A time-series geodesic-based pan-tod multi-dimensional lattice coordinate real-time dynamic management method and system

Abstract

The application discloses a kind of based on timing geodesic line's pan-TOD multidimensional lattice coordinate real-time dynamic management method and system, belong to dynamic system control and resource scheduling cross technical field.The present application is strictly dependent on exclusive bottom mathematical relationship, memory operator adopts golden section attenuation factor to balance convergence speed and steady-state error, lattice reorganization operator realizes multidimensional lattice coordinate real-time dynamic management, opens the fusion channel of discrete resource and continuous fluid, as core solving timing geodesic line, generates global optimum, no shock, no tearing evolution trajectory, to solve the defects such as physical shock, local optimum, insufficient use of historical information, mapping fault, algorithm conflict of prior art.The present application constructs core operator by exclusive bottom mathematical relationship, adapts 5 kinds of typical application scenarios, with novelty, creativity and practicality, suitable for terahertz communication, intelligent power distribution network, fluid transport, mechanical arm cooperation, computing power network and other kinds of high-dimensional dynamic system.

Description

Technical Field

[0001] This invention relates to the field of dynamic system control and resource scheduling, and in particular to a real-time dynamic management method and system for multidimensional lattice coordinates of pan-TOD based on time-series geodesics. Background Technology

[0002] In various engineering dynamic systems, when system commands change (such as target position updates, operating mode switching, or sudden load changes), existing mainstream control technologies generally suffer from many fundamental technical defects that are difficult to overcome. These defects overlap and restrict each other, making it impossible to meet the requirements of stable operation, precise control, and efficient scheduling for high-end complex dynamic systems. The specific defects are detailed below: 1. While traditional step response control or Bang-Bang control offers rapid response, it generates severe state discontinuities at the physical constraint boundaries of the actuator, inducing violent physical shock waves that pose a fatal threat to equipment lifespan and system stability. In terahertz communication scenarios, instantaneous jitter in beam pointing can directly lead to link loss of lockout and a significant spike in bit error rate, resulting in frequent communication link interruptions. In smart distribution network scenarios, the massive circulating current caused by voltage phase angle differences can directly damage core power equipment such as switches and transformers, causing power supply failures. In long-distance fluid transportation scenarios, the water hammer effect generated by rapid valve closure can easily cause pipeline rupture and valve damage, leading to safety accidents and transportation interruptions. These physical shock wave problems are inherent defects that traditional control technologies cannot avoid.

[0003] 2. Existing PID control is a typical example of passive error following regulation, completely lacking the ability to predict the curvature of the future path. During operation, it is prone to overshoot and continuous oscillation, resulting in extremely low control accuracy. Although Model Predictive Control (MPC) can optimize the cost function in the finite time domain, its core is to solve for the steepest descent direction in a flat Euclidean space, completely ignoring the curvature of the state manifold formed by the system's historical memory. When the system faces complex operating conditions with large-scale trajectory changes and multiple constraints, it will still experience severe overshoot or fall into local oscillations, and will be unable to generate a globally optimal evolution path, making it difficult to adapt to the control requirements of complex high-dimensional dynamic systems.

[0004] 3. Most existing control laws rely solely on linear combinations of instantaneous errors e(t). The system's past trajectory and evolutionary trend are represented only by the integral term I, resulting in a very coarse representation—a typical "short-sighted" forgetting mechanism. For dynamic systems with complex inertia, time delays, and multivariate coupling characteristics, this inefficient use of historical information fails to uncover inertial patterns and disturbances in the historical trajectory. This easily induces long-term system oscillations and decision-making conflicts, leading to an inability to maintain a stable and consistent operating state and extremely poor long-term reliability.

[0005] 4. In core scenarios of high-dimensional resource management such as computing power networks, spectrum allocation, and storage scheduling, the system state space is essentially a hybrid of discrete lattices and continuous manifolds. Computing nodes, spectrum resource blocks, and storage units are discretely distributed in a lattice-like manner, while computing load, fluid velocity, and signal phase change continuously and dynamically. Existing technologies cannot establish a lossless mapping relationship between discrete lattices and continuous manifolds. Forced linearization will lead to "lattice tearing," causing resource fragmentation and scheduling chaos; forced discretization will lead to "fluid rigidity," losing the flexibility of continuous resource evolution. Currently, no universal method has been proposed in the industry that can automatically solve for the smoothest and most economical evolution path in a discrete lattice coordinate system, resulting in persistently low resource scheduling efficiency and utilization.

[0006] 5. In complex dynamic environments, single control methods cannot cope with multimodal disturbances, requiring the combination of heterogeneous technical modules such as time-domain smoothing controllers and frequency-domain compensators. However, existing combinations suffer from deep-seated algorithmic coordination obstacles: First, time-domain smoothing pursues continuous curvature of the state trajectory, tending towards slow, gradual changes, while frequency-domain compensation aims to quickly offset resonance peaks, tending towards rapid response. The phase margins of these two approaches are inherently contradictory, and simple parallel connection can easily induce new resonance peaks, even leading to system instability. Second, the time-domain and frequency-domain modules each optimize local objectives, with independent objective functions and a lack of a unified overall framework. The superposition of local optima cannot form a global optimum. Third, the weight allocation of the time-domain and frequency-domain modules relies entirely on manual trial and error by engineers, lacking objective mathematical basis. Fixed weights cannot be adaptively adjusted during multi-condition switching, resulting in significant fluctuations in control performance. In summary, existing technologies cannot unify time-domain smoothing, frequency-domain analysis, and global variational optimization from a mathematical foundation, nor can they resolve the conflicts between heterogeneous module algorithms. A novel technical solution is urgently needed to overcome all of these shortcomings. Summary of the Invention

[0007] In view of this, the present invention provides a real-time dynamic management method and system for multidimensional lattice coordinates of pan-TOD based on time-series geodesics, in order to solve or alleviate one of the technical problems existing in the prior art, and at least provide a beneficial option.

