Computer-implemented method for determining a manipulated variable vector for controlling a system

Abstract

A first general aspect of the present disclosure relates to a computer-implemented method for determining a manipulated variable vector for controlling a system. The method comprises determining a first state vector, receiving a reference trajectory default vector, receiving a manipulated variable default vector, generating a stability rule on the basis of a stability measure and the first state vector, and calculating a manipulated variable vector on the basis of the stability rule, the manipulated variable default vector and the reference trajectory default vector.

Description

[0001] R.410834 - 1 -Description Title: COMPUTER-IMPLEMENTED METHOD FOR DETERMINING A CONTROLLED VARIABLE VECTOR FOR CONTROLLING A SYSTEM State of the Art Safety is considered one of the greatest challenges in driver assistance systems and autonomous driving. Previous techniques describe various extensions of an approach in which an input signal from a given motion controller is checked for safety using a backup controller (safety path), deciding whether applying the motion controller's output signals ensures safety for future points in time. While these extensions enable a basic design and efficient implementation of the desired safety mechanism on control units, the resulting safety interventions only ensure safety specifications such as minimum / maximum lateral forces or acceleration / deceleration.Real-world tests have shown that while safety is guaranteed, interventions are often abrupt and can have a destabilizing effect on the system. To improve the performance and acceptance of such safety concepts for motion control, it is desirable to incorporate traditional stability properties into the safety specifications that are not supported by the existing state of the art. Historically, control engineering methods have focused primarily on stability guarantees. Modern control systems that enter safety-critical areas, such as driver assistance systems, autonomous driving, or robots that interact with humans, must also meet safety requirements. While safety filters, as in R.410834 -. 2 -While safety filters, as mentioned in the previous paragraph, can be used to enforce compliance with state and input constraints, their application in the case of motion control can have the following undesirable side effects: They can cause abrupt vehicle maneuvers, including strong steering and acceleration or braking interventions with unpleasant impacts on the entire system, including destabilizing effects. Examples of this can include oscillating slip angles on low-friction roads (wet, icy). Safety filters can also cause strong oscillations in the vehicle's motion when operated near a safety constraint, such as a maximum permissible lateral force. This effect is exacerbated when the desired and safety-filtered input vary greatly, e.g., during repeated countersteering by the safety filter.In the literature on safety filters, such oscillating effects are referred to as Zeno behavior. These properties are undesirable in most control systems. Furthermore, they can be particularly problematic in autonomous driving, as the effects can be perceived as potentially dangerous and / or uncomfortable, even if formal safety requirements are still met. Thus, there is a fundamental need for improved safety filters in control engineering. Disclosure of the Invention A first general aspect of the present disclosure relates to a computer-implemented method for determining a manipulated variable vector for controlling a system.The method comprises determining a first state vector, receiving a reference trajectory specification vector, receiving a manipulated variable specification vector, generating a stability rule based on a stability measure and the first state vector, and calculating a manipulated variable vector based on the stability rule, the manipulated variable specification vector, and the reference trajectory specification vector. A second general aspect of the present disclosure relates to a computer system configured to implement the computer-implemented method R.410834 -. 3 -for determining a manipulated variable vector for controlling a system according to the first general aspect (or an embodiment thereof). A third general aspect of the present disclosure relates to a computer program designed to carry out the computer-implemented method for determining a manipulated variable vector for controlling a system according to the first general aspect (or an embodiment thereof). A fourth 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 third general aspect (or an embodiment thereof). The method proposed in this disclosure according to the first general aspect (or an embodiment thereof) can be used to provide modular safety control architectures.For example, the proposed method can be particularly advantageous in architectures where safety interventions have a predetermined and limited destabilizing effect on the overall system. The proposed method and the associated improvements can ensure a certain degree of comfort in motion control while observing safety requirements in the context of the established concept of stability. The proposed method can reduce the frequency of abrupt driving maneuvers, such as sharp steering, acceleration, or deceleration, and thus increase passenger comfort. The occurrence of undesirable destabilizing effects can thus be reduced.A further advantage may be that system components, particularly power transmission system components, are protected by reducing abrupt and strong control interventions, thus extending their service life and / or enabling longer maintenance intervals. This can increase the quality of the components themselves as well as the entire vehicle. Furthermore, the techniques of the present disclosure can provide a method that determines a manipulated variable vector based on stability rules in relation to a reference trajectory, which may be variable. In certain cases, the reference trajectory can be subject to continuous replanning or rescheduling, for example, of paths based on R.410834. 