Method for controlling complex systems

Abstract

The invention relates to a method for controlling complex systems by means of a trained network, the method comprising the steps of: detecting one or more system variables of the complex system; determining the temporal development of the complex system to an intermediate state by means of the trained network; determining one or more control variables depending on the predicted temporal development of the complex system, and applying the one or more control variables to the complex system, such that the complex system is transferred to a target state. During the training of the network, the network was not trained on the intermediate state and / or the target state.

Description

[0001] Methods for controlling complex systems

[0002] The present invention relates to a method for controlling complex systems using a trained network. The present invention further relates to a corresponding device and a storage medium.

[0003] Real-world complex systems sometimes exhibit chaotic behavior that is difficult to predict, making it challenging to determine and control the evolution and temporal behavior of such systems. Examples of such real-world complex systems include mechanical, thermodynamic, and / or electronic systems. A simple example of a complex mechanical system that can exhibit chaotic behavior is the double pendulum. Other examples include the flow behavior in a turbine or engine, weather models, and similar phenomena. Predicting the behavior and evolution of the turbine's operating state can be particularly valuable in this context.If the prediction indicates that the engine is entering an undesired operating state, a parameter within the turbine, such as fuel supply, air supply, or flap position, can be appropriately adjusted based on the predicted behavior, thus preventing the undesired operating state. Predicting complex systems can therefore be used to control them effectively. Furthermore, predicting the behavior of complex real-world systems is helpful in the design and development of such systems, enabling the early identification and prevention of design and construction errors.

[0004] Methods for controlling dynamic nonlinear complex systems were first presented in 1990 by Ott et al. (PRL, 64, 1196 (1990)) and subsequently further developed. Initially, all these methods shared the common goal of controlling the chaotic behavior of the nonlinear complex system through small manipulations, such that the complex system is brought into a regular, i.e., periodic, state and then maintained there. This is achieved predominantly through two methods. Either one waits long enough until the trajectory describing the system's behavior is located in the desired target region of phase space (e.g., near a fixed point of a Poincaré section) and controls the locking of the system through small variations of a control parameter. Or one continuously monitors for pre-selected trajectories.Later, control methods were also described that can bring a complex system with regular behavior into a chaotic state. In Haluszczynski et al., Sei Rep 11, 12991 (2021), an AI method for controlling dynamic nonlinear complex systems was developed, which allows nonlinear complex systems to be controlled in a purely data-driven manner in relation to arbitrary target systems. This is based on the availability of data about the target system, which the AI ​​method uses to learn the properties of the target system.

[0005] The current state of the art allows for the purely data-driven control of dynamic systems into target states through the use of AI methods, without needing to know the underlying dynamic equations of the system – Haluszczynski et al., Sei Rep 11, 12991 (2021). This requires sufficient data about the target state beforehand so that the AI ​​method can learn the desired properties of the target state. Dynamic complex systems can exhibit a multitude of different dynamics, which are determined by the framework conditions of the complex system and can be transformed into other dynamics by changing these conditions. The disadvantage of the current state of the art is that the trained AI method used for control can only control the dynamic complex system into one target state precisely determined by the training data.If a different target state is desired, the AI ​​method must be retrained with the dynamics of the desired parameters. Besides the limited applicability of the control mechanism to exactly one target state for each AI method, it follows that control is only possible when data about the target state is available. An AI method that allows dynamic, complex systems to be controlled into different target states using one and the same method, including interpolated or extrapolated target systems for which no training data is available, has not yet been developed.

[0006] The object of the present invention is to provide a method for controlling complex systems which makes it possible to achieve target states that are unknown in advance.

[0007] The problem is solved by a method according to claim 1, a device according to claim 15 and a storage medium according to claim 16.

