An online control method for unknown switching systems based on noise data

Abstract

The method of the present application provides an online control method of unknown switching system based on noise data, collects historical operation data at each time, divides the operation process of the system into four stages according to the operation track of the system, and controls in different stages by using different control rules. In the excitation stage, a set of designed random control sequence is used for the controller side to control the system. In the update stage, a low complexity data-based SDP problem is solved, and the optimal solution is used to construct a state feedback controller to control the system. In the convergence stage and the stable stage, the system does not solve the SDP, but uses the state feedback matrix solved recently to control the system in advance. As can be seen, the present application does not need prior system identification, only needs data sampling and calculation from the self-triggering time, and can perform state closed-loop control on the unknown switching system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent manufacturing, and particularly relates to an unknown switching system online control method based on noise data. BACKGROUND

[0002] In order to promote the transformation and upgrading of traditional manufacturing industry to intelligent manufacturing, it is urgent to solve the problems in production line data acquisition, information processing, equipment management and control, operation scheduling, production plan management and decision-making. In order to meet the personalized needs, the flexible design of the production line has become the focus. Since the production line is constantly changing with the process and various requirements, this system is a typical switching system. This system is frequently used in other modern engineering systems, such as aircraft control systems, power systems, chemical control systems, mobile robot systems, etc.

[0003] In this system, even if each individual subsystem can remain stable, the system may still diverge if the control law and the control law of each subsystem cannot be effectively matched. The early design of the controller for this system mainly focuses on the model-based method, that is, the system model needs to be constructed in advance or the system identification is performed by using the collected data. However, with the continuous increase of the system size, the difficulty and computational complexity of system identification also show exponential growth. In order to solve this problem, data-driven methods have caused a research boom in recent years. This method directly learns the control law of the system from the data, thereby realizing the control of the system. However, the existing methods mostly rely on reinforcement learning, which requires a large amount of data set for pre-training, and cannot achieve the expected control effect in the case of small data samples. At the same time, the noise in data acquisition should also be considered, so that the designed controller has a certain robustness to noise.

[0004] Therefore, at present, a method is urgently needed to directly obtain the control law of the switching system based on the data of the system with noise, so that the unknown system can be stably operated. SUMMARY

[0005] Therefore, the present application provides an unknown switching system online control method based on noise data, which can obtain the control law of the system online based on the data collected by the system, without pre-system identification and closed-loop control of the system.

[0006] In order to achieve the above application purpose, the technical scheme of the present application is as follows:

[0007] An unknown switching system online control method based on noise data, the specific steps comprising:

[0008] S1, setting T=2N-1, wherein N=(n x +1)nu +n x , the unknown switching system collects state data and input data of past T time points during operation, constructs input data matrix U k-1 , state data matrix X k-1 and state data matrix X k of k time point with length T; the initial value of k is T; n x is the state dimension of the unknown switching system, n u is the dimension of the control input;

[0009] S2, U k-1 , X k-1 and X k are brought in, and the SDP optimization problem is solved to obtain the control gain matrix K(k) = U0Q(k)P(k) of k time point -1 and Lyapunov matrix P(k);

[0010] S3, the Lyapunov function V(x(k)) = x(k)'P(k)x(k) is constructed, and it is judged whether the current Lyapunov function of the unknown switching system is greater than a given value, that is, V(x(k)) > δ V is established; if yes, the unknown switching system has not entered the convergence domain, and the unknown switching system uses the online control rule for control until the Lyapunov function of the system is less than the given value; if not, the unknown switching system enters the convergence domain, and the unknown switching system continues to use the control gain matrix K(k-1) of the last time point to control the unknown switching system by using the state feedback control law, and the Lyapunov function matrix continues to use the matrix P(k-1) of k-1 time point until the Lyapunov function of the unknown switching system exceeds the given value, and the online control of the unknown switching system based on noise data is completed;

