Computer-implemented method for determining a proxy model of a state-space model

Abstract

The general aspects of the present disclosure relate to a method for determining a surrogate model of a state space model. The method includes receiving a time-continuous state space model describing a system to be closed-loop controlled. The method further includes forming a time-discrete representation of the state space model describing the system to be closed-loop controlled, wherein at least the time-discrete representation of the state space model has a time dependence based on a stochastic distribution. The method further includes determining a surrogate model of the time-discrete representation of the state space model.

Description

BACKGROUND

[0001] Highly automated or autonomous systems are increasingly gaining focus, for example in the field of robotics and automotive industry. In particular, closed-loop control systems are of increasing significance in the operation of autonomous or highly automated systems. The problem arises in distributed systems in which, for example, a closed-loop control algorithm is executed physically separately from the system to be closed-loop controlled, for example by means of cloud computing or edge computing, and as a result of which time delays occur in the data transmission.

[0002] Due to different physical conditions influencing the signal transmission, or different channel utilizations in vehicle-to-vehicle communication (V2V communication), time delays or fluctuating sampling times can occur, which are non-deterministic and thus uncertain. For example, networked adaptive speed closed-loop control, platooning or cooperative lane merging can be such cases in which the channel utilization is exceptionally high compared to other cases. Non-deterministic delays can occur, for example, in the feedback loop when a distributed E / E architecture participates in the vehicle control function, in the bus communication, and / or in the signal processing and transmission in the sensor system. In a closed-loop control system such as, for example, the longitudinal guidance of a vehicle, non-deterministic time delays can have a disadvantageous effect on the success of the closed-loop control.

[0003] Many solutions in the prior art do not adequately take into account the influence of the uncertain time effects and their mapping in the closed-loop control. Furthermore, there is also a lack of efficient methods for quantifying the uncertain time effects.

[0004] As a result, the system under consideration has to be either adjusted very conservatively or optimized by worst-case analysis, which can lead to poor performance. Alternatively, usually only inefficient and computationally intensive uncertainty quantification methods (Uncertainty Quantification (UQ) in English) are available, which require a large number of simulations (> 3000). Then, it is difficult to perform UQ algorithms online, i.e. at runtime. For example, the monitoring of the influence of the uncertain time effects can only be performed offline at design time. Therefore, there is a need for improved methods to quantify the uncertain time effects in the design of a closed-loop control. SUMMARY

[0005] A first general aspect of this disclosure relates to a method for determining a surrogate model for a state-space model. The method includes: receiving a time-continuous state-space model describing a system to be controlled in a closed loop. The method further includes: forming a time-discrete representation of the state-space model describing the system to be controlled in a closed loop, wherein at least the time-discrete representation of the state-space model has a time correlation based on a random distribution. The method further includes: determining a surrogate model of the time-discrete representation of the state-space model.

[0006] The second general aspect of this disclosure relates to a computer system configured to perform a method for determining a proxy model of a state-space model according to the first general aspect (or an embodiment thereof).

[0007] The third general aspect of this disclosure relates to a computer program configured to perform a method for determining a proxy model of a state-space model according to the first general aspect (or an implementation thereof).

[0008] The fourth general aspect of this disclosure relates to a computer-readable medium or signal that stores and / or contains a computer program according to the third general aspect (or its embodiments).

[0009] The method according to the first general aspect (or its embodiment) presented in this disclosure can be used to provide a method for determining a surrogate model for a state-space model. This method can be used to determine a surrogate model of a state-space model for designing a state-closed-loop controller.

[0010] Furthermore, the proposed method allows for the characterization of uncertain time effects in a closed-loop control system with a single simulation, representing a significant efficiency gain compared to numerous simulations using inefficient UQ methods. This results in savings in both runtime and computational resources required for simulation. Moreover, the computation of the surrogate model can be performed prior to the design of the state-loop controller, reducing the computational power required for its design. By discretizing the time-continuous state-space model while considering time correlations based on random distributions, a better mapping to reality can be created, particularly in distributed closed-loop control systems, and the design of the state-loop controller can be improved. Furthermore, the techniques disclosed herein allow for the mapping of uncertain time effects in data transmission channels and / or the consideration of uncertain time effects when sampling transmitted signals. Furthermore, through resource-efficient computation, uncertainty quantification can be performed at runtime (“online”). This allows for the monitoring and / or prediction of confidence intervals for the target variable at runtime.

