Data-driven state feedback control method and device for periodic piecewise linear circuit system

Abstract

The present invention relates to a data-driven state feedback control method and device for a periodic piecewise linear circuit system. The method comprises: constructing a periodic piecewise linear closed-loop system model to obtain basic system information; performing input-output experiments on each subinterval to obtain input-output data that satisfies a response rank condition; describing the system dynamics of the linear system on the subinterval based on the input-output data with sufficient excitation, and obtaining the closed-loop characteristics of the system represented by the input-output data; constructing a Lyapunov function of the closed-loop periodic piecewise linear system, and using the Schur complement equivalence to construct the stability condition of the linear matrix inequality for the Lyapunov function; substituting the obtained input-output data into the stability condition to solve the controller gain matrix; and substituting the controller gain matrix back into the closed-loop system model to converge the state variables to an equilibrium point. The present invention adopts a data-driven approach to achieve effective control under unknown system parameters and achieve fast and flexible convergence.

Description

Technical Field

[0001] The invention relates to a data-driven state feedback control method and device for a periodic piecewise linear circuit system, and belongs to the field of automatic control. Background Art

[0002] The origins of data-driven control can be traced back to the pioneering work of Ziegler and Nichols, as well as the pioneering work of neural networks. Today, data-driven control has attracted a growing number of researchers, and the scope of research has expanded from PID control to model reference control, output tracking, model prediction, and optimal control. Some of these methods use only a single batch of data for offline controller design, while others are iterative control methods that require multiple online experiments.

[0003] A core issue in data-driven control is how to replace process models with data. For linear systems, Willems proposed in 2005 that the set of trajectories generated by a linear system can be represented by a finite set of trajectories, as long as these trajectories possess sufficiently exciting dynamic characteristics. Simply put, under certain conditions, the dynamics of a linear system can be represented by a finite set of input and output data. Inspired by this, researchers have published numerous research results. For example, a prior art data-driven model-predictive rack cooling system control method establishes a linear time-invariant system model for a rack-based micro-data center and employs a data-driven control method to develop an optimal control method, ultimately maintaining the temperature near a reference value and achieving good control results. Another example is a prior art data-driven rail transit train speed predictive control method, which establishes a linear time-invariant system model for a rail transit train and employs a data-driven model-predictive control method to develop an optimal control method, ultimately achieving train speed tracking and achieving good control results. However, because the controlled model is a linear time-invariant system, this method is not applicable when the actual controlled system has multiple subintervals and may experience switching. Summary of the Invention

[0004] The present invention provides a data-driven state feedback control method and device for a periodic piecewise linear circuit system, aiming to solve at least one of the technical problems existing in the prior art.

[0005] The technical solution of the present invention relates to a data-driven state feedback control method for a periodic piecewise linear circuit system. The method according to the present invention comprises the following steps:

[0006] S100, constructing a periodic piecewise linear closed-loop system model of the circuit system and obtaining basic information of the periodic piecewise linear system;

[0007] S200, performing input-output experiments on each subinterval to obtain input-output data that satisfies the response rank condition; describing the system dynamics of the linear system on the subinterval based on the input-output data with sufficient excitation to obtain the closed-loop characteristics of the system represented by the input-output data;

[0008] S300, constructing a Lyapunov function of a closed-loop periodic piecewise linear system, and constructing a stability condition of a linear matrix inequality using Schur complement equivalence for the Lyapunov function; substituting the obtained input and output data into the stability condition to solve a gain matrix of the controller;

[0009] S400 , substituting the gain matrix of the feedback controller back into the closed-loop system model to make the state variables converge to an equilibrium point.

[0010] Furthermore, the step S100 includes:

[0011] S110. Express the circuit system as a periodic piecewise linear system;

[0012] S120, obtaining basic information of the periodic piecewise linear system; wherein the basic information includes the number of subintervals z, the length of each subinterval L i , the number of state variables n x , the number of input variables m u ;

[0013] S130, selectively re-segmenting each sub-interval according to the length of the sub-interval;

[0014] S140, constructing a state feedback controller; wherein each subinterval has a separate controller gain matrix;

[0015] S150: Substitute the state feedback controller into the original circuit system to form a closed-loop system.

