Data-driven robust model predictive control method of underwater robot propulsion system

Abstract

The invention discloses a data-driven robust model predictive control method for an underwater robot propulsion system, and the method comprises the steps: collecting the input and output data of the underwater robot propulsion system, constructing a data-driven nonlinear ARX model as a system nominal model, and enabling the model not to depend on an explicit dynamical model; setting control input, output and environment disturbance constraints; then designing an LQR controller based on a linear model of the nonlinear ARX model at a balance point, obtaining a local control law and a Lyapunov function, and avoiding robust invariant set calculation; and then a min-max robust optimal control problem containing terminal cost is constructed, and an optimal control law is obtained by solving the problem and is implemented in a rolling manner.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of underwater robot control, and particularly relates to a data-driven robust model predictive control method for an underwater robot propulsion system. BACKGROUND

[0002] The underwater robot propulsion system is the core actuator for realizing underwater attitude adjustment and position movement of the robot, and its running state directly determines the navigation accuracy and stability of the underwater robot. Due to the complex and changeable underwater environment, uncertain factors such as flow disturbance and fluid resistance change exist universally, and the propulsion system often shows significant nonlinear characteristics.

[0003] At present, the control methods for the underwater robot propulsion system mainly include traditional PID control, conventional model predictive control (MPC) and robust control. Among them, the conventional robust model predictive control method usually needs to introduce terminal region constraints based on robust invariant sets in the controller design to ensure system stability. The implementation process of this kind of method is generally as follows: first, an explicit nonlinear dynamics model of the underwater robot propulsion system is established, then the robust invariant set is calculated through complex mathematical derivation and embedded into the optimization problem of model predictive control as a terminal constraint, and finally the control input is obtained by solving the min-max optimization problem.

[0004] In addition, for some systems that are difficult to establish accurate explicit models, there are also a small number of data-driven control attempts in the prior art, but most of them fail to effectively combine the robust model predictive control framework, either the robustness is insufficient and cannot resist complex underwater disturbances, or still need to rely on robust invariant sets for stability guarantee, and cannot break through the design limitations of traditional methods.

[0005] Although the existing control methods have been applied in some scenarios, there are still the following significant defects for the complex working conditions of the underwater robot propulsion system: Robust invariant set calculation is extremely difficult: the underwater robot propulsion system is affected by environmental factors such as water flow and water pressure, and its dynamics is complex and strongly nonlinear. The mathematical derivation and solution process of the robust invariant set is extremely tedious, and even in many actual working conditions, it is difficult to obtain an analytical solution. Especially when the prior model of the system is unknown and only input-output data can be obtained, the construction of the robust invariant set is out of the question.

[0006] Strong dependence on explicit system model: traditional robust model predictive control methods are based on known explicit dynamics models of the system, but in actual operation of the underwater robot propulsion system, component wear, environmental changes and other factors will cause model parameter drift, which will reduce the accuracy of the previously established explicit model and affect the control effect, making it difficult to guarantee robustness.

[0007] High complexity of controller design: The introduction of terminal region constraints not only increases the computational burden of robust invariant sets, but also increases the number of constraint conditions of the optimization problem of model predictive control, improves the dimension of solution, and causes the design process of the controller to be complicated and the real-time performance to be difficult to meet the control requirements of the rapid response of the underwater robot.

[0008] Insufficient robustness of data-driven methods: The existing few data-driven control methods fail to deeply integrate the advantages of the robust model predictive control framework, and the resistance to uncertain factors such as water flow disturbance and measurement noise in the underwater environment is weak, and the system is prone to oscillation or even instability under complex working conditions. SUMMARY

[0009] In view of the problems existing in the prior art, the present application provides a data-driven robust model predictive control method for an underwater robot propulsion system, aiming to solve the problems of traditional robust model predictive control relying on robust invariant sets, high complexity of calculation, and strong dependence on explicit models of the system, and insufficient robustness of data-driven methods.

[0010] The technical solution of the present application is as follows: A data-driven robust model predictive control method for an underwater robot propulsion system is realized based on a nonlinear ARX model; the underwater robot propulsion system comprises a propeller, a drive motor, an attitude sensor, a position sensor and a controller; the method comprises the following steps: S1, collecting input and output data through the sensors of the underwater robot propulsion system to obtain an input and output time series data set; based on the collected input and output time series data set, a nonlinear ARX model is constructed as a nominal model of the underwater robot propulsion system; the state output constraint, the control input constraint and the disturbance constraint of the underwater robot propulsion system are set; S2, based on the constructed nonlinear ARX model, a local control law and a Lyapunov function are designed; S3, a robust model predictive control optimization problem is constructed, and the constraint conditions of the optimization problem are set; S4, the robust model predictive control optimization problem is solved to obtain an optimal control law, and the corresponding optimal control command is sent to the underwater robot propulsion system, and the rolling update of the control law is realized through rolling implementation.