[0011] In step S2, the SDP formula solved at k time point is:

[0012]

[0013] subject to

[0014]

[0015] Wherein, (γ, Q, P, L, M) is a variable to be solved, matrix Q is a T×n x matrix, matrix P is a n x ×n x dimension positive definite symmetric real matrix, matrix L is a n x ×n x matrix, matrix M is a T×T matrix, and α>0 is a noise adjustment parameter, is the maximum value of the noise two-norm;

[0016] In step S3, the method of the on-line control law is that the controller side judges whether the current time is the updating time or the excitation time according to the Lyapunov function of the unknown switched system;

[0017] When the current time is neither the updating time nor the excitation time, which is called the stable running time, the unknown switched system continues to use the control gain matrix K(k-1) of the last time, uses the state feedback control law to control the unknown switched system, and the Lyapunov function matrix continues to use the matrix P(k-1) of the k-1 time;

[0018] When the current time is the updating time, the unknown switched system uses the control gain matrix K(k) solved at the k time, uses the state feedback control law to control the unknown switched system, and the Lyapunov function matrix uses the matrix P(k) solved at the k time;

[0019] When the current time is the excitation time, the controller side does not solve the SDP problem, randomly selects a control sequence with a length of N, which satisfies that each control input in the sequence is in a given range and the minimum singular value of the nx+1 order Hankel matrix composed of the sequence is not less than a set value ρ, and the Lyapunov function matrix continues to use the matrix of the excitation time, and the judgment process of whether the current time is the updating time or the excitation time is not performed until after the N time;

[0020] The judgment condition of whether the current time is the updating time is that for k>2, if V(x(k))>λ0V(x(k-1)) and V(x(k-1))≤λ0V(x(k-2)), the current time is the excitation time, and the time is recorded as k j ; if V(x(k))≤λ0V(x(k-1)) and V(x(k-1))>λ0V(x(k-2)), the time is recorded as k j , the current time is the updating time when k∈{k j +N, …, k j}; and the parameter λ0>0 is a pre-given parameter.

[0021] Advantages

[0022] (1) The method of the present application provides an online control method for unknown switching systems based on noise data. A data matrix composed of data collected at the previous T time points is collected at each time point, and a data-driven SDP problem is solved online to quickly obtain the control matrix and Lyapunov function matrix of the system. Different control rules are used to control the system according to the change rule of the Lyapunov function. As can be seen, the present application does not require prior system identification, and only needs to sample data and calculate the self-triggering time to perform state closed-loop control on the unknown switching system.

[0023] (2) In the method of the present application, the solution of the control matrix of the unknown switching system only needs to be solved by a low-complexity SDP, and the time point determination rule is used, so not all time points need to solve the SDP problem. As can be seen, the amount of calculation required to control the system is small.

[0024] (3) In the method of the present application, the unknown switching system is subjected to bounded noise, and the proposed method can ensure the robustness of the system to noise.

[0025] (4) The method of the present application provides an online control method for unknown switching systems based on noise data. Historical operation data is collected at each time point, and the system operation process is divided into four stages (excitation stage, update stage, stable stage and convergence stage) according to the system operation trajectory. Different control rules are used to control the system in different stages. In the excitation stage, a set of designed random control sequences is used on the controller side to control the system. In the update stage, a low-complexity data-based SDP problem is solved, and the optimal solution is used to construct a state feedback controller to control the system. In the convergence stage and stable stage, the system does not perform SDP solving, but uses the state feedback matrix obtained by the latest solving to control the system. As can be seen, the present application does not require prior system identification, and only needs to sample data and calculate the self-triggering time to perform state closed-loop control on the unknown switching system. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 It is a schematic diagram of the unknown switching system with a controller of the present application.

[0027] Figure 2 It is a flowchart of the method of the present application.

[0028] Figure 3 It is a switching control effect diagram of the F-18 aircraft embodiment of the present application.

