COMPUTER-IMPLEMENTED METHOD FOR GENERATING A COMPLEXITY-REDUCED TIME MODEL OF A DISTRIBUTED SYSTEM

Abstract

A general aspect of the present disclosure relates to a method for generating a reduced-complexity time model of a distributed system. The method comprises receiving time data, receiving a controlled system model, and modeling the received time data as a stochastic process to obtain an original stochastic process. The method further comprises decomposing the original stochastic process into a plurality of modes of the original stochastic process to obtain an approximation of the original stochastic process. The method further comprises performing a sensitivity analysis using the controlled system model and the approximation. The method further comprises selecting a first subset of modes of the approximation based on the comparison and / or a default value, and outputting a reduced-complexity time model based on the first subset of modes.

Description

State of the art

[0001] Highly automated or autonomous systems are increasingly in focus, for example, in robotics and the automotive industry. Control systems, in particular, are becoming increasingly important in the operation of autonomous or highly automated systems.

[0002] Difficulties arise when considering stochastically distributed parameters. While the consideration of stochastically uncertain system parameters in the design of controllers is known, for example, through intrusive uncertainty quantification methods, one example of such a stochastically uncertain parameter is the uniform distribution of vehicle mass in vehicle dynamics models. The uncertainties discussed in the state of the art are always assumed to be time-independent, scalar quantities. If, for example, multiple uncertainties occur, they are still assumed to be uncorrelated.

[0003] Problems arise in distributed systems where, for example, the control algorithm is executed physically separate from the system to be controlled, for example, using cloud or edge computing, resulting in time delays in data transmission. Many state-of-the-art solutions inadequately consider the influence of uncertain timing effects and their representation in the control system. Examples of such time effects include jitter, delay, and / or degradation.

[0004] Due to different physical conditions that influence signal transmission or different channel utilization in vehicle-to-vehicle (V2V) communication, time delays or fluctuating sampling times that are non-deterministic and therefore uncertain can occur. For example, networked adaptive cruise control, group start, or cooperative lane merging can be situations in which channel utilization is unusually high compared to other situations. For example, non-deterministic delays can arise in the feedback loop, in bus communication when distributed E / E architectures are involved in vehicle control functions, and / or in signal processing and transmission in sensor systems. In control systems, such as the longitudinal guidance of a vehicle, the non-deterministic time delay can have a detrimental impact on the control success.As a result, the systems under consideration must either be tuned very conservatively or optimized using worst-case analyses, which can lead to poor performance. Therefore, there is a need for improved methods for quantifying and incorporating stochastically distributed time effects in controller design. Disclosure of the invention

[0005] A first general aspect of the present disclosure relates to a method for generating a reduced-complexity time model of a distributed system. The method comprises receiving time data, receiving a controlled system model, and modeling the received time data as a stochastic process to obtain an original stochastic process. The method further comprises decomposing the original stochastic process into a plurality of modes of the original stochastic process to obtain an approximation of the original stochastic process. The method further comprises performing a sensitivity analysis using the controlled system model and the approximation. The method further comprises selecting a first subset of modes of the approximation based on the comparison and / or a default value, and outputting a reduced-complexity time model based on the first subset of modes.

[0006] A second general aspect of the present disclosure relates to a computer system configured to perform the method for generating a reduced complexity time model of a distributed system according to the first general aspect (or an embodiment thereof).

[0007] A third general aspect of the present disclosure relates to a computer program configured to execute the method for generating a reduced complexity time model of a distributed system according to the first general aspect (or an embodiment thereof).

[0008] A fourth general aspect of the present disclosure relates to a computer-readable medium or signal storing and / or containing the computer program according to the third general aspect (or an embodiment thereof).

[0009] The method proposed in this disclosure according to the first general aspect (or an embodiment thereof) can serve to provide a method for generating a reduced-complexity time model of a distributed system. The method can serve to determine a reduced-complexity time model for the design of a state controller.

