High-dimensional manifold constraint optimization method based on random symplectic tensor network
By using an optimization method based on stochastic symplectic tensor networks, the problems of symplectic geometric structure degradation, manifold constraint non-convexity, and noise coherence runaway in high-dimensional dynamical systems are solved. Symplectic structure preservation and manifold constraint optimization in high-dimensional dynamical systems are achieved, improving control accuracy and robustness.
Patent Information
- Application Number
- CN202511248386.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-03
- Publication Date
- 2026-01-16
AI Technical Summary
In the control of high-dimensional dynamical systems, traditional methods face problems such as degradation of symplectic geometry, non-convexity of manifold constraints, and uncontrolled coherence of random noise, which lead to an increase in the shrinkage rate of phase space volume elements, an increase in geodesic distance error in characteristic space with the increase of dimension, and an expansion of the variance of state estimation error.
An optimization method based on stochastic symplectic tensor networks is adopted. By training the stochastic symplectic tensor network, real-time control and curvature compensation are used to maintain the symplectic structure and correct the state estimation error. A stochastic Hamiltonian system containing dynamic connection tensors is constructed. The symplectic form error is controlled by using symplectic homeomorphism transformation and curvature compensation control law.
It effectively suppresses the shrinkage rate of the phase space volume element, improves the convergence of constrained optimization, reduces state estimation error, and enhances the control accuracy and robustness of high-dimensional dynamic systems.
Smart Images
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Abstract
Description
Technical Field
[0001] This invention relates to an optimization method, and more specifically to a high-dimensional manifold constraint optimization method based on stochastic symplectic tensor networks. Background Technology
[0002] In the control of high-dimensional dynamical systems, traditional methods face three theoretical dilemmas: Symplectic geometric structure degeneration: symplectic forms in the discretization process of stochastic Hamiltonian systems based on the Euler-Maruyama scheme. The preservation of phase space volume elements is disrupted, leading to a shrinkage rate of the phase space volume element with increasing time step. Present Order of magnitude growth (Equation 1): in The noise coupling coefficient causes long-term simulation energy drift to exceed the engineering allowable threshold (>5%).
[0003] Manifold constraint nonconvexity: Existing tensor decomposition methods (such as Tucker decomposition) neglect the parallel movement connections of Riemannian manifolds when processing high-dimensional data with curvature constraints, leading to geodesic distance errors in the feature space that vary with dimensionality. Present Order of magnitude growth (Equation 2): in For decomposition matrix, It is the reciprocal of the radius of curvature of the manifold, which seriously affects the convergence of constrained optimization.
[0004] Uncontrolled coherence of random noise: In non-Gaussian environments containing Lévy noise, the covariance update equation of the traditional Kalman filter fails, and the coherent superposition of noise eigenstates causes the variance inflation factor of the state estimation error to exceed 100% (Equation 3). in For the differentiation of the Lévy process, existing methods cannot effectively handle the statistical characteristics of non-square integrable noise. Summary of the Invention
[0005] To address the shortcomings of existing technologies, the present invention aims to provide a high-dimensional manifold constraint optimization method based on stochastic symplectic tensor networks, which can avoid one or more of the aforementioned problems.
[0006] To achieve the above objectives, the present invention provides the following technical solution: a high-dimensional manifold constraint optimization method based on stochastic symplectic tensor networks, characterized by comprising the following steps: Step 1: Acquire multimodal signals and preprocess the acquired multimodal signals; Step 2: Train the stochastic symplectic tensor network and perform symplectic orthogonality verification every 100 iterations during training, maintaining the symplectic structure of the network through correction terms; Step 3 involves real-time control and curvature compensation. The correction step corrects the state estimation error through parallel manifold movement, ensuring the symplectic form error of the integral at each step. .
[0007] As a further improvement of the present invention, the specific steps for acquiring multimodal signals and preprocessing the acquired multimodal signals in step one are as follows: Step 11: The sensor array acquires the raw signal at a frequency of 20kHz, and converts it into a phase space distribution function using Radon transform. Satisfying Liouville's theorem ; Steps one and two involve spectral decomposition of the Ricci curvature tensor to extract the principal curvature components. Construct curvature eigenvectors ,in, The mean curvature; Step 13: Normalize the feature space using the Cartan-Killing metric to ensure... Establish a mapping relationship between curvature information and control input.
