Data-driven predictive controller establishment method, implementation method and control system

Abstract

The present invention belongs to the field of system control, and specifically relates to a method for establishing a data-driven predictive controller for a parameter-free model, an implementation method, and a control system. One method for establishing a data-driven predictive controller for a parameter-free model is to construct a data-driven predictive controller for a parameter-free model based on an extended version of the basic lemma in a stochastic system, combining the initial input data matrix, the initial output data, and the initial innovation data matrix, and then outputting an optimal control law u according to the output of the data-driven predictive controller for the parameter-free model. f (t) to achieve control of the controlled system. The present invention is based on the estimation and information extraction of innovations. Compared with the noise model parameter identification required by other methods, the estimation of innovations is simpler, easier, and more practical. In addition, the present invention can obtain an optimal control strategy and achieve better predictive control effects under various disturbance conditions.

Description

Technical Field

[0001] The present invention belongs to the field of system control, and in particular relates to a method for establishing and implementing a data-driven predictive controller without a parameterized model, and a control system. Background Art

[0002] Traditional predictive control methods are model-based. This involves first collecting the input and output data of the controlled system and then deriving a parameterized model from this data through system identification. The resulting model and a potential control strategy are then used to predict the system's future output. The potential control strategy is then optimized based on requirements such as the control objective and the input / output range, resulting in the optimal control strategy within a specified definition. This approach, known as model predictive control, primarily involves two steps: modeling and control. However, as the complexity of the controlled system increases, the cost of obtaining an accurate parameterized model becomes increasingly significant, posing a significant challenge to existing model predictive control methods. Consequently, the idea of ​​bypassing the modeling step and directly deriving the optimal control strategy based on the raw input and output data has emerged, leading to the development of data-driven predictive control methods.

[0003] In some existing patent documents, although data-driven control has appeared as the core content, it still remains in the original modeling-control paradigm in essence. Chinese Patent: CN115309042A discloses a method of using data to estimate the time-varying parameters of the identification equation and perform control accordingly. Chinese Patent: CN115616895A also uses data to estimate the state space expression as a control model, and uses this as a basis to achieve closed-loop control of the ball-bar system. Chinese Patent: CN108879690B discloses a method of using an equivalent dynamic linearization data model rather than a traditional mechanism model to perform proportional-integral control. The model in the method in the above patent document is no longer the mechanism model established in the past based on physical and chemical knowledge, but a data model in an equivalent sense, which can be directly identified using data, but this method still belongs to the modeling-control paradigm and still has the problem of modeling difficulty.

[0004] The paper "A note on persistence of excitation," published in the journal Systems & Control Letters, Volume 54, Issue 4, pp. 325-329, provides a method for describing the input and output trajectories of linear time-invariant systems. This method can replace traditional parameterized models in control applications. The significance of this method has earned it the title of the fundamental lemma of data-driven control. The paper "Data-enabled predictive control: In the shallows of the DeePC," published at the 18th European Control Conference in 2019, pp. 307-312, first applied the fundamental lemma to predictive control, resulting in the DeepPC (data-enabled predictive control) method. This method focuses on unperturbed deterministic systems. Control performance is significantly affected by noise in the input and output data. One solution to this problem is to add regularization. The paper "Bridge Direct and Indirect Data-Driven Control Formulations via Regularizations and Relaxations," published in the journal IEEE Transaction on Automatic Control, Volume 68, Issue 2, pp. 883-897, summarizes various regularization forms and explains their underlying principles. In addition, the paper "Distributionally Robust Chance Constrained Data-Enabled Predictive Control," published in the journal IEEE Transaction on Automatic Control, Volume 67, Issue 7, Pages 3289-3304, applies the concept of distributed robust control to constrain disturbances from a probabilistic perspective. A paper to be published in the journal IEEE Transaction on Automatic Control, "On a Stochastic Fundamental Lemma and Its Use for Data-Driven Optimal Control," uses a chaotic polynomial expansion method to describe disturbances in detail, enabling predictive control.