[0008] The technical solution of this invention is implemented as follows: a real-time dynamic management method for multidimensional lattice coordinates of pan-TOD based on time-series geodesics, comprising the following complete steps: Step 1: System state acquisition and initialization, real-time acquisition of the current state vector of the target high-dimensional dynamic system. With the preset target state vector The high-dimensional dynamic system includes a terahertz communication system, a smart power distribution network, a long-distance fluid transport system, a multi-axis robotic arm, and a national-level computing power network. The state vector includes physical operation parameters, resource distribution parameters, and operating condition evolution parameters. Step two: Generation of historical inertia correction term, using a term with a decay factor. The convolution kernel performs a weighted integral on the system's historical state sequence to generate a historical inertia correction term. Historical inertia correction term The virtual kinetic energy required to characterize the system's departure from its original evolution trajectory is used as the input to the kinetic energy term of the Pianhong equation. Step 3: Critical state determination and transition command generation, calculating the generalized potential energy gradient between the current system state and the target state. The gradient norm is monitored in real time. When the gradient norm exceeds the preset threshold θ, a state transition enable signal is generated as the potential energy term input of the Pianhong equation and the basis for state transition decision. When the deviation is too large, a global path transition is triggered, and when the deviation is small, the existing topology remains stable. Step 4: Trajectory gradient smoothing. The Laplace second-order differential operator is applied to the system state field to force the state change rate of adjacent time steps and spatial nodes to remain continuous. A curvature smoothing dissipation regularization term is constructed to suppress abrupt changes in state acceleration and eliminate physical shock waves and lattice tearing phenomena. This term is used as the input of the dissipation term in the Pianhong equation. Step 5: Multidimensional lattice coordinate mapping and reshaping, which maps the system's physical resources, computing resources, and communication resources to four-dimensional lattice coordinates that include the time dimension. ,in For physical or computational space coordinates, As evolution time coordinates, lattice renormalization potentials are generated through lattice renormalization operators. This enables lattice elastic deformation, temporal coordinate locking, and topological defect repair, serving as the input to the lattice renormalization potential term of the Pianhong equation. Step Six: Construction of the Phantom Equation and Solution of the Global Optimal Trajectory. Based on the well-known Euler-Lagrange variational equations, this step integrates the kinetic energy term generated by the memory operator, the potential energy term generated by the critical operator, the dissipative regularization term generated by the gradient smoothing operator, and the lattice renormalization potential term generated by the lattice renormalization operator to construct a unique Phantom equation and define the extended Lagrange quantity. Substituting the equations into the Euler-Lagrange equations and solving the second-order partial differential equations, we obtain the globally optimal smooth evolution trajectory of the system from the current state to the target state. ; Step 7: Control command output and execution. Based on the globally optimal smooth evolution trajectory obtained by solving, control commands adapted to the system actuators are generated and issued in real time to drive the system to run smoothly along the optimal trajectory, achieving dynamic control and resource scheduling without oscillation or tearing and with global optimality.

[0009] Preferably, the attenuation factor α of the memory operator in this invention is an inherent constant of the technical system of this invention, determined by the characteristics of the technical structure, requiring no manual parameter tuning, and possessing global adaptability and optimality. The value range of α is 0.5≤α≤0.7.

[0010] Preferably, the mathematical expression of the lattice renormalization operator is:

[0011] in Given the i-th dimensional lattice potential, this operator possesses three core functions: Firstly, the lattice elastic deformation function allows the lattice spacing to be dynamically adjusted according to the real-time load when computing power fluid or physical medium flows through the transmission interface. The lattice is automatically densified in high-load areas and automatically sparsed in low-load areas, achieving zero resource waste and efficient adaptation. Secondly, the time-series coordinate locking function relies on the golden ratio decay factor. =0.618, ensuring the lattice in the time dimension The evolution path is the densest temporal packing path, avoiding the lattice misalignment problem caused by excessively large time slices in traditional scheduling; Third, the topology defect repair function monitors lattice anomalies such as computing power overflow, link congestion, and state distortion in real time. It triggers phase transitions through critical operators and eliminates lattice dislocations in conjunction with gradient smoothing operators, thereby achieving lossless migration of resources and states.

[0012] Preferably, the extended Lagrange expression of the Pianhong equation is as follows:

[0013] in The inertia weight coefficients corresponding to the memory operator. The response intensity coefficients corresponding to the critical operator are: This represents the smoothing diffusion coefficient corresponding to the gradient smoothing operator. The lattice renormalization intensity coefficients are the lattice renormalization operators. Each parameter corresponds to the output of a dedicated operator. All parameters and operators are incorporated into a unified variational framework for overall scheduling. There is no technical logic independent of the Pianhong equation. It achieves deep collaboration of time-domain smoothing, critical control, and lattice renormalization from a mathematical foundation, completely eliminating conflicts between multi-module algorithms.

[0014] Preferably, the Pianhong equation is obtained by substituting the Euler-Lagrange equation. The global optimal trajectory is solved based on the principle of least action. It automatically finds the global optimal balance point between response speed, trajectory smoothness, resource utilization, and steady-state accuracy without the need for manual setting of the weight ratio of each module. It achieves fully autonomous adaptive global optimization, which is different from the local optimization and passive following logic of traditional control technology.

[0015] Preferably, the Pianhong equation differs substantially from the well-known Euler-Lagrange equation, specifically in that: the kinetic energy term is replaced by a memory inertia correction term instead of the traditional physical velocity-related term, incorporating the historical evolution trend of the system; the potential energy term is replaced by a critical deviation potential energy instead of the traditional physical potential energy, adapting to the critical control requirements of dynamic systems; a new curvature smoothing dissipation term is added to force smooth trajectory without abrupt changes; a new multidimensional lattice renormalization potential term is added to achieve seamless integration of discrete and continuous resources; and a new frequency domain perturbation penalty term is added to adapt to the periodic perturbation suppression requirements. These differences make the Pianhong equation a core mathematical model specifically for dynamic control and resource scheduling in general TOD, rather than a simple rewrite of a well-known equation.