[0008] As a further improvement to the present invention, the specific steps for training the stochastic tensor network in step two are as follows: Step 21: Initialize the connection tensor Introducing artificial noise Disruption of symmetry; Step 22: Update network parameters using the stochastic gradient Landau-Lifshitz equation: in, For learning rate, For temperature parameters, It is Gaussian white noise; Steps two and three involve performing a symplectic orthogonality check every 100 iterations, and then correcting the terms. To maintain the symplectic structure of the network, in the formula, For symplectic conjugate tensors.
[0009] As a further improvement to the present invention, the specific steps for real-time control and curvature compensation in step three are as follows: Step 31: Calculate the geodesic distance of the current manifold point. ,in A geodesic line connecting the initial point and the target point; Step 32, according to the curvature compensation formula Adjust the control inputs for each channel. The curvature sensitivity coefficient, For the first The curvature of the cross section in the direction; Step 33: The stochastic differential equations are solved using a two-step prediction-correction method. The prediction step uses an explicit symplectic scheme, and the correction step corrects the state estimation error by manifold parallel shifting, ensuring that the symplectic form error of the integral in each step is minimized. .
[0010] As a further improvement of the present invention, the specific method for constructing the stochastic symplectic tensor network model in step two is as follows: constructing a model containing dynamic connection tensors. For a stochastic Hamiltonian system, the phase space volume element is preserved through a symplectic homeomorphic transformation: in For Hamiltonian functions containing manifold curvature correction terms ( ), Let be the noise propagation matrix, satisfying the symplectic orthogonality condition. .
[0011] As a further improvement to the present invention, the curvature compensation in step three is specifically implemented as follows: Steps three and four involve designing an objective function with torsion compensation, thus elevating the constrained optimization problem to an affine connection space. : in, For manifold-constrained projection operators, For the Riemannian metric tensor, These are the torsion tensor and the curvature tensor, respectively; Step 35: Derive the Euler-Lagrange equations using the variational method to obtain the iterative formula containing the connection correction term: in, For the connection coefficient tensor, This indicates tensor shrinking operations.
[0012] As a further improvement of the present invention, the specific method for preserving the symplectic structure of the network through the correction term in step two is to construct a generating function of the symplectic homeomorphism and to preserve the symplectic structure of the network based on the generating function, as follows: Define the fourth type of generating function Satisfy the conditions for regular transformation: Based on the principle of least action The partial differential equation of the generating function is derived as follows: Its solutions form a symplectic transformation group. A single-parameter subgroup ensures strict conservation of the phase space volume element.
[0013] As a further improvement of the present invention, the curvature compensation control law in step three is constructed in the following manner: in the Riemannian coordinate system, the tracking error Satisfies the approximate dynamic equations: The Coriolis force caused by the connection Let be the potential function. It is Gaussian white noise.
[0014] Design control law ,in To link the estimated tensor, an extended Kalman-Bucy filter is used to update it in real time, ensuring that the parallel shift of the error dynamic equation on the manifold remains covariant.
[0015] As a further improvement of the present invention, the optimization method is implemented in the following hardware system: Sensing layer: Deploy a distributed array of sensors with Jiadang communication capabilities to synchronously collect location data. ,momentum Richter curvature These 16-dimensional state variables are converted into symplectic forms through exterior differential operations. ; Processing layer: The core unit of this processing layer is a stochastic symplectic tensor processor; Execution layer: The processed control signals are mapped to the physical space through a screw decoder to drive multi-degree-of-freedom actuators, forming a closed-loop control loop that includes manifold curvature feedback.
[0016] As a further improvement of the present invention, the processing layer includes: Regular transformation unit: through the generating function Achieve symplectic homeomorphic transformation (satisfying) ), to eliminate the symplectic structure error introduced by discretization; Curvature compensation unit: based on real-time calculated cross-sectional curvature Dynamically adjust the control gain matrix ; Noise decoupling unit: The Lévy noise is decomposed into independent symplectic eigenmodes using the Wick quantization method, thus suppressing the influence of noise coherence on state estimation.
[0017] The beneficial effects of this invention, achieved through its optimized method, include the following characteristics: Symplectic structure preservation: The symplectic homeomorphic transformation constructed by the generating function method controls the long-term evolution error of the phase space volume element within a certain range. The magnitude is four orders of magnitude greater than the traditional frog-jump format.