[0016] Further, for step S100,

[0017] The basic period of the system is divided into z subintervals, i = 1, 2, ..., z. Then, in the i-th subinterval of each period, the circuit system is dynamically described in the form of a periodic piecewise linear system as follows:

[0018] x(t+1)=A i x(t)+B i u(t)

[0019] Where t represents time, They represent the periodic piecewise linear system n x dimensional state vector and m u dimensional control input vector, where It represents an n-dimensional real column vector space, n can be replaced by any positive integer, and the symbols that appear below all represent the above meanings. i=1,2,…,z means that the system is in the i-th subinterval, the number of subintervals is z, and the number of state variables is n. x , the number of input variables Represent the system matrix and input matrix of the i-th subinterval respectively, where It represents the n×m dimensional real matrix space, n and m can be replaced by any positive integers, and the symbols that appear below all represent the above meanings;

[0020] The state feedback controller is expressed as follows:

[0021] u(t)=K i x(t),t∈t i

[0022] Where, represents the gain matrix of the state feedback controller in the i-th subinterval, t∈t i Indicates that the system is in the i-th subinterval;

[0023] The closed-loop system formed by substituting the state feedback device into the original circuit system is expressed as follows:

[0024] x(t+1)=(A i +B i K i )x(t).

[0025] Furthermore, in step S200,

[0026] The measured X i,0 , U i,0 The following rank conditions are met:

[0027]

[0028] in,

[0029] X i,0 =[x(0)x(1)…x(T i -1)],

[0030] U i,0 =[u(0)u(1)…u(T i -1)]

[0031] Where, X i,0 ,U i,0 They represent the vectors of input and output data obtained in the ith subinterval, x(0)~x(T i-1),u(0)~u(T i -1) represents the input and output data at each moment, T i It indicates the length of experimental data obtained in one experiment.

[0032] Furthermore, in step S200,

[0033] When the rank condition is satisfied, there exists a matrix as an equality constraint satisfy:

[0034]

[0035] The closed-loop characteristics of the periodic piecewise linear system are expressed as follows:

[0036]

[0037] in,

[0038] X i,0 =[x(0)x(1)…x(T i -1)],

[0039] X i,1 =[x(1)x(2)…x(T i )],

[0040] U i,0 =[u(0)u(1)…u(T i -1)],

[0041] Where, X i,1 Indicates that in the i-th subinterval, when the input data is U i,0 Output data in the case of It means n x dimensional identity matrix.

[0042] Furthermore, the step S300 includes:

[0043] S310. Construct the Lyapunov function of closed-loop periodic piecewise linear systems and obtain basic stability conditions.

[0044] S320, using Schur complement equivalence on the stability condition in step S310, and transforming the stability condition into a linear matrix inequality;

[0045] S330 , substituting the obtained data into the inequality and equality conditions given in step S320 to obtain a gain matrix of the state feedback controller.

[0046] Furthermore, in step S310,

[0047] For the i-th subinterval after expansion, i=1,2,…,N, there exists a positive definite matrix matrix Constant 0 < λ i <1, then the exponential stability condition of the basic periodic piecewise linear system is expressed as follows:

[0048]

[0049] P i+1 ≤P i

[0050] I nx =X i,0 G i

[0051] The gain matrix of the state feedback controller is expressed as follows:

[0052] K i =U i,0 G i ,

[0053] Wherein, the above two inequalities are used to make the Lyapunov function decrease and the Lyapunov function not increase at the switching point to constrain the transition of the system dynamics when switching between subintervals; the last equation is used to describe the dynamics of the system in each subinterval based on the collected input and output data.