[0005] For stochastic systems with disturbances and measurement noise, existing approaches can be broadly categorized into two technical approaches. One approach involves modifying Deep Predictive Control (DeePC) to mitigate the effects of disturbances, including introducing regularization terms and utilizing distributed robust control methods. The problem with this approach is that these measures are merely stopgap measures and cannot yield optimal control strategies. Furthermore, control performance remains poor under high disturbance intensity. Another approach involves a specific description of the disturbance, thereby extending the original fundamental lemma to stochastic systems. A representative approach of this approach is to precisely describe the disturbance using chaotic polynomial expansions. However, this approach's precise description of the disturbance is achieved by constructing a general model. Therefore, even slight deviations in the model parameters can significantly reduce the accuracy of the disturbance description, significantly affecting the final control performance. Consequently, this approach is difficult to implement in practice. In summary, existing data-driven predictive control approaches without parameterized models suffer from two main issues: first, they cannot yield optimal control strategies for stochastic systems; second, existing approaches rely heavily on noise models, hindering their practical application.

[0006] In view of this, the present invention is proposed. Summary of the Invention

[0007] To address the aforementioned technical issues in the prior art, the present invention proposes a method for establishing, implementing, and controlling a parameterized model-free data-driven predictive controller. This method is based on the estimation and extraction of innovations, which is simpler and more practical than the noise model parameter identification required by other methods. Furthermore, the present invention achieves an optimal control strategy, achieving better predictive control results under various disturbance conditions.

[0008] The present invention includes the following technical solutions:

[0009] A first aspect of the present invention provides a method for establishing a data-driven predictive controller without a parameterized model, comprising the following steps:

[0010] Collect historical input data U from the controlled system d and historical output data Y d ;

[0011] Using historical input data U d Construct the initial input data matrix;

[0012] Using historical output data Y d Construct the initial output data matrix;

[0013] According to the historical output data Y d Get one-step-ahead forecast value Get the new interest estimate based on the one-step-ahead forecast

[0014] Using innovation estimates Construct the initial innovation data matrix;

[0015] According to the extended version of the basic lemma in random systems, the data initial input data matrix, initial output data and initial innovation data matrix are combined to construct a data-driven predictive controller for the parameter-free model. The optimal control law u is output by the data-driven predictive controller for the parameter-free model. f (t) to realize the control of the controlled system.

[0016] Furthermore, the method further comprises the following steps:

[0017] Set the prediction time domain L f and sliding window length L p ;

[0018] According to the prediction time domain L f and sliding window length L p Divide the initial input data matrix into two segments to obtain the data matrix U f 、U p ; Data matrix U f The number of input elements in each column is equal to the prediction time domain L f , data matrix U p The number of input elements in each column is equal to the sliding window length L p ;

[0019] According to the prediction time domain L f and sliding window length L p Divide the initial output data matrix into two segments to obtain two data matrices Y f 、Y p ; Data matrix Y f The number of output elements in each column is equal to the predicted time domain L f , data matrix Y p The number of output elements in each column is equal to the sliding window length L p ;

[0020] According to the prediction time domain L f and sliding window length L p Divide the initial innovation data matrix into two segments to obtain two data matrices Data Matrix The number of innovation elements in each column is equal to the prediction time domain L f , data matrix The number of innovation elements in each column is equal to the sliding window length L p ;

[0021] According to the extended version of the basic lemma in random systems, combined with the data matrix U f 、U p 、Y f 、Y p 、 Construct a data-driven predictive controller without parameter model, and output the optimal control law u according to the data-driven predictive controller without parameter model. f (t) To realize the control of the controlled system;

[0022] Where: prediction time domain L f is a constant, the sliding window length L p is a constant.