[0011] An advantage lies in the fact that this method can be applied to a wide range of closed-loop control systems. One example for this is the longitudinal guidance of a vehicle. Here, the longitudinal guidance of a vehicle involves the control and stability of its motion along the direction of travel. This longitudinal guidance can include aspects of acceleration, deceleration, and speed closed-loop control, ensuring that the vehicle can travel forward or backward on the road in a desired manner. Particularly in autonomous and / or assisted driving (where multiple vehicles communicate through the same communication point and delays may occur in data transmission), the techniques disclosed herein can lead to improved closed-loop control behavior. In this context, the disclosed method can also lead to improved closed-loop control in the lateral guidance of a vehicle. Further examples can be found in different areas of closed-loop control techniques, such as in robotics, motor control / closed-loop control of motors, building automation, etc. The method can be further packaged and provided, thereby enabling its use by an extended user group, even if that extended user group or individual members of that user group are unaware of its underlying mathematical basis. Because the structure of the surrogate model is similar to or identical to the structure of the original system to a certain extent, integration into existing software architectures is possible. The method also enables the output of the variance and / or confidence interval of the target variable.

[0012] In this disclosure, some terms are used as follows: A surrogate model can be a model that approximates or represents a complex function or a complex primal model. For example, the computational intensity of a surrogate model can be lower than that of the primal model. In one example, a surrogate model can be created using a bottom-up approach with data control. In one example, the exact internal workings can be unknown. For example, the focus can be on the input-output behavior of the surrogate model. In one example, a surrogate model can be created based on a simulator's response to a finite number of data points. For example, a surrogate model can be determined using machine learning methods and / or statistical methods.

[0013] A "state-closed-loop controller" may include an algorithm (i.e., a calculation rule) that feeds back complete or partial state variables (i.e., the internal state of the controlled object) to input variables. The state-closed-loop controller may include parameters capable of weighting the state variables. In some examples, the state-closed-loop controller may execute on a computer system. In some examples, the state-closed-loop controller may execute in a vehicle's control device, in the cloud, or at the edge. For example, the state-closed-loop controller may include a hardware module with inputs and outputs, or a part of such a hardware module.

[0014] "Vehicle" can be any device used to transport passengers and / or goods. A vehicle can be a motor vehicle (such as a PKW or LKW), but it can also be a rail vehicle. A vehicle can also be a motorized two-wheeled or three-wheeled vehicle. However, waterborne (floating) and flying devices can also be vehicles. A vehicle can be at least semi-autonomous or assisted. Attached Figure Description

[0015] Figures 1-A to 1-B schematically illustrate methods for determining surrogate models for state-space models.

[0016] Figure 2 An exemplary closed-loop control loop according to one or more embodiments of this disclosure is schematically illustrated.

[0017] Figures 3-A and 3-B exemplarily illustrate the response of the closed-loop control loop and its confidence interval when the proxy model according to the technology of this disclosure is applied. Detailed Implementation

[0018] First, refer to Figure 1-A, Figure 1-B and Figure 2 The techniques disclosed herein are discussed. Referring to Figures 3-A and 3-B, the possible results and advantages of the methods disclosed herein for determining state-space models are discussed.

[0019] Figure 1 is a flowchart illustrating possible steps of a method 100 for determining a surrogate model for a state-space model. The method 100 for determining a surrogate model for a state-space model includes: receiving 110 a time-continuous state-space model for describing a system 10 to be controlled in a closed loop. The method includes: forming 120 a time-discrete representation of the state-space model for describing the system to be controlled in a closed loop, wherein at least the time-discrete representation of the state-space model has a time correlation based on a random distribution. Further, the method includes: determining 130 a surrogate model of the time-discrete representation of the state-space model. In one example, the method includes designing a state-closed-loop controller based on the surrogate model. In one example, the method includes applying the state-closed-loop controller in functions for controlling and / or monitoring vehicles and / or robots.

[0020] In one example, a time-continuous state-space model can have a delay parameter. Relevant time correlations. In one example, the delay parameter It can be based on a random distribution.

