A method, system, and storage medium for state calculation and action generation of complex systems based on structured constraints.

Abstract

This invention discloses a method, system, and storage medium for complex system state calculation and action generation based on structured constraints, belonging to the technical fields of complex system operation control, state analysis, intelligent calibration, and computer implementation. The method acquires multi-dimensional physical state input of a complex system, performs state calculation based on preset structured constraints, and obtains at least two different-dimensional state representation quantities. These state representation quantities include at least a first state representation quantity representing the degree of deviation of the current state from the target working domain and a second state representation quantity representing the evolution trend or directional relationship of the current state. Based on the state representation quantities, basic action quantities are generated, and based on the basic action quantities and action projection relationships, action output information is generated. Based on the structured constraints, constraint verification, projection correction, or output condition judgment is performed on the action output information, and the processed action output information is output. The action output information includes at least one of control quantities, state classification results, action direction suggestions, priority suggestions, and suggestion adjustment ranges. This allows the invention to cover multiple implementation paths, such as individual judgment, suggestion output, post-judgment control, and direct control, and is applicable to engines, powertrains, wind turbines, rocket vertical recovery, and other multivariable coupled and strongly nonlinear systems.

Description

Technical Field

[0001] This invention relates to the fields of complex system operation control, state analysis, intelligent calibration, industrial data processing, and computer implementation technology, and particularly to a method, system, and storage medium for complex system state calculation and action generation based on structured constraints. The complex system can be a physical operating system with state sensors, controllers, and actuators, or a monitoring, suggestion, or decision support system that receives action output information through a host computer, a manual operation terminal, or a secondary controller. Examples include, but are not limited to, engines, powertrains, electric motor drive systems, wind turbine generators, rocket vertical recovery systems, industrial process systems, robot systems, and other systems with multivariable coupling and strong nonlinearity. Background Technology

[0002] Existing complex system operation schemes typically rely on original physical quantity errors, prediction errors, or empirical rules for judgment and control. Typical paths include proportional-integral-derivative (PI-DE) regulation, gain scheduling, rule triggering, model predictive control, and piecewise control. The control basis of these schemes usually lies directly in scalar errors, local prediction results, or static rules in the physical space. Essentially, they belong to the approach of "first observing the deviation, and then compensating for the deviation."

[0003] In scenarios involving multivariable coupling, strong nonlinearity, rapid shifts in operating conditions, chronic equipment degradation, and difficulty in establishing accurate mechanistic models, relying solely on direct feedback based on raw physical quantities often fails to fully reflect changes in the internal coupling relationships of the system. Judgment logic and control logic are often disconnected, and judgment results tend to remain at the alarm level, making it difficult to continuously and stably translate them into the basis for subsequent actions. When the system approaches its physical limit boundaries, traditional methods are also prone to misjudgment, over-adjustment, oscillation, and ineffective actions.

[0004] Taking engines as an example, compressor surge boundaries, vortex inlet temperature boundaries, speed boundaries, and fuel supply boundaries coexist and are coupled with each other; a single error closed loop is insufficient to promptly identify the state where "although a single sensor value has not exceeded its limit, the entire system is approaching the instability boundary." Taking rocket vertical recovery as an example, minimum thrust constraints, attitude coupling, remaining fuel, and landing structure strength collectively limit the final maneuver space; simply pursuing the instantaneous optimal path may push the system into a region where a soft landing is impossible. Taking wind turbine generators as an example, tower first-order bending, blade aeroelastic response, and generator electromagnetic torque are coupled with each other; a single pitch or torque closed loop often cannot simultaneously consider load life and power point tracking.

[0005] Therefore, a new basic algorithm framework is needed to enable complex systems to complete state calculations based on unified constraints and further generate action outputs consistent with the current state, thereby incorporating "state recognition, feedback correction, action generation, and constraint-based control" into the same logical system. Summary of the Invention

[0006] The purpose of this invention is to provide a method, system, and storage medium for calculating the state and generating actions of complex systems based on structured constraints. This addresses the problem that existing technologies typically rely on feedback, judgment, or control based on physical errors, local prediction results, or static rules during the operation of complex systems, making it difficult to stably achieve state recognition, feedback correction, and subsequent action generation in scenarios involving multivariable coupling, strong nonlinearity, operating condition drift, or long-term operation.

[0007] To achieve the above objectives, this invention proposes a fundamental algorithm framework for complex system operation. This framework first acquires the multidimensional physical state input of the complex system and performs state calculations on the multidimensional physical state input based on preset structured constraints, obtaining at least two different-dimensional state representation quantities. The state representation quantities preferably include: a first state representation quantity representing the degree of deviation of the current state from the target working domain, and a second state representation quantity representing the evolution trend, directional relationship, or regression trend of the current state. Subsequently, this invention generates basic action quantities based on the first state representation quantity, the second state representation quantity, and the structured constraints, and converts the basic action quantities into action output information based on action projection relationships. The action output information can be a control quantity, or a state classification result, action direction suggestion, priority suggestion, or suggestion adjustment magnitude. Before output, constraint verification, projection correction, or output condition judgment can be performed on the action output information based on the structured constraints; when the action output information is a control quantity and meets the output conditions, it can be further output to the actuator.

[0008] Unlike conventional approaches that passively use constraints as optimization boundaries, the structured constraints in this invention continuously participate in the entire process of state calculation, feedback correction, and action output information processing. In other words, structured constraints define "what the target working domain is," "how to determine deviations," and "how to transform deviation information into action basis quantities, and how to form executable, suggestive, or determinate action output information under constraints." Therefore, the essence of this invention lies not in a specific controller, but in a fundamental algorithm for state calculation and action generation centered on structured constraints.