[0029] Figure 4 It is a trajectory diagram of the Lyapunov function change of the F-18 aircraft embodiment of the present application. DETAILED DESCRIPTION

[0030] The application will be described in detail below with reference to the accompanying drawings and examples.

[0031] As Figure 1 shown, for the closed-loop control system designed for the unknown switching system, including the unknown switching system, the controller, the method of the application is designed for the closed-loop control system, and can stabilize the disturbed unknown switching system.

[0032] The method of the application is divided into entering a convergence domain, an updating stage, an excitation stage and a stable operation according to the state of the Lyapunov function at the current time. After entering the convergence domain, the unknown switching system will no longer solve the SDP problem, directly use the control gain matrix at the last time, control the unknown switching system by using the state feedback control law, and the Lyapunov function matrix uses the matrix at the last time.

[0033] In the updating stage, the controller side uses the matrix composed of the data of the previous T time at the current time to solve the SDP problem, controls the unknown switching system by using the state feedback control law through the control gain matrix and the Lyapunov function matrix obtained by solving, calculates a new Lyapunov function, and judges the change trend of the current Lyapunov function, so as to update the stage of the unknown switching system.

[0034] In the excitation stage, the controller side does not solve the SDP problem, controls the unknown switching system by using a column of random control inputs satisfying the condition, and the Lyapunov function uses the matrix at the last time, but does not judge the stage.

[0035] In the stable operation stage, the unknown switching system will no longer solve the SDP problem, directly use the control gain matrix at the last time, control the system by using the state feedback control law, and at the same time, the Lyapunov function matrix uses the matrix at the last time, and judges the change trend of the current Lyapunov function, so as to update the stage of the unknown switching system.

[0036] Wherein, the dynamic equation of the unknown switching system is:

[0037] x(k+1)=A σ(k) x(k)+B σ(k) u(k)+d(k)

[0038] Wherein, x(k), u(k) and d(k) are respectively the state value of the unknown switching system at time k, the control input value of the controller and the bounded disturbance suffered by the system, the state dimension of the unknown switching system is n x , the dimension of the control input is n u ; the noise dimension of the unknown switching system is n x , which is stochastically bounded, that is, for any time k where ||d(k)|| denotes the two-norm of d(k). The switching signal σ: is a piecewise continuous function that maps elements of the natural number set into a finite integer set M, where M {1,2,…,m} with m>1 representing the total number of subsystems of the unknown switched system. The matrix A σ(k) is an n x ×n x dimensional real matrix, the matrix B σ(k) is an n x ×n u dimensional real matrix, and these matrices belong to a finite matrix set S:={(A i ,B i ):i∈M}. It is assumed that for all σ(k)∈M, the matrix pair (A σ(k) ,B σ(k) ) is unknown but controllable.

[0039] As shown in Figure 2 , based on the above description, the present application provides an unknown switched system online control method based on noise data, and the specific steps are as follows:

[0040] S1, a continuously excited input sequence with a length of N(n x +1)n u +n x is constructed and satisfies where ρ is the lower bound of a given minimum singular value, Lambda (A) represents the minimum singular value of the matrix A, is defined as

[0041]

[0042] Such an input sequence is brought into the unknown switched system for operation, and the state of the unknown switched system corresponding thereto is collected The time after the data is collected is set as k=0 moment. The collected data is arranged in time sequence, and the input data matrix U -1 =[u(-N),…,(-1),0,…,0] with a dimension of n u ×T, the state data matrix X -1 =[x(-),…,x(-1),0,…,0] with a dimension of n x ×T, and the state data matrix X0 at the 0 moment X0=[x(-+1),…,(0),0,…,0] with a dimension of n x ×T are constructed; 0 in the three matrices represents a full 0 column vector with a suitable dimension. The matrix U -1 , X-1 and X0into the following SDP problem to solve

[0043]

[0044] subject to

[0045]

