Method for controlling the dynamics of a complex system

Abstract

The invention relates to the field of controlling the dynamics and analyzing the behaviour of complex systems. Proposed is a method based on the parameters of non-equilibrium (ΔN) and duality (ΔD), which characterize the degree of deviation from an equilibrium state and the internal tension between elements of a system, respectively. The method includes determining these parameters, calculating the sensitivity of the system, and determining the rate of structural changes. The values obtained are used to assess the dynamic state of the system and to predict possible phase transitions, including stability, activation, reorganization and collapse. The method can be used in engineering, biology, economics, and cyber systems, and in modelling evolutionary processes. The method can be used to detect critical states, predict the behavior of systems and more efficiently control their dynamics.

Description

[0001] Invention title: Method for controlling the dynamics of a complex system.

[0002] Description

[0003] 1. Field of technology

[0004] The present invention relates to the field of controlling the dynamics of complex systems operating under conditions of disequilibrium and internal structural heterogeneity, and can be used to control, regulate, adapt and stabilize technical, cyber-physical, computing, information, engineering and other complex systems.

[0005] The invention relates, in particular, to methods for generating control effects on complex systems based on an integrated assessment of the rate of their structural changes, determined by the combined influence of external factors and internal structural characteristics of the system.

[0006] 2. State of the art

[0007] Methods of analysis, modeling, forecasting and control of complex systems are known, reflected in scientific and technical literature on nonequilibrium thermodynamics, nonlinear dynamics, self-organization theory, catastrophe theory, system dynamics, classical and modern automatic control theory, as well as methods of machine learning and optimization.

[0008] In particular, the following approaches are known:

[0009] 1. Nonequilibrium thermodynamics and dissipative structures, including the works of I. Prigogine (as well as publications on open nonequilibrium exchange and self-organization), which examine the mechanisms of the emergence of ordered regimes in nonequilibrium systems.

[0010] 2. The theory of self-organized criticality, including the work of P. Buck (including models of critical regimes and cascade transitions), used to describe nonlinear dynamics and transitions in complex systems.

[0011] 3. Catastrophe theory and the qualitative theory of dynamic systems, including the works of R. Thom, devoted to jump-like transitions and bifurcations when changing control parameters.

[0012] 4. System dynamics and modeling of complex processes, including the work of D. Forrester, aimed at describing the behavior of multicomponent systems with feedback and delays.

[0013] 5. Classical and modern methods of automatic control (including methods of feedback, adaptive control, optimal control, and robust control), widely presented in educational and scientific literature on control theory and engineering cybernetics. 6. Methods of machine learning and optimization, including approaches to constructing models of the system state and generating control actions based on observation data and target criteria.

[0014] The indicated approaches are, as a rule, focused either on managing the deviation of individual observed parameters of the system from specified values, or on local optimization of selected metrics, or on predicting the behavior of the system without using a single integral indicator that takes into account the combined influence of external disequilibrium and internal structural heterogeneity (conflict, tension) of the system.

[0015] The known solutions lack a universal method for forming a control effect on the system based on the calculation of the integral indicator of the rate of structural changes, determined by the parameters of nonequilibrium and duality of the system, which complicates the controlled maintenance of the system in an acceptable range of states under changing operating conditions.

[0016] 3. Technical task

[0017] The technical objective of the present invention is to create a method for controlling the dynamics of a complex system, which allows, on the basis of measured or determined parameters of nonequilibrium and internal structural heterogeneity, to generate a control action aimed at:

[0018] - adaptation of the system operating mode;

[0019] - preventing the transition of the system into unstable, critical or undesirable states;

[0020] - maintaining the system within the permissible range of dynamic modes under changing external and internal conditions.

[0021] 4. Technical result

[0022] The technical result achieved by implementing the invention is:

[0023] - formation of a control effect on the system based on an integrated assessment of the rate of its structural changes;

[0024] - increasing the stability of the system’s operation under conditions of non-stationary external influences;

[0025] - reducing the likelihood of uncontrolled phase transitions, collapses or accelerations of the system;

[0026] - ensuring adaptive change of the system operating mode depending on the current state and dynamics of its development;

[0027] - reduction of computational and energy costs by controlling the dynamics of the system, rather than individual local parameters. 5. Essence of the invention

[0028] The specified technical result is achieved by proposing a method for controlling the dynamics of a complex system characterized by parameters of nonequilibrium and internal structural heterogeneity, which includes the following stages.