[0009] This invention offers at least the following advantages: First, by simultaneously introducing state representation quantities with two dimensions—deviation degree and trend / direction—it can identify precursors of complex systems approaching instability boundaries earlier and more robustly than schemes relying solely on a single error. Second, by introducing action basis quantities as an intermediate layer, the state judgment results can be stably and continuously transformed into the basis for subsequent actions, thus being compatible with both "suggested output" and "direct control" deployment paths. Third, through cross-spatial sensitivity mapping, constraint processing, and boundary overflow prediction, the action output information not only reflects the current position deviation but also the future boundary overflow risk, making it more suitable for systems with multivariable coupling, strong nonlinearity, and strict physical boundaries. Fourth, through dynamic maintenance of structured constraints, the system can adaptively calibrate itself to equipment aging, environmental changes, and operating condition migration during long-term operation, while avoiding the erroneous absorption of instability characteristics under abnormal conditions. Boundary Description with Existing Control and Calibration Technologies

[0010] Compared to traditional proportional-integral-derivative (PI-DE) control, this invention does not directly generate control quantities based on a single physical error, its integral term, and its derivative term. Instead, it first constructs at least two state representation quantities with different dimensions, then generates basic action quantities based on these state representation quantities, and forms action output information through action projection relationships. In the direct control implementation, the action output information can be further expressed as a control quantity. Therefore, this invention is not a single error feedback, but a joint drive oriented towards state geometric relationships and evolutionary trends.

[0011] Compared to model predictive control, the structured constraints in this invention are not merely passive boundary conditions that take effect at the end of the solution process in a rolling optimization problem, but rather continuously participate in the calculation of state representation quantities, the generation of basic action quantities, and the processing of action output information. In other words, in this invention, constraints are not secondary conditions for "finally checking for boundary violations," but rather conditions that "define the state, drive the action, and limit the output" throughout the entire process. Even if rolling optimization, quadratic programming, or equivalent solution methods are used to implement constraint verification in the preferred embodiment, the distinctiveness of this basic architecture remains unchanged.

[0012] Compared with simple threshold rule control, this invention does not trigger discrete actions after a single signal reaches a threshold. Instead, it continuously expresses the current position, trend direction, regression trend, and risk level through two or more dimensions of state representation, and transforms them into continuous action base quantities and continuously corrected action output information. Therefore, it can significantly reduce jitter, false triggering, and hysteresis near the boundary. Terminology and Core Definitions

[0013] Structured constraints: Predefined constraint structures used to define the target working domain, state evolution boundaries, and the basis for action generation. They include at least one type of physical hard constraints and logical soft constraints. Physical hard constraints include insurmountable boundaries such as thrust upper and lower limits, current upper limit, temperature limit, valve position boundary, support strength boundary, and maximum pitch rate. Logical soft constraints include stability domain boundaries, comfort boundaries, lifespan priority zones, protection priority zones, and update, freeze, and recovery rules.

[0014] Target working domain: The permissible state domain defined by structured constraints, which can be a closed set, a convex set, a piecewise approximate convex set, or a connected domain formed by splicing together several reachable subdomains. In a preferred embodiment, the target working domain can be defined by a set of inequality constraints and can be switched or scaled according to the running stage.

[0015] First-state representation quantity: A quantity used to characterize the degree of deviation of the current state from the target working domain. It can be a distance quantity, a signed distance quantity, a Mahalanobis distance, a potential function value, or an equivalent index. It is preferably denoted as D1.

[0016] Second-state representation quantity: A quantity used to characterize the evolution trend, directional relationship, or regression trend of the current state. It can be expressed as velocity projection, normal projection, trend score, directional difference quantity, or equivalent index. It is preferably denoted as D2.

[0017] Action baseline quantity: An intermediate output between the state representation quantity and the action output information, used to represent the direction, intensity, channel allocation, recovery priority, or degree of suppression of the next action. Preferably denoted as q.

[0018] Action output information: The final output result formed by the basic action quantities under structured constraints, which may include at least one of the following: control quantity, state classification result, action direction suggestion, priority suggestion, and suggested adjustment range. In the direct control implementation, the control quantity can be regarded as a specific manifestation of action output information.

[0019] Action projection relationship: A mapping relationship that transforms basic action quantities into action output information. In the direct control implementation, the action projection relationship can further transform the basic action quantities into physical actuator spatial actions. This is preferably achieved through a cross-spatial sensitivity mapping J, but is not limited to the explicit matrix inversion of J. Formal mathematical definition (simplified version)

[0020] Let the initial state space of the system be X ⊆ R. n The control input space is U ⊆ R m The target working domain is Ω*⊆ X. Preferably, Ω* can be defined by the constraint function set c. iDefined as (x) ≤ 0, i = 1, ..., r. Let the state mapping model Φ: X → Z, where Z ⊆ R. p For the feature space, p can be less than, equal to or greater than n, but is preferably a low-dimensional or medium-dimensional space that is convenient for characterizing the main coupling relationships.

[0021] In a preferred embodiment, the first state representation quantity D1 is defined as the signed distance or equivalent deviation index from the current state to the target working domain in the feature space. For example, D1(x) = inf z*∈Φ(Ω*) The value ||Φ(x)-z*|| is assigned a sign as needed based on whether it lies within the boundary. The second state characterization quantity D2 is used to characterize the trend of the current state in the direction approaching or moving away from the target working domain boundary. It can be defined as the projection of the state change quantity onto the boundary normal or local regression direction, or its equivalent direction quantity. For non-smooth boundaries, piecewise normals, locally linear approximating normals, or numerical approximating normals can be used.

[0022] The basic motion quantity q can be constructed as follows: q = A1·f(D1) + A2·g(D2) + A3·h(ΔD1, ΔD2); where f, g, and h are linear or nonlinear scalar functions or vector functions, and A1, A2, and A3 are parameter matrices or weights. The motion output information y can be generated from the motion projection relationship, for example, y = Ψ(q, J, C), where Ψ represents the projection, solution, lookup table interpolation, or optimization process, J is the cross-spatial sensitivity mapping, and C is the structured constraint. In the direct control implementation, the motion output information y can be further represented as a control quantity u.

[0023] In a preferred embodiment, the mathematical objective of cross-space sensitivity mapping can be expressed as: given the desired correction direction g z,k In the case of J, solve k Δu should be as close to g as possible. z,k Δu. Preferably, it can be obtained using least squares, constrained least squares, pseudo-inverse, quadratic programming, control barrier function projection, or equivalent methods. If constrained solution is used, in the direct control implementation, the control quantity simultaneously satisfies the actuator hard constraints and the target working domain boundary constraints; in the suggested output implementation, the output result simultaneously satisfies the preset hierarchical, prompt, or decision boundary.

