Online data-driven rolling optimization control method and system for variable-mode system

Abstract

The invention discloses a rolling optimization control method and system for an online data-driven variable-mode system, and relates to the technical field of control of variable-mode systems. The invention aims to solve the problems that an existing data-driven variable-mode system control algorithm is preset to be capable of collecting sufficient data of each mode in an offline stage, neglects an unknown new mode possibly generated during online operation of an actual variable-mode system, and lacks constraint consideration. According to the technical key points, the dynamic change of the system can be captured in real time, the control law is correspondingly updated and optimized according to the dynamic change, an online mixed sampling excitation strategy is provided, and a semi-definite programming problem capable of designing a slow excitation controller online by using rapid sampling data is constructed. And the open-loop excitation time after the new mode is generated is effectively shortened. According to the method, unknown new modals possibly generated during online operation of an actual variable modal system and corresponding constraints are considered, the continuous solvability of optimization control and the asymptotic stability of a closed-loop system can be effectively guaranteed, and the optimization control law is updated in real time by exciting the unknown switching modals online; and the variable-mode rolling optimization control method with wider applicability is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of control of variable mode systems, and in particular to an online data-driven rolling optimization control method and system for variable mode systems. Background Art

[0002] As a special type of hybrid system, the variable modal system consists of several switching subsystems and a switching signal that runs through all subsystems. This type of dynamic system can effectively describe dynamic processes with structural / parameter mutations, so it has attracted widespread attention from academia and industry. However, for complex and large-scale variable modal processes or systems, the cost of modeling and parameter identification is high and often difficult to implement. To solve this problem, many data-based unknown switching system analysis and control methods have emerged in recent years, covering data-based open / closed loop characterization, switching controller design, and unified design of controller and switching law. These methods all assume that sufficient data of each mode can be collected in the offline stage. However, when the variable modal system is running online, new modes caused by system failures, unknown external loads, or sudden changes in the external environment often appear, and these new modes are often unknown. At present, there has been preliminary research on online data-driven variable modal system control methods. This method updates the control law online through real-time data to cope with new modes generated by the system. However, the above existing studies do not consider the system constraints that are commonly present in actual engineering, making it difficult to apply them in practice.

[0003] Rolling optimization control (also known as model predictive control) has been widely used in constrained variable modal systems because of its excellent ability to optimize performance and handle soft / hard constraints. Existing research can be divided into two categories: one is based on the minimum-maximum optimization control framework, and the feedback control law is obtained by repeatedly optimizing the performance upper bound of the infinite time domain. Although this method can ensure stability and continuous feasibility, it is often too conservative; the other is to obtain the control law by optimizing the performance indicators related to the current mode. This method uses set theory analysis to give the residence time conditions that ensure stability and continuous feasibility. However, the above studies are all based on the premise of accurate state space models of all subsystems. Given the difficulty of obtaining accurate models for complex variable modal systems, it is particularly important to develop data-driven rolling optimization control methods for variable modal systems.

[0004] It is worth noting that the latest progress in behavioral system theory has promoted the development of direct data-driven rolling optimal control methods for linear time-invariant systems. This type of method makes full use of the Hankel matrix composed of offline measurement trajectories with continuous excitation input, so that the prediction model in traditional rolling optimal control is replaced by data form. If this method is extended to variable mode systems with online generated modes, it is necessary to use the real-time excitation data of the current mode to update the Hankel matrix and terminal components online. The direct method is to inject a finite length open-loop continuous excitation input sequence into the current subsystem, but this method puts the system in an open-loop state for a long time, which may cause excessive growth of the state trajectory or even constraint violation. Another attempt is to use an asynchronous optimal control law or an optimal control law that gradually updates the Hankel matrix to achieve closed-loop excitation, but the mismatch between the prediction model and the current mode may lead to performance degradation and even destroy the stability guarantee and feasibility of rolling optimal control. Therefore, it is urgent to design an effective method that can not only obtain valid data online, but also improve control performance and reduce the risk of constraint violation.

[0005] The prior art with document number CN119356086A provides an anti-shake model predictive control method and system for a variable mode system, which solves the problem that the traditional anti-shake variable mode control algorithm is difficult to balance the anti-shake control performance and the stabilization control performance, resulting in problems in the stabilization control performance of the control system, such as a significant decrease in convergence speed and a sharp increase in overshoot. It includes establishing a variable mode control system model and designing a cost function, designing linear inequality conditions on stability based on the stability criterion of the variable mode system of the average residence time and the multi-Lyapunov function method and calculating the cost upper limit, designing linear inequality conditions that meet the system constraints and calculating the system control performance cost upper limit, and finally obtaining the multi-modal state feedback control gain according to the designed rolling time domain optimization algorithm and acting on the control system. However, the prior art does not mention how to obtain effective data online and improve control performance and reduce the risk of constraint violation.