[0008] According to one aspect of the invention, a method for controlling complex systems using a trained network is provided. In particular, the network is a neural network, and especially a recurrent neural network. The method comprises the following steps:

[0009] Capturing one or more system variables of the complex system in a given state range of the system - in particular characterized by state parameters;

[0010] Determining the temporal evolution of the complex system into an intermediate state outside the previously recorded state range using the trained network;

[0011] Determining one or more control variables depending on the predicted temporal evolution of the complex system, and

[0012] Applying one or more control variables to the complex system so that the complex system is transformed into a target state, whereby the network was not trained on the intermediate state and / or the target state during its training. The system variables can be variables that characterize the complex system. In a mechanical system, these can be position variables or angles. In a simple example of a double pendulum, the system variables might be the displacement of the two masses relative to the normal. In the example of a jet engine, the system variables might be a flow velocity, pressure, temperature, or the like. The system variables are thus observables of the real complex system, which are primarily accessible through measurement.This can involve energy, a spatial coordinate (as in the previous example), velocity, acceleration, temperature, current, voltage, pressure, concentration, electrical resistance, or the like. The state domain is a parameter range that characterizes the behavior of the complex system. This characterization can be achieved, for example, by one or more state parameters, with the domain encompassing a possible variation of these state parameters at which the complex system's behavior remains unchanged or changes only slightly. The trained network is used to determine the temporal evolution of the complex system. In particular, it identifies an intermediate state of the complex system that the system reaches after a predetermined time period or a predetermined number of magazines. Such a network is known, for example, from D. Köglmayr, C.Räth, “Extrapolating tipping points and simulating non-stationary dynamics of complex systems using efficient machine learning”, Sei Rep 14, 507 (2024), the content of which is incorporated in its entirety into this application. Subsequently, depending on the predicted temporal evolution of the complex system, one or more control variables are determined and applied to the complex system so that it is transformed into a target state. While the system variables are quantities / observables that characterize the complex system itself (such as the position or angles of the masses in the case of a double pendulum), the control variable is an influencing factor that can be used to change the behavior of the system variables. In particular, it is a time-dependent control variable. In the example of the double pendulum, the one or more control variables can be a force acting on the first mass and / or the second mass.The control variable here comprises, in particular, a continuous force that changes over time and acts on the first mass and / or the second mass, causing the double pendulum to move along the desired trajectory. In the example of an engine, this could be, for instance, the air supply, fuel supply, or flap position, which, for example, influences the flow velocity within the engine. Depending on the determined intermediate state or the determined temporal developments of the complex system, this allows the system to be influenced and controlled in such a way that the target state is achieved.

[0013] It has been shown that the network does not need to be trained on the intermediate state and / or the target state during its training. Therefore, no training data encompassing the target state and / or the intermediate state for the corresponding dynamics of the complex system needs to be provided during the network training process. This allows the trained network to determine the temporal evolution of the complex system into previously unseen states. Thus, it is no longer necessary for the network to be specifically trained on the target state or the temporal evolution to the intermediate state. Instead, the trained network can interpolate or extrapolate the system dynamics into unknown parameter ranges. This provides a method for controlling a complex system and transitioning it to a target state.This simplifies network training, enables easy transferability of the trained network to different dynamics of the complex system, and simultaneously creates a reliable control method. Furthermore, successful learning of the system dynamics allows for the extrapolation of state ranges, which can then be used directly as target state ranges. Now, the method can not only be used, as described above, to apply one or more control variables to the system variables of the complex system, but also to determine state parameters that lead to the target state range. This enables another form of control, which allows the transition from the actual state of the system to the target state by means of a state parameter change extrapolated and proposed by the learning method, by effecting a corresponding change in one or more state parameters of the system.Using the example of the double pendulum, a state parameter could be, for example, the length of the pendulum from mass one to mass two, or the weight of mass two itself.