[0024] The mathematical expressions given in this specification are used to illustrate the mathematical framework for implementing the invention, and are not intended to limit the invention to a single formula. Those skilled in the art can implement the invention in equivalent forms without departing from the inventive concept. Algorithm Overall Principle

[0025] The basic algorithm flow of this invention includes: acquiring multi-dimensional physical state input; performing state calculation based on structured constraints; forming at least two different-dimensional state representation quantities; generating basic action quantities based on the state representation quantities; generating action output information through action projection relationships; performing constraint verification, projection correction, or output condition judgment before outputting the action output information; and outputting the processed action output information. In the direct control implementation, the processed action output information can be further output to the actuator.

[0026] Among them, state calculation answers "where the system is now and where it is going"; action base quantity answers "how the system should act next"; action output information answers "what kind of adjustment, suggestion, warning or control result the system should output next"; in the direct control implementation, the control quantity further answers "how to adjust at the physical actuator level". This invention, through the intermediate layer of action base quantity, makes the process between judgment and output no longer a hard switch, but a continuous, adjustable and constrained mapping process.

[0027] In a preferred embodiment, the present invention also introduces feedback correction: based on the relationship between the changes of D1 and D2, the direction term, amplitude term, damping term, recovery term or channel weight in the motion basis quantity are corrected to reduce jitter near the boundary and over-excitation in abnormal states. Implementation forms of structured constraints

[0028] Structured constraints can be implemented in any of the following ways, or in combination of at least two of the following ways: First, software implementation, which exists in the form of parametric models, boundary functions, rule sets, mapping models, state machine logic, configuration files, or combinations thereof, and is executed by a processor to complete state calculations and action generation; Second, fixed constraint implementation, which exists in the form of firmware, dedicated logic, programmable devices, pre-configured control units, fixed circuits, or pre-set hardware logic, and directly participates in state calculations and / or action generation during operation; Third, intrinsic structure implementation, which is formed at least in part by the system's pre-set structural parameters, mechanical coupling relationships, electrical coupling relationships, control connection relationships, pre-configured channel relationships, preset response boundaries, or native design; Fourth, hybrid implementation, which is composed of at least two of the following: software implementation, fixed constraint implementation, and intrinsic structure implementation.

[0029] In a preferred embodiment, structured constraints support dynamic maintenance. When the system is within the target working domain for multiple consecutive sampling periods, some constraint parameters are updated; when the system is in an abnormal, critical, or rapidly deviating state, some constraint parameters are frozen; after the system recovers, the parameters are gradually restored and updated according to preset conditions. To ensure algorithm stability, preferably, an upper limit is set on the amplitude, frequency, or rate of change of each update to avoid the system failing to converge due to "rapid drift of the constraint boundaries themselves." Stability, real-time performance, and robustness specifications

[0030] This invention does not require a universally applicable rigorous mathematical proof for all operating conditions, but in preferred embodiments, candidate discrete energy functions or candidate Lyapunov functions can be constructed, for example, V = 1 / 2·(D1 2 + η·D2 2 When the rate of change of structured constraints is limited, the state mapping is continuous and locally differentiable within the current working interval, and the gain of the basic action quantity satisfies the preset boundary, the V can be made to show a decreasing trend or a non-increasing trend within several consecutive sampling periods by selecting the action projection relationship and constrained projection parameters, thereby supporting the convergence description within the local working interval.

[0031] Regarding real-time performance, this invention preferably employs methods such as local linearization, lookup table interpolation, offline matrix identification, constrained least squares, or low-dimensional quadratic programming to implement action projection and constraint verification, avoiding the need to solve a highly complex global nonlinear optimization problem in each sampling period. For high-frequency sampling scenarios such as power systems, motor control, or rocket attitude control, offline calibration of cross-space sensitivity mapping, online lookup table correction, and fast constraint projection can enable the algorithm to achieve an engineering-acceptable iteration frequency on low-cost MCUs, DSPs, FPGAs, or their collaborative platforms.

[0032] In a preferred low-latency implementation architecture, the Jacobian sensitivity matrix, its regularized pseudo-inverse, or its equivalent local response matrix of the complex dynamic system at the current operating point can be decomposed into the weight distribution of several operator sequences, and the projection results of candidate actions can be calculated in parallel in at least two independent computational loops. Subsequently, cross-loop consistency checks are performed on the candidate results of different computational loops; when the candidate results are consistent within a preset tolerance, and the current D1 and D2 have met the preset accuracy threshold or energy decrease threshold, the calculation can be prematurely terminated within the current sampling period, and the current control increment or its correction value can be directly output. The above implementation is used to reduce the additional latency caused by explicit matrix inversion, multi-round iterative optimization, or complete high-order solution, and can achieve near-zero additional latency determination without changing the essence of this invention, which is to drive state calculation, generation of basic action quantities, and constraint-based control through structured constraints.

[0033] Regarding robustness, this invention preferably maps high-frequency noise, abnormal disturbances, and model uncertainties as: high-frequency fluctuations in the state representation quantity, error boundaries in the prediction model, and a structured constraint update freezing strategy, respectively. When short-term sudden noise or disturbances such as jet bounce, gusts, or sensor spikes are detected, over-excitation can be suppressed through low-pass processing, model freezing, constraint contraction, or a protection-first mode. Simplified numerical implementation example (2×2 MIMO example)

[0034] Unless otherwise stated in this section and subsequent embodiments, the variable symbols in Sections 10 to 15 follow the mathematical definitions in Section 6 and the overall algorithm principles in Section 7; discrete sampling quantities are represented by time k as a subscript, and the symbols in the figures and embodiments are consistent with those in this section.

[0035] To clearly illustrate the feasibility of this invention, a very simplified two-input, two-state embodiment is given below. Let the state vector be x = [x1, x2]. T Where x1 can be understood as position deviation and x2 as velocity deviation; control input u = [u1, u2] T The target working domain is defined as c(x) = a·x1 + b·x2 - c0 ≤ 0, where a, b, and c0 are constants. Preferably, the state mapping Φ is an identity mapping, i.e., z = Φ(x) = x.

[0036] In this embodiment, a first state characterization quantity D1 = max(0, a·x1 + b·x2 - c0) can be defined, which is the non-negative deviation of the current state relative to the boundary of the target working domain; a second state characterization quantity D2 = a·Δx1 + b·Δx2 can be defined, which is the projection of the state change quantity onto the normal direction of the boundary. If D1 increases and D2 is positive, it indicates that the system has not only deviated from the boundary, but is also continuing to move away in a more unfavorable direction; if D1 is small but D2 is positive, it indicates that although the system has not yet deviated significantly, it has a tendency to rapidly approach the boundary.

