COMPUTER-IMPLEMENTED METHOD FOR ADJUSTING A STATE CONTROLLER, ESPECIALLY FOR A VEHICLE, IN THE PRESENCE OF TIME DELAYS AND / OR PACKAGE LOSSES IN COMMUNICATION AND STATIC UNCERTAINTIES

Abstract

One aspect of the present disclosure relates to a computer-implemented method for adapting a state controller by means of a data processing device, wherein the state controller is intended for the control of a technical system, and wherein the state controller and the technical system are contained in a local control system that communicates with the data processing device. The method aims to enable a not overly conservative, yet robust control for a local control system, despite initial lack of knowledge of the statistics or probability distribution of time delays in a local control system as well as of static uncertainties in a technical system to be controlled.

Description

Technical field The present invention relates to techniques for adapting a state controller by means of a data processing device. Related aspects include a computer program, a state controller, a data processing device, a distributed system, and a computer-readable medium or signal. State of the art In recent decades, the rapid development of computing power and communication technology has significantly impacted the infrastructure of today's control systems. While conventional control systems consist of sensors, controllers, and actuators connected by cables, a networked control system (NCS) replaces these connections with a communication network. The advantages of such an NCS are numerous, including reduced cabling and maintenance costs, while the communication topology allows for greater flexibility in distributed systems. Conversely, using a communication network also presents network-related problems, such as random time delays in sensor-to-controller (S2C) and controller-to-actuator (C2A) transmission, for example, due to large distances between nodes or time-varying network traffic.Furthermore, random packet loss can occur, e.g. due to network congestion. Both problems, if not actively addressed, can degrade the performance of the control system and, even worse, lead to instability of the control loop. It should be noted that NCS (Network Communication Systems) are not limited to wireless connections, but are also found in centralized or zone-based E / E architectures, in vehicles where various electronic control units exchange information, or in process control where bus networks replace hard-wired end-to-end connections. Furthermore, static uncertainties can also occur in a controlled technical system. These uncertainties remain constant or vary slowly over time during operation, but differ from one technical system to another. For example, in the case of vehicles as controlled technical systems, the load-dependent yaw inertia and mass of the vehicle, the distances of the vehicle's center of gravity to the axles, etc., can vary from vehicle to vehicle of the same type. This can negatively impact the control performance if these effects are not adequately considered. In the past, various control approaches have been developed to account for random time delays / packet losses, ranging from deterministic to stochastic approaches. While deterministic (robust) approaches are based on describing the worst-case uncertainty, stochastic approaches use additional information in the form of statistics / probability distributions to obtain a less conservative controller. However, the stochastic approach typically assumes complete information about the probability distribution or statistics of the time delay, which makes it difficult to apply in practice. On the other hand, if empirical estimates of the statistics are used, no guarantee can be given for the closed-loop control system. Such guarantees are, however, essential for enabling the control system.Furthermore, some state-of-the-art regulatory approaches do not take into account the additional negative effect of the often unavoidable static uncertainties. Therefore, a problem to be solved that underlies the disclosure can be seen, for example, as providing a method that enables – e.g., despite initial lack of knowledge of the statistics and / or probability distribution of time delays in a local control system as well as of static uncertainties in a technical system to be controlled – a not too conservative, but nevertheless robust control for a local control system. Summary of the invention A first general aspect of the present disclosure relates to a computer-implemented method for adjusting a state controller by a data processing device, wherein the state controller is intended for controlling a technical system, and wherein the state controller and the technical system are contained in a local control system that communicates with the data processing device. The method of the first aspect comprises the data processing device collecting a number of state input pairs of state vectors and input vectors of the state controller at a plurality of timestamps, wherein the timestamp corresponds to a discrete point in time at which the associated state input pair was determined.Furthermore, the techniques of this disclosure include providing a dynamic model for describing the technical system to be controlled, taking into account i) collected state input pairs, ii) the multitude of timestamps, iii) a distribution of time delays and / or packet losses during communication within the local control system, and iv) a distribution of a static parameter vector of the technical system. The static parameter vector influences the behavior of the technical system and contains at least one component that includes a static uncertainty parameter.Furthermore, providing the dynamic model includes: modeling the distribution of time delays and / or packet losses using the collected multitude of timestamps and a discrete-time Markov process; and modeling the distribution of the static parameter vector of the technical system using the collected number of state input pairs of state vectors and input vectors of the state controller and Bayesian inference with respect to the static parameter vector. Finally, the procedure of the first aspect includes adapting the state controller based on the provided dynamic model. A second general aspect of the present disclosure relates to a computer program designed to execute the computer-implemented method for adjusting a state controller according to the first aspect. A third general aspect of the present disclosure relates to a state controller designed to control a technical system, wherein the state controller communicates with the technical system to be controlled, at least partially, via a communication network. The state controller of this third aspect is further designed to send a number of state input pairs of state vectors and input vectors, each with a corresponding timestamp, via a communication network to a data processing device outside of a local control system comprising the state controller and the technical system. From these inputs, a sequence of time delays and a sequence of state input pairs can be derived for the data processing device.Furthermore, the state controller of the third aspect is designed to receive an update from the data processing device, wherein the update comprises a modified state controller, specifically an extended updated feedback matrix, wherein an input vector at a discrete time is connected to an extended state vector at the same discrete time through the extended feedback matrix, the extended state vector comprising a state vector at the same discrete time and time-delayed components of the input vector, described by the number of Markov modes. The state controller is also designed to implement the update. A fourth general aspect of the present disclosure relates to a data processing device designed to execute the computer-implemented method for adjusting a state controller according to the first aspect and / or the computer program according to the second aspect. A fifth general aspect of the present disclosure relates to a distributed system comprising a data processing device according to the fourth aspect. Furthermore, the distributed system comprises a local control system, which includes a state controller and a technical system to be controlled. A sixth general aspect of the present disclosure relates to a computer-readable medium or signal that stores and / or contains the computer program according to the second aspect. The techniques described in the first through sixth general aspects may have one or more of the following advantages. The method proposed here, according to the first general aspect (or an embodiment thereof), allows a state controller in a local control system to be successively adapted and ultimately deployed with improved performance (compared to the performance of the original state controller before adaptation), although (generally unknown in advance) time delays and / or packet losses (in other words, temporal uncertainties) may arise from the communication network between the state controller and the technical system being controlled. The proposed control strategy with respect to temporal uncertainties utilizes a general modeling framework for NCS—referred to as the Markov Jump Linear System (MJLS). Compared to conventional methods, time delay data, i.e.,Measurements are used to construct a Markov transition matrix and an ambiguity set containing the true probability distribution with a user-defined confidence level for each discrete time step. By continuously collecting further time-delay data, the Markov transition matrix can be recursively updated at runtime and the ambiguity set reduced while maintaining the same user-defined confidence level. This updating of the Markov transition matrix and the ambiguity set constitutes a first learning-based mechanism for the state controller of this disclosure. This ensures that an overly conservative design of the control is reduced by successively decreasing the ambiguity set, while still maintaining the probabilistic stability guarantees (due to the confidence level). A further advantage of this invention is that the present techniques, when learning the distribution with respect to time delays and / or packet losses, can simultaneously learn the true (but unknown) static parameters of the technical system to be controlled using Bayesian inference and collected state input pairs. These input pairs are collected from the state controller (e.g., the original state controller or a previously adapted state controller) in operation at timestamps, which are then used to learn the distribution of the time delays and / or packet losses. Compared to conventional methods, state input pair data, i.e., in the form of measurements, can be used to construct, for each discrete time step, a so-called probabilistic parameter set containing the true probability distribution for one or more static parameters with a user-defined confidence level.By continuously collecting