[0011] Further, in S1, the input and output data are collected through the sensors of the underwater robot propulsion system, wherein the input data is the current / voltage of the drive motor; the output data is the attitude angle deviation and position deviation of the underwater robot; the collection scene covers still water environment, different flow rate water flow environment and different load working conditions; the time series length meets the identification requirements of the nonlinear ARX model.

[0012] Further, based on the collected input-output time series data set, a data-driven identification algorithm is used to construct a nonlinear ARX model as the nominal model of the underwater robot propulsion system. The core characteristic of the nonlinear ARX model is that the model input only contains historical input data and historical output data; the historical input data are: ; wherein, is the input delay order, which is set based on the response speed of the underwater robot propulsion system; The historical output data are: ; wherein, is the output delay order, and the model output is the current output prediction value; System state data is constructed from historical input-output data: ; The nonlinear dynamics of the underwater robot propulsion system satisfy: ; The output relationship satisfies: ; wherein, is the system state vector at time t, is the control input vector at time t, is the environment disturbance vector at time t, is the output vector at time t, is the output matrix, is a nonlinear function.

[0013] Further, in S1, the nonlinear ARX model is constructed, specifically including: The collected input-output data time series set is preprocessed to remove abnormal input values and abnormal output values caused by sensor failure, and a moving average method is used to filter measurement noise; The input delay order and the output delay order of the nonlinear ARX model are determined by the AIC information criterion, ensuring that the model is neither under-fitted nor over-fitted; The structure parameters of the nonlinear ARX model are determined by a data-driven identification algorithm, The nonlinear ARX model needs to accurately fit the key characteristics of the propulsion system: the nonlinear relationship between the drive motor current and the attitude angle deviation and position deviation, ensuring that the model output is an accurate prediction value.

[0014] Further, the state output constraint, the control input constraint and the disturbance constraint of the underwater robot propulsion system are set, for the state output constraint, for the control input constraint, for the disturbance constraint; wherein, is a set of attitude deviation and position deviation constraints, which is set based on the operation accuracy requirement of the underwater robot; is a set of driving motor current / voltage constraints, which is set based on the rated power of the propeller and the maximum overload capacity of the motor; is a set of water flow disturbance constraints, which is set based on the historical water flow data of the operation sea area and the input / output data residual statistics.

[0015] Further, the S2 specifically includes: setting a level set initial parameters , determining the equilibrium point of the underwater robot propulsion system; at the equilibrium point, the Taylor expansion is performed on the constructed nonlinear ARX model to obtain a linearized model; designing an LQR controller for the linearized model, selecting a state weight matrix and a control input weight matrix , solving the algebraic Riccati equation to obtain a positive definite matrix and a state feedback gain matrix , constructing a local control law and a quadratic Lyapunov function , and satisfying the constraint condition of assumption 1; wherein, assumption 1 is: there exist a control law , a function and a level set , such that for all , the following is satisfied: is a positive definite function, and there exist a function , satisfying: ; and: , ; that is, the motor current / voltage output by the local control law is within the constraint range, ; The expression for solving the algebraic Riccati equation is: ; wherein, is the state matrix of the linearized model, is the input matrix of the linearized model.

[0016] Further, in the S3, based on the assumption 1 to the assumption 3, a robust model predictive control optimization problem capable of guaranteeing the input-to-state stability of the closed-loop system is constructed, and specifically includes: A min-max robust optimal control problem containing a terminal cost is constructed, and the objective function is: ; Wherein, is the objective function of the robust model predictive control, is the prediction horizon, is the state-control cost function, is the disturbance cost function, is the terminal cost, is the state predicted at the time ; The constraint conditions of the optimization problem include the state recursion constraint: ; Wherein, is the robust optimal control input at the time , that is, the solution of the optimization problem, is the worst-case disturbance at the time , used for min-max robust optimization; The initial state constraint is: ; And the state output constraint, the control input constraint and the disturbance constraint set in the S1; is the robust optimal solution at the time .