4 -curves and / or obstacles, e.g. in autonomous driving, can be (temporally) variable. In these cases, the disclosed method can advantageously take the variable reference trajectory into account when determining the manipulated variable. A further advantage can be seen in the fact that the computer-implemented method can be integrated into existing systems and, for example, can be loaded into existing control units and / or can be provided via cloud and / or edge computing. Some terms are used in the present disclosure in the following way: A “state controller” can 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 can comprise parameters that can weight the state variable. In examples, a state controller can be executed on a computer system.A state controller can, for example, comprise or be part of a hardware module with inputs and outputs. 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. Brief Description of the Figures: Fig. 1 schematically illustrates a computer-implemented method for determining a manipulated variable vector for controlling a system. Fig. 2 schematically illustrates an exemplary control loop according to one or more embodiments of the present disclosure. Detailed Description R.410834 -. 5 -Fig. 1 is a flowchart showing possible method steps of the computer-implemented method 100 for determining a manipulated variable vector for controlling a system. The computer-implemented method 100 for determining a manipulated variable vector for controlling a system 10 includes determining 110 a first state vector ^(^), receiving 120 a reference trajectory specification vector ^^^^(^), receiving 130 a manipulated variable specification vector ^^^^(^), generating 140 a stability rule based on a stability measure ^ ^and the first state vector ^(^), and calculating 150 a manipulated variable vector ^(^) based on the stability rule, the manipulated variable specification vector ^^^^(^), and the reference trajectory specification vector ^^^^(^). In examples, the system 10 can be described by means of a system function ^. For a state vector ^(^ + 1) of a subsequent time step, taking into account an external disturbance variable ^(^), the following can apply: ^(^ + 1) = ^(^(^), ^(^),^(^)). In examples, the state vector ^(^) can be measured or mathematically reconstructed using an observer. In examples, the first state vector ^(^) can comprise one or more state variables (^^,^, ^^,^, ^^,^, …). For the state vector ^(^), the following can apply: ^(^) ∈ℝ ^^ , where ^ ^is a natural number. In some examples, the computer-implemented method 100 may be part of a filter stage 12 that is connected downstream of a conventional and / or already known control system, as shown in Fig. 2. In some examples, the manipulated variable specification vector ^^^^(^) may comprise an output value of a control stage 11. In examples, the manipulated variable specification vector ^^^^(^) may comprise an output value of a non-safe and / or non-certified control stage 11. In examples, the manipulated variable specification vector ^^^^(^) may comprise an input value entered by a human user, for example, in a driver assistance system. In some examples, the reference trajectory specification vector ^^^^(^) may comprise an output value of a control stage 11. In examples, the reference trajectory specification vector ^^^^(^) may be non-zero, orIt may be advantageous for the techniques of the present disclosure if the reference trajectory specification vector ^^^^(^) is not equal to zero. In some examples, the following may apply to the first manipulated variable vector ^(^): ^(^) = R.410834 -. 6 - ^(^(^), ^^^^(^), ^^^^(^)), where ^ in this example stands for the filtering of the manipulated variable specification vector ^^^^(^) by the computer-implemented method 100. In examples, the first manipulated variable vector ^(^) and / or manipulated variable specification vector ^^^^(^) can comprise one or more manipulated variables (^^,^, ^^,^, ^^,^, … ) or manipulated variable specification values ​​(^^^^,^, ^^^^,^, ^^^^,^, … ). For the first manipulated variable vector ^(^), the following can apply: ^(^) ∈ ℝ^^, where ^^ is a natural number. For the manipulated variable specification vector ^^^^(^), the following can apply:^ ^^^^ a natural Number is. The method 100 (120) of the reference trajectory specification vector ^ ^^^(^). In examples, the reference trajectory specification vector can be obtained from a higher-level planning module or defined as the centerline of the lane currently being traveled. In some examples, instability of the system 10 can be determined by fluctuating, increasing, and / or oscillating deviations from the reference trajectory specification vector ^^^^(^). In some examples, the instability can be calculated by weighted differences between the current state vector and / or the control vector and the reference state vector or the reference control variable vector. In examples, the stability measure ^ ^based on a plurality of prediction state vectors ^^|^ , ^^^^|^ a plurality ^ of prediction steps. The first state vector ^(^) can serve as the initial state vector ^^|^ of the plurality of prediction state vectors. In examples, this can mean that, starting from the currently measured / observed state vector ^ ^|^ and a planned future manipulated variable trajectory ^^|^ , ^^^^|^ the future prediction state vectors ^^|^ , ^^^^|^ can be predicted. This can provide the basis for calculating the stability measure ^ ^ .In examples, the received reference trajectory vector (^^^^(^)) may be variable and / or time-dependent. In examples, the stability measure ^ ^based on a plurality of prediction trajectory vectors (^^|^ , ^^^^|^) of a plurality of prediction steps, wherein the plurality of prediction trajectory vectors (^^|^ , ^^^^|^) comprise achievable trajectories determined using a system description of the system. In examples, the plurality of prediction trajectory vectors (^^|^ , ^^^^|^) for a R.410834 - 7 - State controller and / or the filter stage 12 comprise achievable trajectories. In examples, the state controller may comprise the filter stage 12. It may be advantageous, since the received reference trajectory, described by the reference trajectory specification vector ^^^^(^), may represent an unachievable trajectory, to determine an artificial prediction trajectory, described by the plurality of prediction trajectory vectors ^^|^, ^^^^|^, that is achievable. Based on this achievable prediction trajectory, the stability measure ^ ^be determined. In examples, a first component of a prediction trajectory vector ^ ^|^ the majority of prediction trajectory vectors ^^|^ , ^^^^|^ a reachable prediction state vector x ^,^|^ and a second component of a prediction trajectory vector ^^|^ of the plurality of prediction trajectory vectors ^^|^ , ^^^^|^ comprises an achievable prediction manipulated variable vector u^,^|^. For example, the following may apply: ^^|^ = [x^,^|^, u^,^|^] ^ . In examples, the prediction trajectory vector ^^|^ may be non-zero, or it may be advantageous for the techniques of the present disclosure if the prediction trajectory vector ^^|^ is non-zero. In general, system-related safety requirements may necessitate the restriction of possible states ^(^) and / or manipulated variables ^(^). For the states ^(^), a subset ^ of all (theoretically) possible states can generally be defined: ^ ⊂ the manipulated variables^(^) can generally be defined as a subset ^ of all (theoretical) manipulated variables: ^ ⊂ ℝ^^ . An achievable prediction trajectory ^(^) can be defined in examples as a subspace ^ ^ be restricted. For example, this subspace ^^ can be composed of a subset ^^ ⊂ ^ and a subset ^^ ⊂ ^: ^(^) ∈ ^^ ≙ ^^ × ^^. A prediction trajectory ^(^ + 1) of a subsequent time step ^ + 1 can be defined to lie within the set ^^^(^)^, which can be based on the system function ^ and for which: ^ In examples, the stability measure ^ ^by summing a plurality of cost functions over at least a first prediction step ^ and a second prediction step ^ + 1 of the plurality of prediction steps. In examples, each cost function of the plurality of cost functions can be calculated using a prediction state vector of the plurality of prediction state vectors ^^|^ , ^^^^|^ and a prediction manipulated variable vector of a plurality of prediction manipulated variable vectors ^^|^ , ^^^^|^ to a respective prediction step of the first prediction step ^ R.410834 - 8 -or the second prediction step ^ + 1. In some examples, the plurality ^ of prediction steps may be 0 to 10, 0 to 100, 0 to 500, 0 to 1000, or greater than 1000. In examples, the plurality of cost functions may be based on the plurality of prediction trajectory vectors (^^|^ , ^^^^|^). For the calculation of the stability measure ^^, the following may apply for a summation over ^ prediction steps: ^^ = ∑^^^In examples, the cost function may be a predicted trajectory ^ ^|^ , ^^|^ of a ^ in a time step ^ and an achievable prediction trajectory ^^|^ of the same prediction step ^ in the same time step ^. In some examples, the stability measure ^ ^ by a quadratic cost function ℓ. Additionally or alternatively, the difference between a predicted state vector ^ ^|^the plurality of prediction state vectors ^^|^ , ^^^^|^ and a reachable prediction state vector^^,^|^ in some examples with a first weighting matrix ^ and / or a difference between a predicted manipulated variable vector ^^|^ of the plurality of second manipulated variable vectors ^^|^ , ^^^^|^ and a reachable prediction manipulated variable vector ^^,^|^ with a second weighting matrix ^. For example, the quadratic cost function can be expressed as follows: ^ ^ ^ ^^ Weighting matrix ^ can be a positive-definite matrix. For example, by selecting matrices ^ and ^ as positive-definite, the stability measure ^^ can indicate the future deviation with respect to the reference trajectory. For example, persistent oscillations lead to ^ ^ infinite and therefore unstable, while finite values ​​of the stability measure ^ ^can indicate stable system behavior. In some examples, the state vector ^ ^^^|^ the plurality of prediction state vectors of the second prediction step based on a system function ^, the state vector ^ ^|^ the plurality of prediction state vectors of the first prediction step and the manipulated variable vector ^^|^the plurality of second manipulated variable vectors of the first prediction step ^are calculated. For ^^^^|^ the following can then apply: ^^^^|^ = ^(^^|^ , ^^|^ , 0). The system function ^ describes the system. In some examples, the R.410834 - 9 - first state vector ^(^), as initial state vector ^ ^|^ the majority of prediction state vectors. In some examples, the