further state-input pair data, these static parameters can be recursively updated, and the probabilistic parameter set can be reduced by this parameter while maintaining the same user-defined confidence level for the static parameter. This adaptation of the static parameters and the probabilistic parameter set constitutes a second learning-based mechanism for the state controller of the present techniques. This additionally reduces an overly conservative design of the control system by successively reducing the probabilistic parameter set, while still maintaining the probabilistic stability guarantees (due to the confidence level). A further advantage of this invention is that the adapted state controller, according to the present techniques, is robust because it can handle a multitude of probability distributions for time delays / packet losses as well as probability distributions for static uncertainty parameters. At the same time, it is not overly conservative, since it is not designed to accommodate all theoretically possible time delays / packet losses (and their sequences) as well as static uncertainty parameters equally, but rather those that are statistically relevant in the application. The defined state controller can then be considered released immediately or further investigated and, if necessary, released within the framework of a release procedure. Enabling the controller can be a necessary step for enabling the controlled technical system. Furthermore, the state controller defined according to the first aspect can be adjusted as needed, even if it is already in operation. Some terms are used in this disclosure in the following ways: A “state controller” may comprise an algorithm, i.e., a computational procedure, that feeds a complete or partial state variable (i.e., the internal state of the controlled system) back to an input variable. A state controller may include parameters that can weight the state variable. In examples, a state controller may be executed on a computer system. In examples, a state controller may be executed in a vehicle control unit, a cloud, or an edge. A state controller may, for example, comprise or be part of a hardware module with inputs and outputs. In the examples, a state controller may be a controller, part of a controller, or the controller itself. The “technical system to be controlled” in the present disclosure may be designed for installation in a vehicle and / or for controlling a vehicle function (in particular, a driving function). For example, the vehicle function may be a function for autonomous and / or assisted driving. In some examples, the state controller may be designed to run on a vehicle computer system (e.g., of an autonomous, highly automated, or assisted driving vehicle). For example, the computer system may be implemented locally in the vehicle or (at least partially) in a backend that is communicatively connected to the vehicle. For example, the computer system may include a control unit on which the state controller can be executed. In some examples, the vehicle may include a computer system with a communication interface that enables communication with a backend.For example, the state controller can be executed in this backend. In some examples, temporal uncertainties (such as time delays and / or packet loss) can arise from data transmission between the technical system being controlled and the computer system executing the state controller. In one example, "the technical system being controlled" could be a system for lateral and / or longitudinal guidance of the vehicle. In other examples, "a state vector" could be based on velocity or distance information. In other examples, the state vector could include a relative velocity and / or a distance between a first vehicle, a second vehicle, a person, and / or a stationary object. In another example, "the state vector" could include state variables based on at least one of a steering angle, an attitude angle, a yaw rate, a slip angle, and / or a lateral error.In some examples, the state vector can include information from a network, such as motion and / or direction information from other vehicles. This information can be provided via vehicle-to-vehicle (V2V) communication or via a backend (V2X) communication. The state vector can also include state variables based on one or more sensor signals. These sensor signals can be generated by appropriate sensors, such as lidar, radar, cameras, ultrasonic sensors, GPS, accelerometers, temperature sensors, and the like. An input vector can include a steering angle, steering speed, or target values ​​for acceleration and / or braking.In some examples, the "system to be controlled" may be designed for arrangement in a drive control system or drive unit and / or serve to control a motor-related function (in particular, motor control). In other examples, the "technical system to be controlled" may be arranged for arrangement in a drive control system of an electric machine. For example, the "state vector" may contain components that are based on at least one control signal, an operating mode, or a power setting of the electric machine. Within the scope of this disclosure, it is also conceivable that "the technical system to be controlled" may be located in a robot and / or designed to control a robot function (in particular, to control a robot's driving function and / or a robot's movement function, e.g., of robot arms). For example, "the technical system to be controlled" may be a system for lateral and / or longitudinal guidance of the robot. In some examples, the state controller may be executed on a robot's computer system. For example, the computer system may be implemented locally in the robot or (at least partially) in a backend that is communicatively connected to the robot. In some examples, the state controller may be executed in a backend. In some examples, "the state vector" may be based on velocity or distance information.In examples, the "state vector" can include a relative velocity and / or distance between a first robot, a human, another mobile device, and / or a stationary object. In another example, the state vector can include state variables based on at least one steering angle, orientation angle, yaw rate, slip angle, and / or lateral error. In yet another example, the state vector can include information from a network, such as motion and / or direction information from other robots, mobile devices, and / or humans. In yet another example, this information can be provided via direct communication or through a backend. In yet another example, the "state vector" can include state variables based on one or more sensor signals.In examples, these sensor signals can be generated by appropriate sensors, such as lidar sensors, radar sensors, cameras, ultrasonic sensors, GPS, accelerometers, temperature sensors, and the like. In one example, an "input vector" could include a steering angle, a steering speed, or target values ​​for acceleration and / or braking. Furthermore, the "technical system to be controlled" can serve to control distributed systems, for example, for the longitudinal guidance of multiple vehicles (platooning is one example). In addition to longitudinal vehicle guidance, the "technical system to be controlled" can provide the control of distributed systems, such as automated guided vehicles (AGVs). This control system can, for example, be designed to drive and / or coordinate AGVs using a local network (e.g., Local Edge, 5G network, 6G network, etc.) within a limited area, particularly in a logistics center and / or a production facility. As another example, the distributed systems can include robot arms in a local network, for example, in a manufacturing system. The control algorithms of at least these robot arms can be at least partially outsourced (i.e.,at least partially decentralized). For the purposes of this disclosure, "time delays" or "packet losses" that can occur during communication between the state controller and the controlled technical system are considered uncertain (in other words, indeterminate) timing effects that are at least partially nondeterministic (e.g., stochastic) in nature. These uncertain timing effects can occur in the feedback loop of a state controller and thus affect its performance. For example, in distributed systems where the control algorithm is physically separate from the controlled system (e.g., via cloud or edge computing), such timing delays in data transmission can occur. The timing delay can also be associated with sensor signal acquisition. In the following, the term "time delay" may in some cases also include jitter, i.e.,a fluctuation in the accuracy of the transmission clock of computing units of the distributed systems, such as a state controller and an actuator of a vehicle, a sensor of the vehicle and the state controller (or any combination thereof). A "static uncertainty parameter" can be a time-independent uncertainty parameter, which can also be of a non-deterministic (e.g., stochastic) nature, that can occur in the feedback loop of a state controller and thus influence its performance. For example, a "static uncertainty parameter" can mean that it is constant over time for a specific technical system, such as a vehicle or a robot (and / or the environment in which the device operates), and therefore appears as a constant scalar in "a technical system to be controlled," but varies from one technical system to another (and / or from one environment to another in which the technical system operates).Examples include the mass of the vehicle, the road friction on which a vehicle travels, the position of the vehicle's center of gravity, the load-dependent yaw inertia, and the distances of the vehicle's center of gravity to the axles. A "dynamic model" for describing a "technical system to be controlled" can be a model that quantitatively describes one or more functions of a system (e.g., one or more vehicle functions of a vehicle or one or more robot functions of a robot). This quantitative description can include, for example, a temporal and / or spatial dependency of one or more "state variables" and / or one or more "input variables" that represents the behavior of this function or these functions of the technical system. Furthermore, the "dynamic model" can include parameters (e.g., static uncertainty parameters, time delays, and / or packet loss as discussed above) on which the state variables and / or input variables may depend. In some cases, the "dynamic model" can include parameters that can influence the dynamic change of the state variables and / or input variables.The “dynamic model” can be a comprehensive one (in the sense of equations, e.g., a system of coupled equations, such as differential equations for the state variables, input variables, or parameters used to describe the behavior of a function of a technical system). In the context of this disclosure, the term “dynamic model” is to be understood in a broader sense and can also include the modeling of a