[0017] Further, in the S4, specifically includes: Solving the min-max robust optimal control problem, the optimal control law at the time is obtained: ; Wherein, is the optimal control law based on the prediction horizon at the time ; The corresponding optimal control command is sent to the driving motor of the underwater robot propulsion system to adjust the propeller speed; at the next time, the new output data is collected through the attitude sensor and the position sensor, and the state vector is updated in combination with the historical input data : ; With the updated state vector as the initial state, S4 is executed again to realize the rolling update of the control law, adapting to the dynamic changes of the underwater environment.

[0018] Further, the robust optimal control problem also satisfies hypothesis 2 and hypothesis 3, wherein hypothesis 2 is: There exists Class function , , Make the objective function Satisfy: , ; Hypothesis 3 is: There exists a normal number Satisfy for all And , have: ; Wherein, Is a normal number, used to constrain the cost function lower bound when the state exceeds .

[0019] Further, the level set of the optimal cost function is defined: ; Where Is the optimal cost function; When the initial state of the system , the closed-loop system has input-to-state stability, meeting the stability requirements of the underwater robot operation.

[0020] Compared with the prior art, the present application has the following beneficial effects: The present application provides a data-driven robust model predictive control method for underwater robot propulsion system, which collects the input and output data of the underwater robot propulsion system, constructs a data-driven nonlinear ARX model as the nominal model of the system, without relying on the explicit dynamic model; then set the control input, output and environmental disturbance constraints; then design an LQR controller based on the linearization model of the nonlinear ARX model at the equilibrium point, obtain the local control law and Lyapunov function, avoid the calculation of robust invariant set; then construct a min-max robust optimal control problem containing terminal cost, and obtain the optimal control law by solving the problem and rolling implementation.

[0021] The control accuracy is significantly improved: the data-driven nonlinear ARX model can accurately fit the nonlinear dynamic characteristics of the underwater robot propulsion system, combined with the robust min-max optimization strategy, effectively compensating for the errors caused by environmental disturbances and model uncertainties.

[0022] In the complex working conditions such as water flow disturbance and parameter drift, the closed-loop system can still maintain the input-to-state stability, the control input and output always meet the constraint condition, there is no oscillation and instability phenomenon, and the reliability of the system operation is greatly improved.

[0023] The application discards the terminal area constraint, simplifies the controller design process, combines data-driven modeling and robust optimization framework, ensures the input-to-state stability (ISS) of the system in the complex disturbance environment underwater, improves the control precision and operation stability of the propulsion system, and has low engineering implementation cost, fast real-time response, and is suitable for various nonlinear and unknown model underwater robot propulsion systems. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 It is a data-driven robust model predictive control method flowchart of an underwater robot propulsion system provided in an embodiment of the application. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical scheme and advantages of the application clearer, the technical scheme in the embodiment of the application will be described clearly and completely below in combination with the drawings in the embodiment of the application. Obviously, the described embodiments are only a part of the embodiments of the application, not all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor belong to the protection scope of the application.

[0026] EMBODIMENT As Figure 1 A data-driven robust model predictive control method of an underwater robot propulsion system is realized based on a nonlinear ARX model (only relying on input and output data, and the state data is constructed by historical input and output data); ARX is an autoregressive exogenous input model. The English full name is AutoRegressive with eXogenous inputs, and ARX is a commonly used linear time series analysis and system identification model. The underwater robot propulsion system includes a propeller (such as a propeller, a water jet propeller), a driving motor, an attitude sensor (such as a gyroscope, an accelerometer), a position sensor (such as a sonar, an underwater GPS) and a controller; including the following steps: S1, collecting input and output data through the sensors of the underwater robot propulsion system to obtain input and output time series data set; based on the collected input and output time series data set, a nonlinear ARX model is constructed as a nominal model of the underwater robot propulsion system; setting the state output constraint, control input constraint and disturbance constraint of the underwater robot propulsion system; In the S1, the input and output data are collected through the sensors of the underwater robot propulsion system, wherein, Input data Current / voltage for driving motor (control input); armature voltage for driving motor (unit: V), collected by voltage sampling module of controller, sampling accuracy 0.01 V; Output data Attitude angle deviation (roll angle deviation, pitch angle deviation, yaw angle deviation), position deviation (x / y / z axis position deviation) of underwater robot (output quantity representing control effect of propulsion system); contains two core indicators-attitude angle deviation (unit: °) (take the maximum value of roll angle deviation , pitch angle deviation ), position deviation (unit: m) (take the Euclidean distance of x-axis and y-axis direction position deviation); Collect scenarios covering still water environment, different flow rate water environment, different load working conditions (such as the weight change of carried equipment); cover still water environment (water flow speed 0 m / s), low-speed water flow (0.5 m / s), medium-speed water flow (1.0 m / s), high-speed water flow (1.5 m / s) and pulsating water flow (0.5-1.0 m / s periodic change), load working conditions are 50 kg, 75 kg, 100 kg, a total of 4 water flow scenarios x 3 load working conditions = 12 typical working conditions; the length of time series collected meets the identification needs of nonlinear ARX model.