[0046] where U k-1 , X k-1 and X k are the input data matrix at k-1 time, the state data matrix and the state data matrix at k time, (γ, Q, P, L, M) are the variables to be solved, the matrix Q is a T×n x matrix, the matrix P is a n x ×n x positive definite symmetric real matrix, the matrix L is a n x ×n x matrix, the matrix M is a T×T matrix, and α>0 is a noise adjustment parameter. The optimal value obtained at k time is denoted as The Lyapunov matrix is The state feedback matrix control matrix is where is the inverse matrix of the matrix , the Lyapunov function V(x(0))=x(0) T P(0)x(0) is constructed, and the control input u(0)=K(0)x(0) is used to control the system.

[0047] S2, for 1≤k≤N-1. The state and input data newly collected at k time are replaced with the zero column vector in the k+Nth column of the state data matrix constructed at k-1 time, that is, the state data matrix X k at k time is [x(-N+1),…,x(k),0,…,0]. The input data matrix U k-1 at k-1 time is [u(-N),…,u(k-1),0,…,0], the state data matrix X k-1 at k-1 time is [x(-N),…,x(k-1),0,…,0], and the state data matrix X k at k time is brought into the SDP problem in the S1 step to solve, the Lyapunov matrix is The state feedback matrix control matrix is The Lyapunov function V(x(k))=x(k) T P(k)x(k) is constructed, and the control input u(k)=K(k)x(k) is used.

[0048] S3. Let T = 2N-1. When k ≥ T, neither the input data matrix nor the state data matrix has a zero vector column. Therefore, for each new column added, the first column of the current matrix is ​​deleted. That is, the input data matrix at time k-1 is U. k-1 =[u(kT),…,u(k-1)], and the state data matrix is ​​X k-1 = [x(kT),…,x(k-1)], where X is the state data matrix at time k. k = [x(k-T+1),…,x(k)].

[0049] S4. Set a constant δ V If the value is greater than 0, determine whether the Lyapunov function at the current time k is greater than this constant, i.e., V(x(k))>δ. V Whether it is valid or not.

[0050] S4-1. If not, the unknown switching system enters the convergence region. The unknown switching system continues to use the control gain matrix K(k-1) from the previous time step and uses the state feedback control law to control the system. The Lyapunov function matrix continues to use the matrix P(k-1) from time step k-1 until the Lyapunov function of the system exceeds this given value.

[0051] S4-2. If yes, then the system is said to have not entered the region of convergence. The system is controlled using an online control algorithm until the Lyapunov function of the system is less than a given value. During online control, the system's Lyapunov function is used to determine whether it is an update or excitation time. For a given constant 0 < λ0 < 1, a sequence is used... element k in j V(xjk) represents j ))>λ0V(k j -1) and V(x(k) j -1))≤λ0V(k j -2) time points; using sequences element k in j V(x(k) j -1))>λ0V(k j -2) and V(x(k) j ))≤λ0V(k j -1) is the time point.

[0052] S4-2-1, If This is neither the update moment nor the excitation moment, and is called the stable operation moment. The unknown switching system continues to use the control gain matrix K(k-1) of the previous moment, uses the state feedback control law to control the system, and the Lyapunov function matrix continues to use the matrix P(k-1) of the k-1 moment.

[0053] S4-2-2, k is the update time, the matrix U k-1 , X k-1 and X k are brought into the SDP problem in the S1 step to solve, then the Lyapunov matrix is The control matrix is The unknown switching system uses the latest control gain matrix K(k) solved at k time to control the system using the state feedback control law u(k) = K(k)x(k), and the Lyapunov function matrix is updated to V(x(k)) = x(k) T P()x(k).

[0054] S4-2-3, is the excitation time, the controller side does not solve the SDP problem, and a control sequence of length N is randomly selected, which satisfies each control input in the sequence in a given range Where And the minimum singular value of the n x +1 order Hankel matrix composed of this sequence is not less than a set value ρ, that is In the subsequent N time, the Lyapunov function matrix continues to use the matrix at the excitation time, and the S4-1 judgment process is no longer performed until N time.