[0037] The basic motion parameters can be constructed using the following formula: q = [α·D1 + β·D2, γ·D1] T , where α, β, and γ are adjustable parameters. Candidate values ​​for the control quantity can be derived from u. 0 = J·q is generated, where J is a 2×2 offline calibration matrix or local response matrix. If the next time step state x̂ is predicted... k+1 = A·x k + B·u 0 Satisfy c(x̂) k+1 If ) > 0, then for u 0Perform projection correction to obtain c(x̂) k+1 The corrected control quantity u is ≤ 0. Therefore, this invention can fully realize the closed-loop chain of "state calculation—action basis quantity—control quantity—boundary prediction" in a highly simplified system.

[0038] Regarding the statistical basis for determining the first deviation warning threshold: In a preferred embodiment, the warning threshold used to characterize the boundary of the target working domain in the structured constraints is not set empirically, but is determined based on the statistical distribution of the system steady-state samples.

[0039] Specifically, after the first deviation D1 is normalized or standardized, its statistical distribution in the steady-state operating sample can be approximated as a unimodal distribution with a mean of μ and a standard deviation of σ; in a preferred case, it can be further approximated as a normal distribution. Based on this assumption, the exceedance probability corresponding to the 1σ quantile of the upper tail on one side can be used as the preferred statistical basis for the warning threshold.

[0040] According to the cumulative distribution function Φ(z) of the standard normal distribution, when the first deviation after normalization reaches μ+σ, its one-sided overtail exceedance probability is: P(X > μ + σ) = 1 - Φ(1) ≈ 0.15873.

[0041] Therefore, in this preferred embodiment, 0.15873 can be used as a preferred statistical quantile example for the first deviation entering the warning zone, characterizing that the system has entered the early warning interval of upper deviation from the steady-state center region. Using this statistical basis helps to improve the sensitivity of early deviation identification while maintaining a high steady-state tolerance, and reduces the probability of false triggering caused by measurement noise or transient disturbances.

[0042] During the action generation process, when the normalized statistic corresponding to the first deviation reaches or exceeds the warning quantile threshold, the system can switch from maintenance mode to buffer mode or compensation mode, so that the action base quantity transitions from maintenance term to suppression term or compensation term, thereby enabling the adjustment action to intervene when a statistically significant early deviation occurs.

[0043] It should be noted that the aforementioned 0.15873 is merely a preferred statistical example under the condition of normal approximation. In other embodiments, the warning threshold can also be determined based on the empirical quantiles of historical steady-state samples, the estimation results of nonparametric distributions, or, when the first deviation uses a quadratic statistic such as the squared Mahalanobis distance, based on the corresponding chi-square quantile. All of the above different threshold determination methods are optional implementations of the structured constraints of this invention. Enhanced Implementation Example 1: Main Implementation Example of Engine and Powertrain

[0044] This embodiment uses an engine or powertrain with fuel metering, variable stator blades, bleed valve, nozzle adjustment, and torque distribution functions as an example to illustrate the implementation of the present invention in highly coupled, highly nonlinear, and strongly boundary systems. Specific technical problems addressed by this embodiment include: compressor approaching surge boundaries, thermal load approaching upper limits, coupling instability of speed or torque under transient conditions, control reference drift after aging, and over-adjustment due to boundary misjudgment.

[0045] In this embodiment, the multidimensional physical state input preferably includes at least a portion of the following: low-pressure speed N1, high-pressure speed N2, compressor outlet pressure P3, compressor outlet temperature T3, turbine inlet temperature Tt4, fuel flow rate Wf, variable stator blade position VSV, bleed valve opening, nozzle area, vibration signal, lubricating oil parameters, ambient pressure, ambient temperature, thrust command rate of change, and current control output state. Preferably, the above signals are first filtered, normalized, time-aligned, and outlier-value processed to construct a state vector x. k .

[0046] Preferably, the target working domain Ω* is defined by a specific set of inequality constraints: c1(x k c2(x) represents the lower limit constraint of surge margin. k ) represents the upper limit constraint on the vortex inlet temperature, c3(x) k ) represents the boundary constraints for rotational speed and acceleration, c4(x) k ) represents the constraint on the rate of change of the actuator, satisfying c i (x k If Ω* is less than or equal to 0, the state is considered to be within the target working domain. To improve conservatism, a contraction can be applied to Ω* in protected mode to form a safe working domain Ω. s .

[0047] In a preferred embodiment, the state mapping model Φ can employ an offline-trained autoencoder, principal component analysis, piecewise linear mapping, or mechanism-based feature mapping to obtain the feature representation z. k = Φ(x k As a directly achievable method, D1 k It can be defined as D1 k = max i [c i (x k )]_+ or the weighted signed distance on the boundary of the target working domain, used to represent the current state relative to Ω* or Ω. s The deviation range; D2 k It can be defined as the current state increment Δx k = x k - xk-1 In the local boundary normal or local regression direction n k The projection on, i.e., D2 k = n k ^T Δx k Alternatively, an equivalent trend deviation can be used. Thus, D1 k Reflecting "how far from the boundary", D2 k This reflects whether the border is rapidly approaching.

[0048] In a preferred embodiment, the basic motion quantity q k Generate according to the following relationship: q k = A1·sat(D1 k ) +A2·sat(D2 k ) + A3·[ΔD1 k , ΔD2 k ]^T, where A1, A2, and A3 are weight matrices or allocation matrices, and sat(·) is a saturation function or an equivalent bounded function. Preferably, D1 k Primarily determines the baseline for motion intensity, D2 k It primarily determines the direction of suppression, advancement, or recovery, thereby enabling the basic motion quantity to simultaneously carry positional deviation information and trend information.

[0049] The candidate values ​​of the control quantity are determined by q through the action projection relationship. k The transformation is obtained. In a preferred embodiment, the cross-spatial sensitivity mapping uses the local Jacobian sensitivity matrix J. k J k Each element represents the local effect of a unit action in a certain execution channel on a certain state constraint or feature dimension. k Small-amplitude step disturbances can be applied to each execution channel during engine bench testing, and the response of the characteristic space or constraint function can be recorded. Offline calibration can then be performed using the least squares method, recursive least squares method, or equivalent system identification method. During online operation, the J function can be calibrated based on the current operating point. k Perform table lookups, interpolation, or segmented calls. To ensure numerical stability, it is preferable to use J... k Regularization is applied, and its condition number, lookup step size, and single-cycle update magnitude are limited.