[0006] Therefore, the traditional variable modal rolling optimization control algorithm is heavily dependent on the accurate state space model of all subsystems. For complex and large-scale variable modal systems, the computational cost required for system modeling and parameter identification is high, which greatly increases the hardware cost of the control system. The existing data-driven variable modal system control algorithms all assume that sufficient data of each mode can be collected in the offline stage, ignoring the unknown new modes that may be generated when the actual variable modal system is running online, and lack of constraint consideration. Therefore, it is particularly important to propose an innovative online data-driven variable modal system rolling optimization control method, which realizes a more widely applicable variable modal rolling optimization control method by online excitation of unknown switching modes to update the optimization control law in real time. Summary of the invention

[0007] The technical problem to be solved by the present invention is

[0008] In order to solve the existing data-driven variable mode system control algorithms, the present invention assumes that sufficient data of each mode can be collected in the offline stage, ignoring the unknown new modes that may be generated when the actual variable mode system is running online, and lacks constraint consideration. In response to these problems, the present invention proposes an online data-driven variable mode system rolling optimization control method.

[0009] The technical solution adopted by the present invention to solve the above technical problems is:

[0010] A rolling optimization control method for a variable mode system based on online data drive, comprising:

[0011] Step 1: Introduce a variable mode control system, define the system state quantity and input quantity, establish system hard constraints, design a cost function, and collect input-state data under the initial mode offline. The main process is: First, describe the system as a variable mode system composed of multiple sub-modes and variable mode signals, and define the state quantity and input quantity based on the actual scenario. Then, according to the system characteristics and control requirements, set the hard constraints of the state quantity and control input. In addition, based on the control objective, construct a reasonable cost function. Finally, through experimental means, collect sufficiently long input-state data under the initial mode offline.

[0012] Step 2: Design a data-driven rolling optimization control algorithm online. The main process is: first, build a data-driven prediction model based on the input-state trajectory of the current subsystem; then, solve the terminal cost and terminal constraints through semi-definite programming optimization problems to form a rolling horizon optimization framework.

[0013] Step 3: Execute the rolling optimization control strategy and real-time monitoring. The main process is: select a suitable solver to solve the optimization problem, obtain the control input and act on the controlled object. In addition, a mode switching monitor is designed based on the behavioral system theory to monitor the predicted state quantity and the actual state quantity in real time, and trigger the online incentive mechanism when the system mode switches.

[0014] Step 4: Design and execute the hybrid sampling excitation strategy online. The main process is: First, when the switching monitor detects the system mode switching, increase the system sampling frequency, design the continuous excitation control input sequence, and quickly open-loop excite the unknown subsystem to obtain system behavior information. Secondly, based on the fast sampling system trajectory, design a data-driven controller that meets the system constraints and ensures system stability. Then, restore the system sampling frequency to be consistent with the optimization control frequency, and implement closed-loop continuous excitation for the unknown subsystem. Finally, after collecting sufficiently long input-state data, return to step 2, update the prediction model and continue the rolling optimization control process.

[0015] Next, the method is specifically implemented as follows:

[0016] Step 1: Introduce a variable mode control system, define the system state and input quantities, establish system hard constraints, design a cost function, and collect input-state data under the initial mode offline:

[0017] First, the system model obtained by discretizing the satellite platform under the solar panel array expansion mission with a constant sampling period h is described as the following discrete variable mode linear system:

[0018] Σ σ(k) :x(k+1)=A σ(k) x(k)+B σ(k) u(k) (1)

[0019] in Indicates the system status, that is, the satellite platform attitude angular velocity and attitude angle. The attitude angle includes the roll angle φ, the pitch angle θ and the yaw angle ψ, and the angular velocity corresponds to it; Represents the system input, i.e., the satellite platform control torque T cx , T cy and T cz , T cx , T cy and T cz Respectively represent the three-axis control torque; n x and n u They represent the dimensions of state quantity and input quantity respectively, and the dimensions corresponding to x(k)u(k); k is the sampling time; the satellite moment of inertia changes under the solar panel array expansion mission, and the corresponding satellite platform system model presents M sub-modes; the switching signal σ(k) represents the piecewise constant function of the sub-mode of the satellite platform that changes with time k and is right continuous, and its value is taken from the finite set {1,2,…,M}; k j represents the jth switching time and k 0 = 0; define the time interval from the s-1th switching moment to the sth switching moment as the sth switching stage, where s ≥ 1; the matrix pair {A i ,B i} represents the system matrix of the i-th satellite platform subsystem; in this mission scenario, the satellite platform system matrix and switching time are unknown, and only input-state data can be used;

[0020] According to the physical characteristics and safety considerations of the satellite platform itself, the hard constraints of the state quantity and control input (i.e. the allowable range of attitude angular velocity / attitude angle and the allowable range of control torque) are defined as follows:

[0021]

[0022]

[0023] in and are the hard constraint gain matrices of the state variables and control inputs, respectively, where and is the upper limit of state and control constraints, c x With c u Represents the number of constraints on state quantity and input quantity respectively;

[0024] The unknown system dynamic characteristics are obtained through the measured input-state trajectory, and the concept of continuous excitation is introduced;

[0025] Definition: A sequence z of length N [0,N-1] Among them for m is the dimension of the sequence; the sequence is L-order continuously excited if the Hankel matrix of the sequence is full rank:

[0026]

[0027] The prediction model of the subsystem can be represented by the Hankel matrix composed of the collected input-state data; specifically, {u [0,L-1] ,x [0,L]} is an arbitrary L-length input-state trajectory of the subsystem with x(0) as the initial state if and only if there exists a vector Make

[0028]