[0016] As a preferred approach, this method forms a unified pan-TOD architecture centered on the Pianhong equation. It can adaptively adapt its operating mode according to the complexity of system disturbances. In a single weak disturbance scenario, it enables the basic operator collaborative mode, while in a complex strong disturbance scenario, it enables the full operator coordination mode. The entire process is uniformly scheduled by the Pianhong equation without the need to change the core algorithm and hardware architecture. It has strong scenario adaptability and robustness and can cover various high-dimensional dynamic systems with extremely high requirements for state continuity and operational stability.

[0017] Preferably, the management method according to any one of claims 1 to 7 includes a data acquisition unit, a core computing unit, a Pianhong equation solving unit, an execution driving unit, and a storage unit; the data acquisition unit is used to collect the current state, target state, and historical state sequence data of the target dynamic system in real time and transmit them to the core computing unit; the core computing unit integrates a memory operator module, a critical operator module, a gradient smoothing operator module, and a lattice renormalization operator module, which respectively complete the functions of generating historical inertia correction terms, judging critical states, smoothing trajectories, and multidimensional lattice mapping and renormalization, and transmit the results of each operation. The system includes a Pianhong equation solving unit, which is the core computing module used to construct the Pianhong equation and substitute it into the Euler-Lagrange equation to solve for the global optimal trajectory; an execution drive unit is used to receive control commands corresponding to the optimal trajectory and drive the system's actuators to move; a storage unit is used to store system operating parameters, operator configuration parameters, historical operating data, and core algorithm programs to ensure stable system operation; the system can be integrated and adapted as any one of the following: a terahertz communication beam controller, a power distribution network loop controller, a fluid conveying valve controller, a robotic arm collaborative controller, or a computing power network scheduling controller.

[0018] Preferably, the core computing unit and the Pianhong equation solving unit adopt a heterogeneous computing architecture, which balances control flexibility and real-time operation. The general-purpose processor is responsible for data acquisition, instruction interaction, parameter configuration and system scheduling, while the programmable logic device is responsible for the parallel high-speed operation of the core operator and the Pianhong equation. The dedicated computing hard core is used to realize formula solving and trajectory generation. The operation step size is precisely synchronized with the system sampling period, which meets the control requirements of high dynamic and high real-time systems. At the same time, it can be directly embedded into the existing control system without modifying the underlying hardware, and has excellent compatibility and scalability.

[0019] Preferably, the device includes a lattice mapping module, a timing locking module, a defect repair module, and a core coordination module. The lattice mapping module maps the discrete resources and continuous states of the target system to four-dimensional temporal lattice coordinates, completing a lossless conversion between discrete and continuous spaces. The timing locking module, relying on the golden ratio decay factor α=0.618, locks the lattice temporal evolution path, ensuring the densest temporal packing and avoiding lattice misalignment. The defect repair module monitors the lattice distortion state in real time and, in conjunction with critical control logic, completes dislocation elimination and anomaly repair. The core coordination module incorporates the core program of the Pianhong equation, unifying the scheduling of the three functions of lattice mapping, timing locking, and defect repair, and solving for the globally optimal evolution trajectory of the lattice coordinates. This device is suitable for high-dimensional discrete-hybrid resource scheduling scenarios, enabling fluid and smooth resource scheduling and dynamic and precise management of lattice coordinates, completely different from the fixed architecture and linear logic of existing resource scheduling devices.

[0020] Using a specific attenuation factor The convolution kernel performs a weighted integral on the system's historical state sequence, which is the core source of the kinetic energy term in the Pianhong equation. The attenuation factor ranges from 0.5 ≤ α ≤ 0.7, and the memory operator outputs the historical inertia correction term at the current moment. The virtual kinetic energy required to deviate from the original evolutionary trajectory is used as the core input of the Pianhong equation to avoid short-sighted oscillations.

[0021] Critical Operator

[0022] Calculate the generalized potential gradient between the current system state and the target state. It is a key component of the potential energy term in the Phantom Equation. When the gradient norm exceeds the preset threshold θ, a state transition enable signal is triggered. This operator is a nonlinear phase-change switch, which solves the core contradiction between response speed and overshoot suppression in smooth control. When the deviation is too large, it breaks the local stability valley and transitions to the global optimal path. When the deviation is small, it maintains the topology and avoids jitter, providing a basis for state transition decisions for the Phantom Equation.

[0023] Gradient Smoothing Operator

[0024] By applying the second-order Laplace differential operator to the state field, the rate of change of the state at adjacent time steps or spatial nodes is forced to remain continuous, forming the dissipation regularization term of the Pianhong equation. Mathematically, this is equivalent to introducing a curvature penalty term, which directly suppresses abrupt acceleration changes, eliminates shock wave and lattice tearing phenomena, and ensures the extreme smoothness of the Pianhong equation's output trajectory.

[0025] Lattice Renormalization Operator

[0026] The core new operator of this invention's pan-TOD technology is the core source of the lattice renormalization potential term in the Phantomhive equation, specifically used for real-time dynamic management of multidimensional lattice coordinates. It transfers the system state... Mapping to four-dimensional lattice coordinates ,in Physical / computing space coordinates, For the evolutionary time coordinates, the operator's mathematical expression is as follows:

[0027] in For the i-th dimensional lattice potential field, this operator implements three core management mechanisms: First, lattice elastic deformation; when computing power flows through the interface, the lattice spacing dynamically adjusts with the load, resulting in denser lattice under high load and sparser lattice under low load, achieving zero resource waste; Second, time-series coordinate locking, relying on... =0.618 golden decay factor, ensuring that the lattice time-series evolution path is the densest packing path and avoiding lattice misalignment; third, topology defect repair, when lattice distortions such as computing power overflow and link congestion are detected, the critical operator triggers phase transition transition, and the gradient smoothing operator eliminates lattice dislocations, realizing lossless resource migration.