[0029] At the first stage, the nonequilibrium parameter AN is measured or determined, which characterizes the degree of deviation of the system from the equilibrium state under the influence of external factors, such as external load, resource flow, environmental disturbances or other influences.

[0030] At the second stage, the duality parameter AD is measured or determined, which characterizes the internal structural heterogeneity, conflict, tension, or inconsistency of the system’s elements.

[0031] The AD parameter can be determined, in particular, on the basis of:

[0032] - dispersion or heterogeneity of system parameters;

[0033] - entropic or information indicators;

[0034] - covariance, gradients or differences between subsystems;

[0035] - other quantitative characteristics of the system's internal structure. In the third stage, the system excitability function a is calculated as a function of the parameters AN and AD, reflecting the system's sensitivity to changes in external and internal conditions.

[0036] At the fourth stage, the coefficient 0 is determined, reflecting the contribution of the duality parameter AD to the rate of structural changes in the system.

[0037] At the fifth stage, the rate of structural changes of the system dS / dt is calculated using the following equation: dS / dt = a(AN, AD) • AN + 0 • AD

[0038] dS

[0039] — = a(AN,AD) *AN + (3 * AD

[0040] dt

[0041] At the sixth stage, based on the calculated value of dS / dt, a control action U is formed, intended to change the operating mode of the system.

[0042] The control action U can be formed, in particular, by: - ​​limiting or strengthening individual processes;

[0043] - changes in resource distribution;

[0044] - regulation of the intensity of interaction of subsystems;

[0045] - changes in the operating modes of system elements;

[0046] - changes in the structure of interactions between system elements. At the seventh stage, U influences the system, resulting in changes in the system's dynamics toward achieving a stable or target operating mode. 6. Implementation of the control action

[0047] The control action U represents at least one control parameter, signal or set of parameters that act on the elements of the system.

[0048] In particular embodiments of the invention, the control action U is formed depending on the value and dynamics of the change in dS / dt, for example:

[0049] when dS / dt exceeds a given threshold value, the control action is aimed at reducing the intensity of processes or redistributing resources;

[0050] when dS / dt decreases below the permissible range, the control action is aimed at increasing the activity of the system;

[0051] Control can be carried out in discrete or continuous mode.

[0052] The specific form of control action is determined by the type of system and the conditions of its operation and does not limit the scope of legal protection of the invention.

[0053] 7. Examples of implementing the method

[0054] In one example of implementation, the method is used to control a technical system, where the control action is formed by changing the operating mode of the system elements depending on the value of dS / dt.

[0055] In another example, the method is applied in a computing system where the control action is formed by redistributing computing resources between the system components.

[0056] In the third example, the method is applied in a cyber-physical system, where the control action is aimed at changing the structure of interaction of the system elements in order to prevent transition to a critical state.

[0057] 8. Possible areas of application

[0058] The method of controlling the dynamics of a complex system can be used in:

[0059] - technical and engineering systems;

[0060] - computing and information systems;

[0061] - cyber-physical systems;

[0062] - decision support systems;

[0063] - automated and adaptive control systems.

[0064] 9. Advantages of the invention

[0065] The proposed method provides a universal approach to managing the dynamics of complex systems by using an integral indicator of the rate of structural change, taking into account both external disequilibrium and the internal duality of the system, which distinguishes it from known solutions.

[0066] 10. Visualization.

[0067] To clearly explain the operating principle of the claimed method, visualization of changes in the state of the system over time can be used.

[0068] In one of the possible visualization options, the state of the system is displayed in the space of parameters characterizing the nonequilibrium and internal structural heterogeneity of the system, while the sequence of changes in states over time is presented in the form of a trajectory.

[0069] This visualization allows for a clear demonstration of the dynamics of changes in the system state and transitions between operating modes, but is not a mandatory element of the method implementation and does not affect the formation of the control action.

[0070] The provided illustration is intended solely to explain the operating principle of the claimed method and does not limit the scope of legal protection of the invention.