[0029] in, is an N-length input-state trajectory of the subsystem, and the control input sequence is L-order continuous excitation; in order to meet the full rank condition of continuous excitation, the implementation of rolling optimization control with L-step prediction horizon for variable mode systems requires online collection of N-length input-state data under each sub-mode, and the data length must satisfy N ≥ (n x +L)(n u +1)-1; the data collected in the sth switching stage is expressed as The input sequence is continuously stimulated;

[0030] In order to ensure the stability of the system, the system cost function of the sth switching stage is established as follows:

[0031]

[0032] in; and They are respectively the input and state quantities at time k+n predicted at time k; represents the stage cost and is defined as in and are the weight coefficients of attitude angle and input torque respectively; L represents the number of prediction time domain steps; is the terminal cost of the sth switching stage to be designed;

[0033] Finally, the N-length input-state data under the initial mode obtained through the experiment is expressed as

[0034] Step 2: Using the collected data in the current mode, design a data-driven rolling optimization control algorithm online:

[0035] First, we introduce the quadratic terminal cost in Represents the terminal cost weight matrix; and introduces the terminal constraint set in the form of an ellipsoid, which is expressed as follows:

[0036]

[0037] where γ s is the upper bound of the terminal cost;

[0038] The online update method of the terminal component is to ensure the recursive feasibility of the rolling optimization control and the stability of the closed-loop system:

[0039] Solving the following semidefinite programming optimization problem can obtain the terminal cost weight matrix

[0040]

[0041] in and Represent the first-order Hankel matrices of the slow sampling system state and input trajectory respectively, and define the terminal control gain as The symbol * indicates that the term is omitted due to symmetric matrix; I indicates the identity matrix; F s is the process variable in the optimization problem;

[0042] According to the solution of optimization problem (8), the upper bound of the terminal cost can be obtained by solving the following semidefinite programming optimization problem:

[0043]

[0044] On this basis, the online data-driven rolling optimization control problem in the sth switching stage can be expressed as follows:

[0045]

[0046] Where α is the decision variable, is the optimal system cost;

[0047] Step 3: Execute the rolling optimization control strategy and monitor the system status in real time through the variable mode system switching monitor;

[0048] The Yalmip toolbox and Sdpt3 solver are selected to solve the optimization problem. At each sampling time, the semidefinite programming optimization problem shown in equation (10) is solved to obtain the optimal control sequence: where α * The optimal solution found by the optimizer; the first element Act on the controlled object;

[0049] If the predicted state If it is inconsistent with the current actual state quantity x(k), it means that the prediction model does not match the current subsystem. Therefore, by comparing the predicted state quantity with the actual state quantity in real time, it is possible to monitor whether the system has mode switching. The moment when the system switches is observed is expressed as Taking into account the numerical calculation errors existing in actual engineering, the switching moment can be obtained through the following mode switching monitor:

[0050]

[0051] When s = 0 e r Relative error bounds for numerical optimization methods;

[0052] Step 4: Design and execute the mixed sampling incentive strategy online, and return to step 2 after the incentive is completed.

[0053] First, when the mode switching monitor detects that the system has switched, the sampling period is reduced to h f , and a segment N f The long continuous excitation control input sequence is injected into the current subsystem; the fast sampling discrete linear system associated with the sth switching stage can be expressed as:

[0054]

[0055] in represents the system state under fast sampling (i.e. the satellite platform attitude angular velocity and attitude angle under fast sampling), represents the system input under fast sampling (i.e., the satellite platform control torque under fast sampling), is the sampling time, the matrix represents the fast sampling system matrix of the i-th satellite platform subsystem; to prevent switching from occurring within the sampling interval, it is necessary to ensure that there is a positive integer v such that h = vh f, where v is the multiple of the sampling frequency increase; to ensure that the collected data can sufficiently characterize the system characteristics, the fast sampling data length must meet N f ≥(n u +1)n x +n u ;

[0056] On this basis, the high-frequency continuous excitation control input is designed as

[0057]

[0058] in is to randomly generate an arbitrary vector at time k′ to ensure continuous excitation conditions, ∈′ is the upper bound of the infinite norm of the given random vector; in this way, the current subsystem data obtained by fast excitation in the sth switching stage is expressed as

[0059] Secondly, the system sampling frequency is restored to be consistent with the optimized control frequency, and the following closed-loop slow excitation controller is given:

[0060]

[0061] in is the controller gain to be designed, It is to randomly generate an arbitrary vector at time k to ensure that the closed-loop control input meets the continuous excitation condition, ∈s is the upper bound of the infinite norm of the given random vector;

[0062] Then, the controller gain is designed using the fast sampling data of the sth switching stage The slow excitation controller can ensure the stability of the slow sampling system and the satisfaction of the constraints as shown in equation (1);

[0063] For the sth switching stage of the variable mode system, consider the fast sampling subsystem and the input-state trajectory generated by it as shown in equation (12): The control input sequence is continuously excited, and the fast sampling frequency is v times the slow sampling frequency; given the controller design parameters gather Is a collection With Collection Pontrya gold difference, among which represents the infinite norm upper bound of the random vector attached by the controller; if there exists a matrix {P s >0,S s >0,W s ,G s ,Z s} makes the following optimization problem solvable:

[0064]

[0065] in and represent the fast sampling system state and input trajectory Hankel matrices respectively; and Represents algorithm process variables; represents the system closed-loop matrix; Represents the concatenation matrix of the identity matrix and the zero matrix; represents the concatenation matrix of the identity matrix and the negative identity matrix; then the slow excitation controller shown in (14) can ensure that the closed-loop slow sampling system is stable and satisfies the constraints, and its control gain is

[0066] {P s >0,S s >0,W s ,G s ,Z s} are all algorithm decision variables, and their introduction purpose is to determine whether there is a controller that meets the control requirements. s It is used to calculate controller gain;

[0067] Finally, the slow excitation controller shown in (14) is obtained by solving the optimization problem (15) and executing this controller for N steps. Accordingly, the collected N-step input-state data is expressed as And return to step 2, update the prediction model and continue the rolling optimization control process.