[0023] Furthermore, the data-driven predictive controller without parameterized model is:

[0024]

[0025] Obtain the optimal control law u through a data-driven predictive controller without parameterized models f (t) and u f (t) The corresponding predicted output The optimal control law u f (t) Acting as input to the controlled system to control the controlled system;

[0026] Where: p (t), δ f (t) represents the slack variable, g(t) represents the linear combination coefficient, u p (t) represents the sliding window length L before time t p The actual input value of the controlled system, y p (t) represents the sliding window length L before time t p The actual output value of the internal controlled system, Indicates the sliding window length L before time t p The estimated value of the new information in the time domain L is U, which represents the prediction time after time t. f The input range of the controlled system; Y represents the predicted time domain L after time t f Output range of the internal controlled system;

[0027]

[0028]

[0029] Furthermore, the controlled system predicts the time domain L after time t f The input range U includes:

[0030] when When u 1b≤u(t+k)≤u ub ;

[0031] when hour,

[0032] The controlled system predicts the time domain L after time t f The output range within Y includes:

[0033] when hour,

[0034] when hour,

[0035] Where: u 1b Indicates that the controlled system is The upper bound of input when u ub Indicates that the controlled system is The input lower bound when ; Indicates that the controlled system is The upper bound of the input when Indicates that the controlled system is The input lower bound when ;

[0036] y 1b Indicates that the controlled system is The upper bound of the output when y ub Indicates that the controlled system is The output lower bound when ; Indicates that the controlled system is The output upper bound when , Indicates that the controlled system is The output lower bound when ;

[0037]

[0038] Furthermore, The representative function is:

[0039]

[0040] Where: data matrix Q represents the error weight matrix, data matrix R represents the control weight matrix; λ g ,λ p ,λ f represents the penalty factor, y r (t) represents the reference trajectory of the controlled system output, u r (t) represent the reference trajectory of the controlled system input.

[0041] Furthermore, the new interest estimate Obtained by the following formula:

[0042]

[0043] Furthermore, the one-step-ahead forecast value Obtained by the following formula:

[0044]

[0045] Where: φ y 、φ χ 、D by solving

[0046] Get, Y p,d Represents the additional historical output data matrix, U p,d Represents the additional historical input data matrix.

[0047] Furthermore, the data matrix U f 、U p 、Y f 、Y p 、 All use the Hankel matrix form.

[0048] The second aspect of the present invention provides a method for implementing data-driven predictive control of a parameter-free model, comprising the above-mentioned data-driven predictive controller of the parameter-free model, and outputting the optimal control law u through the data-driven predictive controller of the parameter-free model. f (t) to control the controlled system.

[0049] Further, the following steps are included:

[0050] The data-driven predictive controller without parameterized model outputs the optimal control law u f (t), the optimal control law u f (t) as input to the controlled system;

[0051] Collect the output data of the controlled system and use the output data to update u p (t), y p (t),

[0052] Repeat the above steps.

[0053] A third aspect of the present invention provides a parameter-free model data-driven predictive control system for executing the above-mentioned parameter-free model data-driven predictive control implementation method.

[0054] By adopting the above technical solution, the present invention has the following advantages:

[0055] 1. The basis of the present invention lies in the estimation and information extraction of new information. Compared with the noise model parameter identification required by other methods, the estimation of new information is simple, easy and more practical. In addition, in the present invention, the optimal control strategy can be obtained, and better predictive control effects can be obtained under various disturbance conditions.

[0056] 2. This invention can obtain the optimal control strategy under various circumstances and achieve better predictive control effects. This is compared with the method of reducing the impact of disturbances. Based on the original basic lemma, the present invention successfully obtains the extended form of the basic lemma on the random system through the introduction and learning of the new information part, and realizes the accurate description of the disturbance. This is the reason why the present invention can obtain the optimal control strategy, which also determines that the present invention can achieve better predictive control effects. Secondly, the present invention has strong practical application value, which is compared with other methods that attempt to describe disturbances. The basis of this method is the estimation and information extraction of new information, and the estimation of new information is simple, easy and more practical than the noise model parameter identification required by other methods. Moreover, in the present invention, the new information estimation error does not have a particularly large impact on the final control effect. Therefore, the present invention is easier to apply in practice and can obtain better predictive control effects under various disturbance conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0058] Figure 1 This is a flow chart of a data-driven predictive controller for establishing a parameter-free model in an embodiment of the present invention;

[0059] Figure 2 This is a waveform diagram of historical input data in an embodiment of the present invention;