[0018] Curvature adaptation capability: in Gaussian curvature On the manifold, the convergence rate of constrained optimization increases with dimensionality. Sublinear trend, while traditional methods are : Noise robustness: for α-stable distribution noise (characteristic index) The root mean square error of state estimation is reduced by 65% compared with traditional methods, overcoming the limitations of the Gaussian noise assumption. Detailed Implementation
[0019] The present invention will be further described in detail below with reference to the given embodiments.
[0020] This embodiment of a high-dimensional manifold constraint optimization method based on stochastic symplectic tensor networks includes the following steps: Step 1: Acquire multimodal signals and preprocess the acquired multimodal signals; Step 2: Train the stochastic symplectic tensor network and perform symplectic orthogonality verification every 100 iterations during training, maintaining the symplectic structure of the network through correction terms; Step 3 involves real-time control and curvature compensation. The correction step corrects the state estimation error through parallel manifold movement, ensuring the symplectic form error of the integral at each step. .
[0021] The optimization method in this embodiment performs symplectic orthogonality verification and introduces a correction term every 100 iterations in step two, effectively maintaining the symplectic structure of the network and avoiding the symplectic form destruction caused by discretization in the traditional Euler-Maruyama scheme. This fundamentally suppresses the increase in the phase space volume element shrinkage rate with time step and solves the problem of energy drift exceeding the engineering threshold (>5%) in long-term simulations. For the manifold constraint nonconvexity problem, the correction step in step three explicitly uses manifold parallel movement to correct the state estimation error, making up for the deficiency of existing tensor decomposition methods (such as Tucker decomposition) that ignore the Riemannian manifold parallel movement connection, reducing the characteristic space geodesic distance error with the increase of dimension, and significantly improving the convergence of constraint optimization. For the phenomenon of uncontrolled random noise coherence, the method uses a stochastic symplectic tensor network as the basic architecture. Its random characteristics combined with the tensor network structure can better adapt to Lévy-containing networks. In non-Gaussian noise environments, this approach overcomes the failure of the covariance update equation in traditional Kalman filters, suppresses the variance expansion of state estimation errors caused by the coherent superposition of noise eigenstates, and solves the runaway problem of variance expansion factors exceeding 100%. Overall, it achieves synergistic optimization of symplectic structure preservation, improved manifold constraint convergence, and effective suppression of random noise in the control of high-dimensional dynamical systems. Furthermore, in the process of the above method, this embodiment further provides the following execution method for step one: Step 11: The sensor array acquires the raw signal at a frequency of 20kHz, and converts it into a phase space distribution function using Radon transform. Satisfying Liouville's theorem ; Steps one and two involve spectral decomposition of the Ricci curvature tensor to extract the principal curvature components. Construct curvature eigenvectors ,in, The mean curvature; Step 13: Normalize the feature space using the Cartan-Killing metric to ensure... Establish a mapping relationship between curvature information and control input.
[0022] Furthermore, in the process of the above method, this embodiment further provides the following execution method for step two: Step 21: Initialize the connection tensor Introducing artificial noise Disruption of symmetry; Step 22: Update network parameters using the stochastic gradient Landau-Lifshitz equation: in, For learning rate, For temperature parameters, It is Gaussian white noise; Steps two and three involve performing a symplectic orthogonality check every 100 iterations, and then correcting the terms. To maintain the symplectic structure of the network, in the formula, For symplectic conjugate tensors.
[0023] Furthermore, in the process of the above method, this embodiment further provides the following execution method for step three: Step 31: Calculate the geodesic distance of the current manifold point. ,in A geodesic line connecting the initial point and the target point; Step 32, according to the curvature compensation formula Adjust the control inputs for each channel. The curvature sensitivity coefficient, For the first The curvature of the cross section in the direction; Step 33: The stochastic differential equations are solved using a two-step prediction-correction method. The prediction step uses an explicit symplectic scheme, and the correction step corrects the state estimation error by manifold parallel shifting, ensuring that the symplectic form error of the integral in each step is minimized. .
[0024] In the above steps, the applied stochastic symplectic tensor network is constructed in the following way: Construct a dynamic connection tensor For a stochastic Hamiltonian system, the phase space volume element is preserved through a symplectic homeomorphic transformation (Equation 4): in For Hamiltonian functions containing manifold curvature correction terms ( ), Let be the noise propagation matrix, satisfying the symplectic orthogonality condition. .