[0050] As a calculation method that can be directly implemented, we can first calculate based on D1. k and D2 k Construct the desired correction direction g k Then according to Δu k = (J k ^TJ k + λI)^(-1) Jk ^T g k The candidate control increment is obtained by taking its regularized equivalent form, where λ is the regularization parameter and I is the identity matrix; subsequently, the candidate control quantity u is obtained. k 0 = u k-1 + Δu k If the computing power of the ECU / MCU is limited, the full matrix inversion can be performed without explicitly completing it in each sampling period. Instead, J... k Its regularized pseudo-inverse or its equivalent local response is decomposed into the weight distribution of the operator sequence, and candidate control increments are generated in parallel in two or more independent computation loops.

[0051] Subsequently, cross-loop consistency checks are performed on the candidate control increments generated by different computation loops; when the cross-loop difference does not exceed the preset tolerance, and D1 k D2 k When the preset accuracy threshold, energy degradation threshold, or safety margin threshold is met, the calculation is prematurely terminated within the current sampling period, and the candidate control quantity or its constrained correction value is directly output. This reduces the additional latency caused by explicit matrix inversion and multiple iterations without changing the core control logic, making the architecture suitable for low-latency implementation in high-frequency sampling environments of power systems.

[0052] In this embodiment, for u k 0 Perform two levels of constrained projection or verification. The first level is the verification of actuator physical hard constraints, including fuel metering valve opening boundaries, VSV mechanical boundaries, vent valve rate of change boundaries, nozzle area rate of change boundaries, and torque distribution boundaries. The second level is the target working domain out-of-bounds prediction driven by logic soft constraints: predicting the state x at the next moment based on the current control quantity and model error boundaries. pred,k+1 If the surge margin, thermal margin, or speed margin corresponding to the predicted state will be lower than the preset lower limit, or will deviate from Ω* or its contracted Ω, s Then for u k 0 Perform projection correction, control barrier function constraint processing, or constraint contraction processing to obtain the corrected control quantity u. k Among them, the single-cycle cutting amount, constraint shrinkage amount, and equivalent correction amount are preferably not more than the preset boundary.

[0053] To illustrate local convergence, a discrete candidate energy function V can be constructed. k = 1 / 2·(D1 k ^2 + η·D2 k ^2). Under the condition that the rate of change of structured constraints is limited, J kUnder conditions where lookup error and gain of the fundamental motion quantity are limited, by selecting A1, A2, A3, λ, and the projection parameters, V can be made... k+1 - V k Maintain a non-positive or generally declining trend within the preferred working range. If V is detected... k If the system stops descending within the preset window, or if sensor glitches, abnormal combustion, or severe speed fluctuations are detected, the system enters a high-priority compensation mode, freezes some structured constraint updates, and increases the weight of the safety boundary.

[0054] This embodiment preferably employs a three-level response mode: sustain, buffer, and high-priority compensation. The sustain mode is used in D1. k and D2 k Maintain current control when both are within the small disturbance range; buffer mode is used in D2 k When the system is approaching the boundary but has not yet crossed it, the risk is first released through the auxiliary execution channel; the high-priority compensation mode is used in D1 k Exceeding the preset threshold or V k When the temperature stops decreasing, priority is given to ensuring surge, overtemperature, and execution boundary safety. Adjustments to steady-state mapping parameters and J are only permitted when the system is within the target operating domain for multiple consecutive sampling periods and is in sustain or buffer mode. k The system performs small-step updates by looking up table partitions, target working domain center points, or boundary offsets; when the system enters high-priority compensation mode, abnormal state, or rapid deviation state, the update is frozen; after recovery, the system is gradually unfrozen in small steps.

[0055] At the level of infringement comparison assistance, the external response of this embodiment can be manifested as follows: during sudden acceleration or sudden load changes, the fuel channel and the auxiliary execution channel exhibit asymmetric recovery characteristics with a sequential order; when approaching the surge boundary, the system will prioritize releasing the risk through the auxiliary channel before restoring the target output through the main channel; in high-priority compensation mode, the control change rate and boundary margin changes exhibit graded switching characteristics. The above external characteristics can serve as auxiliary evidence at the product behavior level, but are not intended to limit the scope of protection of this invention. Enhanced Example 2: Vertical Recovery and Landing Example of Rocket

[0056] This embodiment uses the vertical recovery and landing of a rocket as an example to illustrate the applicability of the present invention in extreme, highly constrained, time-varying, and high-frequency control scenarios. This embodiment does not make "absolute zero error" a legal commitment, but rather aims to achieve "stable convergence and soft landing within a preset landing tolerance." Specific technical problems include: under conditions where minimum thrust cannot be infinitely reduced, attitude and translation are strongly coupled, gust disturbances occur, jet bounce occurs, and remaining fuel is limited, stably guiding the rocket to a preset landing area and controlling the touchdown velocity, attitude, and lateral deviation within the tolerance range.

[0057] The multidimensional physical state inputs in this embodiment preferably include: altitude, vertical velocity, horizontal velocity, attitude angle, angular velocity, current engine thrust, minimum engine thrust threshold, engine throttling capability, remaining fuel, landing leg status, inertial navigation data, ground relative position information, crosswind estimate, jet backflow estimate, and actuator status. The structured constraints preferably include at least three categories: the first category is physical hard constraints, including upper and lower limits of engine thrust, upper limit of attitude angle, upper limit of angular velocity, lower limit of remaining fuel, and allowable load of the landing support; the second category is landing geometric constraints, including landing zone location boundaries, descent envelope, and grounding attitude boundaries; the third category is logical soft constraints, including protection priority zone, fuel priority zone, soft landing priority zone, and recovery zone.