[0060] Figure 3 This is a waveform diagram of historical output data in an embodiment of the present invention;

[0061] Figure 4 This is a waveform diagram of the estimated value of innovation in an embodiment of the present invention;

[0062] Figure 5 is the optimal control law u output by the data-driven predictive controller without parameterized model in the embodiment of the present invention f (t) Comparison diagram with the reference trajectory of the output of the controlled system. DETAILED DESCRIPTION

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0064] Example 1

[0065] like Figure 1 As shown, this embodiment provides a method for establishing a data-driven predictive controller without a parameterized model, comprising the following steps:

[0066] Collect historical input data U from the controlled system d and historical output data Y d ;

[0067] Set the prediction time domain L f and sliding window length L p ;

[0068] Using historical input data U d Construct the initial input data matrix; according to the prediction time domain L f and sliding window length L p Divide the initial input data matrix into two segments to obtain the data matrix U f 、U p ; Data matrix U f The number of input elements in each column is equal to the prediction time domain L f , data matrix U p The number of input elements in each column is equal to the sliding window length L p ;

[0069] Using historical output data Y d Construct the initial output data matrix according to the prediction time domain L f and sliding window length L p Divide the initial output data matrix into two segments to obtain two data matrices Y f 、Y p ; Data matrix Y f The number of output elements in each column is equal to the predicted time domain L f , data matrix Y p The number of output elements in each column is equal to the sliding window length L p ;

[0070] According to the historical output data Y d Get one-step-ahead forecast value Get the new interest estimate based on the one-step-ahead forecast

[0071] Using innovation estimates Construct the initial innovation data matrix according to the prediction time domain L f and sliding window length L p Divide the initial innovation data matrix into two segments to obtain two data matrices Data Matrix The number of innovation elements in each column is equal to the prediction time domain L f , data matrix The number of innovation elements in each column is equal to the sliding window length L p ;

[0072] According to the extended version of the basic lemma in random systems, combined with the data matrix U f 、U p 、Y f 、Y p 、 Construct a data-driven predictive controller without parameter model, and output the optimal control law u according to the data-driven predictive controller without parameter model. f (t) To realize the control of the controlled system;

[0073] Where: prediction time domain L f is a constant, the sliding window length L p is a constant.

[0074] It should be noted that the prediction time domain L f Represents the future period, the sliding window length L p Indicates the past period. Historical input data U d and historical output data Y d The specific acquisition process is to select a period of time in the control system, in seconds, and collect historical input data and historical output data every second, and finally obtain the historical input data U d and historical output data Y d ; Of course, the time interval does not necessarily have to be in seconds, but seconds are more accurate.

[0075] Furthermore, the data-driven predictive controller without parameterized model is:

[0076]

[0077] Obtain the optimal control law u through a data-driven predictive controller without parameterized models f (t) and u f (t) The corresponding predicted output The optimal control law u f (t) Acting as input to the controlled system to control the controlled system;

[0078] Where: p (t), δ f (t) represents the slack variable, g(t) represents the linear combination coefficient, u p (t) represents the sliding window length L before time t p The actual input value of the controlled system, y p (t) represents the sliding window length L before time t p The actual output value of the internal controlled system, Indicates the sliding window length L before time t p The estimated value of the new information in the time domain L is U, which represents the prediction time after time t. f The input range of the controlled system; Y represents the predicted time domain L after time t f Output range of the internal controlled system;

[0079]

[0080]

[0081] The specific form of the parameter-free model data-driven predictive controller is not limited to the examples in this embodiment, and other forms of parameter-free model data-driven predictive controllers should also fall within the protection scope of the present invention.

[0082] This data-driven predictive controller without parameterized models is different from existing methods using parameterized models and has the advantage of high prediction accuracy.

[0083] It should be noted that U f 、U p 、Y f 、Y p 、 is obtained by the above method, u p (t), y p (t), In the data-driven predictive controller without parameterized models, δ p (t), δ f (t) and g(t) are both unknown variables. express

[0084] u f (t), δ p (t),δ f (t), g(t) minimizes the J function.