distribution of temporal uncertainties (i.e., time delays and / or packet losses) and a distribution of static uncertainty parameters: if, for example, these distributions are updated (in other words, changed) over time, the dynamic model can also be updated; more on this below. A "vehicle" can be any device that transports passengers and / or cargo. A vehicle can be a motor vehicle (for example, a car or a truck), but also a rail vehicle. A vehicle can also be a motorized two- or three-wheeler. However, floating and flying devices can also be vehicles. Vehicles can operate at least semi-autonomously or with assistance. Brief description of the characters Fig. 1a is a flowchart illustrating an example of a computer-implemented procedure for fitting a state controller by a data processing device according to the first aspect. Fig. 1b and Fig. 1c are flowcharts showing further possible procedure steps according to the first aspect. Fig. 2 illustrates an exemplary embodiment of a distributed system comprising a local control system and a data processing device. Fig. 3 schematically illustrates an exemplary local control system with three vehicles performing platooning and, in particular, a group start. Fig. 4 illustrates exemplary successive transition probabilities and associated decreasing ambiguity sets. Fig. 5a illustrates exemplary control processes for a second vehicle during the platooning group start from Fig. 3 as a function of time for two different fitting experiments in the procedure, along with associated 1-σ confidence intervals.Fig. 5b shows, by way of example, the mean value for a radius defined with respect to one of the ambiguity sets as a function of the number of fitting experiments in the procedure, as well as a corresponding 1-σ confidence interval. Fig. 5c shows two exemplary static uncertainty parameters, corresponding to the respective masses of the second and third vehicles from Fig. 3, as a function of the number of fitting experiments in the procedure, as well as corresponding 1-σ confidence intervals. Detailed description As outlined in Figures 1a to 1c, a first general aspect relates to a computer-implemented method for adjusting a state controller 4 by a data processing device 7, wherein the state controller 4 is intended for controlling a technical system 3. The state controller 4 and the technical system of the first aspect are contained in a local control system 2, which communicates with the data processing device 7. The communication between the local control system 2 and the data processing device 7 (e.g., in both directions of communication, as exemplified by dashed arrows in Figure 2) can take place via a non-time-critical communication network 6 (e.g., via appropriate communication interfaces). The non-time-critical communication network 6 within the meaning of the present disclosure means that during the communication between the local control system 2 (e.g.,No time delays and / or packet losses occur between the state controller 4 of the local control system 2 (or another module that is part of the local control system) and the data processing device 7 (or at least these are of a deterministic, controllable nature). In some cases, the data processing device 7 can be an external device with respect to the local control system 2 (as shown by way of example in Fig. 2). In other cases, the data processing device can be part of the local control system 2. As shown by way of example in Fig. 3, the local control system 2 can comprise a plurality of vehicles, which together form the technical system 3 to be controlled and, for example, form a convoy (i.e., perform platooning) and, in particular, carry out a group start. The plurality of vehicles comprises at least two vehicles, or, as shown by way of example in Fig. 3, three vehicles. All vehicles except the first (leading) vehicle are controlled via the communication network 5 by a state controller 4 outside the technical system 3 to be controlled. In this case, it is advantageous for the communication network 5 to be a wireless network. Here, v0 denotes a speed of the first vehicle, v1 a speed of the second vehicle immediately following the first vehicle, and v2 a speed of the third vehicle immediately following the second vehicle.Furthermore, dsafe denotes the required safety distance that should ideally be maintained between successive vehicles or at least not be undercut. Furthermore, e1 denotes a distance deviation from the ideal safety distance dsafe between the first and second vehicle, and e2 denotes a distance deviation from the ideal safety distance dsafe between the second and third vehicle. However, the local control system 2 is not limited to this use case. Another use case is, for example, the control and / or coordination of guided automated vehicles by a local network (local edge, 5G network, etc.) in a limited area, such as logistics centers or production facilities. Yet another use case is, for example, the (partial) outsourcing of the control algorithms of robot arms to local networks, for example, for manufacturing systems. Another use case is the lateral and / or longitudinal control of vehicles at traffic intersections or other control zones, which is outsourced to a local edge or cloud system (e.g., a roadside unit). Further examples are described in detail above. The process steps of the corresponding independent claim are shown in the boxes drawn with solid lines in Figs. 1a to 1c, while the process steps of some dependent claims are shown in the boxes shown with dashed lines. The first step of the procedure involves the data processing device 7 collecting 100 state input pairs of state vectors and input vectors of the state controller 4 at a multitude of timestamps, where the timestamp corresponds to a discrete point in time at which the associated state input pair was determined (in other words: measured). For example, the state controller 4 (e.g., initially a robust state controller) can, during operation, transmit the state input pairs with their respective timestamps (e.g., continuously or at predetermined time intervals according to a schedule in the form of individual messages) to the data processing device 7 via the (in the sense discussed above) non-time-critical communication network 6. Alternatively, a differently designed module of the local control system 2 can be responsible for this transmission.For example, there can be a total of NS state vectors and input vectors in the number of state input pairs. Accordingly, NS timestamps can also constitute the multitude of timestamps. NS can be two or more, ten or more, fifty or more, one hundred or more, one thousand or more. In some cases, the collected state input pairs with their respective timestamps can be stored in a memory 11; 100 (e.g., a non-volatile memory or a cloud associated with this memory 11; 100) of the data processing device 7 (The reference numeral 100 in Fig. 2 indicates that the "collect" process step 100 and the memory 11 are connected in this example). The next procedural step involves providing a dynamic model to describe the system to be controlled, taking into account i) collected state input pairs, ii) the multitude of timestamps, iii) a distribution of time delays and / or packet losses during communication within the local control system, and iv) a distribution of a static parameter vector γ of the technical system. The static parameter vector influences the behavior of the technical system (in other words, its performance) and contains at least one component that includes a static uncertainty parameter. The static parameter vector can include one or more components, two or more components, three or more components, four or more components, or ten or more components. The number of components contained in the static parameter vector can determine its dimension.In the following, the dimension of the parameter vector will in some cases be denoted as np (i.e. γ ∈ ℝnp). It is conceivable that time delays and / or packet losses within the local control system may, in some cases, occur between the state controller 4 and the technical system 3 (e.g., with one or more subsystems of the technical system 3 and the state controller 4, such as the second or third vehicle and the state controller 4 in Fig. 3). In this case, the communication network 5 can be described as a time-critical communication network. Alternatively or additionally, such time delays and / or packet losses may occur within the technical system 3 (e.g., if it comprises several communicating subsystems; not shown in Fig. 3). Examples of a "static parameter" have already been given above: In the example of Fig. 3, the respective (unknown but constant) masses of the second and third vehicles, m1 and m2, can be selected as two static uncertainty parameters.In this non-restrictive case, the static parameter vector can contain two components. For example, γ = (γ1γ2)T with γ1 = m1 and γ2 = m2, where the superscript T stands for transposition. In the techniques of the present disclosure, providing the dynamic model comprises modeling the distribution of time delays and / or packet losses using the collected multitude of timestamps and a discrete-time Markov process. Furthermore, providing the dynamic model comprises modeling the distribution of the static parameter vector of the technical system using the collected number of state input pairs of state vectors and input vectors of the state controller and Bayesian inference (e.g., in the form of Bayesian linear regression) with respect to the static parameter vector γ. In the techniques presented here, the dynamic model for describing the system to be controlled can comprise a continuous-time dynamic model, which can be represented by a predefined function f(x, u, γ). This predefined function can contain the following time-dependent arguments: a state vector x, comprising one or more state variables; an input vector u, comprising one or more input variables and delayed by an indefinite time delay τ, which represents the distribution of time delays and / or packet losses in communication within the technical system; and the static parameter vector y, which influences the behavior of the technical system 3 (as mentioned above). In some examples, the predefined function can include, as an additional time-dependent argument, a noise vector ε, which models noise (e.g.,normally distributed noise with a mean of zero). In some cases, the time-continuous dynamics model can be modeled as a linear time-continuous system with indeterminate time delay τ ∈ ℝ≥0. For example, the linear time-continuous system can be given by the following first-order differential equations with respect to time t: As defined above, x ∈ ℝnx is a state vector, u ∈ ℝnu is an input vector, and ε ∈ ℝnx is a noise vector. Here, Aγ and Bγ can be functions of the parameter vector γ ∈ ℝnp and do not contain any explicit time dependence. Furthermore, providing the dynamic model to describe the system to be controlled can involve creating a discrete-time