[0021] In one example, the continuous state-space model may include an input variable vector u(t). In another example, the input variable vector u(t) may include target preset values ​​for the acceleration and / or braking processes of the vehicle and / or robot. In yet another example, the input variable vector may include voltage and / or current signals, which serve as target preset values ​​for the motor closed-loop control and / or braking device. In yet another example, the input variable vector may include target preset values ​​for the steering unit of the vehicle and / or robot. In yet another example, the input variable vector u(t) may be related to a delay parameter. Relevant. The delay parameter can map the input variable vector. The time delay is uncertain. In one example, the input variable vector can be calculated at a location different from the system to be controlled in the closed loop. This leads to potential time delays in data transmission. In the current disclosure, the time uncertainty is addressed through random independent variables. To express this. In one example, a time-continuous state-space model can be described by the following equation: , where t>0, x(0)=x0.

[0022] In one example, the input variable vector u(t) can be determined by the closed-loop control law u(t) = Kx(t). In one example, the gain matrix K can be time-varying, time-invariant, or constant. In one example, the gain matrix K can be deterministic. In one example, the state-space model can include a vector of state variables that depends on a random distribution. In one example, sensor data (e.g., from a camera system) may be delayed in time, resulting in a vector of state variables that depends on a random distribution. .

[0023] In one example, the temporal correlation of a time-discrete representation could include sampling times based on a random distribution. In another example, it could be the temporal continuous states of a time-continuous state-space model and the sampling times of the signal samples. It can be based on a random distribution. In one example, sampling can be done at multiple time steps t. k Execution. The corresponding time step in multiple time steps can be determined by the sampling time. The multiple is formed. This multiple can be expressed by running the index parameter k. For multiple time steps t k Applicable to: t k =k Let k = 0, 1, 2, .... In a time-continuous state-space model, time t can take a value between each first and second sampling time. In some examples, the second sampling time can be formed by adding the first sampling time to the sampling time. In the examples, time t in a time-continuous state-space model can be applied... In some examples, the delay parameter It can be a uniform distribution. In the example, it can be applied to: In the example, the sampling time... It can be a uniform distribution. In the example, it can be applied to: In the example, the state-space model may include the system matrix. and input matrix . Figure 2 An exemplary closed-loop control loop 10 is schematically illustrated. In this example, the state variable vector may include multiple state variables based on multiple sensor signals. In this example, the multiple sensor signals may be generated by multiple sensors, such as, for example, a lidar sensor, a radar sensor, a camera, an ultrasonic sensor, GPS, an accelerometer, a temperature sensor, etc. In this example, the state variable vector may include state variables containing information from a virtual model (e.g., a digital twin). The closed-loop control loop may further include an observer for simulating the state variable vector x(t) based on one or more measurable output signals (e.g., multiple sensor signals).

[0024] Forming a discrete-time representation of a 120 state-space model can include transforming the general solution of the time-continuous state-space model into a time-discrete domain. In the example, in the discrete time domain, it can be assumed that there exists a piecewise constant vector of input variables between the initial time t0 and time t. In the example, the initial time t0 can be set as the sampling time. Any first (integer) multiple of k. Here, time t can be set as the sampling time. The second (integer) multiple of k+1. Here, the second multiple can be a multiple after the first multiple. In the example, it can be: In one example, the time-discrete representation of a state-space model can be described as follows: k=1, 2, 3, ... .

[0025] One advantage of the method disclosed in this paper is that it can reduce the uncertain sampling time by forming a time-discrete representation of a 120-state-space model. The correlation is transferred to the system matrix and input matrix This allows for the determination of the 130 agent model.

[0026] In some examples, the agent model may include multiple agent matrices. These multiple agent matrices may include an agent system matrix A' and an agent state matrix Z. k The surrogate model consists of a surrogate input matrix B' and an optional surrogate perturbation variable matrix. In the example, the surrogate model may include a surrogate gain matrix K'. For example, the presence of the perturbation variable matrix may depend on whether the state-space model of the original system contains perturbation variables. In some examples, the surrogate model may be described by the following equation: ,in k = 1, 2, 3.