stability rule may include that the stability measure ^ ^ less than or equal to a first upper limit ^ ^ For example, the first upper bound ^ ^act as a design parameter that determines the maximum tolerated deviations from a purely stabilizing controller. In some examples, a larger value of the first upper limit ^ ^ result in the stability-enhancing effect of the computer-implemented method of the present disclosure only being activated when the security of the system 10 is at risk. In contrast, lower values ​​of the first upper limit ^ ^ cause additional safety interventions if entries of the manipulated variable specification vector^ ^^^ (^) can have a destabilizing effect on the system 10. In some examples, a final cost function ^^(^^|^) can be added to the summation of the plurality of cost functions ℓ over at least the first prediction step ^ and the second prediction step ^ + 1 to ensure that ^^ approaches the first upper limit ^^. In some examples, the following can apply: ^^ = ∑ ^^^ In some examples, the computer-implemented method 100 may be repeatedly executed at least at a first time step ^ − 1 and at a second time step ^ . In some examples, the stability rule may include that a difference between a stability measure^^^^ of the first time step ^ − 1 and a stability measure ^^ of the second time step ^ is less than or equal to a second upper limit. In some examples, the stability measure ^^^^ of the first time step ^ − 1 may serve as an input to the filter stage 12 for generating 140 the stability rule. In some examples, the second upper limit may be a minimum selected from a difference between the stability measure ^ ^^^ of the first time step ^ − 1 and the first upper bound ^^ or the value of a cost function based on the initial state vector ^ ^|^, an initial prediction trajectory vector ^^|^, and / or a running manipulated variable vector variable of the second time step. In some examples ^ ^^ ^^ R.410834 - 10 - The stability rule can therefore be fulfilled in the example shown if the stability measure ^ ^ less than or equal to the first upper limit ^ ^ In another example, the stability rule in the example shown can be fulfilled if the difference between the stability measure ^^^^ of the first time step ^ − 1 and the stability measure ^^ of the second time step ^ is less than or equal to the costs ℓ(^0|^, ^0|^, ^0|^)) at the initial step ^ = 0. In one example, in the case of a disturbance event, the second upper limit can be adjusted by means of an addition with a buffer variable ξ. The following can then apply: ^^ − ^^^^ ≤ Example, the buffer variable ξ can only then non-zero if it is necessary to relax the stability rule. By increasing the numerical value ξ the difference between the stability measure ^ ^^^ of the first ^ − 1 and the stability measure ^^ of the second time step ^ increase. In examples, the numerical value of the buffer variable ξ may need to be increased with an increasing strength of an external disturbance. In some examples, calculating 140 the first manipulated variable vector ^(^) may include calculating an extremum. In some examples, calculating 140 the first manipulated variable vector ^(^) may include minimizing a difference between the manipulated variable target vector ^^^^(^) and a current manipulated variable vector variable. In some examples, the Stability specification may be one of a plurality of constraints. In some examples, calculating (150) the manipulated variable vector (^(^)) may comprise (almost) minimizing a difference between the reference trajectory specification vector (^^^^(^)) and each prediction trajectory vector of the plurality of prediction trajectory vectors (^^|^, ^^^^|^). The result of the (almost) minimization may be the first manipulated variable vector ^(^) that (almost) minimizes the difference between the manipulated variable specification vector ^^^^(^) and the current manipulated variable vector variable of the given plurality of constraints. The difference between the manipulated variable specification vector ^^^^(^) and the current manipulated variable vector variable may also comprise the greatest possible reduction of the difference between the Specification vector ^^^^(^) and the current manipulated variable vector variable frame of the plurality ^ of prediction steps. In the plurality of constraints may further comprise at least one of a state vector R.410834 - 11 - domain ^^ of a manipulated variable vector domain ^^. It can hold: ^^ ^^|^ ∈ ^^. In some examples, the plural of further a definition set for a final state vector ^ ^ ^|^ ^ of the plurality of prediction state vectors. The final state vector can be the result of calculating the state vector in the last of the plurality of prediction steps. For example, the following optimization problem can be set up for calculating 150 the manipulated variable vector (^): {^ In one example, ^ can be a scalar. In one example, ^ can be a design parameter that represents the decay of the stability measure. In examples, ^ can be between 0 and 1. For example, the following can hold: ^ ∈ (0, 1). In examples, the optimization problem can (almost) minimize the difference between the received reference trajectory specification vector ^^^^(^) and the prediction trajectory vector of the plurality of prediction trajectory vectors ^ , ^^^^|^ determined in each prediction step: ^ ∑^^^ ^ ^|^^ . In this term can be weighted with a weighting ^In examples, the system 10 to be controlled can be designed for placement in a vehicle, a robot, a building, a power tool and / or a household appliance, and / or for controlling a vehicle function, a robot function, a