[0014] This method allows, on the one hand, the determination of a time-varying control variable to steer the trajectories of the system variables towards the desired state, and on the other hand, the determination of a system parameter change that leads to the desired state of the system. For example, if the desired state of a double pendulum is that of a periodically moving mass two with a specific amplitude, this method makes it possible to extrapolate the exact weight and length of the pendulum from mass one to mass two, so that mass two, with a certain initial potential energy, moves along the desired periodic trajectory with a given amplitude.

[0015] Preferably, if the trained network predicts a deviation of the complex system from the target state, the complex system can be (re)directed to the target state by applying one or more control variables. In other words, if the intermediate state determined by the temporal evolution of the complex system deviates from the desired target state, one or more control variables are determined from the difference and used to control the complex system. This creates a control loop that, thanks to the trained network, allows even complex systems to be controlled efficiently and, in particular, takes into account states for which the network was not specifically trained.

[0016] Preferably, the network is a para meter-aware next generation reservoir computing network, a para meter-aware reservoir computing network, or a parameter-aware minimal reservoir computing network.

[0017] Preferably, the complex system has three or more degrees of freedom.

[0018] Preferably, the complex system exhibits periodic, intermittent and / or chaotic behavior.

[0019] Preferably, the network was not trained on either the intermediate or the target state. Specifically, the trained network did not see either the intermediate or the target state as training data. Thus, no states of the complex system similar to the intermediate and / or the target state were provided to the network as training data. The prediction of the intermediate state or the determination of the target state is therefore achieved through extrapolation or interpolation of the training data provided during the training process.

[0020] Preferably, N denotes the number of states with which the network is trained, and M denotes the number of intermediate or target states that can be predicted by the trained network or toward which the complex system can be controlled. Here, N is smaller than M, and in particular, significantly smaller than M.

[0021] In particular, N is less than or equal to 10, and especially less than or equal to 5. Therefore, training data only needs to be provided for fewer than 10, and especially fewer than 5, states and their dynamics or temporal evolutions of the complex system in these states. Thus, for each of these states, a large number of training data points are provided as a time series for training the network. However, this training data is limited to N states of the complex system.

[0022] In particular, M is greater than 100 and especially greater than 1000, so that a significantly larger number of intermediate and target states can be predicted by the trained network. This greatly simplifies network training, as training data only needs to be provided for a small number of states of the complex system. At the same time, this simplified training method does not limit the versatility of the trained network, so that a large number of intermediate and target states can still be captured by the trained network.

[0023] Preferably, the one or more control variables are continuously varied until the target state is reached. With known networks for controlling complex systems, it is not possible to predict intermediate states with sufficient granularity. Therefore, typically, when a control variable is determined, it is applied immediately to achieve a direct and stepless transition of the complex system to the target state. However, it has been shown that such an abrupt transition of the complex system to the desired target state leads to undesirable side effects, such as a change in system behavior and, in particular, chaotic or transient behavior until the target state is reached.This can lead to significantly longer transition times until the complex system reaches the target state and the undesired behavior of the complex system, caused by the abrupt transition, subsides. Since, according to the present invention, the trained network can also predict unseen states of the complex system, it is possible to change the one or more control variables in small steps and, in particular, continuously, in order to gradually guide the intermediate state, which is determined by the trained network, towards the target state. In this process, a prediction for each of the continuously changed control variables is determined. Thus, a sequence of control variables is determined that transitions the complex system to the target state, particularly without changing the system's behavior.The length of the sequence is determined by the duration of the continuous changes to the one or more control variables and the number of selected intermediate steps for these variables. No corresponding adjustment of the trained network is necessary, as the trained network can also determine previously unseen states. This prevents unintended changes in system behavior. Simultaneously, the target state can be reached more quickly, since the target state is established immediately after the control variable for the target state is reached, without any unwanted intermediate behavior.

[0024] Preferably, the system behavior is maintained for continuously changing control variables. Thus, if, for example, the complex system exhibits periodic behavior, the control variables are changed, or a sequence of control variables is chosen, in such a way that the system behavior remains periodic for the complex system.