[0027] In one example, determining the surrogate model 130 can be performed based on a random distribution. In one example, determining 130 can be performed using polynomial chaotic expansion (PCE). In one example, determining the surrogate model 130 can further include: defining one or more polynomial bases 131 based on the random distribution, wherein the surrogate model is determined using one or more polynomial bases. In one example, each of the plurality of surrogate matrices can be computed using polynomial chaotic expansion (PCE). The polynomial base can correspond to the random distribution. In one example, each polynomial base can be orthogonal to the random distribution it represents. In one example, the one or more polynomial bases can be at least one of Hermitian polynomials, Legendre polynomials, Jacobian polynomials, and / or generalized Laguerre polynomials. In one example, it can be applied to the state variable vector. Among them, Z k,n This represents the so-called chaotic coefficients and the state of the surrogate model. In one example, a polynomial chaotic expansion may include an approximation with a number of time steps of N. In one example, method 100 may include determining the number of time steps N. In one example, the determination of the number of time steps N may be predetermined. For example, a larger number of time steps N may lead to a more accurate approximation but requires longer computation time, while a smaller number of time steps N may lead to a less accurate approximation but achieves shorter computation time. In one example, a polynomial chaotic expansion may be performed on multiple matrices of the surrogate model. Here, the multiple matrices of the surrogate model each include chaotic coefficients of the corresponding polynomial chaotic expansion.

[0028] In one example, the determination of multiple proxy matrices for a proxy model can be specifically applied as follows: .

[0029] In one example, determining the surrogate model 130 may include: specifying multiple quadraturpunkten and multiple quadraturation weights, and computing the surrogate model 133 using numerical quadraturation methods. With the help of numerical quadraturation methods (also known as numerical integration), the integral at these multiple quadraturpunkten can be approximated by using multiple quadraturation weights. For example, matrix A' can be computed using the following equation: In some examples, method 100 may include determining the number of quadrature points J. In one example, the number J may be predetermined. For example, a larger number of quadrature points J may result in a more accurate approximation but requires longer computation time, while a smaller number of quadrature points J may result in a less accurate approximation but achieves shorter computation time.

[0030] In some examples, method 100 may include designing a state-closed-loop controller based on the surrogate model. In some examples, the design of the state-closed-loop controller may include stochastic optimization. Here, stochastic optimization may be performed using an objective function based on the surrogate model. Here, stochastic optimization may include minimizing the objective function. An advantage of the proposed method can be seen as the ability to determine multiple surrogate matrices independently of a specific input variable vector. Further, in examples, the confidence interval of the state trajectory of the closed-loop control loop may be calculated using only one simulation based on the surrogate model. In some examples, the state variable x is a time-discrete representation of the state-space model. k The expected value can be determined based on the proxy model. In one example, state x k The expected value can be obtained through E[x] k ]=CMZ k Calculation. Here, M is an auxiliary matrix obtained from the polynomial chaotic expansion. In some examples, the state variables x in the time discrete representation of the state-space model are... k The variance can be determined based on the surrogate model. In one example, state x k The variance can be obtained through Calculation. Here, V is an auxiliary matrix obtained from the polynomial chaotic expansion.

[0031] This disclosure also relates to a method for controlling a vehicle using a state-closed-loop controller 20 designed by means of the methods of this disclosure. Here, in some examples, the state-closed-loop controller 20 and / or the system to be controlled in a closed loop can be designed as described above.