building automation function, a R.410834 - 12 -Power tool automation function, and / or a household appliance automation function. For example, the vehicle function can be a function for autonomous and / or assisted driving. In some examples, the computer-implemented method 100 can be designed for execution on a computer system of a vehicle (e.g., an autonomous, highly automated, or assisted driving 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 computer-implemented method 100 and / or the filter stage 12 can be executed. In some examples, the vehicle can include a computer system with a communication interface that enables communication with a backend.For example, the computer-implemented method 100 can be executed in this backend. In one example, the system 10 to be controlled can be a system for lateral and / or longitudinal guidance of the vehicle. For example, a state variable of the state vector ^(^) can include one or more position variables, orientation angles, velocity variables, and / or a yaw rate of change. The manipulated variable vector ^(^) and / or manipulated variable command vector ^^^^(^) can include, for example, a steering angle, a parameter associated with the drivetrain, and / or braking parameters. In other examples and as indicated above, the system 10 to be controlled can be arranged in a robot and / or configured to control a robot function (in particular, to control a movement function of a robot). For example, the system to be controlled can be a system for lateral and / or longitudinal guidance of the robot.In some examples, the computer-implemented method 100 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) in a backend communicatively coupled to the robot. In one example, the system to be controlled may be configured for placement in a building and / or may serve to control building functions. R.410834 - 13 -(in particular for controlling building automation functions). For example, the building function may be a function for controlling room temperature, lighting, and / or security equipment. In some examples, the computer-implemented method 100 may be configured to execute 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 communicatively coupled to the building. For example, the computer system may comprise a control system or a building automation control device on which the computer-implemented method 100 may be executed. In examples, the building may have a computer system with a communication interface enabling communication with an external backend. For example, the computer-implemented method 100 may be executed in this backend.In examples, a state vector^(^) can contain variables based on information such as room temperature, brightness, or the presence of people. In some cases, the state vector ^(^) can include a relative temperature difference, illuminance, or distance to a specific location or object in the building. An example of a state 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, in examples, 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 manipulated variable specification vector ^(^) could be... ^^^ ( ^ )For example, a temperature and / or lighting specification, for example in the form of a voltage signal and / or current signal. In other examples, the system 10 to be controlled may be designed for arrangement in a power tool and / or for controlling a power tool function (in particular for controlling a work function of the power tool). In some examples, the computer-implemented method 100 may be executed on a computer system of the power tool. For example, the computer system may be implemented locally in the power tool or (at least partially) in R.410834 - 14 -a backend that is communicatively connected to the power tool. In other examples, the system 10 to be controlled may be designed for placement in a household appliance and / or for controlling a household appliance function (in particular, for controlling a work function of the household appliance). In some examples, the computer-implemented method 100 may be executed on a computer system of the household appliance. For example, the computer system may be implemented locally in the household appliance or (at least partially) in a backend that is communicatively connected to the household appliance. In further examples, the system 10 to be controlled may be designed for placement in a machine tool, a personal assistant, an access control system, and / or a medical device.Furthermore, a computer system is disclosed that is designed to execute the computer-implemented method 100 for determining a manipulated variable vector for controlling a system. The computer system can comprise at least one processor and / or at least one main memory. The computer system can further comprise a (non-volatile) memory. In examples, the computer system can be part of an overall system. For example, the overall system can comprise, in addition to the computer system, the system 10 to be controlled. The overall system can comprise, for example, as mentioned above, a vehicle, a robot, a building, a power tool, a household appliance, a machine tool, a personal assistant, an access control system, and / or a medical device. Furthermore, a computer program is disclosed that is designed to execute the computer-implemented method 100 for determining a manipulated variable vector for controlling a system.The computer program can be in interpretable or compiled form, for example. It can be loaded (even in parts) into a computer's RAM for execution, e.g., as a bit or byte sequence. R.410834 -. 15 - 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