[0054] Further, in step S320,

[0055] For the i-th subinterval after expansion, i=1,2…N, if there exists a positive definite matrix matrix Constant 0 < λ i <1, the inequality constraint of step S310 is converted into a linear matrix inequality by applying the Schur complement equivalence, which is expressed as follows:

[0056]

[0057] M i+1 >M i

[0058] M i =X i,0 N i

[0059] The gain matrix of the state feedback controller is expressed as follows:

[0060]

[0061] Where, where λi is the decay rate, λ i The value is given in advance.

[0062] The technical solution of the present invention also relates to a computer-readable storage medium having program instructions stored thereon, and the above-mentioned method is implemented when the program instructions are executed by a processor.

[0063] The technical solution of the present invention also relates to a data-driven state feedback control system of a periodic piecewise linear circuit system, wherein the system includes a computer device containing the above-mentioned computer-readable storage medium.

[0064] The beneficial effects of the present invention are as follows:

[0065] The present invention provides a data-driven state feedback control method and device for a periodic piecewise linear circuit system. The state feedback controller of the designed periodic piecewise linear system can enable the corresponding closed-loop system to achieve exponential stability. The method is data-driven. Although the nominal system matrix is ​​mentioned in part of the derivation process of the above steps, in actual use, it is not necessary to identify the specific parameters of the system in advance, and the gain matrix of the corresponding controller is directly obtained based on the input and output data. The effectiveness of the method of the present invention is verified based on a periodic piecewise linear circuit system. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 FIG. 4 is a basic flow chart of a control method according to an embodiment of the present invention.

[0067] Figure 2 A scatter plot of the gain matrix of the state feedback controller calculated for a real example of an embodiment of the present invention, wherein each small circle represents a controller parameter in a subinterval;

[0068] Figure 3 This is a schematic diagram of the first state response result of the closed-loop system of the simulation example according to the embodiment of the present invention;

[0069] Figure 4 This is a schematic diagram of the second state response result of the closed-loop system of the simulation example according to the embodiment of the present invention;

[0070] Figure 5 This is a schematic diagram of the third state response result of the closed-loop system of the simulation example according to an embodiment of the present invention;

[0071] Figure 6 A schematic diagram of the Lyapunov function results of a closed-loop system of a simulation example according to an embodiment of the present invention;

[0072] Figure 7 A circuit schematic diagram of a periodic piecewise linear circuit system according to an embodiment of the present invention;

[0073] Figure 8Schematic diagram of each circuit module in the periodic piecewise linear circuit system according to an embodiment of the present invention;

[0074] Figure 9 is a schematic diagram of a Howland current source in a circuit simulation according to an embodiment of the present invention;

[0075] Figure 10 This is a diagram of the state variable response results of the closed-loop system of the PSPICE simulation example according to an embodiment of the present invention. DETAILED DESCRIPTION

[0076] The following will provide a clear and complete description of the concept, specific structure and technical effects of the present invention in conjunction with the embodiments and drawings to fully understand the purpose, scheme and effects of the present invention.

[0077] It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly fixed or connected to the other feature, or it may be indirectly fixed or connected to the other feature. The singular forms "a", "said" and "the" used herein are also intended to include the plural forms, unless the context clearly indicates otherwise. In addition, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art. The terms used in this specification are only for describing specific embodiments and are not intended to limit the invention. The term "and / or" used herein includes any combination of one or more related listed items.

[0078] Should be understood that, although the present disclosure may adopt the term first, second, third etc. to describe various elements, these elements should not be limited to these terms.These terms are only used to distinguish the elements of the same type from each other.For example, without departing from the scope of the present disclosure, the first element may also be referred to as the second element, and similarly, the second element may also be referred to as the first element.The use of any and all examples or exemplary language ("for example", "such as" etc.) provided herein is only intended to better illustrate embodiments of the present invention, and unless otherwise required, will not impose limitations on the scope of the present invention.