[0025] Preferably, the duration of the continuous change of the control variable is determined by predicting its evolution over time, thereby identifying a minimum duration for which the system behavior of the complex system remains unchanged. It has been shown that the probability of the complex system changing its behavior (for example, switching from periodic to chaotic behavior) decreases with increasing duration of continuous changes to one or more control variables until the target state is reached. However, since the trained network is now able to predict the evolution of the complex system over time, even for continuous changes in the control variable or a sequence of applied control variables, such continuous prediction of the evolution over time can be used to determine the minimum duration for which the system behavior of the complex system remains unchanged.In particular, a large number of predictions of the temporal evolution of the complex system are determined for different durations of continuous changes. The minimum duration at which no change in the system's behavior occurs can then be used to control the complex system. Thus, a minimum duration for transitioning the complex system from its initial state to its target state can be determined without unwanted effects and, in particular, without any change in the system's behavior.

[0026] Preferably, for a specific duration of continuous changes to one or more control variables, a control variable or sequence of control variables is determined for which no change in system behavior occurs. This determined control variable is then applied to the complex system, thus transitioning the complex system into its target state. This ensures that the system behavior of the complex system is maintained even if the probability of the complex system transitioning to a different system behavior is greater than zero for the selected duration of the continuous changes to the one or more control variables.

[0027] In this approach, a duration of continuous change is chosen such that the probability of the complex system switching to a different behavior is less than 1. Therefore, there is at least one control variable or sequence of control variables for which no changes in system behavior occur. This control variable or sequence of control variables is then used to control the complex system, ensuring that its behavior remains unchanged.

[0028] To determine the appropriate control variable or sequence of control variables, the system behavior can be consecutively analyzed for a multitude of control variables using suitable metrics, such as the correlation dimension, spatial complexity, or the self-similarity of the attractor. In particular, the first control variable or sequence of control variables that demonstrates a suitable maintenance of the system behavior can be used, and the search can be terminated. Thus, the method for finding the appropriate control variable or sequence of control variables is fast and can be performed in real time.

[0029] As described above, the probability of a complex system changing its behavior decreases with a longer duration of continuous changes in one or more control variables. However, it has been found that the duration of the continuous change does not need to be so long as to guarantee that no change in system behavior occurs. Rather, for shorter durations of continuous changes, and potentially even for abrupt changes in one of the control variables, a control variable (in the case of an abrupt change) or a sequence of control variables (in the case of a continued continuous change) can be found that will bring the complex system into the target state without unwanted intermediate states occurring or requiring a transient response. Thus, it is also possible to achieve this.

[0030] Preferably, one or more system variables are measured quantities and in particular pressure, temperature, voltage, current, voltage, resistance, concentration, motion (position, speed, acceleration) or the like.

[0031] Preferably, the one or more system variables are detected by sensors within the complex system. This allows for the creation of a complete control loop, in which the sensors detect the one or more system variables of the complex system, one or more suitable control variables are determined by the trained network, and then applied to the complex system to control it.

[0032] Preferably, the complex system is a mechanical system, a thermodynamic system, and / or an electronic system. The complex system can be designed to exhibit periodic, quasi-periodic, or chaotic behavior. Preferably, the complex system is, for example, a power grid, a climate model, a turbine, an engine, or the movement of objects such as people or vehicles in a room, or the like. However, the present invention is not limited to this specific application, so that other real-world complex systems can also be considered, and their behavior or temporal evolution can be predicted by the hybrid network of the present invention.

[0033] Furthermore, the present invention relates to a device comprising a processor and a storage medium connected to the processor. The storage medium stores instructions which, when executed by the processor, perform the method described above.

[0034] Preferably, the trained network is implemented by the device. In particular, the network can be hardware-implemented and, for example, provided by specific hardware, or the network can be software-implemented.

[0035] Preferably, the device has one or more sensors for detecting the system variables of the complex system.