R.410834 - 16 - Claims 1. Computerimplementiertes Verfahren (100) zur Bestimmung eines Control variable vector for controlling a system (10) - Bestimmen (110) eines ersten Zustandsvektors (^(^)), - Empfangen (120) eines Referenz-Trajektorie-Vorgabevektors (^^^^(^)), - Empfangen (130) eines Stellgrößen-Vorgabevektors ^^^^(^)), - Erzeugen (140) einer Stabilitätsvorschrift auf der Basis eines Stabilitätsmaßes (^^) und des ersten Zustandsvektors (^(^)), und - Berechnen (150) eines Stellgrößenvektors (^(^)) auf der Basis der Stabilitätsvorschrift, des Stellgrößen-Vorgabevektors (^^^^(^)) und des Referenz- Trajectory specification vector (^ ^^^ (^)).

2. Computerimplementiertes Verfahren (100) gemäß Anspruch 1, wobei das Stabilitätsmaß (^^) auf einer Mehrzahl von Prädiktions-Zustandsvektoren (^^|^ , ^^^^|^) einer Mehrzahl von Prädiktionsschritten basiert, wobei der erste Zustandsvektor (^(^)) als initialer Zustandsvektor ^^^|^^ der Mehrzahl von Prädiktions-Zustandsvektoren dient.