[0079] Reference Figures 1 to 10 In some embodiments, the data-driven state feedback control method for a periodic piecewise linear circuit system according to the present invention comprises at least the following steps:

[0080] S100, constructing a periodic piecewise linear closed-loop system model of the circuit system and obtaining basic information of the periodic piecewise linear system;

[0081] S200, performing input-output experiments on each subinterval to obtain input-output data that satisfies the response rank condition; describing the system dynamics of the linear system on the subinterval based on the input-output data with sufficient excitation to obtain the closed-loop characteristics of the system represented by the input-output data;

[0082] S300, constructing a Lyapunov function of a closed-loop periodic piecewise linear system, and constructing a stability condition for a linear matrix inequality using Schur complement equivalence for the Lyapunov function; substituting the obtained input and output data into the stability condition to solve the controller gain matrix;

[0083] S400: Substitute the gain matrix of the feedback controller back into the closed-loop system model to make the state variables converge to the equilibrium point.

[0084] Specific implementation of step S100

[0085] Step S110: Consider a circuit system with periodic dynamic characteristics, and assume it to be a periodic piecewise linear system in the following form, that is, the basic period of the system is divided into z subintervals, taking i = 1, 2, ..., z. In the i-th subinterval of each period, the corresponding circuit system dynamic description is:

[0086] x(t+1)=A u x(t)+B i u(t)

[0087] Where, They represent the state vector and control input vector of the periodic piecewise linear system respectively, i=1,2,…,z means the system is in the i-th subinterval, Represent the system matrix and input matrix of the i-th subinterval respectively.

[0088] It should be noted that the system matrix A of the present invention i and the input matrix B i They are all nominal parameter matrices, and their specific parameters are unknown. They are only used as nominal approximations of the system model to facilitate subsequent analysis and controller design, and do not require identification to obtain specific parameter values.

[0089] Step S120: Obtain basic information of the periodic piecewise linear system. The quantities that must be known are the number of subintervals z, the length of each subinterval L i , the number of state variables n x , the number of input variables m u It is understandable that the above basic information can be determined based on the basic physical characteristics of the actual system and the number of actuators that generate the control input signal.

[0090] Step S130: In order to improve the control accuracy, each sub-interval is re-divided into n i Parts, 1≤n i ≤L i , then the number of subintervals of the entire cycle is artificially expanded to N = n1 + n2 + ... + n z It is understandable that this step is only performed when the length of a subinterval is too long, because too small a division will greatly increase the complexity of the calculation and may even lead to no solution.

[0091] Step S140: Construct a state feedback controller u(t)=K i x(t),t∈t i , where It represents the gain matrix of the state feedback controller, and each subinterval has a separate controller gain matrix.

[0092] Step S150: Substitute the state feedback device into the original system to form a closed-loop system, which is expressed as follows:

[0093] x(t+1)=(A i +B i K i )x(t).

[0094] Specific implementation of step S200

[0095] Step S210: Select random data of appropriate size as the control input of the system to obtain input and output data. Furthermore, the input control input must be linearly independent, and experiments are generally conducted using random data as the control input.

[0096] Step S220: Select the data that meets the rank condition from the obtained input and output data as the final input and output data. Specifically, the rank condition mentioned above refers to the X obtained by measurement. i,0 , U i,0 The following rank conditions are met:

[0097]

[0098] It should be noted that the present invention adopts the rank condition of the above formula (1) to ensure that the control input has sufficient excitation, so that the obtained input and output data can represent the dynamics of the closed-loop system.

[0099] Step S230: Describe the system dynamics of the linear system on the subinterval according to the input and output data with sufficient excitation, and obtain the closed-loop characteristics of the system represented by the input and output data. Specifically, when the rank condition of the above step S220 formula (1) is satisfied, if there is a matrix satisfy

[0100]

[0101] Then the closed-loop characteristics of the periodic piecewise linear system can be written as follows:

[0102]

[0103] in,

[0104] X i,0 =[x(0)x(1)…x(T i -1)],

[0105] X i,1 =[x(1)x(2)…x(T i )],

[0106] U i,0 =[u(0)u(1)…u(T i -1)],

[0107] It should be noted that the above input and output data can be obtained by performing input and output experiments in each subinterval. The subinterval here refers to the subinterval before expansion, that is, i = 1, 2, …, z. Since artificially expanding the subinterval does not change the system model, the original subinterval is split into multiple smaller subintervals to share the same set of data.