[0010] By reducing complexity, the proposed method can make the generated time model suitable for implementation in a controller and enable controller evaluation online, i.e., in real time. A further advantage of the proposed method is its ability to utilize the correlation between the time courses of the time effects and enable less conservative controller designs. The method can enable the distribution of the control system across multiple physically separate components and the consideration of the resulting time effects, for example, in the design of a controller. The reduced-complexity time model can be applied, for example, in a controller design based on uncertainty quantification.For example, the reduced-complexity time model can allow only one or a few simulations to characterize the influence of uncertain time effects on a control system, which can represent a significant efficiency gain compared to a large number of simulations using inefficient UQ methods. This can lead to savings in terms of runtime and the computing resources required for the simulation.

[0011] Furthermore, the techniques of the present disclosure may map the uncertain timing effects in a data transmission channel and / or account for the uncertain timing effects when sampling transmitted signals.

[0012] One advantage may be that the method can be applied to a variety of control systems. An example of this may be the longitudinal guidance of a vehicle. The longitudinal guidance of a vehicle refers to the control and stability of its movement along the direction of travel. It may include aspects such as acceleration, deceleration and speed control, which ensure that the vehicle can move forwards or backwards on the road in the desired manner. Particularly with regard to autonomous and / or assisted driving, in which a plurality of vehicles communicate via the same communication points and delays in data transmission may occur, such as during a group start (e.g. "traffic light start"), the techniques of the present disclosure can lead to improved control behavior.In this context, the disclosed method can also lead to improved control of the vehicle's lateral guidance.

[0013] Further examples can be found in various fields of control engineering, such as robotics, motor control of electrical machines, building automation, etc. The method can be provided in a further encapsulated form, thus enabling use by an expanded user group, even if this group or individual members of the user group are not familiar with the underlying mathematical principles. Integration into an existing software structure can also be enabled.

[0014] Some terms are used in this disclosure as follows: A "state controller" may comprise an algorithm, i.e., a calculation rule, 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 comprise parameters that may 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 an ECU of a vehicle, a cloud, or an edge. A state controller may, for example, comprise or be part of a hardware module with inputs and outputs.

[0015] A "vehicle" can be any device that transports passengers and / or cargo. A vehicle can be a motor vehicle (e.g., 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 be at least partially autonomous or assisted. Short description of the characters Fig. 1 schematically illustrates a method for generating a complexity-reduced time model of a distributed system. Fig. 2 schematically illustrates an exemplary architecture for executing the method for generating a complexity-reduced time model. Fig. Figures 3A to 3D illustrate exemplary results of the sensitivity analysis for individual modes. Detailed description

[0016] First, with regard to the Fig. 1 and Fig. 2 discusses the techniques of the present disclosure. With respect to Fig. 3A to 3D discuss possible results and advantages resulting from the method disclosed herein for generating a reduced complexity time model.

[0017] Fig. 1 is a flowchart showing possible steps of the method 100 for generating a reduced complexity time model of a distributed system.

[0018] The method 100 for generating a reduced-complexity time model of a distributed system comprises receiving 110 a continuous-time state-space model for describing a system 10 to be controlled. The method 100 comprises receiving 110 time data 210, receiving 120 a controlled system model 240, and modeling 130 the received time data as a stochastic process 220 to obtain an original stochastic process. The method further comprises decomposing 140 the original stochastic process into a plurality of modes of the original stochastic process to obtain an approximation 230 of the original stochastic process. The method comprises performing 150 a sensitivity analysis 250 using the controlled system model 240 and the approximation.The method further comprises selecting 160 a first subset of modes of the approximation based on the comparison and / or a default value, and outputting 170 a complexity-reduced time model 260 based on the first subset of the modes.

[0019] In one example, the method includes designing a state controller based on the reduced complexity time model 260. In one example, the method includes applying the state controller in a function for controlling and / or monitoring a vehicle and / or a robot.