representation of the continuous-time dynamic model by discretizing it in time (e.g., using a known sampling time h ∈ ℝ>0). This discretization can describe the indeterminate time delay τ using the discrete-time Markov process by translating this delay into a discrete-time Markov chain with Markov modes θk for discrete time points. In some cases, each discrete time point can be assigned a corresponding Markov mode from a number of Markov modes. By discretizing time, e.g., using Euler integration, the above equation can be expressed as follows (Equation 1): The continuous time delay τ was translated into a discrete-time Markov chain θk ∈ {0,..., M}. Here, each Markov mode (also: Markov state) i ∈ {0,..., M} represents an integer time delay Δtk = ih (assigned to a corresponding discrete time tk), where M ∈ ℕ denotes the maximum time delay of interest for each application. This discrete-time Markov chain θk can model communication within the imperfect communication network 5 (accompanied by time delays and / or packet loss), which causes discrete time delays up to M. Furthermore, in the equation above, Aγ and Bγ are the matrices that can be developed using the components of the parameter vector y as follows (Equation 2): where A0, B0, Ai, and Bi are independent of γ. In the techniques of the present disclosure, modeling the distribution of time delays and / or packet losses can include deriving a sequence of time delays Δk based on the collected multitude of timestamps. Next, modeling the distribution of time delays and / or packet losses can include converting the sequence of time delays into a sequence of Markov modes M of the discrete-time Markov process. For example, the sequence of time delays can be a sequence of discrete time delays Δk. In some cases, to determine the sequence of Markov modes M, the discrete time delays can be calculated from the respective successive timestamps and expressed as multiples of the sampling time h.This can be achieved, for example, by subtracting the successive timestamps and then rounding the result of this subtraction to a corresponding integer of the sampling time. The sequence of Markov modes M of the discrete-time Markov process can be obtained, for example, as follows (Equation 3): where denotes a floor function and NS∈ ℕ is the set of collected timestamps (in other words, the total sample size over all collected timestamps). Furthermore, modeling the distribution of time delays and / or packet losses can involve determining a number of transition probabilities for transitions from time delays at a first time tk to time delays at a second time tk+1 based on the sequence of Markov modes, where the second time is later than the first. The first time can be, for example, tk = kh, where h is a sampling time and k ∈ ℕ0 is zero or a positive integer. This time can be identified with the integer k; that is, one can speak, for example, of the k-th time. The second time can be, for example, the time immediately following the first time tk+1 = (k + 1)h = tk + h. This time can again be identified with the integer k + 1. Furthermore, modeling the distribution of time delays and / or packet losses can involve determining one or more ambiguity sets around the specified number of transition probabilities, where each of the one or more ambiguity sets represents a measure of the deviation of specified transition probabilities from a fixed time delay at the first time tk to the time delays at the second time tk+1 with respect to corresponding true transition probabilities (more on this below). In the techniques of the present disclosure, the sequence of time delays can be a sequence of discrete time delays, in particular wherein a number of possible transition probabilities for transitions from time delays at the first time to time delays at the second time are arranged in a Markov transition matrix. (The definite number of transition probabilities can also be arranged in the Markov transition matrix.) Furthermore, the fixed time delay can be given by a fixed Markov mode θk = i ∈ {0,...,M} from a number of Markov modes at the first time tk, and each of the time delays at the second time tk+1 can correspond to a (generally different) Markov mode θk+1 = j ∈ {0,...,M} from the number of Markov modes. For example, transition probabilities from the fixed Markov mode θk= i ∈ {0, ... , M} to the Markov mode θk+1= j ∈ {0,...,M} can be denoted as τij= ℙ(k+1= j | θk= i).By iterating through all possible values ​​of the fixed mode θk = i ∈ {0,...,M}, the specific number of transition probabilities (and / or the number of possible transition probabilities) can be written as matrix elements of the Markov transition matrix. In an example, the Markov transition matrix can be expressed as follows (Equation 4):. It should be noted that, as defined above, this involves determining transition probabilities for transitions from delays at the first time tk to delays at the second time tk+1 based on the sequence of Markov modes. In other words, this approach allows the Markov transition matrix to be empirically estimated, which can then be used to solve a stochastic optimization problem. In this sense, the term "sequence of Markov modes" used above differs from the term "number of Markov modes" in that the former refers to the determined timestamps, while the latter refers more generally to the Markov modes; more on this below. Within the scope of the present disclosure, it is conceivable that determining the number of transition probabilities for the transitions from time delays at the first time tk to the time delays at the second time tk+1 may include determining one or more sample sizes, in particular inverse sample sizes ηi, for one or more fixed Markov modes θk= i from the number of Markov modes θk∈ {0,...,M}, corresponding to the respective time delays at the first time tk, wherein the determination of the one or more sample sizes, in particular inverse sample sizes, is carried out recursively by parsing the sequence of Markov modes M. In particular, each sample size, e.g., the i-th sample size, ηi-1∈ ℕ, can be determined recursively as follows: At the beginning of parsing the sequence of Markov modes M, the i-th sample size may have the value zero.Then, once the fixed Markov mode θk = i (the time delay at the first time tk) has been parsed from the sequence of Markov modes M, and a subsequent parsed Markov mode in this sequence of Markov modes M is the Markov mode θk+1 = i (the time delay at the second time tk+1), the i-th sample size, ηi-1, can be incremented by one. Otherwise, a value for the i-th sample size, ηi-1, can remain unchanged if the subsequent parsed Markov mode in this sequence of Markov modes M is the Markov mode θk+1 = j with j ≠ i. In an example, the i-th sample size, ηi-1, can be determined as follows (Equation 5): In some cases, all sample sizes, ηi-1, for i ∈ {0,..., M} can be determined in this way. Furthermore, determining the number of transition probabilities for the transitions from time delays at the first time tk to the time delays at the second time tk+1 can involve recursively determining transition probabilities for each transition from one or more fixed Markov modes θk = i from the number of Markov modes θk ∈ {0, ..., M} at the first time to each Markov mode θk+1 = j from the number of Markov modes θk+1 ∈ {0, ..., M}, representing the respective possible time delays at the second time tk+1, based on one or more determined sample sizes ηi-1, in particular inverse sample sizes, for one or more fixed Markov modes from the number of Markov modes and by parsing the sequence of Markov modes M. In some cases, one or more possible transition probabilities for a fixed Markov mode may be θk= i (e.g.For example, for the i-th mode, a row of the Markov transition matrix is ​​formed from the number of Markov modes θk at the first time point, and for each Markov mode θk+1= j (e.g., for the j-th mode), from the number of Markov modes θk at the second time point tk+1. This row can be denoted, for example, as follows: where i ∈ {0,...,M}. The transition probabilities for transitions from the fixed Markov mode i must be normalized to one at each time point k within a row of the Markov transition matrix, i.e., the following holds: This reflects the fact that the transition from the fixed Markov mode θk= i at the first time tk to one of the possible modes must occur at the second time tk+1. Furthermore, determining the number of transition probabilities for transitions from time delays at the first time tk to time delays at the second time tk+1 can involve assigning initial values ​​to the number of transition probabilities and updating the number of transition probabilities based on the sequence of Markov modes (for example, by the recursive determination described above). In one case, at the beginning of parsing the sequence of Markov modes M, it can be assumed that the transition probabilities within a row (e.g., each row) of the Markov transition matrix are uniformly distributed if no prior knowledge of the transition probabilities is available: This means that a transition from the fixed Markov mode θk= i at the first time tk to any of the possible modes at the second time tk+1 is equally likely.For example, the transition probabilities within the rows can be given by the following expression: (for the Markov transition matrix with dimension M × M). Alternatively, if prior knowledge of the transition probabilities exists (e.g., if the Markov transition matrix was previously determined from an earlier sequence of Markov modes, more on this below), the Markov transition matrix can be initialized accordingly. In some cases, the recursive determination of transition probabilities discussed above, which form a row (e.g., the i-th row) of the Markov transition matrix and which, as described above, each represent a transition from a fixed mode, e.g., a fixed mode i (i.e., θk = i), from the number of Markov modes θk at the first time point to each Markov mode θk+1 = j from the number of Markov modes θk+1 (representing the respective possible time delays at the second time point tk+1), can be determined recursively as follows. First, transition probabilities within the row of the Markov transition matrix can be initialized (e.g., as explained above).These transition probabilities can then be determined recursively once the fixed Markov mode θk = i (the time delay to the first time tk) is parsed from the sequence of Markov modes M by: - ​​recursively deriving transition probabilities within the row of the Markov transition matrix for a next parsing step k + 1 from an immediately preceding parsing step k, starting from initialized transition probabilities, at i) scaling these transition probabilities with a scaling factor that depends on the sample size ηi-1, in particular on the determined inverse sample size ηi, to the preceding parsing step k (e.g., the scaling factor can be equal to or proportional to one minus the determined inverse sample size ηiz to parsing step k); and optionally ii) adding a