[0085] at the same time, It can be understood as the optimal control law u f (t) and uf (t) The corresponding predicted output At the same time, three conditions must be met, namely, to minimize the J function and satisfy the equation Satisfy the value range u f (t)∈U,

[0086] Furthermore, the controlled system predicts the time domain L after time t f The input range U includes:

[0087] when When u 1b ≤u(t+k)≤u ub ;

[0088] when hour,

[0089] The controlled system predicts the time domain L after time t f The output range within Y includes:

[0090] when hour,

[0091] when hour,

[0092] Where: u 1b Indicates that the controlled system is The upper bound of input when u ub Indicates that the controlled system is The input lower bound when ; Indicates that the controlled system is The upper bound of the input when Indicates that the controlled system is The input lower bound when ;

[0093] y 1b Indicates that the controlled system is The upper bound of the output when y ub Indicates that the controlled system is The output lower bound when ; Indicates that the controlled system is The output upper bound when , Indicates that the controlled system is The output lower bound when ;

[0094]

[0095] It should be noted that u 1b 、u ub 、 y 1b 、yub 、 The specific value of can be determined by those skilled in the art based on experience.

[0096] Based on this, the optimal control law u can be obtained f (t) More precise.

[0097] Furthermore, J(u f (t), δ p (t),δ f The function represented by g(t) is:

[0098]

[0099] Where: data matrix Q represents the error weight matrix, data matrix R represents the control weight matrix; λ g ,λ p ,λ f represents the penalty factor, y r (t) represents the reference trajectory of the controlled system output, u r (t) represent the reference trajectory of the controlled system input.

[0100] Furthermore, the new interest estimate Obtained by the following formula:

[0101]

[0102] Furthermore, the one-step-ahead forecast value Obtained by the following formula:

[0103]

[0104] Where: φ y 、φ χ 、D by solving

[0105] Get, Y p,d Represents the additional historical output data matrix, U p,d Represents the additional historical input data matrix.

[0106] It should be noted that It can be understood as φ y ,φ x ,D needs to satisfy two conditions at the same time, namely φ y ,φ x ,D satisfies minimum, while satisfying φ y ,φ x is the Teoplitz matrix.

[0107] Furthermore, the data matrix U f 、U p 、Y f 、Y p 、 Both use the Hankel matrix form, which reduces the amount of calculation and increases the speed.

[0108] This embodiment also provides a method for implementing data-driven predictive control of a parameter-free model, including the above-mentioned data-driven predictive controller of the parameter-free model, and outputting the optimal control law u through the data-driven predictive controller of the parameter-free model. f (t) to control the controlled system.

[0109] Further, the following steps are included:

[0110] The data-driven predictive controller without parameterized model outputs the optimal control law u f (t), the optimal control law u f (t) as input to the controlled system;

[0111] Collect the output data of the controlled system and use the output data to update u p (t), y p (t),

[0112] Repeat the above steps.

[0113] The controlled system inputs u f (t) After the control is realized, the corresponding output data will be output, and the data will be used to update u p (t), y p (t), The data-driven predictive controller without parameterized models re-outputs u according to the updated data. f (t), and this cycle is repeated to achieve precise control of the controlled system. It can be understood that when the interval is in seconds, t = 1, 2, 3..., and this cycle is endless.

[0114] This embodiment also provides a parameter-free model data-driven predictive control system for executing the above-mentioned parameter-free model data-driven predictive control implementation method.

[0115] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be implemented directly using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in random access memory (RAM), internal memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, a hard disk, a removable disk, a CD-ROM, or any other form of readable storage medium known in the art.

[0116] Example 2

[0117] Based on Example 1, this example specifically illustrates the method of the present invention.

[0118] Collect historical input data U from the controlled system d and historical output data Y d Specifically, a sufficiently long historical input data U is obtained in advance from the historical operation database of the controlled system. d ={u d (1),u d (2),u d (3),...u d (N)} and output data Y d ={y d (1),y d (2),y d (3),...y d (N)} and requires historical input data U d It should have rich changes and be able to fully stimulate the controlled system so that the historical output data Y d It can fully reflect the dynamic characteristics of the controlled system.