[0068] The control method is used to perform attitude control on a satellite platform. The variable mode system refers to a satellite platform that performs a solar panel array expansion task. The solar panels deployed on the platform gradually expand, causing its rotational inertia to change, thereby causing the platform to exhibit variable mode characteristics.

[0069] A rolling optimization control system for a variable mode system based on online data drive, the system has a program module corresponding to the steps of the above technical solution, and executes the steps of the rolling optimization control method for a variable mode system based on online data drive during operation.

[0070] A computer-readable storage medium stores a computer program, wherein the computer program is configured to implement the steps of a rolling optimization control method for a variable mode system based on online data drive when called by a processor.

[0071] The present invention has the following beneficial technical effects:

[0072] The present invention is a switching optimization control method of switching mode monitoring-online excitation-updating data model mode for variable mode systems that may generate unknown new modes during online operation. The present invention effectively shortens the open-loop excitation time after the new mode is generated by introducing a mixed sampling excitation strategy. The control method of the present invention can effectively ensure the continuous solvability of the optimization control and the asymptotic stability of the closed-loop system. The research results of the present invention are of great significance in promoting the development of variable mode system control theory and promoting the practical application of data-driven variable mode rolling optimization control theory. The present invention takes into account the unknown new modes and corresponding constraints that may be generated when the actual variable mode system is running online. The present invention innovatively proposes an online data-driven variable mode system rolling optimization control method, which realizes a more widely applicable variable mode rolling optimization control method by online stimulating unknown switching modes to update the optimization control law in real time.

[0073] Aiming at the problem of optimizing control of variable mode systems that may generate new modes online, the present invention proposes an online data-driven variable mode system optimization control algorithm that integrates switching mode monitoring, online data excitation, and rolling optimization control. The specific advantages are as follows: ① Considering the unknown new modes that may be generated when the variable mode system is running online, an end-to-end online data-driven rolling optimization control method is established. This method can capture the dynamic changes of the system in real time and update the optimization control law accordingly, without relying on any system identification steps in the whole process. On the premise of ensuring that various constraints are met, this method guarantees the recursive feasibility of rolling optimization and the stability of the closed-loop system from a theoretical level. ② In order to shorten the inevitable data deficiency stage in the excitation process and reduce the risk of violating constraints, this patent proposes an innovative online hybrid sampling excitation strategy. At the same time, a semi-definite programming problem that can use fast sampling data to design a slow excitation controller online is constructed. This strategy ensures that sufficient continuous excitation data can be collected while the constraints are met, thereby realizing online updating of the optimization control law.

[0074] In summary, the present invention proposes an innovative online data-driven variable modal rolling optimization control method to address the defects of the existing variable modal rolling optimization control, which is over-reliant on precise models and the inability of the existing data-driven variable modal system control to cope with the online generation of new modes. This method directly designs the control strategy through online data in an end-to-end manner without any modeling or system identification steps. After the new mode is generated, the method can achieve closed-loop control that guarantees system constraints with a short open-loop excitation. The method proposed in the present invention not only broadens the application objects and scope of application of such methods, but also shows good engineering application value, and provides new ideas and methods for the development of control theory and practical application of variable modal systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The accompanying drawings are used to provide a further understanding of this patent and constitute a part of the specification. They are used together with the embodiments of this patent to explain the invention and do not constitute a limitation of this patent. In the accompanying drawings:

[0076] Figure 1 It is a flow chart of an online data-driven variable mode system rolling optimization control method;

[0077] Figure 2 Satellite mode switching signal diagram used in simulation experiments;

[0078] Figure 3 is the control input torque curve of the satellite platform under the action of the proposed controller;

[0079] Figure 4 It is the attitude angle response curve of the satellite platform under the action of the proposed controller;

[0080] Figure 5 This is the attitude angular velocity response curve of the satellite platform under the action of the proposed controller. DETAILED DESCRIPTION

[0081] Specific implementation method 1: For the implementation process of an online data-driven variable mode system rolling optimization control method described in the present invention, combined with the attached Figure 1-5 The following is explained:

[0082] Step 1: Introduce a variable mode control system, define the system state and input quantities, establish system hard constraints, design a cost function, and collect input-state data under the initial mode offline.