[0036] Preferably, the device has at least one actuator for generating a control variable which is applied to the complex system. The actuator can be a mechanical actuator, a voltage and / or current source, or the like.

[0037] Furthermore, the present invention relates to a storage medium. The storage medium stores instructions which, when executed by a processor, perform the method described above.

[0038] The invention is explained in more detail below with reference to preferred embodiments and the accompanying figures. These show:

[0039] Figure 1 shows a schematic flowchart of the method according to the present invention.

[0040] Figure 2 shows a representation of the training of the network according to the present invention,

[0041] Figure 3 shows a comparison of the predicted states of the complex system according to the present invention.

[0042] Figures 4A, 4B show exemplary control loops.

[0043] Figures 5A, 5B Comparison of system behavior,

[0044] Figure 6 shows the probability of a change in system behavior depending on the control of the complex system, and

[0045] Figure 7 shows the probability of a change in system behavior depending on the control of the complex system with a selected control variable.

[0046] Reference is made below to Figure 1, which shows a schematic flowchart of the method according to the present invention. The method relates to a method for controlling complex systems using a trained network.

[0047] In step SOI, one or more system variables of the complex system are recorded.

[0048] In step S02, the temporal evolution of the complex system into an intermediate state is determined using the trained network.

[0049] In step S03, one or more control variables are determined based on the predicted temporal evolution of the complex system. In step S04, these one or more control variables are applied to the complex system, thus transforming it into a target state.

[0050] In this case, the network was not trained on the intermediate state and / or the target state during its training.

[0051] The complex system in question could be a dynamic technical system, such as an engine, particularly a rocket engine, an internal combustion engine, or the like. Alternatively, the complex system could be EEG recordings from a patient. Or it could be a fluidic or flow system, where the flow of a fluid within a predefined topology is recorded. Equally conceivable is a system for recording the movement of people, vehicles, mobile elements in a complex interaction, gas particles in a vacuum, bacterial movement, mass transport in living cells, or similar phenomena.

[0052] The control procedure is described below using the example of a jet engine as a real-world system: Such an engine has a multitude of degrees of freedom. Each degree of freedom is determined by at least one measured variable, such as temperature, pressure, vibration, mixture concentration (air-fuel ratio), or the like. Each of these measured degrees of freedom exhibits typical irregular ("chaotic"), but not random, fluctuations in the engine's target state. Knowing the engine's target state allows the behavior of each degree of freedom to be learned and then predicted. Preferably, a machine learning method, such as reservoir computing or next-generation reservoir computing, is used for this purpose. However, if it is computationally expensive to generate training data for each possible target state, e.g., for a slightly modified new mixture concentration, then a machine learning method is more efficient.To generate an experiment, the effort required can be replaced by the AI ​​method presented here, which uses extrapolation or interpolation of the dynamics. During engine operation, a continuous comparison is made between the predicted, extrapolated, or interpolated target behavior and the actual behavior of the variables. If the deviation is significant, the individual physical degrees of freedom (e.g., temperature, pressure) are changed, for example, using an actuator, so that the value of the degree of freedom is brought closer to its target value defined by the prediction. The strength of the influence that the actuator exerts on the respective degree of freedom depends on the difference between the target and actual values ​​and can vary for the different degrees of freedom. Through this continuous measurement, prediction, and complex control, self-reinforcing instabilities, which may otherwise...devastating effects can be avoided.