[0071] Evolution of states in AN-AD coordinates over time

[0072]

[0073] Figure 1

Claims

AMENDED CLAUSE OF THE INVENTION received by the International Bureau on 19 May 2026 (19.05.2026) Independent clause 1 1. A method for controlling the dynamics of a complex computational or cyber-physical system characterized by parameters of nonequilibrium and internal structural heterogeneity, including stages in which: a) measure or determine the nonequilibrium parameter AN, which characterizes the degree of deviation of the system from the equilibrium state under the influence of external factors; b) measure or determine the duality parameter AD, which characterizes the internal structural heterogeneity, conflict or tension of the system; c) calculate the system excitability function a as a function of the parameters AN and AD; d) determine the coefficient P, reflecting the contribution of the duality parameter AD to the rate of structural changes in the system; e) calculate the rate of structural changes of the system dS / dt using the expression: dS / dt = a(AN, AD) • AN + p • AD characterizing in real time a deterministic measure of the intensity of restructuring and change in the complexity of the organizational structure of a computing or cyber-physical system; f) generating a control action U, which is at least one control parameter, based on the calculated value of dS / dt, wherein the generation of said control action is carried out analytically without the use of iterative procedures of stochastic search or fuzzy logical inference; g) influencing the system with the control action U, as a result of which the dynamics of the system changes in the direction of achieving a stable or target operating mode. Independent clause 2 2. A method for assessing the dynamic state of a complex computational or cyber-physical system characterized by parameters of nonequilibrium and internal structural heterogeneity, including the following stages: a) measure or determine the nonequilibrium parameter AN; b) measure or determine the duality parameter AD; c) calculate the systemic excitability function a as a function of the parameters AN and AD; d) determine the coefficient P; e) calculate the rate of structural changes of the system dS / dt using the expression: 8 MODIFIED SHEET (ARTICLE 19)dS / dt = a(AN, AD) • AN + ₽ • AD characterizing in real time a deterministic measure of the intensity of restructuring and change in the complexity of the organizational structure of a computing or cyber-physical system; f) use the calculated value of dS / dt as an integral indicator of the current state and dynamics of the system for analyzing, monitoring or predicting the behavior of the system, including the deterministic prediction of phase transitions between operating modes of the system structure based on the trajectory of change of the specified complexity. Dependent clauses (common to both independent clauses) 3. The method according to paragraph 1 or 2, in which the function a is determined analytically, empirically, or on the basis of observation data of the system.

4. The method according to paragraph 1 or 2, in which the coefficient P is a constant value.

5. The method according to paragraph 1 or 2, in which the coefficient P is determined as a function of the parameters AN and / or AD.

6. The method according to claim 1, in which the control action U is aimed at changing one or more parameters of the system selected from a group including the operating modes of the system elements, the distribution of resources, the intensity of processes and the structure of interaction of subsystems.

7. The method according to paragraph 1 or 2, implemented using computing means.

8. The method according to paragraph 1 or 2, used for controlling or analyzing technical, computing and cyber-physical systems. 9 AMENDED SHEET (ARTICLE 19) EXPLANATION PURSUANT TO ARTICLE 19(1) The Applicant expresses gratitude to the International Searching Authority for conducting an analysis of the state of the art and carefully studied the Written Opinion dated 18.05.2026, prepared by the authorized person D.E. Makeev. The Applicant cannot agree with the examiner's findings regarding the lack of novelty (Article 33(2) PCT) of claim 1 and the lack of an inventive step (Article 33(3) PCT) of claims 1-8. In accordance with Article 19 PCT, the Applicant has submitted replacement sheets of the claims. Notification of changes made to the invention claims:

1. Independent points 1 and 2 have been narrowed: the object of management and assessment is limited to complex “computational or cyber-physical” systems.

2. In paragraphs 1(e) and 2(e), an explicit indication of the deterministic physical-algorithmic nature of the calculated value dS / dt as a measure of change in the organizational complexity of the structure has been introduced.

3. Clause 1 (f) has been clarified to the effect that the formation of the control action is carried out on the basis of a direct deterministic analytical dependence, which excludes the use of stochastic search procedures or fuzzy logical inference.

4. Dependent claim 8 has been amended by deleting the reference to "socioeconomic systems." The scope of the invention in the claims is strictly limited to technical, cyberphysical, computing, and information systems, as well as process control computing platforms. This amendment was made to more clearly emphasize the technical nature of the claimed solution and eliminate redundant related areas. Below are the reasoned arguments refuting the expert's conclusions based on the literal text of the original application and the supporting materials. I. RELATED TO DOCUMENT DI (US 2003 / 0093392 Al, Ulyanov) - INADMISSIBILITY OF EXTENSIVE INTERPRETATION AND SUBSTITUTION OF CONCEPTS The expert asserts that patent D1 (Ulyanov) undermines the novelty (category "X") of independent claim 1, since it discloses the calculation of the rate of change of dS / dt for generating a control action. This conclusion is erroneous and based on an incorrect interpretation of the Applicant's terminology.