term that is computed based on the determined inverse sample size ηiz to parsing step k and a standard basis vector. Otherwise, the transition probabilities within the row of the Markov transition matrix (during the recursive procedure described above) can remain unchanged if the fixed Markov mode θk= j with j ≠ i (j ∈ (0,...,M}) is parsed from the sequence of Markov modes (i.e. the fixed mode θk= j ≠ i) to parsing step k. The recursive determination of transition probabilities within other (e.g., all) rows (j ≠ i) of the Markov transition matrix can be done in the same way. This allows all transition probabilities of the Markov transition matrix to be determined (in other words: the number of transition probabilities for transitions from time delays at a first time tk to time delays at a second time tk+1). In a special, non-restrictive example, the recursive procedure described above can be given by the following expressions (Equation 6): where and are respectively the i-th series of the Markov transition matrix to the parsing steps k and k + 1 respectively, and eΔk+1E ℝM+1 is a standard basis vector with components (eΔk+1)i = δ(k+1)i, i.e., the components are all zero except for the (k + 1)-th component, which is one. Within the scope of the present disclosure, it is conceivable that one or more transition probabilities from the definite number of transition probabilities for each transition from the fixed time delay θk = i at the first time tk to the time delays θk+1 = j at the second time tk+1 is a point in a finite-dimensional vector space corresponding to a transition vector that includes these one or more transition probabilities as components. For example, these one or more transition probabilities could be a row of the Markov transition matrix (e.g., the i-th row i ∈ {0,...,M}, see also the discussion of rows above). In this case, this transition vector could contain this row (or even be this row itself). The ambiguity set for this (definite) transition vector (e.g., the i-th transition vector) could be defined by a sphere centered at the point with radius ri in a finite-dimensional norm (e.g.,q-norm with q=1, 2, 3, 4 or with any other integer or real value). Furthermore, the radius can be based on a user-defined confidence level β and / or a determined sample size of one or more sample sizes ηi-1, in particular an inverse sample size ηi, for a fixed Markov mode i from the number of Markov modes, where this fixed Markov mode corresponds to the fixed time delay θk = i at the first time tk (examples of recursively determining the sample size ηi-1 for the i-th row of the Markov transition matrix, which represents all possible transitions from the fixed Markov mode i to other Markov modes j, are described above). Additionally, a probability that a true transition vector (or, using another notation, belongs to the ambiguity set) can be given by the user-defined confidence level β.In some cases, the radius may decrease with a constant user-defined confidence level and increasing sample size ηi-1, which was determined for a given fixed Markov mode θk= i from the sequence of Markov modes. In some cases, the radius can be determined by a concentration inequality, such as a McDiarmid inequality. For example, the ambiguity set (which is assigned, for instance, at the first time tk) can be determined as follows (Equation 7): where is an i-th probability simplex (or simplex for short). Here, ri(β,ηi-1) is the radius for the fixed Markov mode i, which can depend on a user-defined confidence level β ∈ (0,1) and on the sample size ηi-1. For example, the radius ri for a q-norm with q = 1 can lie in the following range: ri(β,γi-1(k)) ∈ (0,2). In examples, the ambiguity set determined in this way, together with the simplex Si, can lead to a guarantee that a true transition vector belongs to the ambiguity set with a probability given by the user-defined confidence level β. In a specific example, the following expression can hold: with β ∈ (0,1).In other words, it can be statistically guaranteed that the true (but unknown) transition vector belongs to the ambiguity set with probability 1 - β. The above procedure can be illustrated with the help of Fig. 4: In this figure, exemplary points in the form of the cross 21a-b are shown for three parsing steps of the procedure (which do not necessarily have to follow each other immediately), corresponding to the i-th transition vector with the determined transition probabilities (in other words: with the transition probabilities empirically determined by this procedure). The ambiguity set 20a-c can be a non-point-like subset of this higher-dimensional space that includes the point. In Fig. 4, starting from an exemplary ambiguity set that forms a simplex in the space of transition probabilities τi1, τi2, and τi3, further progressively smaller ambiguity sets 20b, 20c are drawn, with all three exemplary ambiguity sets each including the point marked by the cross.The ambiguity set is a measure of the uncertainty of the associated transition probabilities. Figure 4 illustrates how learning by recursively determining transition probabilities influences the empirically determined transition probabilities and the associated ambiguity set. Starting with the simplex (enclosed area of ​​a triangle, indicated by the solid lines in the left panel), which includes both the point 21a (marked by the cross) for the estimated transition probabilities and the true transition probabilities 22a (marked by a filled circle), decreasing ambiguity sets 20b, 20c are defined with subsequent parsing steps. These sets include both the cross 21b and the filled circle 22b and, after a sufficiently large number of parsing steps, converge to a singleton (the cross, which then coincides with the filled circle).In order for the method to converge to the singleton (with a given accuracy), the number of collected timestamps can include NS= 102 or more, NS= 103 or more, or NS= 104 timestamps, depending on the problem. As will be explained in more detail later, the determined one or more ambiguity sets (i ∈ {0,...,M}), e.g. with respective radii ri, can be used in further optimization procedures of the present techniques for the state controller. The previously discussed process step “Modeling 300 of the distribution of time delays and / or packet losses using the collected multitude of timestamps and the discrete-time Markov process” can be carried out in a module 12; 300 of the data processing device 7 (see Fig. 2 ). In the techniques of the present disclosure, the process step "Modeling 400 the distribution of the static parameter vector of the technical system" can include deriving 410 a sequence of state input pairs of state vectors and input vectors from the collected number of state input pairs of state vectors and input vectors of the state controller. As discussed above, these state input pairs are collected to form a multitude of timestamps, the latter being used (or having been used) for the process step "Modeling 300 the distribution of time delays and / or packet losses". Subsequently, the process step “Modeling 400” can include the Bayesian recursive derivation 420 of a posterior distribution for the static parameter vector of the technical system γk+1 for the next discrete time tk+1 based on i) a prior distribution for the static parameter vector of the technical system γk for an (immediately) preceding discrete time tk and ii) the discrete-time representation of the continuous-time dynamic model (such a representation of the continuous-time dynamic model is given in a non-restrictive example by equation (1) above). The recursive derivation can be performed starting from a prior distribution for the static parameter vector of the technical system γ0 that is initial at an initial time t0, where the state vector and the input vector are taken from the derived sequence of state-input pairs of state vectors and input vectors.Furthermore, Bayesian recursive differentiation can be performed for a sequence of discrete points, which is the multitude of timestamps for which the number of state input pairs of state vectors and input vectors of the state controller has been collected. In a preferred case, the initial prior distribution can be a normal distribution. In another case, the initial prior distribution can be a different distribution, which can be characterized in particular by a mean and a covariance. In connection with the process step "Modeling 400", it is conceivable that the formation 220 of the time-discrete representation of the time-continuous dynamics model further comprises: - deriving a matrix Xk, whose matrix elements are calculated from the number of Markov modes based on the state vector for the preceding discrete time tk and the input vector for the preceding discrete time tk with a Markov mode corresponding to this time; and - deriving a vector Yk, whose component is calculated based on the state vector for the preceding discrete time tk, the state vector for the next discrete time tk+1, and the input vector for the preceding discrete time tk with the Markov mode corresponding to this time. In a specific example, the following can be held for the formation of the time-discrete representation of the time-continuous dynamics model starting from the above equations (1) and (2) (equation 8): In the techniques of the present disclosure, “the Bayesian recursive derivation 420” of the a-posteriori distribution for the static parameter vector of the technical system γk+1 can comprise: 1) the recursive determination of a number of parameters for the a-posteriori distribution, in particular a mean µγ,k+1 and a covariance Σγ,k+1, for the next discrete time tk+1 based on a number of parameters for the prior distribution for the static parameter vector of the technical system γk for the preceding discrete time tk; and 2) the time-discrete representation of the time-continuous dynamic model. The recursive derivation can be performed starting from a number of parameters, in particular a mean µγ,0 and a covariance Σγ,0, for the initial prior distribution at the initial time t0. In a specific example, the recursive determination of the mean µγ,k+1 and the covariance Σγ,k+1 of the a-posteriori distribution for the static parameter vector starting from the above equation (8) can be summarized as follows (equation 9): Furthermore, the modeling 400 of the distribution of the static parameter vector of the technical system can further include the determination 430 of a probabilistic parameter set around the static parameter vector γ of the technical system for the next discrete time tk+1 based on the number of parameters of the a-posteriori distribution, in particular the mean µy,k+1 and the covariance Σγ,k+1, which were determined at that time by Bayesian recursive differentiation 420. Here, a first parameter determined at the next discrete time tk+1 from the number of parameters of the a posterior distribution, in particular its mean µγ,k+1, can be a point in a finite-dimensional vector space whose dimension