[0053] The following refers to Figures 2 and 3. Figure 2 shows a bifurcation diagram for a control parameter p for a Lorenz system (Lorenz-63 system), which was solved numerically using a fourth-order Runge-Kutta algorithm ("RK4"). Time series for only four control parameters p, corresponding to four states 100.1, 100.2, 100.3, and 100.4, are used for training the network. All other developments of the complex system for the other control parameters p are therefore unseen states and, in principle, unknown to the trained network. Figure 3 illustrates the prediction of these unknown states using the trained network. As can be seen in Figure 3, the trained network, which was trained only with the four states, is able to determine a wide parameter range of the control variable p and predict it with high accuracy using extrapolation or interpolation.This allows the trained network to be used for complex systems or states of a complex system whose states were not considered during training. For example, the time evolution of the complex system for a control variable p=100.0 can be predicted with high accuracy by the trained network, even though the network neither encountered this state nor was provided with training data for this state during its training. Such a network is known, for example, from D. Köglmayr, C. Räth, “Extrapolating tipping points and simulating non-stationary dynamics of complex systems using efficient machine learning”, Sei Rep 14, 507 (2024), the content of which is incorporated in its entirety into this application.

[0054] The following refers to Figures 4A and 4B. Figure 4A illustrates a conventional control system for a complex system. This involves recording the current states of the system and determining the temporal evolution of the complex system from its current state to an intermediate state. The deviation between the intermediate state and the current state is then determined, and a control variable is derived from this. A switch is depicted as an abrupt change in the control variable, such that when the switch is activated, the control variable intended to transition the complex system from its current state to the target state is applied abruptly.This corresponds to a conventional control system, which is particularly problematic because intermediate states or continuous changes in the control variable cannot be predicted by conventionally trained state-of-the-art networks. This is because conventional networks require specific training for such predictions, and versatile application, especially to unknown target states, is not possible. However, an abrupt change in the control variable affects the behavior of the complex system, which can lead to undesirable effects such as chaotic behavior or complex transient responses. These can, for example, damage the complex system or lead to undesired operating states. Therefore, a continuous change in the control variable is implemented as shown in Figure 4B.This allows a controller to determine how quickly the dynamics of the complex system should change, or over what period of time the controlled variable should change continuously. Subsequently, the transition states are predicted using the trained network. This is possible because the transition states reached by the complex system during the continuous change of the controlled variable do not need to be known during the training process. Thus, the controlled variable changes continuously over a period of time. This is illustrated in Figures 5A and 5B. In Figure 5A, the complex system operates in the region...

[0055] (i) If an actual state exists and the system is to be transitioned to the target state of area (iii), the control variable is abruptly changed according to the sequence shown in Figure 4A. This leads to unintended and unpredictable behavior of the complex system in area (ii). This can cause the complex system to enter an unintended operating state, which can lead to damage to the complex system. In comparison, Figure 5B shows a continuous change of the control parameter, also from p=100.50 to p=99.50, over a period of time within the area.

[0056] (ii) As can be seen from Figure 5B, the system behavior of the complex system remains unchanged and continues to be periodic. This avoids any undesired system behavior.

[0057] Figure 6 shows the probability with which an exemplary complex system transitions from its system behavior to chaotic system behavior, plotted against the duration of the continuous change of the control variable, or transition time. It shows that as the duration of the continuous change of the control variable increases, the probability that the system behavior of the complex system changes to a chaotic system decreases. By predicting the intermediate states along the continuous change of the control variable, it is possible to determine a minimum time period at which the probability of the system behavior changing is minimized. This is illustrated in Figure 6. For example, a transition time of 75 (arb.The system behavior can be selected according to the unit, indicated by the dashed line A, where there is a sufficiently low probability that the system behavior will not change unintentionally but will remain unchanged. This allows for particularly efficient and fast control of the complex system by minimizing the duration of the continuous change, while simultaneously ensuring that unintended system behavior is avoided. Figure 6 shows a simulation and compares it to the prediction of the next-generation reservoir computing network (NGRC). As can be seen in Figure 6, the transition behavior of the complex system can be predicted with high accuracy even for unknown states of the complex system.This allows for the reliable determination of the minimum time required for changes to the control variable, ensuring that the system behavior of the complex system remains unchanged. Furthermore, Figure 6 illustrates a comparison with the system behavior ("control") obtained after applying the control variable.