[0032] In one example, the system to be closed-loop controlled may be designed to be arranged in a vehicle and / or designed to control vehicle functions (especially driving functions). For example, the vehicle functions may be functions for autonomous and / or assisted driving. In some examples, the state closed-loop controller 20 may be designed to execute on a computer system of the vehicle (e.g., 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 device on which the state closed-loop controller 20 may execute. In some examples, the vehicle may include a computer system with a communication interface that enables communication with a backend. For example, the state closed-loop controller 20 may execute in this backend. In some examples, temporal uncertainties may arise due to data transmission between the system to be closed-loop controlled and the computer system executing the state closed-loop controller. In one example, the system to be closed-loop controlled may be a system for lateral and / or longitudinal guidance of the vehicle. In some examples, the state variable vector... It can be based on speed or distance information. In some examples, the state variable vector may include the relative speed and / or distance between a first vehicle, a second vehicle, a person, and / or a stationary object. In one example, the state variable vector of the state-space model... This can include variables based on at least one of the following: steering angle, orientation angle, yaw rate, sideslip angle, and / or lateral error. In the example, the state variable vector... Information may include data from the network, such as motion and / or direction information from other vehicles. In the examples, this information may be provided via vehicle-to-vehicle communication (V2V communication) or via a backend (V2X communication). In one example, the input variables of the input variable vector u(t) may include target preset values ​​for steering speed or acceleration and / or braking processes. In some examples, the system to be closed-loop controlled may be designed to be incorporated into a drive controller or drive unit, and / or used for closed-loop control of motor-related functions (especially for motor closed-loop control). In some examples, the system to be closed-loop controlled may be incorporated into a motor drive closed-loop control unit. For example, the state vector of the state-space model. It may include variables based on at least one of the motor's control signals, operating mode, or power settings.

[0033] This disclosure also relates to a method for controlling a robot using a state closed-loop controller 20 designed by means of the methods of this disclosure. Here, in some examples, the state closed-loop controller 20 and / or the closed-loop system to be controlled can be designed as described above.

[0034] In other examples, the system to be controlled in a closed loop can be located within the robot and / or designed to control robot functions (especially motion functions). For example, the system to be controlled in a closed loop could be a system for lateral and / or longitudinal guidance of the robot. In some examples, the state closed-loop controller 20 can be executed on the robot's computer system. For example, the computer system can be implemented locally within the robot or (at least partially) in a backend that is communicatively connected to the robot. In some examples, the state closed-loop controller 20 can be executed in the backend. In some examples, the state variable vector... It can be based on velocity or distance information. In some examples, the state variable vector can include the relative velocity and / or distance between the first robot, the person, another mobile device, and / or a stationary object. In one example, the state variable vector of the state-space model... This can include variables based on at least one of the following: steering angle, orientation angle, yaw rate, sideslip angle, and / or lateral error. In the example, the state variable vector... This can include information from the network, such as motion and / or orientation information from other robots, mobile devices, and / or humans. In the example, this information may be provided via direct communication or via a backend. In one example, the input variables of the input variable vector u(t) may include target preset values ​​for steering speed or acceleration and / or braking processes.

[0035] This disclosure also relates to a method for controlling functions in building automation using a state-closed-loop controller 20 designed by means of the methods of this disclosure. Here, in some examples, the state-closed-loop controller 20 and / or the system to be controlled in a closed loop can be designed as described above.

[0036] In one example, the system to be closed-loop controlled may be designed for placement within a building and / or for controlling building functions (especially building automation functions). For example, building functions may be for closed-loop control of room temperature, lighting, and / or safety devices. In some examples, the state-closed-loop controller 20 may be designed to execute on a computer system within the building. For example, the computer system may be implemented locally within the building or (at least partially) in a back-end system communicatively connected to the building. For example, the computer system may include a control system or building automation control equipment on which the state-closed-loop controller 20 may execute. In some examples, the building may have a computer system with a communication interface that enables communication with an external back-end system. For example, the state-closed-loop controller 20 may execute in this back-end system. In some examples, temporal uncertainties may arise due to data transmission between the system to be closed-loop controlled and the computer system executing the state-closed-loop controller. In the example, the state variable vector of the state-space model... State variable vectors can include variables based on information such as room temperature, brightness, or the presence of people. In some cases, state variable vectors can include relative temperature differences, illuminance, or distances to specific locations or objects within the building. State variable vectors in the context of building automation. An example could include variables based on parameters such as heating closed-loop control, lighting settings, ventilation speed, or security alarms. In the example, the information could originate from a network, such as sensor data, or settings from other buildings or building components. This information could be provided through communication between buildings or building sections or via an external backend. In one example, the input variables of the input variable vector u(t) could include, for example, temperature presets and / or lighting presets, for example, in the form of voltage and / or current signals.

