A rolling optimization control method and system for online data-driven variable modal systems

Abstract

This invention relates to the field of control technology for variable modal systems, specifically an online data-driven rolling optimization control method and system. To address the shortcomings of existing data-driven variable modal system control algorithms, which presuppose sufficient offline data collection for each mode, neglecting the unknown new modes that may arise during the online operation of the actual variable modal system and lacking constraint considerations, this invention addresses these issues. Key technical points include: real-time capture of system dynamic changes and corresponding updates to the optimization control law; an online hybrid sampling excitation strategy; and the construction of a semidefinite programming problem that allows for online design of a slow excitation controller using rapidly sampled data. By introducing the hybrid sampling excitation strategy, this invention effectively shortens the open-loop excitation time after the generation of a new mode. Furthermore, this invention considers the unknown new modes and corresponding constraints that may arise during the online operation of the actual variable modal system. The control method effectively ensures the continuous solvability of the optimization control and the asymptotic stability of the closed-loop system. By online excitation of unknown switching modes to update the optimization control law in real time, this invention achieves a more widely applicable rolling optimization control method for variable modal systems.

Description

Technical Field

[0001] This invention relates to the field of control technology for variable modal systems, and more particularly to an online data-driven rolling optimization control method and system for variable modal systems. Background Technology

[0002] Variable modal systems, as a special type of hybrid system, consist of several switching subsystems and a switching signal running through all subsystems. These dynamic systems can effectively describe dynamic processes with abrupt structural / parameter changes, thus attracting widespread attention from academia and industry. However, for complex and large-scale variable modal processes or systems, modeling and parameter identification are costly and often difficult to implement. To address this challenge, numerous data-driven methods for analyzing and controlling unknown switching systems have emerged in recent years, covering data-based open / closed-loop characterization, switching controller design, and unified design of controllers and switching laws. These methods all presuppose that sufficient data for each mode can be collected offline. However, when variable modal systems are running online, new modes often arise due to system failures, unknown external loads, or abrupt changes in the external environment; these new modes are often unknown. Currently, there are preliminary studies on online data-driven control methods for variable modal systems, which update the control law online using real-time data to cope with the new modes generated by the system. However, the existing research does not consider the system constraints commonly found in practical engineering, making practical application difficult.

[0003] Rolling optimization control (also known as model predictive control) has been widely used in constrained variable modal systems due to its superior ability to optimize performance and handle both soft and hard constraints. Existing research mainly falls into two categories: one is based on a mini-maximum optimization control framework, which obtains the feedback control law by iteratively optimizing the upper bound of performance in the infinite time domain. While this method ensures stability and continued feasibility, it is often overly conservative. The other category obtains the control law by optimizing performance indices related to the current mode. This type of method uses set theory to analyze and provide the residence time conditions that guarantee stability and continued feasibility. However, all of the above studies are based on the premise of an accurate state-space model of all subsystems. Given the difficulty of obtaining accurate models for complex variable modal systems, developing data-driven rolling optimization control methods for variable modal systems is particularly important.

[0004] It is worth noting that recent advances in behavioral systems theory have facilitated the development of direct data-driven rolling optimal control methods for linear time-invariant systems. These methods fully utilize the Hankel matrix, composed of offline measured trajectories with continuous excitation inputs, replacing the predictive model in traditional rolling optimal control with a data-driven approach. Extending this method to variable modal systems with online generated modes requires updating the Hankel matrix and terminal components online using real-time excitation data from the current mode. A direct approach injects a finite-length open-loop continuous excitation input sequence into the current subsystem; however, this leaves the system in an open-loop state for an extended period, potentially leading to excessive growth of the state trajectory or even constraint violations. Another approach is to use asynchronous optimal control laws or optimal control laws that progressively update the Hankel matrix to achieve closed-loop excitation; however, mismatch between the predictive model and the current mode can lead to performance degradation and even undermine the stability and feasibility of rolling optimal control. Therefore, there is an urgent need to design an effective method that can acquire effective data online while improving control performance and reducing the risk of constraint violations.