[0058] In a preferred embodiment, the first state characterization quantity D1 is used to characterize the degree of deviation of the rocket's current state from the target landing working domain, and can be formed by combining the landing point deviation, vertical velocity deviation, attitude deviation, and remaining fuel margin; the second state characterization quantity D2 is used to characterize the trend of the current state evolving in an unfavorable direction, and can be formed by combining the normal projection in the altitude-velocity phase plane, the normal projection in the attitude-angular velocity phase plane, and the direction of crosswind disturbance. If D1 is small and D2 is significantly positive, it indicates that although the current error is still acceptable, the system may break out of the soft landing envelope in a short period of time.

[0059] In this embodiment, the basic motion quantity q preferably includes: a main thrust adjustment component, an attitude correction component, a lateral correction component, and a soft landing protection component. Through motion projection relationships, q can be projected as engine throttling, attitude control execution, and terminal landing attitude buffer control. To avoid soft landing paradoxes such as "excessive thrust leading to a second bounce" or "insufficient thrust leading to a hard landing" in the minimum thrust region, this embodiment preferably superimposes a control barrier function constraint during the control quantity generation stage, ensuring that the control quantity remains within the feasible motion domain that satisfies the thrust boundary and landing envelope.

[0060] In a preferred embodiment, a candidate energy function V = 1 / 2·(D1) can be constructed. 2 + η·D2 2 By selecting the basic gain of the action, the projection matrix, and the control barrier function parameters, the rocket continuously approaches the convergence targets of D1→0 and D2→0 within the preset landing window. In engineering implementation, this embodiment does not advocate a globally rigorous proof for all wind fields, all deviations, and all model errors. Instead, it advocates that under the conditions of optimized constraint boundaries, optimized remaining fuel, and optimized thrust margin, the candidate energy function shows a decreasing trend, thereby supporting the engineering description of the landing area as a "local attractor" or "optimal attraction domain".

[0061] Regarding real-time performance, this embodiment preferably achieves high-frequency closed-loop operation through local linearization mapping, offline matrix identification, fast table lookup, and low-dimensional quadratic programming. Compared to high-complexity global optimization schemes that require large-scale rolling solutions, the motion base quantities and motion projection chains in this invention can shift most of the complexity to offline calibration and online small-scale correction, thus making it more suitable for operation under high-frequency flight control computing resources. For the preferred control frequency of 500Hz to 1kHz, this invention can meet real-time requirements through dimensionality reduction mapping, boundary shrinkage, and local solutions.

[0062] Regarding robustness, when the rocket recovery stage encounters transient disturbances caused by gusts or engine jet bounce, these disturbances manifest as complex coupled disturbances of altitude, velocity, and attitude in the original physical space. However, in the state characterization quantities, they can be represented as high-frequency disturbance components of D1, short-term transitions of D2, or synchronous abrupt changes of both. This embodiment preferably freezes the structured constraint update upon detecting a sudden disturbance, preventing noise contamination of the core boundary, and performs filtering or low-pass processing on D1 and D2 to prevent the controller from over-acting due to false signals.

[0063] At the verification level, this embodiment preferably adopts the following methods for engineering verification: First, Monte Carlo simulation is used to randomly sample the wind field, sensor noise, thrust deviation, and initial attitude deviation to statistically analyze the distribution of landing position deviation, vertical touchdown velocity, and touchdown attitude; Second, phase plane trajectories of altitude-velocity and attitude angle-angular velocity are plotted to observe whether the trajectories converge toward the target origin within the preset landing window; Third, the calculation time of a single iteration is evaluated to verify the real-time performance on the target flight control platform. Enhanced Implementation Example 3: Wind Turbine Generator Set Implementation Example

[0064] This embodiment uses a wind turbine generator set as an example to illustrate the implementation of the present invention in a scenario where "load life, resonance avoidance, and power control" are equally important. This embodiment does not present a fixed conclusion regarding the specific improvement rate, but rather uses "reducing fatigue damage rate, extending tower and blade life, and reducing resonance risk" as preferred verification objectives. Specific technical problems include: strong coupled oscillations between tower bending moment, blade root load, aeroelastic coupling, and electromagnetic torque, as well as resonance amplification under gust impact.

[0065] The preferred multidimensional physical state inputs include: wind speed, wind direction change rate, blade pitch angle, impeller speed, generator torque, tower top acceleration, tower bending moment, blade root strain, nacelle sway, and converter state variables. Structural constraints include at least: tower stress boundary, pitch change rate boundary, generator current boundary, rated power boundary, resonance-sensitive region boundary, and lifespan priority region.

[0066] In this embodiment, the first state characterization quantity D1 can be used to characterize the degree of deviation of the current state from the "joint working domain of stress safety domain and power safety domain"; the second state characterization quantity D2 can be used to characterize whether the tower bending moment, nacelle oscillation, and blade aerodynamic modes are developing towards resonance amplification. When D2 increases abnormally before the actual stress peak value, the controller can intervene in advance before the stress reaches the peak value, thereby suppressing greater fatigue damage with smaller control actions.

[0067] The preferred basic control quantities include: pitch pre-adjustment component, generator torque buffer component, vibration suppression component, and recovery component. These control quantities can be further reflected in the pitch command and electromagnetic torque command. Since wind turbine fatigue damage is nonlinearly sensitive to load amplitude, when this invention identifies D2 in advance and suppresses amplitude before the peak arrives, even achieving only a moderate level of peak suppression can potentially bring more significant benefits in the lifetime dimension. Therefore, the preferred effect of this invention on wind turbines is not "more aggressively pursuing instantaneous power," but rather achieving a more controllable balance between power generation performance, load lifetime, and resonance avoidance.

[0068] At the verification level, this embodiment preferably compares the tower stress history, cyclic load count, pitch action spectrum, and recovery curve under wind speed disturbance to illustrate the ability of the present invention to implement "cancellation" suppression or "early unloading" suppression before resonance amplification by jointly driving D1 and D2. Enhanced Implementation Example 4: Electric Motor and Drive System Implementation Example

[0069] This embodiment uses a motor controller as an example to illustrate the implementation of the present invention in scenarios involving high-frequency sampling, magnetic weakening, magnetic saturation, and rapid load changes. Specific technical problems include: efficiency degradation in the high-speed magnetic weakening region, current vector oscillation during instantaneous acceleration and deceleration, high-frequency electromagnetic noise, and overshoot during sudden load changes.

[0070] The preferred multidimensional physical state inputs include: d-axis current, q-axis current, motor speed, DC bus voltage, flux linkage estimate, winding temperature, load torque estimate, inverter state, and command change rate. Structured constraints include: current boundary, voltage boundary, temperature rise boundary, field weakening operating boundary, magnetic saturation sensitive zone boundary, and comfort boundary.