[0058] Figure 7 again shows the comparison between the simulation and the prediction, analogous to Figure 6. Furthermore, Figure 7 also shows the comparison with the system behavior ("control") obtained after applying the control variable. However, for each transition period, a control variable or sequence of control variables was determined for which no undesired system behavior occurs. This control variable or sequence of control variables was applied to the complex system, and the probability with which the controlled complex system exhibits chaotic behavior was plotted. As can be seen in Figure 7, even with an abrupt change in the control variable, i.e., a transition period of 0 (arb. units), a control variable can be found that precisely avoids chaotic behavior of the complex system. Such a control variable or sequence of control variables is then used to calculate the probability of chaotic behavior.A sequence of control variables can be found iteratively, whereby, starting from a short transition period, the temporal behavior of the complex system is assessed for different control variables to determine whether it exhibits chaotic or undesirable system behavior. This can be done, for example, using suitable key figures that characterize the complex system or via a look-up table (LUT). The first such control variable found represents the minimum transition period at which maintaining the system behavior is ensured by applying the identified control variable. Thus, according to the present invention, the property of a trained network to predict even unseen and unknown states of a complex system with high precision is exploited.Thus, it is possible to accurately predict the temporal evolution of a complex system even as the control variable influencing it changes continuously, thereby suppressing any changes in system behavior. Alternatively, a control variable or sequence of control variables can be found that does not result in any changes in system behavior.

Claims

Patent claims 1. Method for controlling complex systems using a trained network, comprising the following steps: Capturing one or more system variables of the complex system; Determining the temporal evolution of the complex system into an intermediate state using the trained network; Determining one or more control variables depending on the predicted temporal evolution of the complex system, and Applying one or more control variables to the complex system so that the complex system is transformed into a target state, whereby the network was not trained on the intermediate state and / or the target state during its training.

2. The method of claim 1, wherein the complex system has 3 or more degrees of freedom.

3. A method according to claim 1 or 2, wherein the trained network has not seen either the intermediate state or the target state as training data during its training.

4. Method according to any one of claims 1 to 3, wherein N is the number of states with which the network is trained and M is the number of intermediate states that can be predicted by the trained network or the number of possible target states, wherein N < M.

5. Method according to claim 4, wherein N is less than or equal to 10, in particular less than or equal to 5.

6. Method according to claim 4 or 5, wherein M is greater than 100, in particular greater than 1000.

7. Method according to any one of claims 1 to 6, wherein the one or more control variables are continuously changed until the target state is reached.

8. Method according to claim 7, in which a prediction for the respective intermediate states reached is determined for the continuously changed control variables.

9. Method according to claim 7 or 8, wherein the system behavior is maintained for the continuously changing control variables.

10. Method according to one of claims 7 to 9, wherein the duration of the continuous change of the control variable is determined based on the prediction of the temporal development, wherein a minimum duration is determined for which the system behavior of the complex system remains unchanged.

11. Method according to one of claims 7 to 9, wherein, for a certain duration of continuous change of one or more control variables, a control variable is determined at which no change in system behavior occurs, wherein this determined control variable is applied to the complex system so that the complex system is transformed into a target state.

12. Method according to any one of claims 1 to 11, wherein the one or more system variables are measured quantities, in particular pressure, temperature, voltage, current, resistance, concentration, motion, position, acceleration.

13. Method according to any one of claims 1 to 12, wherein the one or more system variables are detected by means of sensors in the complex system.

14. Method according to any one of claims 1 to 13, wherein the complex system is a mechanical system, a thermodynamic and / or an electronic system.

15. Method according to any one of claims 1 to 14, wherein the complex system is a power grid, a climate model, a turbine, an engine or the movement of objects.

16. Device comprising a processor and a storage medium, wherein the storage medium stores instructions which, when executed by the processor, perform the method according to any one of claims 1 to 15.

17. Storage medium, wherein the storage medium stores instructions which, when executed by a processor, perform the method according to any one of claims 1 to 15.

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