[0027] Collecting parameters: sampling frequency 100 Hz, single working condition collecting time 600 s, single working condition data amount 60000 groups, total collecting data amount 12x60000=720000 groups, ensuring that the data cover the full working range of the system and meet the identification needs of nonlinear ARX model.

[0028] Based on the collected input and output time series data set, a data-driven identification algorithm (such as recursive least squares method, neural network identification method) is used to construct a nonlinear ARX model as the nominal model of the underwater robot propulsion system; The core characteristics of the nonlinear ARX model are that the model input only contains historical input data and historical output data; the historical input data is: ; Wherein, is the input delay order, which is set based on the response speed of the underwater robot propulsion system; The historical output data is: ; Wherein, is the output delay order, and the model output is the current output prediction value; System state data is constructed from historical input and output data: ; The nonlinear dynamic relationship of the underwater robot propulsion system satisfies: ; The output relationship satisfies: ; in, for The system state vector at any given time. for Control the input vector at all times. for Environmental disturbance vector at any given time. for Output vector at each time step For the output matrix, It is a nonlinear function.

[0029] In S1, constructing a nonlinear ARX model specifically includes: The time series of collected input and output data is preprocessed to remove abnormal input and output values ​​caused by sensor failure, and the moving average method is used to filter measurement noise (such as output data fluctuations caused by water flow disturbance). The input delay order of the nonlinear ARX model is determined using the AIC information criterion. and output delay order This ensures that the model is neither underfitted nor overfitted. AIC stands for Akaike Information Criterion. The core of AIC is to impose a penalty on complex models in order to balance model fit and complexity.

[0030] The structural parameters of the nonlinear ARX model are determined using data-driven identification algorithms (such as recursive least squares with a forgetting factor). Nonlinear ARX models need to accurately fit the key characteristics of the propulsion system: namely, the nonlinear relationship between the drive motor current (input) and the attitude angle deviation and position deviation (output), to ensure that the model outputs accurate predicted values.

[0031] Define the state output constraints, control input constraints, and disturbance constraints for the underwater robot's propulsion system. State output constraints, To control input constraints, For disturbance constraints; in, The set of attitude and position deviation constraints is set based on the accuracy requirements of underwater robot operations. The current / voltage constraint set for the drive motor is set based on the rated power of the thruster and the maximum overload capacity of the motor. The water flow disturbance constraint set is based on historical water flow data of the operation sea area and input and output data residual statistics.

[0032] Specifically, the collected raw data is preprocessed, and the specific steps are as follows: Outlier rejection: 3σ criterion is used to identify abnormal data (σ is the standard deviation of data), and the voltage mutation value (such as single sampling voltage > 30V or < 0V) and the attitude angle jump value (such as single jump > 5°) caused by poor sensor contact are removed, a total of about 1200 groups of abnormal data are removed, accounting for 0.17% of the total data amount; Noise filtering: sliding average method is used to filter measurement noise, and the sliding window length is set to 5 (i.e. the average value of the current sampling point and the previous 4 sampling points is taken as the effective data).

[0033] Nonlinear ARX model construction: Based on the preprocessed input and output time series data set, recursive least squares method (data-driven identification algorithm) is used to construct a nonlinear ARX model as the nominal model of the propulsion system, and the core parameters and principles are as follows: Model order determination: the model order is determined by AIC information criterion (Akaike information criterion), and the AIC criterion expression is is the number of model parameters, is the likelihood function value). After calculation, when the input delay order and the output delay order , the AIC value is minimum , at this time, the model neither under-fitting (training set fitting error < 2%) nor over-fitting (test set fitting error < 3%); System state construction: according to claim 3, the system state vector is constructed by historical input and output data, that is , wherein is the motor voltage of the previous 3 time points, is the output (attitude angle deviation + position deviation comprehensive value) of the previous 2 time points; Model structure and parameters: the nonlinear function of the nonlinear ARX model uses polynomial nonlinear terms (the highest order is 2), that is , , are the model parameters identified). After recursive least squares identification, the specific parameters are obtained: , , , , , , ;​​ Model verification: The identified nonlinear ARX model is compared with the actual system output. In the still water environment, under the working condition of 75 kg load, the average error between the model prediction output and the actual output is 1.8%; under the working condition of 1.0 m / s water flow and 100 kg load, the average error is 2.9%, which meets the requirement of "accurately fitting the nonlinear relationship between the motor voltage and the attitude angle deviation, position deviation".

