field and intensity distribution using a phase distribution prediction model; and generate the kinoform diagram according to the current phase distribution.

[0098] In order to execute the method corresponding to the above-mentioned embodiment 1 to achieve the corresponding functions and technical effects, the present invention also provides a robust control system based on phase information pattern coding, which is characterized in that it includes: at least one processor, at least one memory and computer program instructions stored in the memory, and when the computer program instructions are executed by the processor, the described method is implemented.

[0099] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0100] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A robust control method based on kinoform coding, characterized in that: include: Construct a control system based on the incident light field, intensity distribution and corresponding phase distribution; Based on the control system, the robust model predictive control algorithm and soft constraints are used to generate the attraction domain, and a data set is constructed based on the attraction domain; According to the data set, the segmentation method based on data density is used to expand the data set; Based on the expanded data set, a symmetric neural network is trained to determine the phase distribution prediction model; According to the current incident light field and intensity distribution, a phase distribution prediction model is used to determine the current phase distribution; and a kinoform diagram is generated according to the current phase distribution; The segmentation method based on the data set and the data density is used to expand the data set, specifically including: Define data density as the number of samples per unit area; Determine the data density based on the sampling step size; The dataset is sampled according to the data density to obtain the expanded dataset.

2. The robust control method based on kinoform coding according to claim 1, characterized in that: The control system is constructed according to the incident light field, intensity distribution and corresponding phase distribution, specifically including the following formula: ； ； in, represents the incident light field at k sampling time, is the control system state, represents the incident light field at k+1 sampling time, represents the phase distribution, which is the input of the control system, is a random number, , and is the system model at different sampling times.

3. The robust control method based on kinoform coding according to claim 2, characterized in that: Based on the control system, the robust model predictive control algorithm and soft constraints are used to generate an attraction domain, and a data set is constructed based on the attraction domain, which specifically includes the following formulas: ； in, Based on the attraction domain The constructed dataset, is a positive definite weight matrix, is a robust performance indicator function greater than 0.

4. A robust control system based on kinoform coding, used to implement the robust control method based on kinoform coding according to any one of claims 1 to 3, characterized in that: include: A control system building module, used to build a control system according to the incident light field and intensity distribution and the corresponding phase distribution; A data set construction module is used to generate an attraction domain based on a control system using a robust model predictive control algorithm and soft constraints, and to construct a data set based on the attraction domain; The data set expansion module is used to expand the data set according to the data set and the data density-based segmentation method; A phase distribution prediction model determination module is used to train a symmetric neural network based on the expanded data set to determine the phase distribution prediction model; The kinoform diagram generation module is used to determine the current phase distribution according to the current incident light field and intensity distribution using a phase distribution prediction model; and generate the kinoform diagram according to the current phase distribution.

5. A robust control system based on kinoform coding, characterized in that: include: At least one processor, at least one memory, and computer program instructions stored in the memory, which implement the robust control method based on kinoform coding according to any one of claims 1 to 3 when the computer program instructions are executed by the processor.

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