[0119] For historical input data U d The best way to measure the richness of the change is to use whether the incentive is continuous. If the historical input data and historical output data Y d The data matrix If the row rank is full, it can be considered that the input data has historical output data L = L p +L f The nature of the continuous excitation of order L can be considered that the input data has rich changes. f represents the prediction time domain, L p Indicates the sliding window length, L f ≥0, L p ≥0.

[0120] According to the historical input data U d and historical output data Y d Estimated value of new interest To extend the original basic lemma to random systems, the innovation estimate is introduced to achieve an accurate description of the disturbance. Specifically, according to the historical input data U d and historical output data Y d , we can get the historical output data Y d One-step-ahead forecast value And through the formula Get new interest estimate

[0121] For historical output data Y d One-step-ahead forecast value The best method for obtaining , considering both accuracy and ease of use, is to use the least squares method, that is, to solve the following optimization problem:

[0122]

[0123] Among them: Teoplitz matrices means Toeplitz data matrix;

[0124]

[0125]

[0126] By solving the above optimization problem, we can obtain the Markov parameter φ y 、φ χ , D, then through the formula Calculated

[0127] In addition, we get the one-step-ahead forecast value Other methods include the N2SID method in the paper "N2SID: Nuclear norm subspace identification of innovation models" published in the journal Automatica, Vol. 72, pp. 57-63, 2016, or the LRSID method in the repository 'https: / / github.com / wangyibo-png / LRSID'. However, these methods are more computationally intensive.

[0128] Data matrix U f 、U p 、Y f 、Y p 、 The best form of construction is the Hankel data matrix form, with U p 、U f For example:

[0129]

[0130]

[0131] The data matrix Y f 、Y p 、 The Hankelization construction method is similar to this and will not be described in detail here.

[0132] In addition, the data matrix can be constructed in the following manner: the data matrix in the paper 'Distributionally Robust Chance Constrained Data-Enabled Predictive Control' in the journal IEEE Transaction on Automatic Control, Volume 67, Issue 7, pages 3289-3304, or the Mosaic Hankel data matrix in the paper 'Willems' Fundamental Lemma for State-Space Systems and Its Extension to Multiple Datasets' in the journal IEEE Control Systems Letters, Volume 4, Issue 4, pages 602-607, 2020.

[0133] Using the Hankel matrix has the advantage of reducing the amount of offline data used, that is, reducing the historical input data U d and historical output data Y d Reducing the amount of data not only facilitates collection, but also reduces the amount of calculation and improves calculation efficiency.

[0134] According to the extended version of the basic lemma in stochastic systems, combined with the above data matrix, a data-driven predictive controller with no parameterization model is constructed:

[0135]

[0136] Solve it to get the optimal control law u at the corresponding time f (t). Comprehensively consider all aspects of control requirements to obtain the optimal control strategy within a certain period of time in the future.

[0137] For the actual input value u of the controlled system in the data-driven predictive controller without parameterized model p (t), actual output value y p The specific way to obtain (t) is: according to the past sliding window length L p The input data and additional output data are used to construct up (t), y p (t), i.e.

[0138]

[0139]

[0140] For t=1 The acquisition can be obtained by solving the following optimization problem:

[0141]

[0142] It should be noted that It can be understood as g(1), Two conditions need to be met at the same time, namely Minimum, satisfying the equation

[0143] For t>1 It is based on the past sliding window length L p The innovation estimate within is constructed, namely:

[0144]

[0145] Objective function and the constraint u p (t)∈U,y p The choice of (t)∈Y depends on the specific requirements of control quality, control objectives and other factors. The following is a set of optional objective functions and constraints. Given a target signal that needs to be tracked by the system, it is necessary to design an optimization problem to achieve the tracking of the target signal with the lowest possible control cost. Therefore, the objective function J(u f (t), g(t),δ p (t),δ f (t)) can be: Used to measure output tracking error, It is used to measure the control cost, while the matrix Q represents the error weight matrix and R represents the control weight matrix. By adjusting the size of the elements in these two matrices, different control objectives can be achieved. For example, if you are more concerned about the gap between the output signal and the target signal, you can increase Q and reduce R appropriately. If you are more concerned about the control cost, you can change it in the opposite direction. The last part is the regularization term, λ g ,λ p ,λ f Represents the penalty factor, which serves as an additional restriction on other optimization variables in the optimization problem.