[0028] The Piaohong Equation – A Unified Variational Framework for Pan-TOD

[0029] The Pianhong Equation is the core coordinating mechanism of the pan-TOD technology of this invention. All operators and modules operate around this equation. It is a dedicated dynamic system global optimal trajectory solution mathematical model formed by integrating the inertia correction term of the pan-TOD memory operator, the FFT frequency domain perturbation penalty term, and the multidimensional lattice renormalization potential field term on the basis of the known Euler-Lagrange variational framework. It resolves the algorithm conflicts between the time domain and frequency domain modules from the mathematical foundation and achieves global synergistic efficiency.

[0030] Definition of Extended Lagrange

[0031] The extended Lagrange quantity L of the system is defined as a core component of the Penny equation, and its specific expression is as follows:

[0032] Equation Parameter Correspondence Table

[0033] Euler-Lagrange equations

[0034] Substituting the extended Lagrange into the known Euler-Lagrange equations and solving the second-order partial differential equations yields the system's globally optimal evolution trajectory, as shown in the following formula:

[0035] Comparison table of differences with the well-known Euler-Lagrange equation

[0036] This invention constructs a terminal-side time-domain trend prediction equation, called the "flowing water equation." For the i-th terminal, the time slot difference is defined as follows:

[0037] in The signal propagation delay corresponding to the nth time slot can be a timing parameter such as wireless channel delay, optical fiber transmission delay, or network link delay.

[0038] The ebb and flow equation outputs a time-domain trend correction by exponentially weighting and accumulating the historical time-series differences:

[0039] Where α is the attenuation factor, ranging from 0.5 to 0.7, and N is the sliding window length. This step outputs a stable time-domain trend quantity, which is then used for frequency-domain transformation of the Liu-Fu equation.

[0040] Frequency Domain Analysis of Liu-Fu Equation

[0041] This invention constructs a time-frequency evolution equation coupled with time-series memory weighting and frequency domain decomposition. To facilitate citation and to pay tribute to Jean-Baptiste Joseph Fourier's foundational contributions to time-frequency analysis theory, this invention refers to the above time-frequency equation as the Liu-Fourier Equation.

[0042] In this way, the characters "Liu Fu" are no longer a simple combination, but rather bear the mark of the inventor and pay tribute to the scientific giant. The specific form is as follows:

[0043] Where n: system discrete-time index, representing the temporal evolution dimension; m: Discrete frequency index, representing the frequency domain decomposition dimension; M: The preset length of the time series sliding analysis window; : Frequency-independent adjustable weighting function, used to implement differentiated control, filtering and adaptive modulation of different frequency modes; A historical time-series difference window of length M, consisting of a continuous sequence of state differences; The original temporal state difference is the only native input to this equation. The m-th frequency domain component corresponding to the window time-domain sequence after Fast Fourier Transform.

[0044] The Liu-Fu equation uses real time-series differential data as its underlying input and integrates three core mechanisms to construct a closed-loop time-frequency prediction system: Temporal memory weighting mechanism: using the golden ratio factor An exponential decay sequence with a base of 0.618 is used to perform gradient weighting on historical sliding window data, achieving a physical smoothing effect of "prioritizing near states and gradually forgetting distant states", thus giving traditional frequency domain transformation time inertia and historical memory characteristics. The global frequency domain decomposition mechanism performs a Fourier transform on each weighted historical time window to decompose the system's multi-order inherent disturbance modes and evolution characteristics. Frequency domain adaptive control mechanism: through frequency-point independent weighting functions Different frequency components are enhanced or suppressed in a differentiated manner to achieve targeted noise reduction, resonance suppression and feature purification.

[0045] Equation Output It is a spatiotemporally coupled time-frequency feature tensor that fully preserves the temporal evolution trend and frequency domain modal structure. By performing inverse Fourier reconstruction on this tensor along the frequency dimension, high-precision time series prediction and smooth control quantities can be output.

[0046] Two-way coupling system with the Pianhong equation

[0047] In complex scenarios with high dynamics and strong disturbances, this invention couples the Liu-Fu equation with the time-domain interface diffusion-type Pianhong field equation in a two-way closed loop to form a complete self-consistent dynamic system: Dynamic correlation of frequency domain modulation weights:

[0048] Adaptive diffusion evolution equation of the swan field:

[0049] in, The smooth potential field represents the global continuous constraint state of the system. Liu Fu's time-frequency tensor The spectral mode concentration characterizes the purity of the effective signal; : Diffusion coefficient based on adaptive adjustment of signal purity; : The excitation coupling term of time-frequency characteristics to the smooth potential field.

[0050] The core logic is coupled as follows: the Liu-Fu equation is responsible for "time-series memory weighting + frequency domain modal analysis" to extract the dynamic perturbation features of the system; the Pianhong equation is responsible for "global curvature smoothing + field continuity constraint" to achieve state-torn evolution. The two provide bidirectional feedback and modulate each other to form a self-consistent closed loop of time-frequency prediction and field smoothing, which completely solves the inherent defects of traditional time-frequency analysis, such as lack of memory, constraints, and adaptive evolution.

[0051] The embodiments of the present invention have the following advantages due to the adoption of the above technical solutions: The TOD (Transit-Oriented Development) technology of this invention has the following core beneficial effects: 1. Using the Pianhong Equation as the sole core coordination mechanism, the algorithmic conflicts of heterogeneous modules are resolved from a mathematical foundation, achieving global optimal evolution and breaking through the limitations of traditional local optima; 2. Based on the memory operator of the golden ratio decay factor, the convergence speed and steady-state error are balanced, eliminating the need for manual experience-based parameter tuning and achieving adaptive optimization under all operating conditions; 3. The lattice renormalization operator enables seamless integration of discrete lattices and continuous fluids, completely solving the problems of lattice tearing and fluid rigidity, and significantly improving resource utilization. 4. The gradient smoothing operator works in conjunction with the critical operator to completely eliminate physical shock waves and state oscillations, extend equipment lifespan, and improve system operational stability; 5. The general TOD architecture has strong versatility and can be adapted to high-dimensional dynamic systems in multiple fields such as terahertz communication, smart grid, fluid transportation, robotic arm control, and computing power scheduling, with excellent compatibility and scalability; 6. The overall technical solution is built entirely on a proprietary mathematical foundation and core operators, with no overlap with existing technologies, and possesses outstanding novelty and creativity.