[0034] Constraint setting: According to the setting of the state output constraint, the control input constraint and the disturbance constraint of the system, the specific values are as follows: State output constraint : Based on the underwater robot operation accuracy requirement (such as underwater detection operation accuracy , ), the attitude angle deviation , the position deviation is set, so the constraint set , , , }( is the Euclidean distance of the position deviation); Control input constraint : Based on the rated parameters of the thruster (rated voltage 24V, maximum overload voltage 30V), the motor voltage constraint is set to , so the constraint set ; Disturbance constraint : Based on the experimental pool water flow historical data (the maximum water flow disturbance causes the attitude angle deviation increment to be less than or equal to 0.5°, and the position deviation increment to be less than or equal to 0.05m) and the input-output data residual statistics (the residual standard deviation ), the disturbance vector ( is the attitude angle deviation disturbance increment, is the position deviation disturbance increment), and the constraint set .

[0035] S2, based on the constructed nonlinear ARX model, design a local control law and a Lyapunov function; In S2, it specifically includes: Set the initial parameters of the level set , determine the equilibrium point of the underwater robot propulsion system (corresponding to the stable output state: attitude angle deviation is 0°, position deviation is 0m, at this time the historical input-output data constitutes the equilibrium state vector); Taylor expansion is performed on the constructed nonlinear ARX model at the equilibrium point to obtain a linearized model; An LQR controller is designed for the linearized model, where LQR is Linear Quadratic Regulator, a classical optimal control method in control theory, mainly used for optimal regulation of linear systems to make the performance index of the system optimal. The state weight matrix and the control input weight matrix are selected, the positive definite matrix and the state feedback gain matrix are obtained by solving the algebraic Riccati equation (ARE), the local control law and the quadratic Lyapunov function are constructed, and the constraint condition of hypothesis 1 is met. Hypothesis 1 is: There exist control law , function and level set , so that for all , the following is met: is a positive definite function, there exist class functions , satisfy: ; and: , ; wherein and are class functions, used to describe the positive definite property of Lyapunov function , is a certain norm of state vector , used for the positive definite property description of Lyapunov function; , that is, the motor current / voltage output by the local control law is within the constraint range ; The expression for solving the algebraic Riccati equation is: ; wherein is the state matrix of the linearized model, is the input matrix of the linearized model.

[0036] Specifically, the local control law and Lyapunov function are designed based on the constructed nonlinear ARX model, the LQR local control law and the quadratic Lyapunov function are designed, and the specific process and parameters are as follows: Linearized model construction: Set the level set The initial parameters of the underwater robot are set as γ = 10, and the equilibrium point of the propulsion system is determined as (i.e., the attitude angle deviation and the position deviation are both 0 at the rated voltage of the motor). A first-order Taylor expansion of the nonlinear ARX model is performed at the equilibrium point to obtain a linearized model: where the linearized state matrix and the input matrix are calculated by partial derivatives.

[0037] LQR controller design: The state weight matrix and the control input weight matrix are selected, where is a diagonal matrix, and the weights are assigned according to the importance of the states (the attitude angle deviation and the position deviation are given higher weights than the historical voltage): ; is used to constrain the amplitude of the control input.

[0038] The algebraic Riccati equation is solved: and the positive definite matrix (5x5 matrix, the main diagonal elements are 1.2, 1.5, 2.1, 15, and 200, respectively) and the state feedback gain matrix (1x5 matrix) are obtained by using the care function of Matlab.

[0039] The local control law is constructed as Substituting the expression of the state vector , we obtain It is verified that the motor voltage output by the local control law is within the range of 0-30 V (i.e., ), and the output under the linearized model is the output matrix, used to extract the attitude angle deviation and the position deviation.