[0020] In some examples, the received time data 210 may include transmission times obtained by measuring or simulating a transmission of data between components of a distributed system. In examples, the components of the distributed system may include controller components. In examples, the components may include sensors, state controllers, and / or actuators. In examples, the components may include computer programs implemented in software. In examples, the computer programs may each be executed in a cloud, an edge, or on a local computer system, such as a control unit. In examples, the time data 210 may include time records of communication protocols between the components of the distributed system. In examples, a virtual simulation of the distributed system may be performed to obtain the time data 220.In some examples, the time data 210 may be obtained by measurement in a real distributed system.

[0021] In examples, the decomposition 140 of the original stochastic process 220 into a plurality of modes of the original stochastic process may be based on a Karhunen-Loève expansion. In examples, the following may apply to the decomposition: XtruncN​(t,ω)=∑i=1Nλiζi(ω)ei(t) In this example, XtruncN​(t,ω) the approximation 230 of the original stochastic process. In this example, λ i the eigenvalue of each mode, ζ i (ω) of an independent random variable and e i (t) is the eigenvector of each mode. For example, in the limit N → ∞, it can hold that XtruncN​(t,ω) corresponds to the original stochastic process. In examples, the first subset of modes may comprise a number N of modes. For example, decomposing the original stochastic process into the plurality of modes may be advantageous to exploit a possible correlation between the individual temporal data.

[0022] In some examples, the influence of the modes of the first subset on the approximation 230 of the original stochastic process may be greater than the influence of the modes of a second subset of the approximation 230 whose modes are not part of the first subset, and the default value includes a threshold associated with the influence of the modes. For example, the method may include an analysis of how sensitive certain modes, into which the original stochastic process is decomposed, react to changes.

[0023] In some examples, the sensitivity analysis 250 may include performing a comparison of the approximation 230 and the original stochastic process 220 using the controlled system model 240. In Fig. 3A to 3D show sensitivities of individual modes of the original stochastic process. Fig. 3A to 3D show some of the majority of modes of the stochastic process in a control system during a group start (so-called "traffic light start") of several vehicles. The controlled system model 240 can be part of the control system. In this example, in a convoy of vehicles, a target acceleration is specified for each vehicle following behind. The delay in the feedback loop ("feedback delay") of the acceleration control is represented in the model as a stochastic process, and its modes are used as uncertain parameters in a subsequent UQ experiment. Target variables in the present analysis are the distance ( Fig. 3A, Fig. 3C) and the relative speed ( Fig. 3B, Fig. 3D) to the vehicle in front. In examples, the target variable can include the manipulated variable of the control system. In the diagrams, the delay in seconds is plotted on the horizontal axis (x-axis) and the sensitivity of the respective mode on the vertical axis (y-axis). For example, it can be seen that mode 1 reacts more sensitively to changes than mode 2, so that the influence of mode 1 on the overall process is greater and mode 1 is more relevant for simulating the stochastic process than mode 2. The first subset of modes can include the modes that simulate the stochastic process better, i.e. with smaller deviation, than the modes in the second subset.

[0024] In examples, selecting the first subset of modes may include determining a scalar characteristic from the time courses of the approximation. In examples, the characteristic may include the normalized area under the respective curves. For example, normalization may be performed on the sum of all areas and thus the modes whose sum exceeds a certain threshold may be selected. In examples, the default value may include this threshold. In examples, the modes whose area sum results in a certain percentage may be grouped into the first subset. In examples, the default value may include the certain percentage. In examples, selecting the first subset of modes may include determining an approximation error.In examples, the approximation error between iteratively combined individual modes of the plurality of modes and the original stochastic process can be determined. In examples, one or more modes can be added in each iteration step, and the approximation error between the original stochastic process and the modes combined (total) for this step can be determined. In examples, this approximation error can converge towards a value and / or stabilize. In examples, the modes combined in each iteration step can result in a stochastic process that has an approximation error compared to the original stochastic process.