[0005] Document CN119356086A provides a model predictive control method and system for anti-jittering of variable modal systems. It addresses the problem that traditional anti-jittering variable modal control algorithms struggle to balance anti-jittering and stabilizing control performance, leading to issues such as significantly reduced convergence speed and drastically increased overshoot in the stabilizing control performance of the control system. The method includes establishing a variable modal control system model and designing a cost function; designing linear inequality conditions related to stability based on the mean residence time variable modal system stability criterion and the multi-Lyapunov function method, and calculating the upper limit of the cost; designing linear inequality conditions satisfying system constraints and calculating the upper limit of the system control performance cost; and finally, obtaining the multimodal state feedback control gain based on the designed rolling time-domain optimization algorithm and applying it to the control system. However, this prior art does not address how to acquire effective data online and improve control performance or reduce the risk of constraint violations.

[0006] Therefore, traditional variable modal rolling optimization control algorithms heavily rely on accurate state-space models of all subsystems. For complex and large-scale variable modal systems, the computational costs for system modeling and parameter identification are prohibitively high, significantly increasing the hardware cost of the control system. Existing data-driven variable modal system control algorithms all assume sufficient data for each mode can be collected offline, neglecting unknown new modes that may arise during the online operation of the actual variable modal system and lacking constraint considerations. Therefore, proposing an innovative online data-driven rolling optimization control method for variable modal systems, which updates the optimization control law in real time by online excitation of unknown switching modes, is particularly important as it achieves a more widely applicable variable modal rolling optimization control method. Summary of the Invention

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

[0008] To address the shortcomings of existing data-driven variable modal system control algorithms, which all assume sufficient data for each mode can be collected offline, neglecting the unknown new modes that may arise during the online operation of the actual variable modal system and lacking constraint considerations, this invention proposes an online data-driven rolling optimization control method for variable modal systems.

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

[0010] A rolling optimization control method for variable modal systems based on online data-driven approaches, comprising:

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

[0012] Step 2: Online design of a data-driven rolling optimization control algorithm. The main process is as follows: First, based on the input-state trajectory of the current subsystem, a data-driven prediction model is constructed; then, the terminal cost and terminal constraints are solved through a semidefinite programming optimization problem to form a rolling time-domain optimization framework.

[0013] Step 3: Execute the rolling optimization control strategy and real-time monitoring. The main process is as follows: select a suitable solver to solve the optimization problem, obtain control inputs, and apply them to the controlled object. In addition, a mode switching monitor is designed based on behavioral system theory to monitor the predicted and actual state variables in real time. When a system mode switch occurs, an online excitation mechanism is triggered.

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

[0015] Next, the specific implementation process of the method is as follows:

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

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

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

[0019] in This indicates the system state, namely the satellite platform's attitude angular velocity and attitude angles. The attitude angles include roll angle φ, pitch angle θ, and yaw angle ψ, and the angular velocity corresponds to them. This represents the system input, specifically the satellite platform control torque T. cx T cy and T cz T cx T cy and T cz These represent the three-axis control torques respectively; n x and n u Let x(k) and u(k) represent the dimensions of the state and input variables, respectively; k is the sampling time; under the extended solar panel array mission, the satellite's moment of inertia undergoes M variations, corresponding to M sub-modes in the satellite platform system model; the switching signal σ(k) represents a right-continuous piecewise constant function of the satellite platform's sub-modes changing with time k, taking values ​​from the finite set {1,2,…,M}; k j Let $k$ represent the j-th switching time and $k0 = 0$; define the time interval from the (s-1)-th switching time to the s-th switching time as the s-th switching stage, where $s ≥ 1$; 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 are available.

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

[0021]

[0022]

[0023] in and These are the hard constraint gain matrices for the state variables and the control input, respectively. and c is the upper limit of state and control constraints. x With c u These represent the number of constraints for state variables and input variables, respectively.