[0083] First, the system model obtained by discretizing the satellite platform under the solar panel array expansion mission with a constant sampling period h is described as the following discrete variable mode linear system:

[0084] Σ σ(k) :x(k+1)=A σ(k) x(k)+B σ(k) u(k) (1)

[0085] in Indicates the system status (i.e., the satellite platform attitude angular velocity and attitude angle), represents the system input (i.e., satellite platform control torque), n x and n u Respectively represent the state quantity and input quantity dimension, k is the sampling time; under the solar panel array expansion mission, the satellite moment of inertia changes in M ​​kinds of changes, corresponding to the satellite platform system model presents M sub-modes. The switching signal σ(k) represents the piecewise constant function of the sub-mode of the satellite platform that changes with time k and is right continuous, and it takes values ​​from the finite set {1,2,…,M}; kj represents the jth switching time and k 0 = 0; define the time interval from the s-1th switching moment to the sth switching moment as the sth switching stage, where s ≥ 1; the matrix pair {A i ,B i} represents the system matrix of the i-th satellite platform subsystem; in this mission scenario, the satellite platform system matrix and switching time are unknown, and only the input-state data can be used.

[0086] According to the physical characteristics and safety considerations of the satellite platform itself, the hard constraints of the state quantity and control input (i.e. the allowable range of attitude angular velocity / attitude angle and the allowable range of control torque) are defined as follows:

[0087]

[0088] in and are the hard constraint gain matrices of the state variables and control inputs, respectively, where and is the upper limit of state and control constraints, c x With c u Represents the number of constraints on state quantity and input quantity respectively;

[0089]

[0090] in and are the hard constraint gain matrices of the state variables and control inputs, respectively, where and is the upper limit of state and control constraints, c x With c u Represent the number of constraints on state quantities and input quantities respectively.

[0091] In this application, the concept of continuous excitation is introduced to obtain the unknown system dynamic characteristics through the measured input-state trajectory.

[0092] Definition 1: Consider a sequence z of length N [0,N-1] Among them for The sequence is called L-order continuously excited if the Hankel matrix of the sequence is full row rank:

[0093]

[0094] According to the basic lemma of behavioral system theory, the prediction model of the subsystem can be represented by the Hankel matrix composed of the collected input-state data. Specifically, {u [0,L-1] ,x [0,L]} is an arbitrary L-length input-state trajectory of the subsystem with x(0) as the initial state if and only if there exists a vector Make

[0095]

[0096] in, is an N-length input-state trajectory of the subsystem, and the control input sequence is an L-order continuous excitation. In order to meet the full rank condition of continuous excitation, the implementation of rolling optimization control with L-step prediction horizon for variable mode systems requires online collection of N-length input-state data under each sub-mode, and the data length must satisfy N ≥ (n x +L)(n u +1)-1. The data collected in the sth switching stage is expressed as The input sequence is continuously stimulated.

[0097] In addition, to ensure the stability of the system, the system cost function of the sth switching stage is established as follows:

[0098]

[0099] in; and They are respectively the input and state quantities at time k+n predicted at time k; represents the stage cost and is defined as in and are weight coefficients respectively; L represents the number of prediction time domain steps; is the terminal cost of the sth switching stage to be designed.

[0100] Finally, the N-length input-state data under the initial mode obtained through the experiment is expressed as

[0101] Step 2: Using the collected data under the current mode, design a data-driven rolling optimization control algorithm online.

[0102] In this step, we first introduce the quadratic terminal cost in Represents the terminal cost weight matrix. And introduces the terminal constraint set in the form of an ellipsoid, which is expressed as follows:

[0103]

[0104] where γ s is the upper bound of the terminal cost.

[0105] The online updating method of the terminal components is given below to ensure the recursive feasibility of the rolling optimization control and the stability of the closed-loop system.

[0106] Solving the following semidefinite programming optimization problem can obtain the terminal cost weight matrix

[0107]

[0108] in and Represent the first-order Hankel matrices of the slow sampling system state and input trajectory respectively, and define the terminal control gain as The symbol * indicates the omitted term due to the symmetric matrix. According to the solution of the optimization problem (8), the upper bound of the terminal cost can be obtained by solving the following semidefinite programming optimization problem:

[0109]

[0110] On this basis, the online data-driven rolling optimization control problem of the sth switching stage can be expressed as follows:

[0111]

[0112] Where α is the decision variable, is the optimal system cost.

[0113] Step 3: Execute the rolling optimization control strategy and monitor the system status in real time through the variable mode system switching monitor.

[0114] In this embodiment, the Yalmip toolbox and the Sdpt3 solver are selected to solve the optimization problem. At each sampling time, the semidefinite programming optimization problem shown in formula (10) is solved to obtain the optimized control sequence where α * is the optimal solution found by the optimizer. Act on the controlled object.

[0115] According to the basic lemma of behavioral system theory, if the predicted state quantity If it is inconsistent with the current actual state quantity x(k), it means that the prediction model does not match the current subsystem. Therefore, by comparing the predicted state quantity with the actual state quantity in real time, it is possible to monitor whether the system has mode switching. The moment when the system switches is expressed as Taking into account the numerical calculation errors existing in actual engineering, the switching moment can be obtained through the following mode switching monitor:

[0116]

[0117] When s = 0 er Represents the relative error bound of the numerical optimization method.

[0118] Step 4: Design and execute the mixed sampling incentive strategy online, and return to step 2 after the incentive is completed.