[0146] It should be noted that Q, R, λ g ,λ p ,λ f The specific value of can be set by those skilled in the art based on experience.

[0147] As for the selection of constraint conditions, in order to facilitate the solution, the following convex constraints can be selected: When u 1b ≤u(t+k)≤u ub ;when hour, when hour, when hour,

[0148] The optimal control law obtained Including the prediction time domain L starting from time t f Internal control law.

[0149] Example 3

[0150] Based on Example 1 and Example 2, this embodiment will further illustrate the present invention with reference to a simulation example:

[0151] The system selected for this simulation experiment is a second-order discrete state space model with a single input and single output, and the sampling time interval is 1s:

[0152]

[0153] y(t)=[0 1.4142]x(t)+v(t)

[0154] Where w(t) and v(t) are process noise and output noise respectively.

[0155] The control goal of this simulation experiment is to obtain the optimal control law by using the method proposed by the present invention under the premise of a given reference output trajectory, so as to make the output of the system as close to the reference output trajectory as possible while reducing the control cost as much as possible.

[0156] First, the offline data preparation part requires designing historical input data that meets the continuous excitation property and collecting historical output data within the corresponding time period. In order to make the historical input data meet the continuous excitation conditions, this simulation experiment uses a zero-mean Gaussian sequence with a variance of 0.01 superimposed on a rectangular wave with an amplitude of 2, a period of 50%, and a duty cycle of 50%. The length of the collected historical input and output data is N = 400s. The final historical input data is as follows Figure 2 As shown, and the historical output data is as follows Figure 3 As shown. At the same time, select the prediction time domain L f= 25s and sliding window length L p =50s.

[0157] This experiment uses the least squares method to calculate Y d One-step forecast value Make an estimate and get Figure 4 The estimated value of the innovation shown Then the data matrix U f 、U p 、Y f 、Y p 、 It is constructed in Hankel matrix form.

[0158] The data-driven predictive controller without parameterized model constructed in this experimental example is as follows:

[0159]

[0160] Among them: g(t) is a 326-dimensional column vector, u f (t), They are all 25-dimensional column vectors, the control weight and error weight matrices are R = 0.01, Q = 1, and the penalty factor is λ p =λ f =100, the reference trajectory to be tracked is selected as y r (t) = sin(2πm / T), m = 1, 2, 3, ..., T, T = 500s. Considering that the sampling period is 1s, a total of 500 steps will be executed in the end (i.e., k = 500).

[0161] The final predictive control output is as follows: Figure 5 As shown in the figure, the reference path is the u output by the data-driven predictive controller without parameterized model. f (t) Controlled path. By comparing the reference path with the actual path, it can be seen that the parameter-free predictive control method of the present invention has high control accuracy.

[0162] Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for establishing a data-driven predictive controller without a parameterized model, characterized in that: The steps include: Collect historical input data from the controlled system and historical output data ; Leveraging historical input data Construct the initial input data matrix; Using historical output data Construct the initial output data matrix; Output data based on history Get one-step-ahead forecast value , obtain the new interest estimate based on the one-step-ahead forecast value ; Using innovation estimates Construct the initial innovation data matrix; According to the extended version of the basic lemma in random systems, the data-driven predictive controller of the parameter-free model is constructed by combining the initial input data matrix, the initial output data and the initial innovation data matrix. The optimal control law output by the data-driven predictive controller of the parameter-free model is obtained. To realize the control of the controlled system; Among them, the extended version of the basic lemma in random systems is to describe the dynamic characteristics and behavior of the random system using the linear combination of the system trajectory composed of the extended input and output on the basis of combining the input with the new information to obtain the extended input.