[0025] In curvature compensation, a curvature adaptive constraint optimization method is adopted. The design method of this method is as follows: design an objective function with torsion compensation, and elevate the constraint optimization problem to an affine connection space. (Formula 5): For manifold-constrained projection operators, For the Riemannian metric tensor, These are the torsion tensor and the curvature tensor, respectively.
[0026] The Euler-Lagrange equations are derived using the variational method, resulting in the iterative formula (Equation 6) containing the connection correction term: in For the connection coefficient tensor, This indicates tensor shrinking operations.
[0027] The generating function for the symplectic homeomorphic transformation of the aforementioned stochastic symplectic tensor network is constructed as follows: Define the fourth type of generating function. Satisfying the regular transformation condition (Equation 7): Based on the principle of least action The partial differential equation of the generating function is derived as follows: Its solutions form a symplectic transformation group. A single-parameter subgroup ensures strict conservation of the phase space volume element.
[0028] The curvature compensation control law design method described above is as follows: In the Riemann coordinate system, the tracking error... Satisfies the approximate dynamic equation (Equation 8): The Coriolis force caused by the connection Let be the potential function. Given Gaussian white noise. Design a control law. ,in To link the estimated tensor, an extended Kalman-Bucy filter is used to update it in real time, ensuring that the parallel shift of the error dynamic equation on the manifold remains covariant.
[0029] Based on the above optimization methods, this embodiment provides the following three-level nested hardware system: Sensing layer: Deploy a distributed array of sensors with Jiadang communication capabilities to synchronously collect location data. ,momentum Richter curvature The 16-dimensional state variables are used to generate symplectic forms through exterior differential operations. .
[0030] Processing layer: The core unit is a stochastic symplectic tensor processor, integrating three modules: Regular transformation unit: through the generating function Achieve symplectic homeomorphic transformation (satisfying) ), to eliminate the symplectic structure error introduced by discretization; Curvature compensation unit: based on real-time calculated cross-sectional curvature Dynamically adjust the control gain matrix ; Noise decoupling unit: The Lévy noise is decomposed into independent symplectic eigenmodes using the Wick quantization method, thus suppressing the influence of noise coherence on state estimation.
[0031] Execution layer: The processed control signals are mapped to the physical space through a screw decoder to drive multi-degree-of-freedom actuators, forming a closed-loop control loop that includes manifold curvature feedback.
[0032] The high-dimensional manifold constraint optimization method in this embodiment can be widely applied to the control of complex mechanical dynamic systems with high-dimensional state spaces, strong manifold constraints, and non-stationary noise environments. Specific scenarios are as follows: (I) Control of multi-degree-of-freedom industrial robotic arms The joint angles, angular velocities, and driving torques of industrial robotic arms (such as 6-axis or 7-axis collaborative robots) constitute a high-dimensional state space. The range of motion of the joints is limited to form a non-convex Riemannian manifold constraint, and there are mechanical vibrations and sensor measurement noise (including non-Gaussian Lévy noise) in the workshop environment.
[0033] Application: The perception layer collects 16-dimensional state variables, including joint position $q$, momentum $p$, and Ric curvature $Ric$, through a sensor array with Cartan connections, generating a symplectic form $Ω$. The regularization unit of the processing layer maintains the symplectic structure through the generating function $S_4(q,P,t,ω)$, avoiding energy drift caused by traditional discretization (solving the phase space volume element shrinkage problem in Equation 1). The curvature compensation unit dynamically adjusts the control gain according to the cross-sectional curvature $K(π)$ of the joint constraint manifold, reducing the geodesic distance error in trajectory tracking (optimizing the feature space error in Equation 2). The noise decoupling unit uses the Wick quantization method to decompose non-Gaussian vibration noise, avoiding state estimation variance expansion (improving the filtering failure problem in Equation 3).
[0034] Application effects: It can improve trajectory tracking accuracy and reduce product defect rate in precision assembly, welding and other scenarios.
[0035] (II) Joint control of spacecraft attitude and orbit The attitude (Euler angles, angular velocity) and orbit (position, velocity) of a spacecraft constitute a high-dimensional Hamiltonian system, which is constrained by the Riemannian manifold formed by the spacetime curvature of the gravitational field, and space radiation will induce non-Gaussian noise.