is equal to a dimension of the parameter vector. (As mentioned above, the number of components contained in the static parameter vector can determine its dimension, e.g., γ ∈ ℝnp.) The probabilistic parameter set around the static parameter vector γ can be enclosed by a sphere around the point with a radius Ri in a finite-dimensional norm (e.g., a q-norm with q=1, 2, 3, 4, or with another integer or real value). Furthermore, the radius Ri can be based on a user-defined confidence level p for the parameter vector and / or a second parameter determined at the next discrete time tk+1 from the number of parameters of the a posterior distribution, in particular its covariance Σγ,k+1. Additionally, the probability that a true (but unknown) parameter vector y* belongs to the probabilistic parameter set can be given by the user-defined confidence level p for the parameter vector. In some cases, the radius Ri can decrease if the confidence level of the parameter vector remains constant and the number of steps (k ∈ {1,..., NS- 1}) during the iteration of the Bayesian recursive differentiation procedure 420 of the a posterior distribution increases. For example, the following expression can hold for the probabilistic parameter set (equation 10): Here, all variables are already defined above. In another, even more specific example, the probabilistic parameter set can be determined as follows, if the radius Ri is defined by a quantile function of the chi-square distribution: In some examples, the probabilistic parameter set determined in this way can guarantee that a true (but unknown) parameter vector y* belongs to the probabilistic parameter set with a probability given by the user-defined confidence level p for the parameter vector γ. In a specific example, the following expression may hold: ℙ (γ* ∈ Pk+1) ≥ 1 - p with p ∈ (0,1). In some cases, worst-case realizations of the discrete-time representation of the continuous-time dynamics model can be described by a number of parameter vector vertices nv of the probabilistic parameter set. Parameter vector vertices of the probabilistic parameter set can, in some cases, be understood as (numerical) realizations of parameter vector γ that lie at the boundary of the probabilistic parameter set: e.g., in the sense of equation (10), if |γi- [µγ,k+1]i| = Ri(p,Σγ,k+1). Within the scope of the present invention, this number of parameter vector vertices of the probabilistic parameter set can be referred to in particular as V = {γ(1)), γ(2),..., γ(nv)}. The set of parameter vector vertices V can preferably comprise nv∈ ℕ≥1 elements. As will be explained in more detail later, the probabilistic parameter set around the static parameter vector γ of the technical system, e.g. the determined number of parameter vector vertices nvin, can be used in further optimization procedures of the present techniques for the state controller. The previously discussed process step “Modeling 400 of the distribution of the static parameter vector of the technical system” can be performed in a module 14; 400 of the data processing device 7. In the example of Fig. 2, the module 14; 400 and the aforementioned module 12; 300 are shown as two separate modules. In another example, the two process steps “Modeling 300 of the distribution of time delays and / or packet losses” and “Modeling 400 of the distribution of the static parameter vector of the technical system” can be performed within a single module that is part of the data processing device 7. The two process steps 300 and 400 can be performed on the data processing device 7 in any chronological order: In one example, process step 300, "Modeling the distribution of time delays and / or packet losses," can be performed first, followed by process step 400, "Modeling the distribution of the static parameter vector of the technical system." In another example, process step 400, "Modeling the distribution of the static parameter vector of the technical system," can be performed first, followed by process step 300, "Modeling the distribution of time delays and / or packet losses." In yet other examples, the two process steps can be performed in parallel or with temporal overlap. Finally, the first aspect of the present disclosure includes the adaptation of the state controller based on the provided dynamic model. In the techniques of the present disclosure, it is conceivable that the adaptation 500 of the state controller based on the provided dynamics model may involve solving 510 a stochastic optimization problem to determine a feedback matrix K that describes the state controller. This stochastic optimization problem can be reformulated into a deterministic optimization problem so that it may be solvable (e.g., numerically with a given accuracy). In this context, one can also speak of “controller synthesis” instead of “stochastic optimization” (i.e., the stochastic optimization problem serves controller synthesis). The stochastic optimization problem can be solved using the discrete-time representation of the continuous-time dynamics model and using one or more (e.g.,All of the following specific quantities can be solved: i) the number of specific transition probabilities for the transitions from time delays at the first time tk to time delays at the second time tk+1; ii) the one or more specific ambiguity sets around the specific number of transition probabilities; and iii) the specific probabilistic parameter set around the static parameter vector γ of the technical system. Furthermore, stochastic optimization can be performed using an objective function J based on the discrete-time representation of the continuous-time dynamics model. In some cases, using ii) the one or more specific ambiguity sets around the specific number of transition probabilities may involve using the finite norm for the ambiguity sets introduced above. For example, using iii) the specific probabilistic parameter set Pk+1 may mean using the number of parameter vector vertices V = {γ(1), γ(2),..., γ(nv)} of the probabilistic parameter set. Furthermore, the input vector u, comprising one or more input variables, can be connected to the state vector x, comprising one or more state variables, via the feedback matrix of the state controller. Within the scope of the present disclosure, it is conceivable that this input vector-state vector connection can be rewritten using an augmented state vector ξk and the feedback matrix K, which is an augmented feedback matrix. In this case, the augmented state vector ξk at a discrete time (e.g., at the first time tk, at the second time tk+1, or at another discrete time) can comprise the state vector xk at the same discrete time and time-delayed components of the input vector u, which are described by the number of Markov modes θk ∈ {0, ..., M}.The input vector uk at a discrete time can be connected to the augmented state vector ξk at the same discrete time by the augmented feedback matrix K. For example, the following formula can hold: uk = K ξk. The augmented state vector can be written as follows: ξk = (xk, uk-1, uk-2, ..., uk-M)T. In some cases of the present disclosure, the stochastic optimization problem can be performed for the number of parameter vector vertices V = {γ(1), γ(2), ..., γ(nv)} of the probabilistic parameter set (e.g., independently for each parameter vector vertex). The examples of the discrete-time representation of the continuous-time dynamics model (in which time delays are translated into the discrete-time Markov chain with Markov modes for discrete time points) have already been discussed above in connection with equations (1) and (2). In some cases, the discrete-time representation of the continuous-time dynamics model can lead to a Markov jump linear system, which is formulated using the extended state vector ξk.This means that in some cases the stochastic optimization problem can be transformed into a deterministic optimization problem using a set of Markov jump linear systems in connection with the number of parameter vector vertices V = {γ(1), γ(2), ..., γ(nv)}, the probabilistic parameter set, and the ambiguity set. This set of MJLS can contain nv Markov jump linear systems. In some cases, the following may hold (Equation 11): where δ(i,j) denotes, in particular, a Dirac delta, which is defined as δ(i,j) = 1 when i = j and as zero otherwise (the other quantities are already defined in the context of Equations (1) and (2)). Thus, Markov-step linear systems extend, in particular, the local control system by an imperfect communication network that includes time delays of up to M steps. Furthermore, the procedure can include updating the dynamic model when one or more new state input pairs of state vectors and input vectors of the state controller with one or more corresponding new timestamps have been determined. (The state input pairs with their respective timestamps are part of the dynamic model as described above.) This can occur, for example, when the current state controller (described, for example, by a current feedback matrix K) is in operation and sends the new state input pairs with their respective timestamps to the data processing device 7 (continuously or at predetermined time intervals according to a schedule). The one or more new state input pairs can be appended to the number of state input pairs, and the one or more new timestamps can be appended to the multitude of timestamps.This leads to learning by repetition of the procedure described above, in that the newly determined transition probabilities (e.g., together with ambiguity sets) more accurately reflect the current distribution of delays and / or packet losses in the imperfect communication network 5 (with this newly acquired data). Alternatively or additionally, by repeating the procedure, the probabilistic parameter set (e.g., together with its parameter vector vertices V) can be updated, thus more accurately representing the current distribution of the probabilistic parameter set (y) of the technical system. The procedure can then include adapting the state controller based on the updated dynamic model. Specifically, the stochastic optimization problem (in a preferred example, the stochastic optimization problem is a controller synthesis) can be solved taking into account newly determined transition probabilities (e.g., in the form of the Markov transition matrix), ambiguity sets, and / or the probabilistic parameter set. This allows for the determination of an updated feedback matrix that describes the state controller and more accurately reflects the current distribution of delays and / or packet losses in the imperfect communication network 5, as well as the distribution of the static parameter vector of the technical system, potentially leading to improved performance of the updated state controller. The previously discussed process step “adjusting 500 of the state controller” can, for example, be carried out in a module 15; 500 of the data processing device 7 (see Fig. 2). Within the scope of the present disclosure, it is conceivable that