[0025] In examples, performing 150 the sensitivity analysis may include at least two simulations of a control system using the received controlled system model 240. In examples, a first simulation may be performed based on the original stochastic process 220 to obtain a first simulation result. In examples, a second simulation may be performed based on the approximation 230. For example, the first subset may include modes of the approximation whose simulation result is more similar to the first simulation result than a simulation result of a second subset of the approximation whose modes are not part of the first subset. In examples, an error value may be calculated between the first simulation result and the simulation result of the second subset. In examples, the first subset may be selected 160 based on a threshold value for the error value.In examples, the modes can be selected according to their influence on the target variables, such as the . Fig. 3A to Fig. 3D described above. For example, the modes whose cumulative sensitivity exceeds a threshold can be selected. For example, S i the sensitivity of a fashion. Furthermore, S cum be the sum of all determined sensitivities and α a threshold value. Then the following applies: ∑ i∈Isel S i ≥ S cum · α, if I selcomprises the index set of the selected sensitivities. In examples, the threshold value α can be 0.9. In examples, the threshold value α can be 0.92, ..., 0.95, ... 0.98. For example, it is not important that the sensitivities follow the sequence 1, 2, 3, .... In examples, the selected sensitivities can comprise any index. As already described above, the target variables can comprise the control variables. For example, the target variables for longitudinal control of two vehicles can comprise the distance between the vehicles and / or the relative speed.

[0026] In examples, the modeling 130 of the received time data 210 may be performed as a stochastic process 220 based on a Gaussian process regression.

[0027] In examples, the received time data 210 may include transmission times obtained by measuring or simulating a transmission of data between components of a distributed system. In examples, the original stochastic process 220 may be used to model timing effects, where the timing effects include at least one of jitter, delay, and / or degradation. In examples, the reduced-complexity timing model 260 may be used to control and / or regulate a vehicle function, a robot function, a building automation function, a power tool automation function, and / or a home appliance automation function.

[0028] In examples, the distributed system may include a system to be controlled and components for controlling the system. In examples, components of the distributed system may be located in a cloud, an edge, or in local units such as a vehicle, a robot, a building, a household appliance, or a power tool. In examples, the timing effects may arise from data transmission between the components of the distributed system. In examples, the timing effects may arise from data transmission between the system to be controlled and the components for controlling the system.

[0029] In examples, the method may include designing a state controller using the reduced-complexity time model 260. In examples, the design of the state controller may be based on intrusive uncertainty quantification. In examples, the method may include applying the reduced-complexity time model 260 to a computer system of a vehicle, a robot, a building, a power tool, and / or a household appliance. In examples, the method may include using the reduced-complexity time model 260 for control. In examples, the method may include using the reduced-complexity time model 260 for control at runtime. In examples, the method may include using the reduced-complexity time model 260 for controller design, observer design, and / or model-predictive control.The method may also include determining the manipulated variables of a control system using the reduced-complexity time model 260.

[0030] In examples, the reduced-complexity time model 260 can be used to control and / or regulate a vehicle function (in particular, to control a driving function). For example, the vehicle function can be a function for autonomous and / or assisted driving. In some examples, the reduced-complexity time model can be suitable for execution on a computer system of a vehicle (e.g., an autonomous, highly automated, or assisted vehicle). For example, the computer system can be implemented locally in the vehicle or (at least partially) implemented in a backend that is communicatively connected to the vehicle. For example, the computer system can include a control unit on which the reduced-complexity time model 260 is implemented and / or used. In some examples, the vehicle can include a computer system with a communication interface that enables communication with a backend.For example, the reduced complexity time model 260 can be implemented and / or used in this backend.