[0119] First, when the mode switching monitor detects that the system has switched, the sampling period is reduced to h f , and a segment N f The long continuous excitation control input sequence is injected into the current subsystem. The fast sampling discrete linear system related to the sth switching stage can be expressed as:

[0120]

[0121] in represents the system state under fast sampling (i.e. the satellite platform attitude angular velocity and attitude angle under fast sampling), represents the system input under fast sampling (i.e., the satellite platform control torque under fast sampling), is the sampling time, the matrix represents the fast sampling system matrix of the i-th satellite platform subsystem. To prevent switching from occurring within the sampling interval, it is necessary to ensure that there is a positive integer v such that h = vh f , where v is the multiple of the sampling frequency increase. To ensure that the collected data can adequately characterize the system characteristics, the fast sampling data length must meet N f ≥(n u +1)n x +n u .

[0122] On this basis, the high-frequency continuous excitation control input is designed as

[0123]

[0124] in is to randomly generate an arbitrary vector at time k′ to ensure continuous excitation conditions, and ∈′ is the upper bound of the infinite norm of the given random vector. In this way, the current subsystem data obtained by fast excitation in the sth switching stage is expressed as

[0125] Secondly, the system sampling frequency is restored to be consistent with the optimized control frequency, and the following closed-loop slow excitation controller is given:

[0126]

[0127] in is the controller gain to be designed, It is to randomly generate an arbitrary vector at time k to ensure that the closed-loop control input meets the continuous excitation condition, and ∈ is the upper bound of the infinite norm of the given random vector.

[0128] Then, the controller gain is designed using the fast sampling data of the sth switching stage The slow excitation controller can ensure the stability of the slow sampling system and the satisfaction of the constraints as shown in equation (1).

[0129] Theorem 1: For the sth switching stage of the variable mode system, consider the fast sampling subsystem and the input-state trajectory generated by it as shown in equation (12): The control input sequence is continuously excited and the fast sampling frequency is v times the slow sampling frequency. Given the controller design parameters gather Is a collection With Collection Pontrya gold difference, among which represents the infinite norm upper bound of the random vector attached by the controller. If there exists a matrix {P s >0,S s >0,W s ,G s ,Z s} makes the following optimization problem solvable:

[0130]

[0131] in and represent the fast sampling system state and input trajectory Hankel matrices respectively; and Represents algorithm process variables; represents the system closed-loop matrix; Represents the concatenation matrix of the identity matrix and the zero matrix; represents the concatenation matrix of the identity matrix and the negative identity matrix. Then the slow excitation controller shown in (14) can ensure the stability of the closed-loop slow sampling system and satisfy the constraints, and its control gain is

[0132] Finally, the slow excitation controller shown in (14) is obtained by solving the optimization problem (15) and executing this controller for N steps. Accordingly, the collected N-step input-state data is expressed as And return to step 2. Specific implementation method 2:

[0134] In this embodiment, a satellite platform performing a solar panel array expansion mission is controlled.

[0135] Based on step 1, the dynamic characteristics of the control system can be described by the following linearized variable modal system model:

[0136]

[0137] Where φ, θ and ψ represent the roll angle, pitch angle and yaw angle respectively (corresponding to the angles along the X, Y and Z axes respectively); T cx , T cy and T cz Respectively represent the three-axis (X, Y, Z axis) control torque; ω 0 =0.0011rad / is the orbital angular velocity; Represents the satellite's moment of inertia, which has the characteristic of piecewise constant. The change process is as follows:

[0138]

[0139] The numbers in the superscript represent the sub-mode numbers of the system. Note that the system model and parameters are actually completely unknown. They are given here only for the purpose of illustration. Only input quantities and state quantities can be used in the online process. The system variables are defined as The control input quantity is defined as In addition, the maximum attitude angle, maximum angular velocity, and maximum control input are set to 15 degrees, 2.25 degrees per second, and 1 Newton meter, respectively. The prediction time domain is L = 5, and the weight matrix in the cost function is set to and The initial state of the system is φ = 5 degrees, θ = 3 degrees, ψ = 6 degrees and The initial modal trajectory is generated offline by N-length continuous excitation input.

[0140] The slow sampling frequency and the fast sampling frequency are set to h = 0.1s and h respectively. f =0.02s. Accordingly, the slow sampling data length and the fast sampling data length are set to N=43 and N f =30. The design parameters in the incentive strategy are set as ε=0.99, ′=10 -3 and Control is performed according to the rolling optimization control algorithm, switching monitor and variable sampling excitation strategy given in step 2, step 3 and step 4. Figure 2 The variable mode switching signal used in this embodiment is shown in the simulation results. The control input curve, attitude angle response curve, and attitude angular velocity response curve under the action of the proposed variable mode system rolling optimization controller are recorded, as shown in FIG. Figure 3 , Figure 4 and Figure 5As shown in the figure, it can be seen that the proposed algorithm can effectively stabilize the variable mode system that generates new modes during online operation and can meet the constraints. The simulation results verify the effectiveness of the method described in the patent.

[0141] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this application can be executed in parallel, sequentially or in different orders, as long as the expected results of the technical solution disclosed in this application can be achieved, they are all within the scope of protection of the present invention.