[0071] The first state characterization quantity D1 can be used to characterize the degree to which the current state deviates from the efficient or safe operating domain; the second state characterization quantity D2 can be used to characterize whether the current vector, speed, and torque are evolving rapidly in an unfavorable direction. Through these fundamental action quantities, the present invention can proactively correct the current vector based on D2 before the error significantly increases, and maintain continuous constraints on the voltage, current, and flux linkage boundaries through structured constraints in the weak magnetic region or magnetic saturation region. Preferably, the fundamental action quantities are mapped to a voltage vector reference, torque correction quantity, or channel weight adjustment quantity.

[0072] In terms of implementation effectiveness, this invention can unify "dynamic response, efficiency optimization, and noise suppression" under the same constraint framework. For high-frequency scenarios such as motor control at the microsecond to sub-millisecond level, this invention preferably reduces the amount of online computation by using pre-computation mapping, local interpolation, and low-dimensional projection, rather than solving a highly complex global model in each iteration. Enhanced Implementation Example 5: Monitoring and Recommendation Output Example

[0073] In deployments that do not directly connect to the actuator, this invention can output only the state classification results and adjustment suggestion signals. For example, for older equipment that has not yet been converted into a closed-loop execution system, it can collect its multi-dimensional state inputs and perform state calculations based on structured constraints to output state levels such as "stable, warning, critical, and recovery," as well as suggested action directions, priorities, and suggested adjustment ranges. Because this invention still retains the intermediate layer of basic action quantities, even without directly outputting control quantities, it can provide a basis for action with constraint meaning for the host computer, manual operation, or secondary controller. Enhanced Implementation Example 6: Lateral Control and Obstacle Avoidance Implementation Example for Autonomous Vehicles

[0074] In this embodiment, the complex system is an intelligent vehicle with autonomous driving capabilities, whose task is to achieve lane keeping assist (LKA) and active obstacle avoidance on highways or structured urban roads. The system's multidimensional physical state inputs include: the vehicle's lateral distance $y_{err}$ relative to the lane centerline, the heading angle deviation $\theta_{err}$, the current vehicle speed $v$, and the road curvature $\kappa$, all identified by onboard vision sensors or LiDAR.

[0075] In this scenario, the structured constraints $C / \Omega$ are defined as follows: Target working domain boundary: the safe lateral driving space determined by subtracting half the vehicle width from the physical boundary of the lane lines, and the safe corridor boundary generated based on the dynamic obstacle avoidance algorithm; Physical hard constraints: the maximum steering angle limit $\delta_{max}$ and the maximum steering angle change rate limit $\dot{\delta}_{max}$ of the steering actuator; Logical soft constraints: the maximum lateral acceleration threshold (e.g., $0.3g$) set to ensure passenger comfort and prevent sideslip.

[0076] The state calculation process is as follows: The first state characteristic $D1$ represents the degree of lateral deviation of the vehicle. It is defined as the ratio of the current lateral distance $y_{err}$ to the safe half-lane width $L_{safe}$. When $|D1| \to 0$, it indicates that the vehicle is in the center of the lane; when $|D1| \to 1$, it indicates that the vehicle's tires are about to touch the lane edge constraint. The second state characteristic $D2$ represents the trend of the vehicle's return or deviation. It is calculated based on the heading angle deviation $\theta_{err}$ and the lateral velocity, reflecting the vehicle's evolution direction over a short predicted timeframe. If $D1$ is positive and $D2$ is negative, it indicates that although the vehicle is veering to the right, it is returning to the centerline.

[0077] The motion generation logic is as follows: Motion base quantity $q$: The system determines the base steering intensity based on the value of $D1$ and introduces differential compensation or damping based on the trend signal of $D2$. For example, when strong crosswinds are detected causing $D2$ to increase rapidly (exacerbating the deviation trend), even if $D1$ is still small, the motion base quantity $q$ will generate a significant reverse correction intention in advance. Projection and verification: The generated motion base quantity $q$ is mapped to the front wheel steering angle command through a local Jacobian matrix. Subsequently, truncation is performed based on the physical hard constraints (steering limit) in the structured constraints, and the steering increment is smoothed based on the logical soft constraints (lateral acceleration limit) to ensure that the output information does not violate the vehicle dynamics limits.

[0078] In this embodiment, the action output information directly affects the electronic power steering (EPS) system. Through the calculation under the above structured constraints, when the vehicle faces a curve with large curvature or a sudden obstacle avoidance maneuver, it can achieve smooth trajectory correction before touching the lane boundary through the coordinated drive of $D1$ and $D2$. Compared with traditional PID control, the convergence speed near the boundary is faster, and overshoot can be effectively prevented. Confirmatory descriptions and recommended validation schemes

[0079] To enhance the verifiability and specification support of this invention, the following scheme is preferred for engineering verification: First, Monte Carlo simulation. Random sampling is performed on random wind fields, sensor noise, thrust deviation, load changes, model disturbances, and initial deviations to observe the statistical distribution of D1 and D2, the number of boundary crossings, recovery time, and peak control action. Second, phase plane analysis. Phase plane trajectories are plotted for key state pairs (such as height-velocity, attitude angle-angular velocity, torque-speed, tower displacement-bending moment) to verify whether the trajectories converge towards the attraction zone within the target working domain center or boundary under preferred conditions. Third, computational power evaluation. The single iteration time is measured on the target processing platform to confirm that state calculation, basic action quantity calculation, mapping solution, and constraint verification can be completed within the specified sampling period. Fourth, comparative verification. The number of boundary crossings, recovery time, overshoot, control peak value, and number of abnormal mode triggers can be compared with traditional PID, rule control, or conventional MPC under the same simulation conditions. However, in this application, the comparison results are preferably described in text rather than using tables as the sole expression method.

[0080] The present invention provides a method, system, and storage medium for calculating the state and generating actions of complex systems based on structured constraints. These can be deployed on general-purpose processor platforms, edge computing nodes, industrial controllers, embedded systems, dedicated control units, devices with fixed constraint logic, or complex systems where some constraint logic is carried by the system's native structure. By continuously involving structured constraints in state calculation, feedback correction, generation of basic action quantities, and constraint processing of action output information, this invention can form a unified basic algorithm framework in software deployment scenarios, fixed logic scenarios, direct control scenarios, and suggested output scenarios, exhibiting good engineering adaptability and industrial application value.