[0031] In examples, the time effects may result from the data transmission between a system to be controlled and the computer system, which, for example, executes a state controller. In one example, the system to be controlled may be a system for lateral guidance and / or longitudinal guidance of the vehicle. In examples, a state variable vector of a control may be based on speed information or distance information. In examples, the state variable vector may have a time dependence that is described by means of the reduced-complexity time model 260. In examples, the state variable vector may include a relative speed and / or a distance between a first vehicle, a second vehicle, a person, and / or a stationary object.In one example, a state variable vector of an associated state-space model may include variables based on at least one of a steering angle, an orientation angle, a yaw rate, a slip angle, and / or a lateral error. In examples, the state variable vector may include information from a network, such as movement and / or direction information from other vehicles. In examples, this information may be provided via vehicle-to-vehicle communication (V2V communication) or via a backend (V2X communication). In one example, an input variable of an input variable vector may include a steering speed or target specifications for acceleration and / or braking operations. In examples, the system to be controlled may be designed for arrangement in a drive control or a drive unit and / or may serve to control an engine-related function (in particular for engine control).In examples, the system to be controlled may be arranged for arrangement in a drive control system of an electric machine. For example, the state vector of the state-space model may contain variables based on at least one of a control signal, an operating mode, or a power setting of the electric machine.

[0032] The present disclosure also relates to methods for controlling and / or regulating a robot using a reduced complexity time model 260 generated by the methods of the present disclosure.

[0033] In other examples, the reduced-complexity time model 260 may be used to control and / or regulate a robot function (in particular, to control a movement function of a robot). For example, the robot function may be a function for lateral guidance and / or longitudinal guidance of the robot. In some examples, the reduced-complexity time model 260 may be executed on a computer system of a robot. For example, the computer system may be implemented locally in the robot or (at least partially) implemented in a backend that is communicatively connected to the robot. In some examples, the reduced-complexity time model 260 may be executed in a backend. In examples, a state variable vector of a robot control may be based on velocity information or distance information.In examples, the state variable vector may have a time dependence that can be described using the reduced-complexity time model 260. In examples, the state variable vector may include a relative velocity and / or a distance between a first robot, a human, another mobile device, and / or a stationary object. In one example, a state variable vector of an associated state-space model may include variables based on at least one of a steering angle, an orientation angle, a yaw rate, a slip angle, and / or a lateral error. In examples, the state variable vector may include information from a network, such as motion and / or direction information from other robots, mobile devices, and / or humans. In examples, this information may be provided via direct communication or via a backend.In one example, an input variable of an input variable vector may include a steering speed or target specifications for acceleration and / or braking operations.

[0034] The present disclosure also relates to methods for controlling and / or regulating functions in building automation using a reduced-complexity time model 260 generated by the methods of the present disclosure.

[0035] In one example, the reduced-complexity time model 260 may be used to control building functions (in particular, to control building automation functions). For example, the building function may be a function for regulating room temperature, lighting, and / or security equipment. In some examples, the reduced-complexity time model 260 may be suitable for execution on a computer system within the building. For example, the computer system may be implemented locally in the building or (at least partially) implemented in a backend that is communicatively connected to the building. For example, the computer system may include a control system or a building automation control device on which the reduced-complexity time model 260 may be executed. In examples, the building may have a computer system with a communication interface that enables communication with an external backend.For example, the reduced-complexity time model 260 can be executed in this backend. In examples, the time effects can result from the data transfer between a system to be controlled and the computer system executing a state controller. A state variable vector of an associated state-space model can, in examples, contain variables based on information such as room temperature, brightness, or the presence of people. In some cases, the state variable vector can include a relative temperature difference, illuminance, or distance to a specific location or object in the building. In examples, the state variable vector can have a time dependence that can be described using the reduced-complexity time model 260.An example of a state variable vector in the context of building automation could contain variables based on parameters such as heating control, lighting settings, ventilation speed, or security alarms. Information can originate from a network, such as sensor data or settings from other buildings or building components. This information can be provided through communication between buildings or building components or via an external backend. In one example, an input variable of the input variable vector could include, for example, a temperature and / or lighting setting, for example, in the form of a voltage and / or current signal.