[0108] Based on the above derivation, the closed-loop characteristics of the periodic piecewise linear system are derived by a data-driven method. i 、B i , K i Then it is transformed into the known X i,1 and G constrained by formula (2) i In the subsequent calculation process of the gain matrix of the state feedback controller, these data are directly used in the calculation without the need for system identification steps.

[0109] Specific implementation of step S300

[0110] Step S310: constructing the Lyapunov function of the closed-loop periodic piecewise linear system to obtain basic stability conditions.

[0111] Specifically, for each subinterval after expansion, consider the following piecewise Lyapunov function V(t), that is, on each subinterval:

[0112] V(t)=x T (t)P i x(t)

[0113] Among them, P iis a symmetric positive definite matrix. According to Lyapunov's stability theory, to prove that the system is asymptotically stable, we only need to prove that ΔV(t) < 0 and that it can be extended to all periods to satisfy asymptotic stability, where ΔV(t) = V(t+1) - V(t). Therefore, consider the following derivation:

[0114] ΔV(t)=V(t+1)-V(t)=x T (t+1)P i x(t+1)-x T (t)P i x(t)

[0115] The superscript letter T in the formula represents the transpose of a vector or matrix. Substituting the condition of step S230 into the above formula yields:

[0116]

[0117] According to the above formula, maintaining asymptotic stability in each subinterval does not guarantee stability in all cycles. When the system dynamics switches and changes in different subintervals, the degree of change in the system energy is unconstrained. Therefore, it is necessary to consider exponential stability on the basis of asymptotic stability. The goal is to ensure that the system can achieve exponential stability in all cycles and obtain the corresponding stability conditions. In order to meet the exponential stability, a parameter 0<λ is introduced in each subinterval after expansion. i <1, i represents the i-th subinterval, such that V(t+1)<λ i V(t), and there is V(t) at the switching point between every two sub-intervals i+1 <V(t) i When these two inequalities hold, for a certain time t0 of the ith subinterval, any t>t0, if there is no subinterval transition between t and t0, then Then you can get If a sub-interval transition is experienced, it only shows the result of one transition. Multiple transitions can be superimposed on each other. Assuming that the transition point is t1, then there is so In the i-th subinterval, Right now so Let λ=max{λ i+1 ,λ i},So Extended to the case of multiple subintervals, any t>t0, where λ = max i＝1,…,N λ i , we can know that the system satisfies exponential stability.

[0118] On this basis, the exponential stability condition of the basic periodic piecewise linear system is constructed:

[0119] Specifically, for the i-th subinterval after expansion, i=1,2,…,N, if there exists a positive definite matrix matrix Constant 0 < λ i <1, so that the following inequalities and equalities hold:

[0120]

[0121] P i+1 ≤P i

[0122] I nx =X i,0 G i

[0123] Then the periodic piecewise linear system under the action of the state feedback controller is exponentially stable, and the gain matrix of the state feedback controller can be obtained as:

[0124] K i =U i,0 G i

[0125] In the above conditions, the role of the first two inequalities is to ensure that the Lyapunov function decreases and that the Lyapunov function does not increase at the switching point, thereby constraining the transition of the system dynamics when switching between subintervals; the role of the last equation is to ensure that the collected input and output data can be used to describe the dynamics of the system in each subinterval.

[0126] Step S320: applying Schur complement equivalence to the stability condition in step S310 to convert the stability condition into a linear matrix inequality.

[0127] To more conveniently calculate the controller's gain matrix, we provide another stability condition for periodic piecewise linear systems. The inequality in the stability condition of S301 appears as a bilinear matrix inequality. To facilitate the solution of the gain matrix, the above inequality constraint can be converted into a linear matrix inequality by applying the Schur complement equivalence.