the method further comprises sending an update from the data processing device 7 to the state controller 4 (or to a module of the local control system 2), wherein the update includes the adapted state controller (e.g. the extended updated feedback matrix K), in particular wherein the update is configured such that the state controller 4 is replaced by the adapted state controller (e.g. by the extended updated feedback matrix K). Furthermore, the procedure can include the collection of a (new) number of state input pairs of state vectors and input vectors of the adapted state controller by the data processing device 7 at a (new) multitude of timestamps. In other words, the adapted state controller 4 can now be operated, and, for example, the local control system 2 (e.g., the state controller 4) can supply these state input pairs with their respective timestamps to the data processing device 7. The above procedures, including stochastic optimization (e.g., controller synthesis), can now be performed repeatedly so that the state controller is adapted a second time. These adaptation experiments for the state controller (e.g.,For the extended feedback matrix K), the following can then be performed recursively: The number of fitting experiments Nexp for the state controller can be ten or more, fifty or more, one hundred or more, or one thousand or more. To illustrate this, the example of a group start with three vehicles using unreliable communication via a communication network 5, as shown in Figures 2 and 3, is explained in more detail here. The leading (first) vehicle is uncontrolled (with respect to distance control) and travels, for example, at a constant speed v0, followed by two controlled (with respect to their respective distance control) vehicles with control inputs F1 and F2, respectively. The masses of the second and third vehicles, γ1 and γ2, respectively, are examples of two static uncertainty parameters. The goal can be to control the distance error e1 and e2 from the origin; that is, the dashed vertical lines in Figure 3 indicate that the necessary safety distance dsafe is maintained. It can be assumed here that the vehicles are controlled by their forces F1 and F2 (which result in vehicle accelerations).The state and input vectors in this example can be written as follows: x = [e1, v1- v2, e2, v0- v2]T and u = [F1, F2]T, where v1 and v2 are the speeds of the second and third vehicles, respectively (the leading vehicle is the first vehicle). The static parameter vector can be given by the following expression: γ = [γ1,γ2]T. Fig. 5a illustrates exemplary mean values ​​for the distance error e1 (solid curves) for the second vehicle during the platooning group start for two different exemplary fitting experiments in the procedure, namely for Nexp = 1 (corresponding to the control process by the initial state controller) and Nexp = 50 (corresponding to the control process by the final state controller), as well as the corresponding 1-σ confidence intervals around the respective mean values ​​(dashed / dotted curves). It can be seen that the final state controller converges significantly faster for Nexp = 50 than the initial state controller for Nexp = 1 and can reach the target within the depicted time interval (with the accuracy given by the confidence interval).Figure 5b shows, by way of example, the mean value (a solid curve) for a radius ri (on a log scale) defined with respect to an ambiguity set, as a function of the number of fitting experiments Nexp in the procedure, as well as a corresponding 1-σ confidence interval (two dashed curves). Figure 5b shows, in particular, how the radius ri decreases with an increasing number of fitting experiments Nexp, resulting in a smaller ambiguity set. Figure 5c shows, by way of example, the mean values ​​for the masses of the second and third vehicles γ1 and γ2, respectively (solid curves), together with corresponding 1-σ confidence intervals (dashed / dotted curves). Figure 5c illustrates, in particular, how the masses of the second and third vehicles γ1 and γ2 converge to their respective true (but unknown) masses with an increasing number of fitting experiments Nexp. The methods of the first aspect can be used in the design of the state controller or during its operation. Furthermore, a computer program is disclosed that is designed to execute the computer-implemented procedure for adjusting a state controller 4 according to the first aspect. The computer program can be in interpretable or compiled form, for example. It can be loaded (even partially) into a computer's RAM for execution, for example as a bit or byte sequence. A state controller 4 is further disclosed, which is designed to control a technical system 3, wherein the state controller 4 communicates with the technical system 3 to be controlled at least partially via a communication network 5. The communication network 5 can, for example, comprise or be a wireless network. In some cases, the communication network 5 can be a time-critical communication network (in the sense defined above). The state controller 4 is further designed to send a number of state input pairs of state vectors and input vectors with respective timestamps via an external communication network 6 to a data processing device 7 outside a local control system 2, which comprises the state controller 4 and the technical system 3. From these, a sequence of time delays and a sequence of state input pairs for the data processing device 7 can be derived.The external communication network 6 can be a non-time-critical communication network (in the sense defined above). Furthermore, the state controller 4 is designed to receive an update from the data processing device 7, wherein the update comprises a modified state controller, specifically an extended updated feedback matrix K, where an input vector uk at a discrete time is connected to an extended state vector ξk at the same discrete time by the extended feedback matrix K, where the extended state vector ξk includes a state vector xk at the same discrete time and time-delayed components of the input vector uk, described by the number of Markov modes θk. The state controller 4 is also designed to implement (i.e., colloquially, install) the update (or updates). A data processing device 7 is further disclosed, which is designed to execute the computer-implemented method for adapting a state controller 4 according to the first aspect and / or the computer program according to the second aspect. The data processing device 7 of the third aspect may be designed to receive a number of state input pairs of state vectors and input vectors of a state controller 4 at a plurality of timestamps from the state controller 4. Furthermore, the data processing device 7 of the third aspect may be designed to send an update from the data processing device 7, comprising an adapted state controller, to the state controller 4. As described above, in a non-limiting example, the data processing device 7 may comprise at least one memory 11; 100, one module 12; 300, one module 14; 400, and one module 15; 500.The data processing device 7 can have at least one interface for inputs and outputs. Furthermore, a distributed system 1 is disclosed, comprising a data processing device 7 according to the fourth aspect. In addition, the distributed system 1 comprises a local control system 2, which includes a state controller 4 and a controlled technical system 3. An example of a distributed system 1 is shown in Fig. 2. Furthermore, a computer-readable medium or signal is disclosed that stores and / or contains the computer program according to the second aspect. The medium can, for example, include RAM, ROM, EPROM, HDD, SSD, etc., on / in which the signal is stored.

Claims

A computer-implemented method for adjusting a state controller (4) by a data processing device (7), wherein the state controller (4) is intended for controlling a technical system (3), wherein the state controller (4) and the technical system are contained in a local control system (2) that communicates with the data processing device (7), and wherein the method comprises the following steps: - collecting (100) a number of state input pairs (D = { (xk , uk )} k ∈ ℕ ) of state vectors and input vectors of the state controller (4) by the data processing device (7) to a plurality of timestamps, wherein the timestamp corresponds to a discrete time point ( tk S t ) corresponds to the state input pair for which the associated state input pair was determined; - Providing (200) a dynamic model to describe the technical system to be controlled, taking into account i) collected state-input pairs, ii) the multitude of timestamps, iii) a distribution of time delays and / or packet losses in the context of communication within the local control system, and iv) a distribution of a static parameter vector (y) of the technical system, wherein the static parameter vector influences a behavior of the technical system (3) and contains at least one component that includes a static uncertainty parameter, and wherein providing (200) the dynamic model includes: - Modeling (300) the distribution of time delays and / or packet losses using the collected multitude of timestamps (tk S t ) and a discrete-time Markov process; and - Modeling (400) the distribution of the static parameter vector of the technical system using the collected number of state input pairs of state vectors and input vectors of the state controller and a Bayesian inference with respect to the static parameter vector (y); - Adjusting (500) the state controller based on the provided dynamics model. The method of claim 1, wherein the dynamic model for describing the technical system to be controlled comprises a time-continuous dynamic model, wherein the time-continuous dynamic model is represented by a predetermined function (f(x, u, y)) which contains the following time-dependent arguments: a state vector (x) comprising one or more state variables; an input vector (u) comprising one or more input variables and delayed by an indefinite time delay (τ) which represents the distribution of time delays and / or packet losses in the context of communication within the technical system;and the static parameter vector (y) that influences the behavior of the technical system (3), wherein providing (200) the dynamic model to describe the technical system to be controlled includes: - forming (220) a time-discrete representation of the time-continuous dynamic model by time discretization of the time-continuous dynamic model, wherein the indeterminate time delay (τ) is described by the time-discrete Markov process by translating this time delay into a time-discrete Markov chain with Markov modes (θk) for discrete time points, optionally wherein each discrete time point is assigned a corresponding Markov mode from a number of Markov modes.; Method according to claim 1 or 2, wherein the modeling (300) of the distribution of time delays and / or packet losses comprises: - deriving (310) a sequence of time delays (Δk) based