[0024] The dynamic characteristics of an unknown system are obtained by measuring the 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 an L-order continuous excitation if the Hankel matrix of the sequence has full row rank as follows:

[0026]

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

[0028]

[0029] in, It is an N-length input-state trajectory of this subsystem, and the control input sequence It is an L-order continuous excitation; to satisfy the full-rank condition of continuous excitation, implementing rolling optimization control with L-step prediction time domain for a variable modal system requires online collection of N-length input-state data for each sub-mode, and the data length must satisfy N≥(n x +L)(n u +1)-1; The data collected in the s-th switching phase is represented as The input sequence is continuously excited;

[0030] To ensure the system's stabilization performance, the system cost function for the s-th switching phase is established as follows:

[0031]

[0032] in; and These are the input and state variables predicted at time k+n, respectively; Represent the stage cost and define it as follows: in and These are the weighting coefficients for the attitude angle and the input torque, respectively; L represents the prediction time-domain steps; It is the terminal cost of the s-th switching phase to be designed;

[0033] Finally, the N-length input-state data representation under the initial mode was obtained through experiments as follows:

[0034] Step 2: Using the collected data under the current modality, design an online data-driven rolling optimization control algorithm:

[0035] First, we introduce the cost of a secondary terminal. in Let the terminal cost weight matrix be represented; and an ellipsoidal set of terminal constraints be introduced, which is represented as follows:

[0036]

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

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

[0039] Solving the following semidefinite programming optimization problem yields the terminal cost weight matrix.

[0040]

[0041] in and Let the first-order Hankel matrices represent the state and input trajectory of the slow-sampling system, respectively. Define the terminal control gain as... The symbol * indicates a term omitted due to symmetry; I represents the identity matrix; F s To optimize the process variables in the problem;

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

[0043]

[0044] Based on this, the online data-driven rolling optimization control problem in the s-th switching phase can be expressed as follows:

[0045]

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

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

[0048] The Yalmip toolbox and Sdpt3 solver are used 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 obtained by the optimizer; the first element It acts on the controlled object;

[0049] If predicting state variables If the predicted state variable x(k) is inconsistent with the current actual state variable, it means that the predicted model does not match the current subsystem. Therefore, mode switching can be monitored by comparing the predicted state variable with the actual state variable in real time. The moment when the system switch is observed is denoted as... Considering the numerical calculation errors that exist in actual engineering, the switching moment can be obtained through the following mode switching monitor:

[0050]

[0051] Where s = 0 e r Represents the relative error bound of numerical optimization methods;

[0052] Step 4: Design and execute the hybrid sampling excitation strategy online. After excitation is complete, return to Step 2.

[0053] First, once the mode switching monitor detects a system switch, the sampling period is reduced to h. f And a segment N f A long, continuous excitation control input sequence is injected into the current subsystem; the correlation fast-sampled discrete linear system in the s-th switching phase can be represented as:

[0054]

[0055] in This represents the system state under fast sampling (i.e., the satellite platform's attitude angular velocity and attitude angle under fast sampling). This represents the system input under fast sampling (i.e., the satellite platform control torque under fast sampling). For the sampling time, matrix pair Let represent 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 exists a positive integer v such that h = vh. f Where v is the factor by which the sampling frequency is increased; to ensure that the collected data can sufficiently characterize the system characteristics, the length of the fast sampling data must satisfy N.f ≥(n u +1)n x +n u ;

[0056] Based on this, the high-frequency continuous excitation control input is designed as follows:

[0057]

[0058] in At time k′, an arbitrary vector is randomly generated to ensure continuous excitation conditions, where ∈′ is a given upper bound of the infinite norm of the random vector; in this way, the current subsystem data obtained through fast excitation in the s-th switching phase is represented 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 It is the gain of the controller to be designed. At time k, an arbitrary vector is randomly generated to ensure that the closed-loop control input meets the continuous excitation condition, and ∈s is the upper bound of the infinite norm of the given random vector;

[0062] Then, using the fast-sampled data from the s-th switching phase, the controller gain is designed. This ensures that the slow excitation controller can guarantee the stability and constraint satisfaction of the slow sampling system as shown in equation (1);

[0063] For the s-th switching phase of the variable modal system, consider the fast sampling subsystem as shown in equation (12) and the input-state trajectory it generates. 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 It is a set With sets Pontryagin difference, among which Denotes the upper bound of the infinite norm of the random vector attached to the controller; if there exists a matrix {P} s >0,S s >0,W s G s Z s This makes the following optimization problem solvable:

[0064]

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

[0066] {P s >0,S s >0,W s G s Z s} are all algorithmic decision variables, introduced to determine whether a controller that meets the control requirements exists. Z s It is used to measure controller gain;

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

[0068] The control method is used to perform attitude control on the satellite platform. The variable mode system refers to the satellite platform performing the solar panel array expansion mission. As the solar panels deployed on the platform gradually expand, their rotational inertia changes, which in turn causes the platform to exhibit variable mode characteristics.