[0128] For the first inequality of the stability condition in step S310 The bilinear matrix inequality can be transformed into a linear matrix inequality using the first Schur complement equivalence, and we get:

[0129] For the i-th subinterval after expansion, i=1,2…N, if there exists a positive definite matrix matrix Constant 0 < λ i <1, so the following inequality holds:

[0130]

[0131] M i+1 >M i

[0132] And make the following equation true:

[0133] M i =X i,0 N i

[0134] Then the periodic piecewise linear system under the action of the state feedback controller is exponentially stable. And the gain matrix of the controller can be obtained as

[0135]

[0136] In the relevant conditions of step S320, In the actual operation, in order to make the above inequality into a linear matrix inequality, λ i The value of λ needs to be given in advance. i The meaning of the decay rate is λ i The smaller the value, the faster the state variables converge to the equilibrium point. It is understandable that a too small λ i This may lead to unsolvable linear matrix inequalities, so λ needs to be chosen carefully. i The numerical value of .

[0137] Step S330: Substitute the obtained data into the inequality and equality conditions given in step S320 to obtain the gain matrix of the state feedback controller.

[0138] In order to verify the effectiveness of the data-driven state feedback control method for a periodic piecewise linear circuit system proposed in the present invention, the present invention is further described through an example of a control system of an approximate periodic piecewise circuit.

[0139] Specifically, the simulation example:

[0140] Consider a circuit system model with periodic dynamic characteristics:

[0141]

[0142] Where: C1, C2 are the capacitance values ​​of the two capacitors (F);

[0143] v1, v2——the voltage on capacitors C1 and C2 respectively (V);

[0144] R, R0——resistance value (Ω);

[0145] g(t)——represents the negative resistance (Ω) that changes with time

[0146] L——the inductance value of inductor L (H);

[0147] i L ——Current on inductor L (A);

[0148] u——Current source control input (A).

[0149] Using the forward difference method, the model is discretized to

[0150]

[0151] Where, T s represents the sampling time, T s = 0.001s, which is the step size of the discretized model. The parameters of each component in the circuit are set as follows: R = 10 / 7, R0 = 0, C1 = 1 / 9, C2 = 1 / 9, and L = 1 / 7. The units are consistent with the units of the physical quantities corresponding to the above circuit system model. In the formula, g(t) is a periodic piecewise function approximated with a period of 300 steps in discrete time. Taking the first period as an example, the function is expressed as follows:

[0152]

[0153] Where G a1 =-4.5,G a2 =-3,G a3 =-2.

[0154] It can be seen that the system has a total of 3 subintervals, and the length of each subinterval is 100 steps. Select u(t) = rand(1) as the control input, and you can get the data X in each subinterval. i,0 ,x i,1 ,U i,0 It should be noted that these data do not necessarily need to be obtained in one experiment, as long as each data satisfies the corresponding relationship.

[0155] In order to improve the control accuracy, the 3 subintervals are divided into 10 equal parts, and the length of each small subinterval is 10 steps, so there are now a total of 30 subintervals.

[0156] After obtaining the data, substitute these data into the stability condition of step S320 and set By solving the linear matrix inequality in the stability condition of S302, the gain matrix of the state feedback controller can be obtained. Figure 2 .

[0157] Connect the calculated state feedback controller to the system and select x(0) = [10, 10, -10] T As an initial point, we can get Figure 3 、 Figure 4 and Figure 5 The closed-loop system state response is shown in Figure 2. It can be seen that under the initial condition x(0), each state variable can quickly converge to the equilibrium point within a finite time. Figure 6 The curve graph of the Lyapunov function is shown, from which it can be seen that the energy of the system can converge to 0 very well, indicating that the data-driven state feedback control method proposed in the present invention can effectively stabilize the periodic piecewise linear circuit system.

[0158] Furthermore, in order to better verify the practicality of the present invention, a circuit simulation corresponding to the above-mentioned periodic segmented circuit system model was built in PSPICE electronic circuit professional simulation software, and the control effect of the proposed method was verified by the input and output data obtained by the simulation.