[0037] The advantages of this disclosure over prior art will be illustrated below with the aid of Figures 3-A and 3-B. The figures illustrate an example of a convoy of multiple vehicles starting up. The state variable vector is x=[e,w]. T One aspect includes the distance error e=d between the two vehicles. ref - d. This distance error is the reference distance d. ref The difference between the actual distance *d* between the two vehicles. On the other hand, the state variable vector includes the relative speed between the two vehicles. The results of corresponding closed-loop control using the first closed-loop controller K1 and the second closed-loop controller K2 are compared, particularly regarding the probability of potential safety-critical situations occurring in the closed-loop control system. A safety-critical situation could be when the actual distance is less than the reference distance (d...). ref >d), or when the distance error is greater than zero (e>0). In the current example, the first closed-loop controller K1 is a conventional closed-loop controller designed according to prior art, and the second closed-loop controller K2 is a closed-loop controller designed by means of the method of this disclosure. The distance errors of the two exemplary closed-loop controls are shown in Figure 3-A. In this example, line 50 represents the distance error caused by the first closed-loop controller K1. In this example, line 60 represents the distance error caused by the second closed-loop controller K2. Areas 51 and 61 represent - Confidence interval. It can be seen that closed-loop control using the first closed-loop controller results in a higher proportion of distance errors greater than zero than closed-loop control using the second closed-loop controller. This could pose a safety risk, especially with a large number of vehicles. As shown in Figure 3-B, the first closed-loop controller drives the system faster than the second closed-loop controller (line 62), but introduces more oscillations (line 52).

[0038] A computer system is further disclosed, configured to perform a method 100 for determining a surrogate model of a state-space model. The computer system may include at least one processor and / or at least one working memory. The computer system may further include (non-volatile) memory. In some examples, all steps of method 100 may be performed by the computer system. In some examples, individual steps of method 100 may be performed by the computer system. Optionally, the results of individual method steps not performed by the computer system may be received by the computer system.

[0039] A computer program is further disclosed, configured to perform a method 100 for determining a proxy model of a state-space model. This computer program may exist, for example, in an interpretable or compilable form. It may (and may also be partially) loaded into the computer's RAM, for example, as a sequence of bits or bytes, for execution.

[0040] A computer-readable medium or signal is further disclosed, which stores and / or contains the computer program or at least a portion thereof. The medium may include, for example, one of RAM, ROM, EPROM, HDD, SDD, ... on which the signal is stored.

Claims

1. A method (100) for determining a surrogate model for a state-space model, wherein, The method (100) includes the following steps: - Receive (110) a time-continuous state-space model for describing the system to be controlled in a closed loop. - Forming a time-discrete representation of the state-space model (120) for describing the system to be controlled in a closed loop, wherein at least the time-discrete representation of the state-space model has a time correlation based on a random distribution. - Determine the surrogate model for the time discrete representation of the state space model described in (130).

2. The method (100) according to claim 1, wherein, The time-continuous state-space model has a time correlation with a delay parameter based on the random distribution.

3. The method (100) according to claim 2, wherein, The time-continuous state-space model includes a vector of input variables related to the delay parameter.

4. The method (100) according to claim 1, 2 or 3, wherein, The temporal correlation of the discrete temporal representation includes sampling time based on the random distribution.

5. The method (100) according to any one of claims 1 to 4, wherein, The proxy model includes multiple proxy matrices, which include a proxy system matrix, a proxy state matrix, a proxy input matrix, and an optional proxy perturbation variable matrix.

6. The method (100) according to any one of claims 1 to 5, wherein, The determination of the agent model (130) further includes: - Specify (132) multiple quadrature points and multiple quadrature weights, and - The surrogate model described in (133) is computed using a numerical quadrature method.

7. The method (100) according to any one of claims 1 to 6, wherein, The determination of the surrogate model is performed using polynomial chaotic expansion.

8. The method (100) according to any one of the preceding claims, wherein, The system to be closed-loop controlled is designed to be deployed in vehicles and / or robots, and / or designed to control and / or monitor vehicle functions and / or robot functions.

9. A computer system designed to perform a method (100) for determining a proxy model of a state-space model according to any one of claims 1 to 8.

10. A computer program comprising instructions that, when executed by a computer system, cause the computer system to perform a method (100) for determining a surrogate model of a state-space model according to any one of claims 1 to 8.

11. A computer-readable medium or signal that stores and / or contains a computer program according to claim 10.

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