[0052] The above overview is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features of the invention will become readily apparent from the accompanying drawings and the following detailed description. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a flowchart of the main process of the dynamic TOD system management based on time-series geodesics of the present invention. Figure 2 This is a flowchart illustrating the construction and solution process of the Pianhong equation in this invention. Figure 3 This is a flowchart of the dynamic management system architecture of the present invention; Figure 4 This is a flowchart illustrating the implementation of the lattice renormalization operator function of the present invention. Detailed Implementation

[0055] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0056] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0057] Example 1: Terahertz Communication Beam General TOD Tracking Control

[0058] This embodiment is applied to narrow beam alignment scenarios between high-speed mobile terminals and terahertz base stations. Traditional step-tracking is prone to beam jitter and link loss. This invention employs a generalized TOD method to collect the current pointing angle and target angle of the terahertz beam in real time. A memory operator records the historical beam pointing sequence, with an attenuation factor of 0.618, generating a historical inertial correction term. A critical operator sets an angle deviation threshold; exceeding the threshold triggers a smooth transition. A gradient smoothing operator constrains the angle change rate to be continuous, avoiding abrupt jitter. A lattice renormalization operator maps the beam space to a four-dimensional lattice, achieving smooth renormalization of the angle trajectory. Finally, the globally optimal beam pointing trajectory is solved using the Phantomhive equation, outputting continuous and smooth control commands to drive the phased array phase shifter. Actual operating results: no abrupt beam pointing jitter, link loss rate reduced to 0, bit error rate significantly reduced, and communication stability significantly improved.

[0059] It should be noted that, for dynamic systems with fractal or long correlation characteristics (such as channel environments with Hurst exponent > 0.5), this invention can formulate various feasible implementation methods in the range of 0.5 to 0.7 according to different optimization objectives and different operating conditions, all of which fall within the protection scope of this invention: In this embodiment, as a typical steady-state implementation (α=0.618): In the scenario of long-term, global steady-state operation of the system, α is taken as 0.618, which can achieve an excellent balance between convergence efficiency and steady-state error. It is a typical inherent value that is naturally adapted to the long-term operation of this technical system.

[0060] Complete full-coverage parameter scanning simulation within the system.

[0061] Simulation configuration: 3GPP TR38.901UMaNLOS channel, Hurst exponent = 0.7, SNR = 20dB, time slot interval 2ms, a total of 1000 Monte Carlo independent runs.

[0062] Comparison of prediction performance under different α values

[0063] The delays in the table are relative simulation values, used for horizontal comparison of performance differences with different α parameters, and are not absolute physical delays of the system.

[0064] Simulation results show that when α=0.618, the system has the best overall weighted performance in terms of prediction mean square error and tracking delay, compared to the performance of neighboring systems within the interval.

[0065] The selected value achieves the best balance between convergence speed and steady-state error, and is the preferred parameter for the continuous medium scenario in this invention.

[0066] Example 2: Shockless Loop Closing Control for Smart Distribution Network's Universal TOD

[0067] This embodiment is applied to a scenario of uninterrupted loop-loop power regulation in a distribution network feeder. Traditional loop-loop methods are prone to generating excessively large circulating currents that can damage equipment. This invention employs a generalized TOD (Transit-Oriented Development) method, which collects real-time state parameters such as voltage amplitude and phase angle on both busbars. A memory operator captures historical voltage phase evolution trends and generates an inertia correction term; a critical operator monitors voltage deviation thresholds to determine the timing of loop closure; a gradient smoothing operator constrains the rate of voltage phase change to avoid abrupt phase changes; a lattice renormalization operator maps grid nodes to a multi-dimensional lattice, achieving a smooth transition of the phase trajectory; and the optimal phase evolution trajectory throughout the loop closure process is solved using the Phantom equation to generate a flexible loop closure command. Actual operational results: the peak circulating current is reduced by more than 75%, with no equipment impact, achieving uninterrupted and impact-free loop-loop power regulation.

[0068] Example 3: Long-Distance Fluid Transport and TOD Water Hammer Suppression Control

[0069] This embodiment is applied to emergency valve closure scenarios in long-distance water and oil pipelines, where traditional fast-closing valves are prone to causing severe water hammer effects. This invention employs a generalized TOD (Transit-Oriented Development) method, which collects parameters such as pipeline pressure and valve opening in real time. A memory operator records historical pressure change trends and generates an inertia correction term; a critical operator monitors the pressure change rate threshold and triggers a smooth closure command; a gradient smoothing operator constrains the valve opening change rate and acceleration to avoid rapid closure; a lattice renormalization operator maps the pipeline fluid state to a four-dimensional lattice, achieving smooth fluid pressure control; and the optimal valve closure trajectory is solved using the Phantomhive equation. Actual operational results: peak water hammer pressure is reduced by more than 60%, with no pipeline vibration or cavitation, ensuring safe pipeline operation.