[0159] Specifically, first build the circuit system's main framework (see Figure 7 ), where the negative resistance is realized by an operational amplifier, such as Figure 8 The time period dynamics in the system comes from periodic switching, and the periodic control signal is formed by two PWM signals and a NOT gate, as shown in the left figure. Figure 8 As shown in the middle figure, each signal is high only when it is in its own sub-interval. The electronic switch consists of two diodes and two MOS tubes, as shown in Figure 8 As shown in the right figure.

[0160] The voltage-controlled current source as the control input is realized by the ideal components of the ABM library in the simulation process of this embodiment of the present invention. In the actual circuit, the Howland current source structure can be used. Its schematic diagram is as follows Figure 9 It should be noted that for the convenience of simulation, the subintervals are not expanded in the PSPICE simulation, that is, the original three subintervals are maintained.

[0161] Build the corresponding modules of the controlled circuit system and conduct simulation experiments to obtain input and output data, calculate and solve the gain of the data-driven state feedback controller and implement it in the circuit system, and obtain the results as follows Figure 10 As shown, it can be obtained that the three states can converge to the equilibrium point quickly within a finite time under the action of the controller, indicating that the proposed data-driven state feedback control method can effectively stabilize the periodic piecewise linear circuit system.

[0162] It should be noted that, considering that the systems in actual production processes are often very complex, it is almost impossible to accurately identify their system parameters, so a method of directly generating a controller from data is very necessary. The present invention proposes a data-driven state feedback control method and device for a periodic piecewise linear circuit system, which requires less prior knowledge of the system to be controlled and can be controlled under conditions where the system parameters are unknown. The data-driven method used not only avoids the parameter identification process, but also enables the design of the controller by collecting data. The exponential convergence of each state has a faster convergence speed than the asymptotic convergence. At the same time, in the process of designing the controller, the designer can flexibly adjust the convergence rate according to requirements, which will have better transient performance overall.

[0163] It should be appreciated that the method steps in the embodiments of the present invention can be implemented or executed by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable memory. The method can use standard programming techniques. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with the computer system. However, if desired, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. In addition, for this purpose, the program can be run on a programmed application-specific integrated circuit.

[0164] Furthermore, the operations of the processes described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by the context. The processes described herein (or variations and / or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) that is executed collectively on one or more processors, by hardware, or a combination thereof. The computer program includes a plurality of instructions that can be executed by one or more processors.

[0165] Further, the method can be implemented in any type of computing platform that is operably connected to a suitable computer, including but not limited to a personal computer, a minicomputer, a mainframe, a workstation, a network or distributed computing environment, a separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, etc. Various aspects of the present invention can be implemented as machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, an optical read and / or write storage medium, an RSM, a ROM, etc., so that it can be read by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the process described herein. In addition, the machine-readable code, or portions thereof, can be transmitted over a wired or wireless network. When such media includes instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor, the invention described herein includes these and other different types of non-transitory computer-readable storage media. When programmed according to the methods and techniques of the present invention, the present invention can also include the computer itself.

[0166] The computer program can be applied to input data to perform the functions described herein, thereby converting the input data to generate output data that is stored in a non-volatile memory. The output information can also be applied to one or more output devices such as a display. In a preferred embodiment of the present invention, the converted data represents a physical and tangible object, including a specific visual depiction of the physical and tangible object produced on the display.

[0167] The above description is merely a preferred embodiment of the present invention. The present invention is not limited to the aforementioned embodiments. As long as the technical effects of the present invention are achieved by the same means, any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention. Within the scope of protection of the present invention, various modifications and variations of the technical solutions and / or implementation methods are possible.