1. The requirement for literal interpretation: dS / dt as the rate of structural change The expert opinion unjustifiably ascribed physical meanings to the Applicant's parameters that were absent from the application materials. The expert equated the value of dS / dt with the "rate of entropy production." The Applicant draws attention to the fact that in the text of the original description and claims, the symbol dS / dt is literally and unambiguously defined exclusively as "the rate of structural changes in the system" (see claims 1(d), 1(e), as well as Section 5 and Section 9 of the description). The materials of the present application completely omits any mention of thermodynamic entropy or probabilistic chaos as the basis for the calculation framework. Insisting on a literal interpretation of the application, the Applicant points out the inadmissibility of replacing original terms with terms from opposing sources.

2. Differences in the physical and mathematical nature of parameters In the DI document (Ulyanov): The value S represents the Shannon information or statistical entropy (S_plant), which is a probabilistic measure of chaos and uncertainty in signals. The goal of control in D1 is to suppress chaos and minimize entropy production (dS / dt -> 0) (paragraph 14 of formula D1). In the claimed method: The value S defines a deterministic measure of the intensity of restructuring and change in the complexity of the organizational structure of a computing or cyber-physical system over time. An increase in complexity (dS / dt > 0) reflects a process of beneficial architectural evolution, adaptation, or controlled phase transition of the structure, which is fundamentally different from the concept of degradation or chaos in D1.

3. Direct deterministic calculation versus stochastic methods In document D1: The method is based on soft computing principles. The signal is generated iteratively using fuzzy neural networks (FNN) and a genetic algorithm (GA) that performs a random (stochastic) search for optimal weights (see Section 13 of formula D1). - In the claimed method: The control action is generated based on the direct deterministic analytical relationship of equations (1) and (2) by calculating the system excitability function a(AN, AD) in real time. The method does not use random enumeration, chromosome population generation, or fuzzy logical inference, which ensures a fixed response time for the technical system and reduces the load on computing resources. II. RELATIVELY TO DOCUMENTS D2 AND D3 (Category "U" - Obviousness of Combination) Since the Applicant has narrowed the independent claims to computing and cyber-physical systems, and has also amended dependent claim 8 by excluding socio-economic systems, the inclusion of documents D2 and D3 as discrediting the inventive step is unlawful.

1. Document D2 (Dryuk O.V., 2022): This is a "Collection of Problems and Exercises in Physical Chemistry." The expert committed a methodological error by ignoring the literal text of the application and unjustifiably equating the Applicant's parameter with thermodynamic entropy. On page 45 (problems 1, 3, 4) of the D2 manual, it is explicitly stated that the entropy production rate (diS / dt) is considered exclusively for chemical processes, thermal conductivity, and diffusion phenomena (characterizing energy dissipation and heat loss). The transfer of mathematical models of chemical thermodynamics to algorithms for the deterministic management of the organizational complexity of cyber-physical devices is not obvious to a computer scientist.

2. Document D3 (Tyrsin A.N., 2022): This monograph is devoted to vector entropy modeling of multidimensional stochastic systems, where objects are represented as random vectors using methods of mathematical statistics (correlation and dispersion matrices). The proposed method completely eliminates the stochastic analysis of random variables and utilizes measurable invariants of a deterministic nature (AN and AD). None of the documents D 1, D2, D3, either individually or in combination, contain any indication of the possibility of controlling the structure of a cyber-physical object based on the calculation of the system excitability function of two parameters a(AN, AD) and a direct analytical calculation of the rate of change of organizational complexity (dS / dt). The claimed technical result—preventing computational collapses and ensuring a stable response in real time—is achieved through an original deterministic mathematical architecture, which proves the presence of an inventive step. CONCLUSION Based on the above, taking into account the amendments made (including the strict limitation of the field of application in Article 8 to technical and computational frameworks and the explicit textual delineation of parameters), the claimed invention fully satisfies the patentability criteria of “novelty” (Article 33(2) of the PCT) and “inventive step” (Article 33(3) of the PCT). The applicant requests the International Preliminary Expert Authority (IPEA) to issue a positive International Preliminary Report (IPRP) under Chapter II of the PCT.

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