[0069] A rolling optimization control system for a variable modal system based on online data-driven operation is provided. The system has program modules corresponding to the steps of the above-described technical solution, and executes the steps in the rolling optimization control method for a variable modal system based on online data-driven operation during runtime.

[0070] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps of the online data-driven variable modal system rolling optimization control method.

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

[0072] This invention proposes a switching optimization control method for modal systems that may generate unknown new modes during online operation. This method involves switching modes, monitoring online, and updating the data model. By introducing a hybrid sampling excitation strategy, this invention effectively shortens the open-loop excitation time after the generation of a new mode. The control method effectively ensures the continuous solvability of the optimized control and the asymptotic stability of the closed-loop system. The research results of this invention are of significant importance in promoting the development of modal system control theory and facilitating the practical application of data-driven modal rolling optimization control theory. This invention considers the unknown new modes and corresponding constraints that may arise in practical modal systems during online operation. It innovatively proposes an online data-driven rolling optimization control method for modal systems, which updates the optimized control law in real time by online excitation of unknown switching modes, thus achieving a more widely applicable modal rolling optimization control method.

[0073] This invention addresses the optimization control problem of variable-modal systems that may generate new modes online. It proposes an online data-driven optimization control algorithm for variable-modal systems that integrates switching mode monitoring, online data excitation, and rolling optimization control. Specific advantages include: ① Considering the unknown new modes that may arise during the online operation of the variable-modal system, 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. Under the premise of ensuring that all constraints are met, this method theoretically guarantees the recursive feasibility of rolling optimization and the stability of the closed-loop system. ② To shorten the unavoidable data shortage stage during the excitation process and reduce the risk of constraint violation, this patent proposes an innovative online hybrid sampling excitation strategy. Simultaneously, a semidefinite programming problem is constructed that can utilize rapidly sampled data to design a slow excitation controller online. This strategy ensures that sufficient continuous excitation data can be collected while satisfying the constraints, thereby achieving online updating of the optimization control law.

[0074] In summary, this invention addresses the shortcomings of existing variable modal rolling optimization control methods, which rely excessively on precise models and cannot handle the online generation of new modes. It proposes an innovative online data-driven variable modal rolling optimization control method. This method designs control strategies directly from online data in an end-to-end manner, without any modeling or system identification steps. After a new mode is generated, this method can achieve closed-loop control that guarantees system constraints with a brief open-loop excitation. The proposed method not only broadens the application scope and applicability of such methods but also demonstrates significant engineering application value, providing new ideas and methods for the development and practical application of control theory for variable modal systems. Attached Figure Description

[0075] The accompanying drawings are provided to further illustrate this patent and form part of the specification. They are used in conjunction with the embodiments of this patent to explain the invention and do not constitute a limitation thereof. In the drawings:

[0076] Figure 1 A flowchart of an online data-driven rolling optimization control method for variable modal systems;

[0077] Figure 2 This is a diagram of the satellite mode switching signal used in the simulation experiment.

[0078] Figure 3 The diagram shows the control input torque curve of the satellite platform under the action of the proposed controller.

[0079] Figure 4 The diagram shows the attitude angle response curve of the satellite platform under the action of the proposed controller.

[0080] Figure 5 The graph shows the attitude angular velocity response of the satellite platform under the action of the proposed controller. Detailed Implementation

[0081] Specific Implementation Method 1: This section describes the implementation process of an online data-driven rolling optimization control method for variable modal systems, as described in this invention, in conjunction with the appendix. Figure 1-5 The following explanation is provided:

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

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

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

[0085] in This indicates the system state (i.e., the satellite platform's attitude angular velocity and attitude angle). Indicates the system input (i.e., the control torque of the satellite platform), n x and n u Let represent the dimensions of the state and input variables, respectively, and k be the sampling time. Under the extended solar panel array mission, the satellite's moment of inertia undergoes M variations, corresponding to M sub-modes in the satellite platform system model. The switching signal σ(k) represents a right-continuous piecewise constant function of the satellite platform's sub-modes changing with time k, taking values ​​from the finite set {1,2,…,M}; kj Let $k$ represent the j-th switching time and $k0 = 0$; define the time interval from the (s-1)-th switching time to the s-th switching time as the s-th switching stage, where $s ≥ 1$; 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 the switching time are unknown, and only the input-state data can be used.