Claims

1. A rolling optimization control method for a variable mode system based on online data drive, wherein the control method is used to perform attitude control on a satellite platform, and the method comprises the following steps: Step 1: Introduce the variable mode control system, define the system state quantity and input quantity and establish the system hard constraints, design the cost function, and collect the input-state data under the initial mode offline; The system is described as a variable mode system composed of multiple sub-modes and variable mode signals, and the state quantity and input quantity are defined based on the actual scenario; then, hard constraints on the state quantity and control input are set according to the system characteristics and control requirements; a reasonable cost function is constructed based on the control objective; finally, sufficiently long input-state data under the initial mode is collected offline through experimental means; Step 2: Using the collected data under the current mode, design a data-driven rolling optimization control algorithm online; First, a data-driven prediction model is constructed based on the input-state trajectory of the current subsystem. Then, the terminal cost and terminal constraint are solved through the semidefinite programming optimization problem to form a rolling horizon optimization framework. Step 3: Execute the rolling optimization control strategy and monitor the system status in real time through the variable mode system switching monitor; Select a suitable solver to solve the optimization problem, obtain the control input and act on the controlled object; in addition, design a mode switching monitor based on behavioral system theory to monitor the predicted state quantity and the actual state quantity in real time, and trigger the online incentive mechanism when the system mode switches; Step 4: Design and execute the mixed sampling excitation strategy online. After the excitation is completed, return to step 2 and proceed to the next stage of rolling optimization control.

2. According to the method for rolling optimization control of a variable mode system based on online data drive according to claim 1, the basic feature is that the specific implementation process of step 4 is: First, when the switching monitor detects the system mode switching, the system sampling frequency is increased, the continuous excitation control input sequence is designed, and the unknown subsystem is quickly open-loop excited to obtain system behavior information; secondly, based on the fast sampling system trajectory, a data-driven controller that meets the system constraints and ensures system stability is designed; then, the system sampling frequency is restored to be consistent with the optimization control frequency, and the unknown subsystem is subjected to closed-loop continuous excitation; finally, after collecting sufficiently long input-state data, return to step 2, update the prediction model and continue the rolling optimization control process.