on the collected plurality of timestamps (tk S t ); - Converting (320) the sequence of time delays into a sequence of Markov modes (M) of the discrete-time Markov process; - Determine (330) a number of transition probabilities ( T ^ ij ) for transitions from time delays to a first point in time (t k ) to time delays at a second point in time (t k+1 ) based on the sequence of Markov modes, where the second time point is later than the first time point, - Determine (340) one or more ambiguity sets ( A ( T ^ i : ) ; 20 a − c ) around the specified number of transition probabilities, where each of the one or more ambiguity sets represents a measure of a deviation of certain transition probabilities from a fixed time delay at the first time (t). k ) to the time delays to the second time point (t k+1 ) in relation to corresponding true transition probabilities. The method of claim 3, wherein the sequence of time delays is a sequence of discrete time delays, in particular wherein a number of possible transition probabilities for transitions from time delays at the first time to time delays at the second time are in a Markov transition matrix (T^) are arranged. Method according to claim 3 or 4, wherein the fixed time delay is given by a fixed Markov mode (θk= i) from a number of Markov modes at the first time (tk) and each of the time delays at the second time (tk+1) corresponds to a Markov mode (θk+1= j) from the number of Markov modes. The method of claim 5, wherein determining (330) the number of transition probabilities for the transitions from time delays at the first time to the time delays at the second time comprises: - determining one or more sample sizes, in particular inverse sample sizes (ηi), for one or more fixed Markov modes (θk= i) from the number of Markov modes (θk) corresponding to the respective time delays at the first time (tk), wherein determining the one or more sample sizes, in particular inverse sample sizes, is carried out recursively by parsing the sequence of Markov modes (M), and - recursively determining transition probabilities ( T ^ ij ) for each transition from one or more fixed Markov modes (θ k = i) from the number of Markov modes (θ k ) at the first time point for each Markov mode (θ k+1 = j) from the number of Markov modes (θ k+1 ), the respective possible time delays to the second time point (t k+1 ) represent, based on one or more determined sample sizes (η i -1 ), in particular inverse sample sizes, for one or more fixed Markov modes from the number of Markov modes and by parsing the sequence of Markov modes (M), optionally wherein one or more possible transition probabilities for a fixed Markov mode (θ) k = i) from the number of Markov modes (θ k ) at the first time point for each Markov mode (θ k = j) from the number of Markov modes (θ k+1 ) at the second time point (t k+1 ) form a row of the Markov transition matrix. Method according to claim 5 or 6, wherein one or more transition probabilities (T^ij) from the specific number of transition probabilities ( T ^ ij ) for each transition from the fixed time delay (θ k = i) at the first time (t k ) to the time delays (θ k+1 = j) at the second time point (t k+1 ) is a point in a finite-dimensional vector space that corresponds to a transition vector ( T ^ i : ) This corresponds to one or more of these transition probabilities ( T ^ ij ( ) as components, and where the ambiguity set ( A ( T ^ i : ) ) for this transition vector ( T ^ i : ) by a sphere around a point with a radius (r i ) is encompassed in a finite-dimensional norm, and wherein the radius is defined at a user-defined confidence level (β) and / or a determined sample size of one or more sample sizes (η). i -1 ), in particular an inverse sample size (η i ), for a fixed Markov mode based on the number of Markov modes, where this fixed Markov mode is the fixed time delay (θ k = i) at the first time (t k ) corresponds, optionally, where the radius at constant user-defined confidence level and increasing sample size, which for a given fixed Markov mode (θ) k = i) determined from the sequence of Markov modes, decreases. A method according to any one of the preceding claims 2 to 7, if dependent on claim 2, wherein the modeling (400) of the distribution of the static parameter vector of the technical system comprises: - deriving (410) a sequence of state input pairs of state vectors and input vectors from the collected number of state input pairs ( D = { ( xk , uk )} k ∈ ℕ ) of state vectors and input vectors of the state controller; - Bayesian recursive derivation (420) of an a-posteriori distribution ( N ( μ γ , k + 1 , ∑ γ , k + 1 ) ) for the static parameter vector of the technical system (γ k+1 ) for the next discrete time (t k+1 ) based on i) a prior distribution ( N ( μ γ , k , ∑ γ , k ) ) for the static parameter vector of the technical system (γ k ) for a previous discrete time (t k ) and ii) the time-discrete representation of the time-continuous dynamics model, where the recursive derivation starting from a at an initial time (t 0 ) initial prior distribution ( N ( μ γ ,0 , ∑ γ ,0 ) ) for the static parameter vector of the technical system (γ 0 ) is performed, where the state vector and the input vector are taken from the derived sequence of state input pairs of state vectors and input vectors, and where Bayesian recursive differentiation is performed for a sequence of discrete points, which is the plurality of timestamps for which the number of state input pairs D = { ( xk , uk )} k ∈ ℕ was collected from state vectors and input vectors of the state controller. Method according to claim 8, wherein the Bayesian recursive derivation (420) of the a-posteriori distribution for the static parameter vector of the technical system (γk+1) comprises: - recursive determination of a number of parameters for the a-posteriori distribution ( N ( μ γ , k + 1 , ∑ γ , k + 1 ) ) , in particular a mean value (µ γ,k+1 ) and a covariance (Σ γ,k+1 ), for the next discrete time (t k+1 ) based on a number of parameters for the prior distribution ( N ( μ γ , k , ∑ γ , k ) ) for the static parameter vector of the technical system (γ k ) for the preceding discrete time (t k ) and ii) the time-discrete representation of the time-continuous dynamics model, wherein the recursive derivation starting from a number of parameters, in particular a mean value (µ) γ,0 ) and a covariance (Σ γ,0 ), for the initial prior distribution ( N ( μ γ ,0 , ∑ γ ,0 ) ) for the starting time (t 0 ). Method according to claim 9, wherein the modeling (400) of the distribution of the static parameter vector of the technical system further comprises: - Determining (430) a probabilistic parameter set (P k + 1 ) to determine the static parameter vector (γ) of the technical system for the next discrete time (t) k+1 ) based on the number of parameters of the a posteriori distribution, in particular the mean (µ) γ,k+1 ) and the covariance (Σ γ,k+1 ), which at that time were determined by Bayesian recursive derivation (420), optional, where one is at the next discrete time (t k+1 ) certain first parameter from the number of parameters of the a posteriori distribution, in particular its mean (µ) γ,k+1 ), is a point in a finite-dimensional vector space whose dimension is equal to a dimension of the parameter vector, where the probabilistic parameter set (P k + 1) around the static parameter vector (γ) through a sphere around the point with a radius (R i ) is encompassed in a finite-dimensional norm, and where the radius is at a user-defined confidence level (p) for the parameter vector and / or at the next discrete time (t) k+1 ) determined second parameter from the number of parameters of the a posteriori distribution, in particular their covariance (Σ γ,k+1 ), based. A method according to any one of the preceding claims 2 to 10, when dependent on claim 10, wherein the adaptation (500) of the state controller based on the provided dynamics model comprises: - solving (510) a stochastic optimization problem to determine a feedback matrix describing the state controller, wherein the stochastic optimization problem is solved using the discrete-time representation of the continuous-time dynamics model and using one or more of the following specific quantities: i) the number of specific transition probabilities (T^ij) for the transitions from time delays to the first time point (t k ) to time delays at the second time point (t k+1 ); ii) of one or more specific sets of ambiguity ( A ( T ^ i : ) ) to determine the specific number of transition probabilities, and iii) the definite probabilistic parameter set ( P k + 1 ) around the static parameter vector (γ) of the technical system, where stochastic optimization is carried out using an objective function (J) based on the time-discrete representation of the time-continuous dynamics model. Method according to any one of the preceding claims 1 to 11, wherein the method further comprises: - updating the dynamic model when one or more new state input pairs ( D = { ( xk , uk )} k ∈ ℕ ) of state vectors and input vectors of the state controller with corresponding one or more new timestamps (tk S t ) were determined, whereby the one or more new state input pairs are added to the number of state input pairs and the one or more new timestamps (tk S t ) to be appended to a large number of timestamps; - Adjusting the state controller based on the updated dynamics model. Computer program designed to execute the computer-implemented method for adjusting a state controller (4) according to any one of the preceding claims 1 to 12. State controller (4) designed to control a technical system (3), wherein the state controller (4) communicates at least partially with the technical system (3) to be controlled via a communication network (5), wherein the state controller (4) is further designed to: - send a number of state input pairs of state vectors and input vectors with respective timestamps via an external communication network (6) to a data processing device (7) outside a local control system (2) comprising the state controller (4) and the technical system (3), from which a sequence of time delays and a sequence of state input pairs for the data processing device (7) can be derived;- to receive an update from the data processing device (7), wherein the update comprises a modified state controller, in particular an extended updated feedback matrix (K), wherein an input vector (uk) at a discrete time is connected to an extended state vector (ξk) at the same discrete time by the extended feedback matrix (K), wherein the extended state vector (ξk) comprises a state vector (xk) at the same discrete time and time-delayed components of the input vector (uk) described by the number of Markov modes (θk); and - to implement the update. Data processing device (7) designed to execute the computer-implemented method for adjusting a state controller (4) according to any one of the preceding claims 1 to 12 and / or the computer program according to claim 13.

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