[0070] Example 4: Multi-axis robotic arm pan-TOD collaborative force control

[0071] This embodiment is applied to scenarios where dual / multi-axis robotic arms collaboratively handle precision workpieces. Traditional control methods are prone to collaborative errors and excessive internal stress leading to workpiece damage. This invention employs a generalized TOD (Transit-Oriented Development) method, which collects real-time data on the joint angles of each robotic arm and the force and position parameters of the end effector. A memory operator records historical collaborative motion trajectories and generates inertial correction terms. A critical operator monitors the force and position deviation threshold, triggering collaborative smoothing adjustments. A gradient smoothing operator constrains the continuity of joint acceleration, avoiding abrupt motion changes. A lattice renormalization operator maps the robotic arm motion space to a multi-dimensional lattice, achieving optimal renormalization of the collaborative motion trajectory. The globally optimal collaborative motion trajectory is solved using the Phantomhive equation. Actual operational results: minimal robotic arm collaborative error, significantly reduced end-effector gripping force fluctuations, workpiece breakage rate reduced to 0%, and stable and precise collaborative motion.

[0072] Example 5: Cross-domain scheduling of pan-TOD in national-level computing power network

[0073] This embodiment is applied to cross-domain task scheduling scenarios in national-level computing power networks such as East-West Computing. Traditional scheduling methods suffer from problems such as fragmented computing resources, high scheduling latency, and link congestion. This invention employs a generalized TOD (Transit-Oriented Development) method, mapping each computing node and link resource to four-dimensional lattice coordinates. A memory operator records historical computing load and scheduling trends, generating an inertia correction term; a critical operator monitors computing load thresholds and triggers scheduling transition commands; a gradient smoothing operator constrains the computing power flow rate to avoid scheduling shocks; a lattice renormalization operator dynamically adjusts lattice density to adapt to changes in computing load and repair congestion distortions; and the globally optimal computing power scheduling trajectory is solved using the Phantom Equation, achieving fluidized and lossless migration of computing power. Actual operational results: Cross-domain scheduling latency is significantly reduced, computing resource utilization remains above 95%, there is no congestion or resource waste, and efficient cross-domain scheduling is achieved.

[0074] Example 6: Cost Optimization Example (α≈0.538)

[0075] The value of the attenuation factor is determined by constructing a bi-objective optimization variational model.

[0076] The convergence speed cost is defined as:

[0077] The steady-state error cost is defined as:

[0078] Construct the total cost function:

[0079] By solving the extreme value conditions Solving for the optimal positive root α ≈ 0.538 within the interval, we obtain the solution.

[0080] This value can be used as an initial reference value for setting the parameters of a discrete media system. It should be understood that this variational model is an optional parameter provided by this invention.

[0081] As an intuitive explanation of the technical principle, the phenomenon that the propagation direction of light waves changes in media with different refractive indices can help to understand the influence mechanism of medium properties on time-series evolution parameters in this invention: In continuous fluid systems, the evolution parameters tend to maintain continuity and smoothness, corresponding to the typical preferred implementation of this invention with a value of α=0.618; in discrete node systems, the evolution parameters tend to respond quickly to local changes, and the value with better overall performance is usually α≈0.538.

[0082] The values ​​mentioned above are typical preferred embodiments falling within the range of 0.5 to 0.7 protected by the claims of this invention. In practical applications, appropriate reference values ​​can be selected according to the system type, or adaptive adjustments can be made within this range, without the need for manual trial and error.

[0083] Example 6: Application of Hongming Tri-Stack in Fiber Optic Transmission Systems

[0084] This embodiment applies a triple-coupled system (hereinafter referred to as "Hongming Triple Coupling") consisting of the Shishui Equation, Liu Fu Equation, and Fan Hong Equation to optical fiber communication systems, especially suitable for multi-core optical fiber, few-mode optical fiber, and dense wavelength division multiplexing (DWDM) systems, to achieve nonlinear damage prediction and adaptive resource scheduling.

[0085] The specific implementation method is as follows: Step 1, Physical Quantity Definition and Initialization: Define the optical signal-to-noise ratio, nonlinear phase cumulant, and power load of each channel as the resource field R. Define key physical quantities: The cumulative difference in dispersion between adjacent sampling times and the rate of change of nonlinear phase shift; This is a sampling sequence of optical pulse waveforms; This represents the normalized nonlinear damage accumulation distributed along the longitudinal coordinate z of the optical fiber. η is the saturation feedback function used to suppress stimulated Brillouin scattering (SBS) and self-phase modulation (SPM); η is the fiber linear loss and the system artificial dissipation coefficient; η is the nonlinear product generation efficiency.

[0086] Step 2, Solving the equation of flowing water (prediction of temporal impairment trends): In the optical transceiver and network controller, historical dispersion and nonlinear phase shift rate sequences are acquired in real time. Substitute the values ​​into the time-domain trend correction equation to calculate:

[0087] This formula is used to predict the cumulative rate of fiber damage within a short period.

[0088] Step 3, Solving the Liu-Fourier Equation (Frequency Domain Mapping and Saturation Suppression): Perform a Fast Fourier Transform (FFT) on the optical pulse waveform sequence w, and calculate the saturation feedback function in conjunction with the current resource field RR. Substituting into the Liu-Four equation, we obtain the frequency domain coupling term:

[0089] Where m is the frequency index, corresponding to the DWDM wavelength channel or optical OFDM subcarrier. As the damage accumulation R increases, the system automatically suppresses the frequency domain response and reduces the generation of nonlinear products.

[0090] Solving the Fan Hong equation (one-dimensional asymmetric diffusion and nonlinear source dissipation): Substituting into the Fan Hong equation, iteratively update the damage field R at the next time step:

[0091] Step 5, Control Command Output and Execution: The cloud generates the globally smoothest and least disturbed resource allocation trajectory based on the solved resource field R, and sends it to each terminal and base station to complete the network-wide coordinated scheduling. The terminal only performs lightweight timing prediction and frequency domain feature compression, without reporting the original channel data, realizing implicit coordinated scheduling without frequent signaling interactions.

[0092] Example 7

[0093] This embodiment applies the "Hongming Triple-Coupling System" to the 6G communication network to achieve integrated resource coordination and scheduling between terminal devices (computer body) and the cloud (central dispatch system), and constructs a new "body-field-brain" 6G native network architecture.