Claims

1. A data-driven state feedback control method for a periodic piecewise linear circuit system, characterized in that: The method comprises the following steps: S100, constructing a periodic piecewise linear closed-loop system model of the circuit system and obtaining basic information of the periodic piecewise linear system; S200, performing input-output experiments on each subinterval to obtain input-output data that satisfies the response rank condition; describing the system dynamics of the linear system on the subinterval based on the input-output data with sufficient excitation to obtain the closed-loop characteristics of the system represented by the input-output data; S300, constructing a Lyapunov function of a closed-loop periodic piecewise linear system, and constructing a stability condition of a linear matrix inequality using Schur complement equivalence for the Lyapunov function; substituting the obtained input and output data into the stability condition to solve a gain matrix of the controller; S400, substituting the gain matrix of the feedback controller back into the closed-loop system model to make the state variables converge to an equilibrium point; Wherein, the step S100 includes: S110. Express the circuit system as a periodic piecewise linear system; S120, obtaining basic information of the periodic piecewise linear system; wherein the basic information includes the number of subintervals , the length of each subinterval , the number of state variables , the number of input variables ; S130, selectively re-segmenting each sub-interval according to the length of the sub-interval; S140, constructing a state feedback controller; wherein each subinterval has a separate controller gain matrix; S150, substituting the state feedback controller into the original circuit system to form a closed-loop system; Wherein, for the step S100, Among them, the basic period of the system is divided into subintervals, take the count , then in each cycle The circuit system is dynamically described as a periodic piecewise linear system on the subintervals: Where, represents the time variable, and They represent the periodic piecewise linear system dimensional state vector and dimensional control input vector, so that and ,in, represents a real column vector space, is the number of state variables and is represented as the dimension of the real column vector space, is the number of input variables and is represented as the dimension of the real column vector space, and Representing the The system matrix of the subintervals and the input matrix make , ; The state feedback controller is expressed as follows: Where, It means the The gain matrix of the state feedback controller is Indicates that the system is in In the subintervals; The closed-loop system formed by substituting the state feedback device into the original circuit system is expressed as follows: ； Wherein, in the step S200, The measured The following rank conditions are met: in, Where, Respectively represent the The vector of input and output data obtained from the subintervals, It represents the input and output data at each moment. It represents the length of the experimental data obtained; Wherein, the step S300 includes: S310. Construct the Lyapunov function of closed-loop periodic piecewise linear systems and obtain basic stability conditions. S320, using Schur complement equivalence on the stability condition in step S310, and transforming the stability condition into a linear matrix inequality; S330 , substituting the obtained data into the inequality and equality conditions given in step S320 to obtain a gain matrix of the state feedback controller.

2. The method according to claim 1, characterized in that In the step S200, When the rank condition is satisfied, there exists a matrix as an equality constraint satisfy: The closed-loop characteristics of the periodic piecewise linear system are expressed as follows: in, ， Where, Indicates in The subintervals are The output data in the case of It means dimensional identity matrix.

3. The method according to claim 2, characterized in that In the step S310, For the expansion after subintervals, , there exists a positive definite matrix ,matrix ,constant , then the exponential stability condition of the periodic piecewise linear system is expressed as follows: The gain matrix of the state feedback controller is expressed as follows: ， Wherein, the above two inequalities are used to make the Lyapunov function decrease and the Lyapunov function not increase at the switching point to constrain the transition of the system dynamics when switching between subintervals; the last equation is used to describe the dynamics of the system in each subinterval based on the collected input and output data.

4. The method according to claim 3, characterized in that In the step S320, For the expansion after subintervals, , if there exists a positive definite matrix ,matrix ,constant , by applying the Schur complement equivalence, the inequality constraint of step S310 is transformed into the form of a linear matrix inequality, which is expressed as follows: The gain matrix of the state feedback controller is expressed as follows: Where, ;in is the attenuation rate, The value is given in advance. 5 . A computer-readable storage medium having program instructions stored thereon, wherein the program instructions are executed by a processor to implement the method according to claim 1 .

6. A data-driven state feedback control system for a periodic piecewise linear circuit system, characterized in that: include: A computer device comprising the computer-readable storage medium according to claim 5.

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