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

[0087]

[0088] in and These are the hard constraint gain matrices for the state variables and the control input, respectively. and c is the upper limit of state and control constraints. x With c u These represent the number of constraints for state variables and input variables, respectively.

[0089]

[0090] in and These are the hard constraint gain matrices for the state variables and the control input, respectively. and c is the upper limit of state and control constraints. x With c u These represent the number of constraints for state variables and input variables, respectively.

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

[0092] Definition 1: Consider a sequence z of length N. [0,N-1] Among them, for This sequence is called an L-order continuous excitation if the sequence has a full-rank Hankel matrix as follows:

[0093]

[0094] Based on the fundamental lemma of behavioral systems theory, the predictive model of a subsystem can be represented by a Hankel matrix composed of the collected input-state data. Specifically, {u [0,L-1] ,x [0,L]Let} be any L-length input-state trajectory of the subsystem with initial state x(0), if and only if there exists a vector Make

[0095]

[0096] in, It is an N-length input-state trajectory of this subsystem, and the control input sequence It is an L-order continuous excitation. To satisfy the full-rank condition of continuous excitation, implementing rolling optimization control with L-step prediction time domain for a variable modal system requires online collection of N-length input-state data for each sub-mode, and the data length must satisfy N ≥ (n x +L)(n u +1)-1. The data collected in the s-th switching phase is represented as The input sequence is continuously excited.

[0097] Furthermore, to ensure the system's stabilization performance, the system cost function for the s-th switching phase is established as follows:

[0098]

[0099] in; and These are the input and state variables predicted at time k+n, respectively; Represent the stage cost and define it as follows: in and These are the weighting coefficients; L represents the number of prediction time-domain steps. It is the terminal cost of the s-th switching phase to be designed.

[0100] Finally, the N-length input-state data representation under the initial mode was obtained through experiments as follows:

[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 Let represent the terminal cost weight matrix. An ellipsoidal set of terminal constraints is also introduced, represented as follows:

[0103]

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

[0105] The following describes an online update method for terminal components to ensure the recursive feasibility of rolling optimization control and the stability of the closed-loop system.

[0106] Solving the following semidefinite programming optimization problem yields the terminal cost weight matrix.

[0107]

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

[0109]

[0110] Based on this, the online data-driven rolling optimization control problem in the s-th switching phase can be expressed as follows:

[0111]

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

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

[0114] In this embodiment, 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 optimized control sequence. Where α * The optimal solution found by the optimizer. The first element... It acts on the controlled object.

[0115] According to the fundamental lemma of behavioral systems theory, if the predicted state variables... If the predicted state variable x(k) is inconsistent with the actual state variable, it means that the predicted model does not match the current subsystem. Therefore, mode switching can be monitored by comparing the predicted and actual state variables in real time. The moment when a mode switch is observed is denoted as... Considering the numerical calculation errors that exist in actual engineering, the switching moment can be obtained through the following mode switching monitor:

[0116]

[0117] Where s = 0 er This represents the relative error bound of the numerical optimization method.

[0118] Step 4: Design and execute the hybrid sampling excitation strategy online. After excitation is complete, return to Step 2.

[0119] First, once the mode switching monitor detects a system switch, the sampling period is reduced to h. f And a segment N f A long, continuous excitation control input sequence is injected into the current subsystem. The correlated fast-sampled discrete linear system in the s-th switching phase can be represented as:

[0120]

[0121] in This represents the system state under fast sampling (i.e., the satellite platform's attitude angular velocity and attitude angle under fast sampling). This represents the system input under fast sampling (i.e., the satellite platform control torque under fast sampling). For the sampling time, matrix pair Let represent 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 exists a positive integer v such that h = vh. f Where v is the factor by which the sampling frequency is increased. To ensure that the collected data can sufficiently characterize the system features, the length of the fast sampling data must satisfy N. f ≥(n u +1)n x +n u .