[0040] Lyapunov function construction: A quadratic Lyapunov function is constructed, and it is verified that the function satisfies the assumption 1 in claim 6:  is a positive definite function, and there exist functions and that satisfy ; For all and , calculate , and substitute and to obtain .

[0041] S3, construct a robust model predictive control optimization problem, set the constraint conditions of the optimization problem; In S3, based on assumptions 1 to 3, a robust model predictive control optimization problem is constructed to ensure the stability of the closed-loop system input to state, specifically including: A min-max robust optimal control problem with terminal cost is constructed, and the objective function is: ; Where, is the objective function of the robust model predictive control, is the prediction horizon, is the state-control cost function, is the disturbance cost function, is the terminal cost, is the predicted state of the step at time ; The constraint conditions of the optimization problem include state recursion constraints: ; Where, is the robust optimal control input at time , that is, the solution of the optimization problem, is the worst-case disturbance at time , used for min-max robust optimization; Initial state constraints: and state output constraints, control input constraints and disturbance constraints set by S1; is the robust optimal solution at time .

[0042] Specifically, the robust model predictive control optimization problem is constructed, based on assumptions 1 to 3 (assumptions 2 and 3 are described in S4), a min-max robust optimal control problem with terminal cost is constructed, and the core parameters and constraints are as follows: Objective function setting: The objective function is , where the parameters are set as follows: Prediction horizon (According to the controller operation ability, the time consumed by single solution at time is , which meets the requirement of 100Hz sampling frequency); Terminal cost , (consistent with the local Lyapunov function), for guaranteeing the stability of the closed-loop system.

[0043] Constraint setting, the constraint of the optimization problem includes: State recursion constraint: , where is the robust optimal control input, is the disturbance in the worst case (i.e., the disturbance that maximizes the objective function); Initial state constraint: , the actual state vector at time is updated by real-time data acquisition by the sensor; Output, input and disturbance constraint: , , , , .

[0044] S4, solve the robust model predictive control optimization problem to obtain the optimal control law, and send the corresponding optimal control command to the underwater robot propulsion system to realize the rolling update of the control law through rolling implementation.

[0045] In the S4, specifically comprising: Solving the min-max robust optimal control problem to obtain the optimal control law at time ; wherein, is the optimal control law based on the prediction time domain at time ; Send the corresponding optimal control command to the drive motor of the underwater robot propulsion system to adjust the propeller speed; at the next time, the new output data is collected by the attitude sensor and the position sensor, and the state vector is updated in combination with the historical input data ; ; Take the updated state vector as the initial state; execute S4 again to realize the rolling update of the control law and adapt to the dynamic changes of the underwater environment.

[0046] The robust optimal control problem also satisfies hypothesis 2 and hypothesis 3; wherein, hypothesis 2 is: There exists a class function , , such that the objective function satisfies:​​ , ; Assumption 3 is: There exists a positive constant satisfying for all and , ; where, is a positive constant used to constrain the lower bound of the cost function when the state exceeds .

[0047] Define the level set of the optimal cost function: ; where is the optimal cost function; When the initial state of the system , the closed-loop system has input-to-state stability (ISS), which meets the stability requirements of the underwater robot operation.

[0048] The definition of the level set of the optimal cost function is based on Assumption 2 and Assumption 3, combined with the prediction horizon N and the level set parameter, to finally define the level set of the optimal cost function. It has been mentioned in S3.

[0049] Specifically, the optimization problem solving and the implementation of the rolling control, the optimization problem solving: The above min-max robust optimal control problem is solved using the interior point method (the interior point method solving library is integrated in the embedded controller), and the optimal control law at time is obtained. Taking as an example, when the system state , the optimal control law is obtained by solving, and the corresponding worst disturbance .

[0050] Control command execution and state update: The optimal control command is sent to the drive motor, and the propeller speed is adjusted to 1800 r / min to correct the attitude angle and position. At the next time ( ), the new attitude angle deviation is collected by the attitude sensor, and the new position deviation is collected by the position sensor, combined with the historical input data , the state vector is updated: .

[0051] Rolling control implementation: The updated state vector For the initial state, the flow of solving the optimization problem of step S4 is executed again, and the optimal control law of the time is obtained Optimal control law at time The rolling update of the control law is realized. The rolling process is executed once every 0.01s (synchronized with the sampling frequency), which ensures that the controller can adapt to dynamic scenes such as underwater flow disturbance and load change in real time.