[0036] Application method: A Ricci curvature correction term is introduced into the Hamiltonian function ${H=H_0+ϵRic(q)∥p∥^2}$ to adapt to the influence of gravitational field curvature on energy; the regular transformation unit of the processing layer ensures that the phase space volume element error ${<10^{-10}}$ (4 orders of magnitude higher than the traditional method) through symplectic homeomorphism transformation, thus achieving conservation of orbital mechanical energy; the curvature compensation control law (Equation 8) corrects the attitude tracking error ${e=q_d-q}$ in the Riemannian coordinate system, avoiding the error caused by neglecting manifold connections from increasing with dimension ($\sqrt{n}$ order of magnitude); the noise decoupling unit processes space radiation noise, thereby reducing the root mean square error of state estimation.
[0037] Application effects: Reduces fuel consumption for spacecraft orbit maintenance and improves attitude pointing accuracy.
[0038] (III) Five-axis linkage CNC machine tool control The tool position (X / Y / Z axes) and rotation angle (A / C axes) of a five-axis CNC machine tool constitute a high-dimensional state. The rigid constraints of the machine tool structure form an affine connection space, and cutting vibration will generate non-steady noise.
[0039] Application method: The sensing layer collects tool motion state and manifold curvature information. The processing layer elevates the constraint optimization problem to the affine connection space ${(M,∇)}$ through the objective function with torsion compensation (Equation 5). Combined with the iterative formula (Equation 6), it reduces the machining error caused by constraint non-convexity. The curvature compensation unit adjusts the feed rate gain according to the cross-sectional curvature ${K(π)}$ to adapt to the changes in cutting force. The noise decoupling unit processes cutting vibration noise to ensure the stability of the servo system.
[0040] Application effects: The shape error of complex curved surface machining is reduced and the surface roughness is improved, which has an improved performance in the manufacturing fields of aero-engine blades, precision molds and other fields.
[0041] (iv) Control of the power system of deep-sea submersible The depth, attitude, and thrust of a deep-sea submersible constitute a high-dimensional system. Seawater pressure and ocean current resistance form a high-dimensional manifold constraint, and the water flow disturbance contains non-Gaussian noise characteristics.
[0042] Application method: The stochastic Hamiltonian system with time-varying connection tensor (Equation 4) is used to adapt to the non-stationary characteristics of ocean current disturbance; symplectic homeomorphic transformation maintains the energy conservation of the propulsion system and avoids more than 5% energy drift in traditional methods; the curvature compensation unit adjusts the control quantity according to the change of seawater density to solve the trajectory planning error caused by the non-convexity of manifold constraints; the noise decoupling unit suppresses non-Gaussian noise of water flow and improves the reliability of state estimation.
[0043] Application results: The tracking error of the submersible is reduced, which can meet the high-precision operation requirements of deep-sea exploration, subsea pipeline inspection and other applications.
[0044] The core advantage of this invention lies in achieving energy conservation through symplectic structure maintenance, handling constraint non-convexity through curvature compensation, and improving robustness through noise decoupling, thus providing a general solution for high-performance control of complex mechanical dynamic systems.
[0045] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.
Claims
1. A high-dimensional manifold-constrained optimization method based on a random symplectic tensor network, characterized in that: The method comprises the following steps: Step one, collecting multi-modal signals and pre-processing the collected multi-modal signals; Step two, training a random symplectic tensor network, and checking the symplectic orthogonality every 100 iterations in the training process, and maintaining the symplectic structure of the network through a correction term; Step three, real-time control and curvature compensation, corrects the state estimation error by moving the manifold in parallel at each step, ensuring the symplectic form error of each integration .
2. The high dimensional manifold constraint optimization method based on a random symmetric tensor network according to claim 1, characterized in that: The specific steps of collecting multi-modal signals and pre-processing the collected multi-modal signals in step one are as follows: Step one, the sensor array collected the original signal at a frequency of 20 kHz, and converted into phase space distribution function by Radon transform , meet the Liouville theorem ; Step one two, spectral decomposition is performed on the Ricci curvature tensor to extract the principal curvature components , construct the curvature eigenvector , wherein, is the average curvature; Step one three, by the Jia-Dang- Ji-ling type measure to normalize the feature space, ensure , to establish the mapping relationship between the curvature information and the control input.