[0122] Based on this, the high-frequency continuous excitation control input is designed as follows:

[0123]

[0124] in At time k′, an arbitrary vector is randomly generated to ensure continuous excitation, where ∈′ is a given upper bound of the infinite norm of the random vector. In this way, the current subsystem data obtained through rapid excitation in the s-th switching phase is represented 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 It is the gain of the controller to be designed. At time k, an arbitrary vector is randomly generated 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, using the fast-sampled data from the s-th switching phase, the controller gain is designed. This enables the slow excitation controller to ensure the stability and constraint satisfaction of the slow sampling system as shown in equation (1).

[0129] Theorem 1: For the s-th switching stage of a variable modal system, consider the fast sampling subsystem shown in Equation (12) and the input-state trajectory it generates. 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 It is a set With sets Pontryagin difference, among which This represents the upper bound of the infinite norm of the random vector attached to the controller. If there exists a matrix {P} s >0,S s >0,W s G s Z s This makes the following optimization problem solvable:

[0130]

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

[0132] Finally, the slow-excitation controller shown in (14) is obtained by solving the optimization problem (15), and this controller is executed for N steps. Accordingly, the collected N-step input-state data is represented as follows: Then return to step two. Specific Implementation Method Two:

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

[0135] Based on step one, the dynamic characteristics of this 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); T cx T cy and T cz These represent the control torques of the three axes (X, Y, and Z axes); ω0 = 0.0011 rad / is the orbital angular velocity; The moment of inertia of a satellite exhibits piecewise constancy. Its variation process is as follows:

[0138]

[0139] The superscript numbers represent the sub-mode numbers of the system. Note that the actual system model and parameters are completely unknown; they are provided here only for illustrative purposes. During online operation, only input and state variables can be used. System variables are defined as follows: The control input is defined as In addition, the maximum attitude angle, maximum angular velocity, and maximum control input are set to 15 degrees, 2.25 degrees / s, and 1 N·m, 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 = 5deg, θ = 3deg, ψ = 6deg 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 to ε = 0.99 and ′ = 10 respectively. -3 and Control is performed based on the rolling optimization control algorithm, switching monitor, and variable sampling excitation strategy given in steps two, three, and four. For example... Figure 2 The figure shows the variable mode switching signal used in this embodiment. The simulation results record the control input curve, attitude angle response curve, and attitude angular velocity response curve under the proposed variable mode system rolling optimization controller, as shown below. Figure 3 , Figure 4 and Figure 5As shown in the figure, the proposed algorithm can effectively stabilize modal systems that generate new modes during online operation and can satisfy the constraints. Simulation results verify the effectiveness of the method described in the patent.

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

Claims

1. A rolling optimization control method for a variable modal system based on online data-driven approaches, characterized in that, The control method is used for attitude control of a satellite platform, and the method includes the following steps: Step 1: Introduce a variable modal control system, define the system state variables and input variables, establish system hard constraints, design the cost function, and collect input-state data offline under the initial mode. The system is described as a variable modal system consisting of multiple sub-modes and variable modal signals. State variables and input variables are defined based on the actual scenario. Then, hard constraints on state variables and control inputs are set according to 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 methods. 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 constraints are solved by a semidefinite programming optimization problem to form a rolling time-domain optimization framework. Step 3: Implement the rolling optimization control strategy and monitor the system status in real time through the variable modality system switching monitor; Select an appropriate solver to solve the optimization problem, obtain control inputs and apply them to the controlled object; in addition, design a mode switching monitor based on behavioral system theory to monitor the predicted state variables and actual state variables in real time, and trigger an online excitation mechanism when the system mode switches. Step 4: Design and execute the hybrid sampling excitation strategy online. After the excitation is completed, return to Step 2 and proceed to the next stage of rolling optimization control.

2. The rolling optimization control method for a variable modal system based on online data-driven approach according to claim 1, characterized in that, The specific implementation process of step four: First, when the switching monitor detects a system mode switch, the system sampling frequency is increased, and a continuous excitation control input sequence is designed to quickly open-loop excite the unknown subsystem to obtain system behavior information. Second, based on the fast-sampled system trajectory, a data-driven controller that satisfies system constraints and ensures system stability is designed. Then, the system sampling frequency is restored to be consistent with the optimized control frequency, and closed-loop continuous excitation is implemented on the unknown subsystem. Finally, after collecting a sufficiently long amount of input-state data, the process returns to step two, the prediction model is updated, and the rolling optimization control process continues.