[0036] Also disclosed is a computer system configured to execute the method 100 for generating a complexity-reduced time model of a distributed system. The computer system may comprise at least one processor and / or at least one main memory. The computer system may further comprise a (non-volatile) memory. In examples, all steps of the method 100 may be executed by the computer system. In some examples, individual steps of the method 100 may be executed by the computer system. Optionally, results of individual method steps that are not executed by the computer system may be received by the computer system.

[0037] Also disclosed is a computer program designed to execute method 100 for generating a reduced-complexity time model of a distributed system. The computer program can be in interpretable or compiled form, for example. It can be loaded (even in parts) into the RAM of a computer for execution, for example, as a bit or byte sequence.

[0038] Further disclosed is a computer-readable medium or signal that stores and / or contains the computer program or at least a portion thereof. The medium may, for example, comprise one of RAM, ROM, EPROM, HDD, SDD, etc., on / in which the signal is stored.

Claims

[1] Computer-implemented method (100) for generating a complexity-reduced time model of a distributed system, the method comprising the following steps: - receiving (110) time data (210), - receiving (120) a controlled system model (240), - modeling (130) the received time data as a stochastic process (220) to obtain an original stochastic process, - decomposing (140) the original stochastic process into a plurality of modes of the original stochastic process to obtain an approximation (230) of the original stochastic process, - performing (150) a sensitivity analysis (250) using the controlled system model (240) and the approximation, - selecting (160) a first subset of modes of the approximation based on the comparison and / or a default value, and - Outputting (170) a complexity-reduced time model (260) based on the first subset of the modes. [2] The computer-implemented method (100) of claim 1, wherein the influence of the modes of the first subset on the approximation (230) of the original stochastic process is greater than the influence of the modes of a second subset of the approximation (230) whose modes are not part of the first subset, and wherein the default value comprises a threshold value associated with the influence of the modes. [3] The computer-implemented method (100) of claim 1 or 2, wherein the sensitivity analysis (250) comprises performing a comparison of the approximation (230) and the original stochastic process (220) using the controlled system model (240). [4] Computer-implemented method (100) according to claim 1, 2, or 3, wherein performing (150) the sensitivity analysis comprises at least two simulations of a control using the received controlled system model (240), wherein a first simulation is carried out on the basis of the original stochastic process (220) to obtain a first simulation result, and a second simulation is carried out based on the approximation (230), and wherein the first subset comprises modes of the approximation whose simulation result is more similar to the first simulation result than a simulation result of a second subset of the approximation whose modes are not part of the first subset. [5] The computer-implemented method (100) of any preceding claim, wherein decomposing (140) the original stochastic process (220) into a plurality of modes of the original stochastic process is based on a Karhunen-Loève expansion. [6] Computer-implemented method (100) according to one of the preceding claims, wherein the modeling (130) of the received time data (210) is performed as a stochastic process (220) based on a Gaussian process regression. [7] Computer-implemented method (100) according to one of the preceding claims, wherein the received time data (210) comprises transmission times obtained by measuring or simulating a transmission of data between components of a distributed system. [8] The computer-implemented method (100) of any preceding claim, wherein the original stochastic process (220) is to model timing effects, the timing effects comprising at least one of jitter, delay, and / or degradation. [9] Computer-implemented method (100) according to one of the preceding claims, wherein the complexity-reduced time model (260) serves to control and / or regulate a vehicle function, a robot function, a building automation function, a power tool automation function, and / or a household appliance automation function. [10] Computer system adapted to execute the computer-implemented method (100) for generating a complexity-reduced time model of a distributed system according to any one of the preceding claims 1 to 9. [11] Computer program comprising instructions which, when the computer program is executed by a computer system, cause the computer system to execute the computer-implemented method (100) for generating a complexity-reduced time model of a distributed system according to one of the preceding claims 1 to 9. [12] A computer-readable medium or signal storing and / or containing the computer program according to claim 11.

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