[0052] The application provides a data-driven robust model predictive control method for an underwater robot propulsion system, solves the problem that traditional robust model predictive control relies on a robust invariant set, is complex to calculate and difficult to implement, simplifies the controller design process, and avoids the cumbersome calculation of the robust invariant set.

[0053] The application breaks through the dependence of traditional methods on the explicit model of the system, constructs a data-driven nonlinear ARX model by collecting the input and output data of the underwater robot propulsion system, and realizes accurate control without an explicit model.

[0054] The application guarantees the robustness of the controller in a complex disturbance environment underwater, and through the design of a reasonable cost function and a local control law, combined with the min-max robust optimization framework, the influence of flow disturbance and the like on the propulsion system is resisted.

[0055] The application ensures the input-to-state stability (ISS) of the system, improves the control accuracy and running stability of the underwater robot propulsion system under the premise of meeting the control input and output constraints.

[0056] The data-driven robust model predictive control method for an underwater robot propulsion system provided by the application has low design complexity and strong practicality: the calculation link of the robust invariant set is omitted, the controller structure is simple, the constraint conditions of the optimization problem are fewer, the solving efficiency is higher, and the real-time control requirements of the underwater robot propulsion system can be met, and the method is easy to implement in engineering.

[0057] The robustness is outstanding, and the complex underwater environment is adapted: the environmental disturbance in the worst case is directly considered through the min-max optimization problem, and the data-driven model is combined with the accurate fitting of the characteristics of the system, so that the controller can effectively resist the influence of uncertain factors such as flow and measurement noise, and improve the stability of the system in complex working conditions.

[0058] The stability has strict theoretical support: the designed method meets the recursive feasibility proof and the input-to-state stability, and the initial state range of the stable operation of the system is determined, so that the system constraints are always met within the range, and the system runs stably and reliably.

[0059] Those skilled in the art can make various modifications and changes to the above embodiments according to the disclosure and teachings herein. Therefore, the application is not limited to the specific embodiments disclosed and described above, and some modifications and changes to the application shall fall within the protection scope of the claims of the application. In addition, although some specific terms are used in the specification, these terms are only for convenience of description and do not constitute any limitation on the application.

Claims

1. A data-driven robust model predictive control method for an underwater robot propulsion system, based on a nonlinear ARX model; the underwater robot propulsion system includes a thruster, a drive motor, an attitude sensor, a position sensor, and a controller; characterized in that, Includes the following steps: S1. Collect input and output data through the sensors of the underwater robot propulsion system to obtain the input and output time series dataset; based on the collected input and output time series dataset, construct a nonlinear ARX model as the nominal model of the underwater robot propulsion system; set the state output constraints, control input constraints and disturbance constraints of the underwater robot propulsion system. S2. Based on the constructed nonlinear ARX model, design the local control law and Lyapunov function; S3. Construct a robust model predictive control optimization problem and set the constraints for the optimization problem; S4. Solve the robust model predictive control optimization problem to obtain the optimal control law, and send the corresponding optimal control command to the underwater robot propulsion system. The control law is updated by rolling implementation.

2. The data-driven robust model predictive control method for an underwater robot propulsion system according to claim 1, characterized in that, In step S1, input and output data are collected by sensors in the underwater robot's propulsion system, wherein the input data... For the current / voltage of the drive motor; output data The data collection covers attitude angle and position deviations of underwater robots; the data collection scenarios include still water environments, water flow environments with different flow velocities, and different load conditions; and the data collection time series length meets the requirements for nonlinear ARX model identification.

3. The data-driven robust model predictive control method for an underwater robot propulsion system according to claim 2, characterized in that, Based on the collected input and output time series dataset, a data-driven identification algorithm is used to construct a nonlinear ARX model as the nominal model of the underwater robot propulsion system. The core characteristic of nonlinear ARX models is that the model input only includes historical input data and historical output data; the historical input data is: ； in, The input delay order is set based on the response speed of the underwater robot propulsion system. Historical output data is as follows: ； in, The output delay order is used, and the model output is the current predicted output value. System status data Constructed from historical input and output data: ; The nonlinear dynamic relationship of the underwater robot propulsion system satisfies: ； The output relationship satisfies: ； in, for The system state vector at any given time. for Control the input vector at all times. for Environmental disturbance vector at any given time. for Output vector at each time step For the output matrix, It is a nonlinear function.