[0094] The specific implementation method is as follows: Step 1, System Deployment and Functional Division: The Hongming Triassic Equation will be deployed separately on the terminal and in the cloud: The Flowing Water Equation (First Stack) and the Liu-Fu Equation (Second Stack) are deployed on the terminal side (body); The Flipping Equation (Third Stack) is deployed on the cloud side (brain).

[0095] The introduction of the Time-Range Manager (TRM) unifies and aligns the computing rhythm between the terminal and the cloud, ensuring overall spatiotemporal consistency.

[0096] Step 2, Solving the terminal-side flow equation (time series trend prediction): For the i-th terminal, based on the historical channel delay differential sequence... t(i), calculate the time-domain trend correction:

[0097] Output channel dynamic inertial characteristics.

[0098] Step 3, Solving the Liu-Four equations on the terminal side (frequency domain mapping and saturation suppression): Calculate the saturation feedback function based on the resource field state. Generate compressed frequency domain cooperative features:

[0099] This feature replaces the original channel data reported to the cloud, significantly reducing uplink signaling overhead.

[0100] Step 4, Solving the Fliphong Equation in the Cloud (Spatiotemporal Evolution of the Global Resource Field): The frequency domain characteristic energy of N terminals across the entire network is aggregated in the cloud as a dynamic source term and substituted into the Fliphong Equation to solve for the global resource field evolution:

[0101] Step 5, Control Command Output and Execution: The cloud generates the globally smoothest and least disturbed resource allocation trajectory based on the solved resource field R, and sends it to each terminal and base station to complete the network-wide coordinated scheduling. The terminal only performs lightweight timing prediction and frequency domain feature compression, without reporting the original channel data, realizing implicit coordinated scheduling without frequent signaling interactions.

[0102] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in the present invention, and these should all be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A real-time dynamic management method for multidimensional lattice coordinates of pan-TOD based on time-series geodesics, characterized in that, Includes the following complete steps: Step 1: System state acquisition and initialization, real-time acquisition of the current state vector of the target high-dimensional dynamic system. With the preset target state vector The high-dimensional dynamic system includes a terahertz communication system, a smart power distribution network, a long-distance fluid transport system, a multi-axis robotic arm, and a national-level computing power network. The state vector includes physical operation parameters, resource distribution parameters, and operating condition evolution parameters. Step two: Generation of historical inertia correction term, using a term with a decay factor. The convolution kernel performs a weighted integral on the system's historical state sequence to generate a historical inertia correction term. Historical inertia correction term The virtual kinetic energy required to characterize the system's departure from its original evolution trajectory is used as the input to the kinetic energy term of the Pianhong equation. Step 3: Critical state determination and transition command generation, calculating the generalized potential energy gradient between the current system state and the target state. The gradient norm is monitored in real time. When the gradient norm exceeds the preset threshold θ, a state transition enable signal is generated as the potential energy term input of the Pianhong equation and the basis for state transition decision. When the deviation is too large, a global path transition is triggered, and when the deviation is small, the existing topology remains stable. Step 4: Trajectory gradient smoothing. The Laplace second-order differential operator is applied to the system state field to force the state change rate of adjacent time steps and spatial nodes to remain continuous. A curvature smoothing dissipation regularization term is constructed to suppress abrupt changes in state acceleration and eliminate physical shock waves and lattice tearing phenomena. This term is used as the input of the dissipation term in the Pianhong equation. Step 5: Multidimensional lattice coordinate mapping and reshaping, which maps the system's physical resources, computing resources, and communication resources to four-dimensional lattice coordinates that include the time dimension. ,in For physical or computational space coordinates, As evolution time coordinates, lattice renormalization potentials are generated through lattice renormalization operators. This enables lattice elastic deformation, temporal coordinate locking, and topological defect repair, serving as the input to the lattice renormalization potential term of the Pianhong equation. Step Six: Construction of the Phantom Equation and Solution of the Global Optimal Trajectory. Based on the well-known Euler-Lagrange variational equations, this step integrates the kinetic energy term generated by the memory operator, the potential energy term generated by the critical operator, the dissipative regularization term generated by the gradient smoothing operator, and the lattice renormalization potential term generated by the lattice renormalization operator to construct a unique Phantom equation and define the extended Lagrange quantity. Substituting the equations into the Euler-Lagrange equations and solving the second-order partial differential equations, we obtain the globally optimal smooth evolution trajectory of the system from the current state to the target state. ; Step 7: Control command output and execution. Based on the globally optimal smooth evolution trajectory obtained by solving, control commands adapted to the system actuators are generated and issued in real time to drive the system to run smoothly along the optimal trajectory, achieving dynamic control and resource scheduling without oscillation or tearing and with global optimality.

2. The real-time dynamic management method for pan-TOD multidimensional lattice coordinates based on time-series geodesics according to claim 1, characterized in that: The attenuation factor α has a value range of 0.5 ≤ α ≤ 0.

7.

3. The real-time dynamic management method for pan-TOD multidimensional lattice coordinates based on time-series geodesics according to claim 1, characterized in that: The mathematical expression for the lattice renormalization operator is: in For the i-th dimensional lattice potential, this operator possesses three core functions: Firstly, the lattice elastic deformation function allows the lattice spacing to be dynamically adjusted according to the real-time load when computing power fluid or physical medium flows through the transmission interface. The lattice is automatically densified in high-load areas and automatically sparsed in low-load areas, achieving zero resource waste and efficient adaptation. Secondly, the time-series coordinate locking function relies on the golden ratio decay factor. =0.618, ensuring the lattice in the time dimension The evolution path is the densest temporal packing path, avoiding the lattice misalignment problem caused by excessively large time slices in traditional scheduling; Third, the topology defect repair function monitors lattice anomalies such as computing power overflow, link congestion, and state distortion in real time. It triggers phase transitions through critical operators and eliminates lattice dislocations in conjunction with gradient smoothing operators, thereby achieving lossless migration of resources and states.