3. According to the rolling optimization control method of a variable mode system based on online data drive according to claim 1 or 2, the basic feature is that the specific implementation process of the method is: Step 1: Introduce a variable mode control system, define the system state and input quantities, establish system hard constraints, design a cost function, and collect input-state data under the initial mode offline: First, the system model obtained by discretizing the satellite platform under the solar panel array expansion mission with a constant sampling period h is described as the following discrete variable mode linear system: Σ σ(k) :x(k+1)=A σ(k) x(k)+B σ(k) u(k) (1) in Indicates the system status, that is, the satellite platform attitude angular velocity and attitude angle. The attitude angle includes the roll angle φ, the pitch angle θ and the yaw angle ψ, and the angular velocity corresponds to it; Represents the system input, i.e., the satellite platform control torque T cx , T cy and T cz , T cx , T cy and T cz Respectively represent the three-axis control torque; n x and n u They represent the dimensions of state quantity and input quantity respectively, and the dimensions corresponding to x(k)u(k); k is the sampling time; the satellite moment of inertia changes under the solar panel array expansion mission, and the corresponding satellite platform system model presents M sub-modes; the switching signal σ(k) represents the piecewise constant function of the sub-mode of the satellite platform that changes with time k and is right continuous, and its value is taken from the finite set {1,2,…,M}; k j represents the jth switching moment and k0=0; the time interval from the s-1th switching moment to the sth switching moment is defined as the sth switching stage, where s≥1; the matrix pair {A i ,B i } represents the system matrix of the i-th satellite platform subsystem; in this mission scenario, the satellite platform system matrix and switching time are unknown, and only input-state data can be used; According to the physical characteristics of the satellite platform and safety considerations, the hard constraints of the state quantity and control input (i.e. the allowable range of attitude angular velocity / attitude angle and the allowable range of control torque) are defined as follows: in and are the hard constraint gain matrices of the state variables and control inputs, respectively, where and is the upper limit of state and control constraints, c x With c u Represents the number of constraints on state quantity and input quantity respectively; The unknown system dynamic characteristics are obtained through the measured input-state trajectory, and the concept of continuous excitation is introduced; Definition: A sequence z of length N [0,N-1] Among them for m is the dimension of the sequence; the sequence is L-order continuous excitation if the Hankel matrix of the sequence is full rank: The prediction model of the subsystem can be represented by the Hankel matrix composed of the collected input-state data; specifically, {u [0,L-1] ,x [0,L] } is an arbitrary L-length input-state trajectory of the subsystem with x(0) as the initial state if and only if there exists a vector Make in, is an N-length input-state trajectory of the subsystem, and the control input sequence is L-order continuous excitation; in order to meet the full rank condition of continuous excitation, the implementation of rolling optimization control with L-step prediction horizon for variable mode systems requires online collection of N-length input-state data under each sub-mode, and the data length must satisfy N ≥ (n x +L)(n u +1)-1; the data collected in the sth switching stage is expressed as The input sequence is continuously stimulated; In order to ensure the stability of the system, the system cost function of the sth switching stage is established as follows: in; and They are respectively the input and state quantities at time k+n predicted at time k; represents the stage cost and is defined as in and are the weight coefficients of attitude angle and input torque respectively; L represents the number of prediction time domain steps; is the terminal cost of the sth switching stage to be designed; Finally, the N-length input-state data under the initial mode obtained through the experiment is expressed as Step 2: Using the collected data in the current mode, design a data-driven rolling optimization control algorithm online: First, we introduce the quadratic terminal cost in Represents the terminal cost weight matrix; and introduces the terminal constraint set in the form of an ellipsoid, which is expressed as follows: where γ s is the upper bound of the terminal cost; The online update method of the terminal component is to ensure the recursive feasibility of the rolling optimization control and the stability of the closed-loop system: Solving the following semidefinite programming optimization problem can obtain the terminal cost weight matrix in and Represent the first-order Hankel matrices of the slow sampling system state and input trajectory respectively, and define the terminal control gain as The symbol * indicates that the term is omitted due to symmetric matrix; I indicates the identity matrix; F s is the process variable in the optimization problem; According to the solution of optimization problem (8), the upper bound of the terminal cost can be obtained by solving the following semidefinite programming optimization problem: On this basis, the online data-driven rolling optimization control problem in the sth switching stage can be expressed as follows: Where α is the decision variable, is the optimal system cost; Step 3: Execute the rolling optimization control strategy and monitor the system status in real time through the variable mode system switching monitor; The Yalmip toolbox and Sdpt3 solver are selected to solve the optimization problem. At each sampling time, the semidefinite programming optimization problem shown in equation (10) is solved to obtain the optimal control sequence: where α * The optimal solution found by the optimizer; the first element Act on the controlled object; If the predicted state If it is inconsistent with the current actual state quantity x(k), it means that the prediction model does not match the current subsystem. Therefore, by comparing the predicted state quantity with the actual state quantity in real time, it is possible to monitor whether the system has mode switching. The moment when the system switches is observed is expressed as Taking into account the numerical calculation errors existing in actual engineering, the switching moment can be obtained through the following mode switching monitor: When s = 0 e r Relative error bounds for numerical optimization methods; Step 4: Design and execute the mixed sampling incentive strategy online, and return to step 2 after the incentive is completed. First, when the mode switching monitor detects that the system has switched, the sampling period is reduced to h f , and a segment N f The long continuous excitation control input sequence is injected into the current subsystem; the fast sampling discrete linear system associated with the sth switching stage can be expressed as: in represents the system state under fast sampling (i.e. the satellite platform attitude angular velocity and attitude angle under fast sampling), represents the system input under fast sampling (i.e., the satellite platform control torque under fast sampling), is the sampling time, the matrix represents the fast sampling system matrix of the i-th satellite platform subsystem; to prevent switching from occurring within the sampling interval, it is necessary to ensure that there is a positive integer v such that h = vh f , where v is the multiple of the sampling frequency increase; to ensure that the collected data can adequately characterize the system characteristics, the fast sampling data length must meet N f ≥(n u +1)n x +n u ; On this basis, the high-frequency continuous excitation control input is designed as in is to randomly generate an arbitrary vector at time k′ to ensure continuous excitation conditions, ∈′ is the upper bound of the infinite norm of the given random vector; in this way, the current subsystem data obtained by fast excitation in the sth switching stage is expressed as Secondly, the system sampling frequency is restored to be consistent with the optimized control frequency, and the following closed-loop slow excitation controller is given: in is the controller gain to be designed, It is to randomly generate an arbitrary vector at time k to ensure that the closed-loop control input meets the continuous excitation condition, ∈ s is the upper bound of the infinite norm of a given random vector; Then, the controller gain is designed using the fast sampling data of the sth switching stage The slow excitation controller can ensure the stability of the slow sampling system and the satisfaction of the constraints as shown in equation (1); For the sth switching stage of the variable mode system, consider the fast sampling subsystem and the input-state trajectory generated by it as shown in equation (12): The control input sequence is continuously excited, and the fast sampling frequency is v times the slow sampling frequency; given the controller design parameters gather Is a collection With Collection Pontrya gold difference, among which represents the infinite norm upper bound of the random vector attached by the controller; if there exists a matrix {P s >0,S s >0,W s ,G s ,Z s } makes the following optimization problem solvable: in and represent the fast sampling system state and input trajectory Hankel matrices respectively; and Represents algorithm process variables; represents the system closed-loop matrix; Represents the concatenation matrix of the identity matrix and the zero matrix; represents the concatenation matrix of the identity matrix and the negative identity matrix; then the slow excitation controller shown in (14) can ensure that the closed-loop slow sampling system is stable and satisfies the constraints, and its control gain is {P s >0,S s >0,W s ,G s ,Z s } are all algorithm decision variables, and their introduction purpose is to determine whether there is a controller that meets the control requirements. s It is used to calculate controller gain; Finally, the slow excitation controller shown in (14) is obtained by solving the optimization problem (15) and executing this controller for N steps. Accordingly, the collected N-step input-state data is expressed as And return to step 2, update the prediction model and continue the rolling optimization control process.

4. According to the rolling optimization control method of a variable mode system based on online data drive as described in claim 1, 2 or 3, the basic feature is that the variable mode system refers to a satellite platform performing a solar panel array expansion task, and the solar panels deployed by the platform gradually expand, causing its rotational inertia to change, thereby causing the platform to exhibit variable mode characteristics.

5. A rolling optimization control system for a variable mode system based on online data drive, characterized in that: The system has a program module corresponding to the steps of any one of claims 1 to 4 above, and executes the steps in the rolling optimization control method of a variable mode system based on online data drive during operation.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of a rolling optimization control method for a variable mode system based on online data drive according to any one of claims 1 to 4 when called by a processor.

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