2. The method for establishing a data-driven predictive controller without a parameterized model according to claim 1, wherein: The following steps are also included: Set the prediction time domain and sliding window length ; According to the prediction time domain and sliding window length Divide the initial input data matrix into two segments to obtain the data matrix 、 ; Data matrix The number of input elements in each column is equal to the prediction time domain , data matrix The number of input elements in each column is equal to the sliding window length ; According to the prediction time domain and sliding window length Divide the initial output data matrix into two segments to obtain two data matrices 、 ; Data matrix The number of output elements in each column is equal to the prediction time domain , data matrix The number of output elements in each column is equal to the sliding window length ; According to the prediction time domain and sliding window length Divide the initial innovation data matrix into two segments to obtain two data matrices 、 , data matrix The number of innovation elements in each column is equal to the prediction time domain , data matrix The number of innovation elements in each column is equal to the sliding window length ; According to the extended version of the basic lemma in random systems, combined with the data matrix 、 、 、 、 、 Construct a data-driven predictive controller with a parameter-free model and output the optimal control law based on the data-driven predictive controller with a parameter-free model To realize the control of the controlled system; Among them: prediction time domain is a constant, the sliding window length is a constant.

3. The method for establishing a data-driven predictive controller without a parameterized model according to claim 2, wherein: The data-driven predictive controller without parameterized model is: ； Obtaining the optimal control law via a parameter-free model-based data-driven predictive controller and with The corresponding prediction output , the optimal control law Acting as the input of the controlled system to realize the control of the controlled system; in: , represents the slack variable, represents the linear combination coefficient, Indicates the sliding window length before time t The actual input value of the controlled system, Indicates the sliding window length before time t The actual output value of the controlled system, Indicates the sliding window length before time t The estimated value of the new information within Indicates the prediction time domain after time t Input range of the internal controlled system; Indicates the prediction time domain after time t Output range of the internal controlled system; ； ； ； 。 4. The method for establishing a data-driven predictive controller without a parameterized model according to claim 3, wherein: The controlled system predicts the time domain after time t Input range within include: when hour, ; when hour, ; The controlled system predicts the time domain after time t Output range within include: when hour, ; when hour, ; in: Indicates that the controlled system is The upper bound of the input when Indicates that the controlled system is The input lower bound when ; Indicates that the controlled system is The upper bound of the input when Indicates that the controlled system is The input lower bound when ; Indicates that the controlled system is The output upper bound when , Indicates that the controlled system is The output lower bound when ; Indicates that the controlled system is The output upper bound when , Indicates that the controlled system is The output lower bound when ; 。 5. The method for establishing a data-driven predictive controller without a parameterized model according to claim 3, wherein: The representative function is: ； Where: data matrix represents the error weight matrix, data matrix represents the control rights matrix; 、 、 represents the penalty factor, represents the reference trajectory of the controlled system output, They represent the reference trajectory of the controlled system input respectively.

6. The method for establishing a data-driven predictive controller without a parameterized model according to claim 2, wherein: Innovation estimate Obtained by the following formula: 。 7. The method for establishing a data-driven predictive controller without a parameterized model according to claim 2, wherein: One-step-ahead forecast value Obtained by the following formula: ； in: 、 、 By solving get, represents the additional historical output data matrix, represents the additional historical input data matrix, Represents the matrix variable to be optimized.

8. The method for establishing a data-driven predictive controller without a parameterized model according to claim 2, wherein: Data Matrix 、 、 、 、 、 All use the Hankel matrix form.

9. A method for implementing data-driven predictive control without parameterized models, characterized in that: The method comprises establishing a data driven predictive controller without parameter model according to any one of claims 1 to 8, and outputting an optimal control law through the data driven predictive controller without parameter model. To control the controlled system.

10. The method for implementing data-driven predictive control without parameterized models according to claim 9, wherein: The steps include: The optimal control law is output by the data-driven predictive controller without parameterized model , the optimal control law As input to the controlled system; Collect the output data of the controlled system and use the output data to update 、 、 ; Repeat the above steps.

11. A data-driven predictive control system without parameterized models, characterized in that: A data-driven predictive control implementation method for executing a parameter-free model as described in any one of claims 9 or 10.

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