[0055] It should be noted that when the average dwell time between adjacent switching times of the switching system satisfies τ ≥ T, the system can be stabilized.

[0056] As Figures 3-4 shown is an embodiment running on the F-18 flight control system for 200 units of time. The system includes two subsystems, 0.3 Mach, 26 thousand feet in height and 0.7 Mach, 14 thousand feet in height, and the corresponding system matrices are:

[0057]

[0058]

[0059] The set parameters are T = 15, δ V = 0.05, α = 1, λ0 = 0.945, the switching signal is randomly generated, and the average dwell time of the switching signal satisfies τ ≥ 15. The system initial value is x0 = [0.5, 0.5] T . The simulation results show the effectiveness of the invented online control method for unknown switching systems based on noise data.

[0060] To sum up, the above is only the preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. An online control method for an unknown switching system based on noise data, characterized in that... The specific steps include: S1, Settings T =2 N -1, where, During operation, the unknown switching system collects state data and input data from the past T time steps, constructing a k-1 time step input data matrix of length T. State data matrix and the state data matrix at time k The initial value of k is T. To switch the state dimension of the unknown system, To control the dimensions of the input; S2, Substitution , and Solve the SDP optimization problem to obtain the control gain matrix at time k. and Lyapunov matrix ; S3. Constructing Lyapunov functions Determine whether the current Lyapunov function of an unknown switching system is greater than a given value. ,Right now If the condition is true, the unknown switching system has not entered the region of convergence, and the unknown switching system is controlled by an online control law until the Lyapunov function of the system is less than the given value; if the condition is false, the unknown switching system has entered the region of convergence, and the unknown switching system continues to use the control gain matrix from the previous time step. The unknown switching system is controlled using a state feedback control law, and the Lyapunov function matrix continues to use the matrix at time k-1. The online control of the unknown switching system based on noise data is completed until the Lyapunov function of the unknown switching system exceeds this given value. In step S2, the SDP formula obtained at time k is: in, Let Q be the variable to be solved, and let matrix Q be... The matrix P is A positive definite symmetric real matrix of dimension L, wherein matrix L is The matrix M is The matrix, These are noise adjustment parameters. This represents the maximum value of the noise L2 norm; In step S3, the method of online control is as follows: the controller side determines whether the current time is an update time or an excitation time based on the Lyapunov function of the unknown switching system; When the current moment is the excitation moment, the controller does not solve the SDP problem. Instead, it randomly selects a set of control sequences of length N, where each control input in the sequence is within a given range. And constituted by this sequence The minimum singular value of a Hankel matrix of order 1 is not less than a predetermined value. In the subsequent N time steps, the Lyapunov function matrix continues to use the matrix of the excitation time, and no longer performs the process of determining whether the current time step is an update time or an excitation time, until after N time steps.

2. The online control method for an unknown switching system based on noise data according to claim 1, characterized in that: When the current moment is neither an update moment nor an excitation moment, it is called a stable operating moment. In an unknown switching system, the control gain matrix from the previous moment is continued to be used. The unknown switching system is controlled using a state feedback control law, and the Lyapunov function matrix continues to use the matrix at time k-1. .

3. The online control method for an unknown switching system based on noise data according to claim 1, characterized in that: When the current time is the update time, the unknown switching system uses the control gain matrix that was latest solved at time k. The unknown switching system is controlled using a state feedback control law, and the Lyapunov function matrix is ​​the latest matrix solved at time k. .

4. The online control method for an unknown switching system based on noise data according to claim 1, characterized in that: The criterion for determining whether the current time is the update time is: for ,if and This is the motivating moment, and it should be recorded as... ;if and Then record this moment as ,exist The time is the update time; parameters These are pre-defined parameters.

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