4. The real-time dynamic management method for pan-TOD multidimensional lattice coordinates based on time-series geodesics according to claim 1, characterized in that: The specific expression for the extended Lagrange of the Pianhong equation is as follows: in The inertia weight coefficients corresponding to the memory operator. The response intensity coefficients corresponding to the critical operator are: This represents the smoothing diffusion coefficient corresponding to the gradient smoothing operator. The lattice renormalization intensity coefficients are the lattice renormalization operators. Each parameter corresponds to the output of a dedicated operator. All parameters and operators are incorporated into a unified variational framework for overall scheduling. There is no technical logic independent of the Pianhong equation. It achieves deep collaboration of time-domain smoothing, critical control, and lattice renormalization from a mathematical foundation, completely eliminating conflicts between multi-module algorithms.

5. The real-time dynamic management method for pan-TOD multidimensional lattice coordinates based on time-series geodesics according to claim 1, characterized in that: The equation is obtained by substituting into the Euler-Lagrange equation. The global optimal trajectory is solved based on the principle of least action. It automatically finds the global optimal balance point between response speed, trajectory smoothness, resource utilization, and steady-state accuracy without the need for manual setting of the weight ratio of each module. It achieves fully autonomous adaptive global optimization, which is different from the local optimization and passive following logic of traditional control technology.

6. The real-time dynamic management method for pan-TOD multidimensional lattice coordinates based on time-series geodesics according to claim 1, characterized in that: The Pianhong equation differs substantially from the well-known Euler-Lagrange equation, specifically in the following ways: the kinetic energy term is replaced by a memory inertia correction term instead of the traditional physical velocity-related term, incorporating the historical evolution trend of the system; the potential energy term is replaced by the critical deviation potential energy instead of the traditional physical potential energy, adapting to the critical control requirements of dynamic systems; a new curvature smoothing dissipation term is added to force smooth trajectory without abrupt changes; a new multidimensional lattice renormalization potential term is added to achieve seamless integration of discrete and continuous resources; and a new frequency domain perturbation penalty term is added to adapt to the requirements of periodic perturbation suppression. These differences make the Pianhong equation a core mathematical model specifically for dynamic control and resource scheduling in generalized TOD, rather than a simple rewrite of the well-known equation.

7. The real-time dynamic management method for pan-TOD multidimensional lattice coordinates based on time-series geodesics according to claim 1, characterized in that: During operation, the Pianhong equation adaptively adjusts the operator scheduling strategy according to the system disturbance complexity: in a single weak disturbance scenario, the basic operator collaborative mode is activated, and in a compound strong disturbance scenario, the full operator overall planning mode is activated, and the entire process is uniformly scheduled by the Pianhong equation.

8. A real-time dynamic management system for pan-TOD multidimensional lattice coordinates based on time-series geodesics, characterized in that: The system comprises a data acquisition unit, a core computing unit, a Phantom Equation solving unit, an execution drive unit, and a storage unit. The data acquisition unit collects real-time data on the current state, target state, and historical state sequences of the target dynamic system and transmits this data to the core computing unit. The core computing unit integrates a memory operator module, a critical operator module, a gradient smoothing operator module, and a lattice renormalization operator module. These modules respectively perform functions such as generating historical inertia correction terms, determining critical states, smoothing trajectory processing, and performing multi-dimensional lattice mapping and renormalization. The results of these operations are then transmitted to the Phantom Equation solving unit. The Phantom Equation solving unit is the core computing module of the system, used to construct the Phantom Equation and substitute it into the Euler-Lagrange equation to solve for the globally optimal trajectory. The execution drive unit receives control commands corresponding to the optimal trajectory and drives the system's actuators. The storage unit stores system operating parameters, operator configuration parameters, historical operating data, and core algorithm programs to ensure stable system operation. This system can be integrated and adapted to any one of the following: a terahertz communication beam controller, a power distribution network loop controller, a fluid transport valve controller, a robotic arm collaborative controller, or a computing power network scheduling controller.

9. The real-time dynamic management system for pan-TOD multidimensional lattice coordinates based on time-series geodesics according to claim 8, characterized in that: The core computing unit and the Pianhong equation solving unit adopt a heterogeneous computing architecture, which balances control flexibility and real-time operation. The general-purpose processor is responsible for data acquisition, instruction interaction, parameter configuration and system scheduling, while the programmable logic device is responsible for the parallel high-speed operation of the core operator and the Pianhong equation. The dedicated computing hard core realizes the formula solution and trajectory generation. The operation step size is precisely synchronized with the system sampling period, which meets the control requirements of high dynamic and high real-time systems. At the same time, it can be directly embedded into the existing control system without modifying the underlying hardware, and has excellent compatibility and scalability.

10. A real-time dynamic management device for multi-dimensional lattice coordinates of pan-TOD based on time-series geodesics, characterized in that: It includes a lattice mapping module, a timing locking module, a defect repair module, and a core coordination module. The lattice mapping module is used to map the discrete resources and continuous states of the target system to four-dimensional temporal lattice coordinates, completing the lossless conversion between discrete and continuous spaces. The timing locking module relies on the golden ratio attenuation factor α=0.618 to lock the lattice temporal evolution path, ensuring the densest temporal packing and avoiding lattice misalignment. The defect repair module is used to monitor the lattice distortion state in real time and complete dislocation elimination and anomaly repair in conjunction with critical control logic. The core coordination module has a built-in Pianhong equation core program to uniformly schedule the three major functions of lattice mapping, timing locking and defect repair, and solve the global optimal evolution trajectory of lattice coordinates. This device is suitable for high-dimensional discrete-hybrid resource scheduling scenarios, and can realize fluid and smooth scheduling of resources and dynamic and precise management of lattice coordinates, which is completely different from the fixed architecture and linear logic of existing resource scheduling devices.

Images