[0081] This invention is particularly applicable to complex systems that require long-term stable operation, are difficult to reliably calibrate using a single error feedback, and have multiple physical boundary constraints. For engines and powertrains, this invention helps improve boundary recognition capabilities, reduce boundary misjudgments, and enhance long-term adaptive calibration capabilities; for rocket vertical recovery, this invention helps improve the interpretability, real-time performance, and robustness of soft landing control under high constraint conditions; for wind turbine generators and electric motor drive systems, this invention helps achieve a more stable trade-off between dynamic performance, structural lifespan, and operational efficiency. Attached Figure Description

[0082] Figure 1 This is a schematic diagram of the overall algorithm flow of the present invention, corresponding to the overall principle of the algorithm in Section 7.

[0083] Figure 2 This diagram illustrates the relationship between state calculation, basic action quantities, and action output information, corresponding to the overall algorithm principle in Section 7 and the simplified numerical implementation in Section 10.

[0084] Figure 3 To enhance the core algorithm flowchart of the engine and powertrain in Example 1, see Section 11.

[0085] Figure 4 To enhance the control logic diagram for the vertical recovery and landing of the rocket in Example 2, see Section 12.

[0086] Figure 5 This diagram illustrates the unified applicable path of the present invention in different physical systems and different output levels, corresponding to Sections 11 to 15.

Claims

1. A method for calculating the state and generating actions of a complex system based on structured constraints, characterized in that, Includes the following steps: A multidimensional physical state input of a complex system is acquired, including sensor data, operational state quantities, process variables, equipment response quantities, or combinations thereof. Based on preset structured constraints, state calculations are performed on the multidimensional physical state input to obtain a first state representation quantity D1 and a second state representation quantity D2. D1 characterizes the degree of deviation of the current state from the target working domain boundary, and D2 characterizes the approach, departure, or regression trend or directional relationship of the current state relative to the target working domain boundary. Based on D1, D2, and the structured constraints, basic action quantities are generated. Based on the basic action quantities and the action projection relationship defined by the structured constraints, action output information is generated. Based on the structured constraints, the action output information is subjected to constraint verification, projection correction, or output condition judgment. The processed action output information is output; wherein the action output information includes at least one of control quantity, state classification result, action direction suggestion, priority suggestion and suggestion adjustment range, for use in the calibration, control, early warning, decision support of complex system, or to enable the complex system to return to, maintain or recover to the target working domain defined by the structured constraints.

2. The method according to claim 1, characterized in that, The structured constraints are preset constraint structures used to define the target working domain, state evolution boundary, and action generation basis of a complex system. They include at least: a boundary function or a set of constraint inequalities for defining the target working domain; and at least one of physical hard constraints or logical soft constraints for defining the action generation boundary. The structured constraints also include at least one of state mapping model, action projection relationship, update rule, freeze rule, and recovery rule.

3. The method according to claim 1, characterized in that, The state calculation includes: calculating D1 based on the structured constraints, where D1 is the signed distance, weighted distance, or equivalent deviation index from the current state to the boundary of the target working domain; and calculating D2 based on the change in the current state and the local boundary normal, local regression direction, or historical principal direction, where D2 is the projection of the rate of change of the current state in the direction or the equivalent directional deviation.

4. The method according to claim 1, characterized in that, The basic action quantity at least characterizes the direction and intensity of the system's next action, and is generated jointly by D1 and D2; wherein, D1 is used to determine the action intensity baseline, and D2 is used to determine the direction of suppression, advance, recovery or channel allocation, so that the action generation simultaneously reflects the current position deviation information and evolution trend information.

5. The method according to claim 1, characterized in that, When the action output information is a control quantity, generating the action output information based on the action base quantity and the action projection relationship defined by the structured constraints includes: based on the local Jacobian sensitivity matrix J k Alternatively, it can be used to map the basic motion quantity into a control increment in the physical actuator space, or based on equivalent local response mapping, lookup table interpolation mapping, piecewise call mapping, or constrained optimization solution mapping, to generate a control quantity; and based on the structured constraints, perform at least one of the following on the control quantity: amplitude limiting, rate of change verification, boundary overflow prediction, projection correction, control barrier function constraint processing, or constraint contraction processing; and when the control quantity meets the output conditions, output the processed control quantity to the actuator.

6. The method according to claim 1, characterized in that, When the method is deployed without directly connecting to the actuator, the action output information includes at least one of the following: status classification result, action direction suggestion, priority suggestion, and suggested adjustment range; wherein, the status classification result includes at least one of the following: stable, early warning, critical, and recovery status levels; and the action output information is output to the host computer, manual operation terminal, or secondary controller for auxiliary calibration, alarm handling, or subsequent control decision-making.

7. The method according to claim 1, characterized in that, The method employs a hierarchical response mechanism that includes at least a maintenance mode, a buffer mode, and a high-priority compensation mode; at least a portion of the parameters in the structured constraints are updated only when the system is within the target working domain and in maintenance mode or buffer mode for multiple consecutive sampling periods. When the system is in a high-priority compensation mode, an abnormal state, or a rapid deviation state, at least some of the parameters in the structured constraints are frozen; when the system recovers from the abnormal state, it is gradually restored and updated according to preset conditions; and the magnitude, frequency, or rate of change of the update does not exceed a preset boundary.

8. A system for calculating the state and generating actions of a complex system based on structured constraints, characterized in that, It includes a state input interface, an action output interface, a processor, and a memory; the memory stores structured constraint parameters and computer-executable instructions, and the processor executes the computer-executable instructions to complete: acquiring the multidimensional physical state input of the complex system; Based on the structured constraints, state calculations are performed to obtain D1 and D2; Based on D1, D2, and the structured constraints, generate basic motion quantities; based on the basic motion quantities and the motion projection relationships defined by the structured constraints, generate motion output information; Based on the structured constraints, the action output information is subjected to constraint verification, projection correction, or output condition judgment; and the processed action output information is output through the action output interface; wherein, the action output information includes at least one of control quantity, state classification result, action direction suggestion, priority suggestion, and suggestion adjustment range.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 7.

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