3. The rolling optimization control method for a variable modal system based on online data-driven approach according to claim 1 or 2, characterized in that, The specific implementation process of the method is as follows: Step 1: Introduce a variable modal control system, define the system state variables and input variables, establish hard constraints for the system, design the cost function, and collect input-state data offline under the initial mode: First, the satellite platform performing the solar panel array expansion mission will operate at a constant sampling period. The discretized system model can be described as a discrete variable-modal linear system as follows: (1) in This indicates the system state, namely the satellite platform's attitude angular velocity and attitude angles, including roll angle. Pitch angle and yaw angle Angular velocity corresponds to this; This represents the system input, specifically the satellite platform control torque. , and , , and These represent the control torques of the three axes, respectively. and These represent the dimensions of the state variables and the input variables, respectively. The corresponding dimension; The sampling time; changes in satellite rotational inertia occur during the solar panel array extension mission. These changes, and the corresponding satellite platform system model, presents Submodal; switching signal This represents the sub-modes of the satellite platform over time. A piecewise constant function that varies and is right-continuous, derived from a finite set. Take the value from; Indicates the first Each switching moment and ; Define from the first The switching moment to the first The time interval between the switching moments is the first... There are several switching phases, among which ; matrix pairs Indicates the first The system matrix of each satellite platform subsystem is unknown in this mission scenario; only the input-state data is available. Based on the physical characteristics and safety considerations of the satellite platform itself, hard constraints are defined for state variables and control inputs. Hard constraints refer to the allowable range of change of attitude angular velocity / attitude angle and the allowable range of change of control torque. The hard constraint is: in and These are the hard constraint gain matrices for the state variables and the control input, respectively. and For upper limits of state and control constraints, and These represent the number of constraints for state variables and input variables, respectively. The dynamic characteristics of an unknown system are obtained by measuring the input-state trajectory, and the concept of continuous excitation is introduced. Definition: a segment long sequences Among them, for , , Let be the dimension of the sequence; the sequence is For a sequence with continuous excitation, if the Hankel matrix has full row rank as follows: The predictive model of the subsystem can be represented by a Hankel matrix composed of the collected input-state data; specifically, This subsystem is For any initial state A long input-state trajectory exists if and only if there exists a vector Make (5) in, It is a subsystem Long input-state trajectories and control input sequences yes The continuous excitation is of order; to satisfy the full-rank condition of continuous excitation, a method with specific characteristics is implemented for the variable modal system. The rolling optimization control in the predictive time domain requires online collection of data for each sub-mode. Long input-state data, and the data length must meet the following requirements. ;No. The data collected during each switching phase is represented as follows: The input sequence is continuously excited; To ensure the system's stabilization performance, the first The system cost function for each switching phase is established as follows: (6) in; and They are in Time prediction Input and state variables at any given time; Represent the stage cost and define it as follows: ,in and These are the weighting coefficients for attitude angle and input torque, respectively. Indicates the number of prediction steps in the time domain; It is the first one to be designed Terminal cost of each switching phase; Finally, the initial mode was obtained through experiments. Long input-state data is represented as ; Step 2: Using the collected data under the current modality, design an online data-driven rolling optimization control algorithm: First, we introduce the cost of a secondary terminal. in Let the terminal cost weight matrix be represented; and an ellipsoidal set of terminal constraints be introduced, which is represented as follows: (7) in This is the upper bound of the terminal cost; The online update method for terminal components is as follows: to ensure the recursive feasibility of rolling optimization control and the stability of the closed-loop system: Solving the following semidefinite programming optimization problem yields the terminal cost weight matrix. : (8) in and Let the first-order Hankel matrices represent the state and input trajectory of the slow-sampling system, respectively. Define the terminal control gain as... The symbol * indicates a term omitted due to the symmetric nature of the matrix; Represents the identity matrix; To optimize the process variables in the problem; Based on the solution to optimization problem (8), the upper bound of the terminal cost can be obtained by solving the following semidefinite programming optimization problem: (9) Based on this, the first The online data-driven rolling optimization control problem for each switching phase can be represented as follows: (10) in As decision variables, The optimal system cost; Step 3: Implement the rolling optimization control strategy and monitor the system status in real time by switching the monitor through the variable modality system; The Yalmip toolbox and Sdpt3 solver are used 