4. The data-driven robust model predictive control method for an underwater robot propulsion system according to claim 3, characterized in that, In S1, constructing a nonlinear ARX model specifically includes: The time series set of collected input and output data is preprocessed to remove abnormal input and output values ​​caused by sensor failure, and the moving average method is used to filter measurement noise. The input delay order of the nonlinear ARX model is determined using the AIC information criterion. and output delay order This ensures that the model is neither underfitted nor overfitted. The structural parameters of the nonlinear ARX model are determined using a data-driven identification algorithm. Nonlinear ARX models need to accurately fit the key characteristics of the propulsion system: namely, the nonlinear relationship between the drive motor current and the attitude angle deviation and position deviation, to ensure that the model outputs accurate predictions.

5. The data-driven robust model predictive control method for an underwater robot propulsion system according to claim 3, characterized in that, Define the state output constraints, control input constraints, and disturbance constraints for the underwater robot's propulsion system. State output constraints, To control input constraints, For disturbance constraints; in, The set of attitude and position deviation constraints is set based on the accuracy requirements of underwater robot operations. The current / voltage constraint set for the drive motor is set based on the rated power of the thruster and the maximum overload capacity of the motor. The set of constraints for water flow disturbance is set based on historical water flow data of the operating sea area and the residual statistics of input and output data.

6. The data-driven robust model predictive control method for an underwater robot propulsion system according to claim 5, characterized in that, Specifically, S2 includes: Set level set initial parameters The equilibrium point of the underwater robot propulsion system is determined; at the equilibrium point, the constructed nonlinear ARX model is expanded using Taylor to obtain a linearized model. Design an LQR controller for the linearized model and select the state weight matrix. and control input weight matrix Solving the algebraic Riccati equation yields the positive definite matrix. and state feedback gain matrix Constructing local control laws and quadratic Lyapunov functions And it satisfies the constraints of Assumption 1; Among them, assumption 1 is: Existence of control law ,function and level set This makes it possible for all ,satisfy: It is a positive definite function, and it exists. Class function , satisfy: ;and: ， ； in, and for Class functions are used to describe Lyapunov functions. Positive definite properties, State vector A certain norm of is used to describe the positive definite properties of Lyapunov functions; That is, the motor current / voltage output by the local control law is within the constraint range. ; The expression for solving the algebraic Riccati equation is: ； in, For the state matrix of the linearized model, This is the input matrix for the linearized model.

7. The data-driven robust model predictive control method for an underwater robot propulsion system according to claim 6, characterized in that, In S3, based on assumptions 1 to 3, a robust model predictive control optimization problem is constructed that can guarantee the stability of the closed-loop system from input to state, specifically including: Construct a min-max robust optimal control problem including terminal costs, with the objective function as follows: ； in, It is the objective function of robust model predictive control. To predict the time domain, For the state-control cost function, Let be the disturbance cost function. For terminal costs, for The first time predicted Step state; The constraints of the optimization problem include state recursion constraints: ； in, for The robust optimal control input at time t, i.e., the solution to the optimization problem. for The worst-case perturbation at time step 1 is used for min-max robust optimization. Initial state constraints: ； And the state output constraints, control input constraints and disturbance constraints set by S1; for Robust optimal solution at all times.

8. The data-driven robust model predictive control method for an underwater robot propulsion system according to claim 7, characterized in that, Specifically, S4 includes: Solving the min-max robust optimal control problem yields the following results: Optimal control law at time: ； in, for Time based on prediction time domain The optimal control law; The corresponding optimal control command is sent to the drive motor of the underwater robot's propulsion system to adjust the thruster speed; in the next moment, new output data is collected through attitude sensors and position sensors. Combined with historical input data Update the state vector: ； The updated state vector is used as the initial state; S4 is executed again to realize the rolling update of the control law and adapt to the dynamic changes of the underwater environment.

9. The data-driven robust model predictive control method for an underwater robot propulsion system according to claim 8, characterized in that, The robust optimal control problem also satisfies assumptions 2 and 3; where assumption 2 is: exist Class function , , , so that the objective function satisfy: ， ； Assumption 3 is: There are positive numbers Satisfy all and ,have: ； in, A positive constant is used to constrain state overflow. The lower bound of the cost function at time t.

10. The data-driven robust model predictive control method for an underwater robot propulsion system according to claim 9, characterized in that, Define the level set of the optimal cost function: ； in The optimal cost function; When the system is in its initial state At that time, the closed-loop system has input-to-state stability, which meets the stability requirements of underwater robot operation.

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