3. Computerimplementiertes Verfahren (100) gemäß Anspruch 1 oder 2, wobei das Stabilitätsmaß (^^) auf einer Mehrzahl von Prädiktions-Trajektorie-Vektoren (^^|^ , ^^^^|^) einer Mehrzahl von Prädiktionsschritten basiert, wobei die Mehrzahl der Prädiktions-Trajektorie-Vektoren (^^|^ , ^^^^|^) erreichbare Trajektorien umfassen, die unter Verwendung einer Systemfunktion des Systems (10) be determined.

4. Computerimplementiertes Verfahren (100) gemäß Anspruch 1, 2 oder 3, wobei the stability measure (^ ^ ) by summing a plurality of K ostenfunktionen über mindestens einen ersten Prädiktionsschritt (^) und einen zweiten Prädiktionsschritt (^ + 1) der Mehrzahl von Prädiktionsschritten berechnet, wherein each cost function of the plurality of cost functions is determined by means of a prediction state vector of the plurality of prediction state vectors ( ^^|^ , ^^^^|^) und eines Prädiktions-Stellgrößenvektors von einer Mehrzahl von Prädiktions-Stellgrößenvektoren (^^|^ , ^^^^|^) zu einem jeweiligen Prädiktionsschritt des ersten Prädiktionsschritts (^) oder des zweiten Prädiktionsschritts (^ + 1) gebildet wird. R.410834 - 17 - 5. Computerimplementiertes Verfahren (100) gemäß Anspruch 4, wobei die Majority of cost functions on the majority of prediction trajectories- V ektoren (^^|^ , ^^^^|^) basieren.

6. Computerimplementiertes Verfahren (100) gemäß einem der vorhergehenden Ansprüche, wobei die Stabilitätsvorschrift umfasst, dass das Stabilitätsmaß (^^) less than or equal to a first upper limit (^ ^ ) is.

7. Computerimplementiertes Verfahren (100) gemäß einem der vorhergehenden Ansprüche, wobei das Berechnen (140) des Stellgrößenvektors (^(^)) das Calculating an extremum.

8. Computerimplementiertes Verfahren (100) gemäß einem der vorhergehenden Ansprüche, wobei das Berechnen (140) des Stellgrößenvektors (^(^)) das Minimizing a difference between the manipulated variable specification vector (^ ^^^ (^)) and nd einer laufenden Stellgrößenvektorvariable wobei die Stability rule is a constraint of a plurality of constraints.

9. Computerimplementiertes Verfahren (100) gemäß einem der vorhergehenden Ansprüche, wobei das Berechnen (140) des Stellgrößenvektors (^(^)) das Minimizing a difference between the reference trajectory specification vector ( ^^^^(^)) und jeweils einem Prädiktions-Trajektorie-Vektor der Mehrzahl von Prädiktions-Trajektorie-Vektoren (^^|^ , ^^^^|^) umfasst.

10. Computerimplementiertes Verfahren (100) gemäß einem der vorhergehenden Claims, wherein the system (10) to be controlled is designed for arrangement in a vehicle, a robot, a building, a power tool and / or a household appliance, and / or for controlling a vehicle function, e iner Roboterfunktion, einer Gebäudeautomatisierungsfunktion, einer power tool automation function, and / or a household appliance automation function.

11. Computersystem, dafür ausgelegt, das computerimplementierte Verfahren (100) to determine a manipulated variable vector for controlling a system according to one of the preceding claims 1 to 10. R.410834 - 18 - 12. Computerprogramm, umfassend Befehle, die bei der Ausführung des computer program by a computer system causing the c omputerimplementierte Verfahren (100) zur Bestimmung einesmanipulated variable vector for controlling a system according to one of the preceding claims 1 to 10.

13. Computerlesbares Medium oder Signal, das das Computerprogramm gemäß Claim 12 stores and / or contains.

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