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. in The optimal solution obtained by the optimizer; the first element It acts on the controlled object; If predicting state variables With the current actual state quantity Inconsistency indicates a mismatch between the prediction model and the current subsystem; therefore, mode switching can be monitored by comparing the predicted and actual state variables in real time. The moment when a mode switch is observed is denoted as... Considering the numerical calculation errors that exist in actual engineering, the switching moment can be obtained through the following mode switching monitor: (11) Among them when hour , Represents the relative error bound of numerical optimization methods; Step 4: Design and execute the hybrid sampling excitation strategy online. After excitation is complete, return to Step 2. First, once the mode switching monitor detects a system switch, the sampling period is reduced to [missing information]. And a section A long, continuous excitation control input sequence is injected into the current subsystem; the first The fast-sampling discrete linear system with each switching phase can be represented as: (12) in This represents the system state under fast sampling, specifically the satellite platform's attitude angular velocity and attitude angle under fast sampling. This represents the system input under fast sampling, specifically the satellite platform control torque under fast sampling. For the sampling time, matrix pair Indicates the first The fast sampling system matrix of each satellite platform subsystem; to prevent switching from occurring within the sampling interval, it is necessary to ensure the existence of positive integers. Make ,in This is a multiple of the increased sampling frequency; to ensure that the collected data sufficiently characterizes the system, the fast sampling data length must meet certain requirements. ; Based on this, the high-frequency continuous excitation control input is designed as follows: (13) in Is To ensure continuous excitation, an arbitrary vector is randomly generated at each step. Let be the upper bound of the infinite norm of a given random vector; in this way, in the th... The current subsystem data obtained through rapid excitation during each switching phase is represented as follows: ; 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: (14) in It is the gain of the controller to be designed. Is To ensure that the closed-loop control input meets the continuous excitation condition, an arbitrary vector is randomly generated at each step. Let be the upper bound of the infinite norm of a given random vector; Then, using the first Fast sampling of data during each switching phase; designing controller gain. This ensures that the slow excitation controller can guarantee the stability and constraint satisfaction of the slow sampling system as shown in equation (1); For the variable modal system During the switching phase, consider the fast sampling subsystem as shown in equation (12) and the input-state trajectory it generates. The control input sequence is continuously excited, and the fast sampling frequency is the same as the slow sampling frequency. Times; given controller design parameters ,gather It is a set With sets Pontryagin difference, among which Denotes the upper bound of the infinite norm of the random vector attached to the controller; if a matrix exists... This makes the following optimization problem solvable: (15) in , and These represent the Hankel matrices of the fast sampling system state and the input trajectory, respectively. ,and Represents variables in the algorithm process; Represents the closed-loop matrix of the system; This represents the concatenation of the identity matrix and the zero matrix. Let represent the concatenation of the identity matrix and the negative identity matrix; then, as shown in (14), the slow excitation controller can ensure the stability of the closed-loop slow sampling system and satisfy the constraints, and its control gain is . ; These are all decision variables for the algorithm, and their purpose is to determine whether a controller that meets the control requirements exists. It is used to measure controller gain; Finally, the slow excitation controller shown in (14) is obtained by solving the optimization problem (15), and this controller is executed. Step, accordingly, the collected Step input-state data is represented as Then return to step two, update the prediction model, and continue the rolling optimization control process.

4. A rolling optimization control method for a variable modal system based on online data-driven approach according to claim 1 or 2, characterized in that, A variable-mode system refers to a satellite platform that performs a solar panel array expansion mission. As the solar panels deployed on the platform gradually expand, their rotational inertia changes, resulting in the platform exhibiting variable-mode characteristics.

5. The rolling optimization control method for a variable modal system based on online data-driven approach according to claim 3, characterized in that, A variable-mode system refers to a satellite platform that performs a solar panel array expansion mission. As the solar panels deployed on the platform gradually expand, their rotational inertia changes, resulting in the platform exhibiting variable-mode characteristics.

6. A rolling optimization control system for a variable modal system based on online data-driven operation, characterized in that: The system has a program module corresponding to the steps of any one of the claims 1-5 above, and executes the steps in the online data-driven variable modal system rolling optimization control method described above when running.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the online data-driven rolling optimization control method for a variable modal system as described in any one of claims 1-5.

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