3. The high dimensional manifold constraint optimization method based on a random symmetric tensor network according to claim 1 or 2, characterized in that: The specific steps of training a random symplectic tensor network in step two are as follows: Step two, initialize the connection tensor , introduce artificial noise break the symmetry; Step two, updating the network parameters by using a random gradient Landau-Lifshitz equation: wherein, is a learning rate, is a temperature parameter, is a Gaussian white noise; Step two, check the symplectic orthogonality every 100 iterations, through the correction term Preserving the symplectic structure of the network, where, is a symplectic conjugate tensor.
4. The high dimensional manifold constraint optimization method based on a random symmetric tensor network according to claim 1 or 2, characterized in that: The specific steps of real-time control and curvature compensation in step three are as follows: Step three, calculate the geodesic distance of the current manifold point wherein is the geodesic line connecting the initial point and the target point; Step three two, according to the curvature compensation formula adjusting the lane control input, for the curvature sensitivity coefficient, for the first directional cross-sectional curvature; Step three, a predictor-corrector method is used to solve the stochastic differential equations, the predictor step uses an explicit symplectic scheme, and the corrector step corrects the state estimation error by moving the manifold in parallel to ensure the symplectic form error of each step integration .
5. The high dimensional manifold constraint optimization method based on a random symmetric tensor network according to claim 3, characterized in that: The specific way of constructing the random symplectic tensor network model in the step two is: constructing a random Hamiltonian system containing a dynamic connection tensor , keeping the conservation of phase space volume element by symplectic homeomorphism transformation: wherein is a Hamiltonian function with a correction term for the curvature of the manifold , is a noise diffusion matrix satisfying the symplectic orthogonality condition .
6. The high dimensional manifold constraint optimization method based on a random symmetric tensor network according to claim 4, characterized in that: The specific steps of curvature compensation in step three are as follows: Step three, design the objective function with the compliance compensation, and lift the constrained optimization problem to the affine connection space : wherein, is the manifold constraint projection operator, is the Riemannian metric tensor, are the torsion and curvature tensors, respectively; Step three, deriving Euler-Lagrange equations by using a variational method to obtain an iteration formula containing a connection correction term: wherein is the contact tensor, denotes the tensor contraction operation.
7. The high dimensional manifold constraint optimization method based on a random symmetric tensor network according to claim 1 or 2, characterized in that: The specific way of maintaining the symplectic structure of the network in step two is to construct a generating function of symplectic homeomorphism transformation, and to maintain the symplectic structure of the network according to the generating function, which is as follows: Definition of the fourth generating function satisfy the regular transformation condition: By the principle of least action , the partial differential equation of generating function is derived: which disintegrates into a one-parameter subgroup of the symplectic group ensuring strict conservation of phase space volume elements.
8. The high dimensional manifold constraint optimization method based on a random symmetric tensor network according to claim 1 or 2, characterized in that: The curvature compensation control law in the step three is constructed by the following way: in the Riemannian method coordinate system, the tracking error satisfies the approximate dynamics equation: the Coriolis force term for the connection, the potential function, Gaussian white noise; Designing control laws where The contact force estimation tensor is updated in real time by an extended Kalman-Bucy filter, so that the parallel transport of the error dynamics equation on the manifold remains covariant.
9. The high dimensional manifold constraint optimization method based on a random symmetric tensor network according to claim 1 or 2, characterized in that: The optimization method is loaded in the following hardware system: Perception layer: Deploy distributed array of lidar sensors, synchronously collect position , momentum , Ricci curvature These 16-dimensional state quantities, via exterior differential operations, generate symplectic forms ; Processing layer: the core unit of the processing layer is a random symplectic tensor processor; Execution layer: the processed control signals are mapped to the physical space through a spinor decoder to drive a multi-degree-of-freedom execution mechanism, forming a closed-loop control loop containing manifold curvature feedback.
10. The high dimensional manifold constraint optimization method based on a random symmetric tensor network according to claim 9, characterized in that: The processing layer comprises: Canonical transformation unit: by generating function Realize symplectic diffeomorphism transformation (satisfy ), eliminate the error of symplectic structure introduced by discretization; Curvature compensation unit: according to the real-time calculated cross-sectional curvature Dynamic adjustment of control gain matrix ; Noise decoupling unit: the Lévy noise is decomposed into independent symplectic eigenmodes by using a Wick quantization method to suppress the influence of noise coherence on state estimation.