Circuit system iterative learning control method for processing local Lipscherz nonlinearity under unknown state

Abstract

The invention discloses a circuit system iterative learning control method for processing local Lipscherz nonlinearity under an unknown state. According to the method, a self-adaptive gain state observer based on a reference model is constructed aiming at the practical problem that the current of a circuit system is unknown. An iteration length selection index is constructed, so that the output of the system and the observer does not violate a given limit range. An iterative learning controller is constructed to control a circuit system with local Lipscherz nonlinearity. Compared with a traditional control method needing an accurate mathematical model, the control algorithm provided by the invention is more novel and simple in application condition. When the method is used for repeated task operation, the control precision is effectively improved, and the method has good engineering application value.

Description

Technical Field

[0001] The invention relates to a control method for a circuit system, and in particular to an iterative learning control method for a circuit system for processing local Lipschitz nonlinearity under unknown state. Background Art

[0002] Circuit systems are the cornerstone of modern communications. For example, in mobile phone communications, from signal transmission and reception, complex radio frequency circuits and digital signal processing circuits are involved to achieve information modulation, demodulation and long-distance transmission, ensuring that people can conduct voice calls, data transmission and other communication activities anytime and anywhere. Circuit systems have many different manifestations of complexity, mainly including multiple variables and multiple physical quantities, nonlinear characteristics and complex dynamic behaviors caused by various circuit devices, time-varying, high control difficulty caused by large-scale, randomness caused by noise interference, etc. Considering the complexity of the above aspects, the control of circuit systems is very challenging, and it is necessary to study and adopt advanced technologies and methods to deal with it. Summary of the invention

[0003] The purpose of the present invention is to propose an iterative learning control method for a circuit system for processing local Lipschitz nonlinearity under unknown states, which can effectively solve the problems of multiple variables and multiple physical quantities, nonlinearity, time-varying, high control difficulty, randomness, etc. existing in the circuit system and achieve good control effect.

[0004] The specific technical solution of the present invention is as follows: an iterative learning control method for a circuit system for processing local Lipschitz nonlinearity under unknown state, comprising the following steps:

[0005] For the following circuit system:

[0006] In the formula, x k (t) = [x 1，k (t)x 2，k (t)] T represents the loop current, x 1,k (t), x 2,k (t) is x k (t) is the sub-state, k is the number of iterations, R1, R2 are resistances, L1, L2, M are inductors, u k (t) represents the controller, θ(t) represents the unknown matrix time-varying function, ζ(x k (t)) represents the local Lipschitz nonlinear function related to the current. A and B are consistent with the coefficients in the circuit model. The system output is y k (t) = Cx k (t), where C is the system output matrix;

[0007] The reference orbit of the system is generated by the following reference model:

[0008] In the formula, x r (t) represents the reference state, u r (t) represents the reference input, y r (t) represents the reference output;

[0009] Aiming at the practical problem of unknown current in the circuit system, an adaptive gain state observer based on the reference model is constructed:

[0010] In the formula, x r,k (t) represents the estimated current value, represents the bounded adaptive gain, y r,k (t) represents the observer output;

[0011] The construction of the iteration length selection indicator is as follows:

[0012] Where, T k represents the actual running time of each iteration of the system, t∈[0,T] represents the time variable, where T represents the ideal running length of each iteration of the system, β1, are the constraints on the system output and the observer output, ||.|| represents the Euclidean norm, represents t∈[0,T] on ||y r (t)||'s maximum value;

[0013] Construct the state estimation error e in the following form x,k (t) and tracking error e y，k (t): e x，k (t) = x k (t)-x r，k (t) e y，k (t) = y k (t)-y r，k (t)

[0014] The constructed controller looks like this: t≤T k

[0015] In the formula, represents the estimated value of θ(t) and is bounded, ξ(x r，k (t)) represents the local Lipschitz nonlinear function associated with the current estimate;

[0016] The estimated current value has the following relationship:

[0017] In the formula, ψ represents the transformation matrix, from which we can get x r，k (t) is bounded, and we can conclude that u k (t) is bounded;

[0018] The relationship between loop current and controller is as follows:

[0019] In the formula, α1, α2 represent k-type functions, because u k (t) is bounded, so x k (t) is bounded;

[0020] The local Lipschitz nonlinearity has the following relationship: z k (t) = h(t)x k (t)+(1-h(t))x r,k (t)

[0021] In the formula, represents the local Lipschitz function, α3 represents the k-type function, h(t) represents a function greater than zero and less than one, is a function greater than or equal to zero, because x k (t), x r，k (t) is bounded, so z k (t) is bounded, and we can conclude that is bounded and satisfies where β z is an unknown constant greater than zero;

[0022] The design parameter update law is as follows:

[0023] In the formula, proj θ (.),proj L (.) indicates parameter update projection, Indicates a gain greater than zero, (.) T Represents the transpose of a vector or matrix;

[0024] In order to ensure the continuity of the analysis, the virtual tracking error ω is defined as follows: x，k (t):

[0025] Construct a composite energy function to analyze the convergence of the tracking error. The proof process is as follows:

[0026] C001: Select a composite energy function in the following form:

[0027] C002: Wherein, where β θ ≥||θ(t)|| is an unknown constant greater than zero, λ1 is an eigenvalue greater than zero, and tr(.) represents the trace of a matrix;

[0028] C003: Consider the case of t ≤ T k for the difference ΔE k (t) between E k-1 (t) and E k (t). Assume that PB = C, where P is a positive definite matrix, and where:

[0029] C004: According to C003, the following formula can be obtained:

[0030] C005: Consider the case of T k < t ≤ T for the difference ΔE k (t) between E k-1 (t) and E k (t), where:

[0031] C006: According to C005, the following formula can be obtained:

[0032] C007: According to C004 and C006, ΔE k (t) for the case of 0 < t ≤ T can be obtained:

[0033] C008: Wherein,

[0034] C009: Consider the boundedness of E1(t) for the case of t ≤ T k :

[0035] C010: According to C009, the boundedness of E1(t) for the case of t ≤ T k can be obtained;

[0036] C011: Consider Tk Boundedness of E1(t) when <t≤T:

[0037] C012: According to C011, the boundedness of E1(t) when <t≤T can be obtained; k Boundedness of E1(t) when <t≤T;

[0038] C013: According to C009 and C011, the boundedness of E1(t) when 0<t≤T can be obtained;

[0039] C014: Give the proof of the convergence of the tracking error:

[0040] C015: From the positive definiteness of E k (t) and the boundedness of E1(t), the convergence form of the virtual estimation error can be obtained as follows:

[0041] C016: From C015, it can be obtained that Furthermore, it can be obtained that e y，k (t) converges when t∈[0, T k , and when t∈[0, T k , x r，k (t) = x r (t), y k (t) = y r,k (t) = y r (t), which indicates that at time T k y k (t), y r，k (t) does not touch the boundary. According to the proof by contradiction, it can be shown that Description of the Drawings

[0042] Figure 1 Is the flowchart of the method of the embodiment of the present invention;

[0043] Figure 2 Is the system output tracking diagram using the method proposed by the present invention;

[0044] Figure 3 Is the observer output tracking diagram using the method proposed by the present invention;

[0045] Figure 4 Is the tracking error convergence diagram using the method proposed by the present invention; Detailed Embodiment

[0046] The present invention is further illustrated below in conjunction with examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0047] like Figure 1 As shown, an iterative learning control method for a circuit system for processing local Lipschitz nonlinearity under unknown state includes the following steps:

[0048] Step 1: Set the initial value of the parameter;

[0049] Step 2: Update algorithm parameters;

[0050] Step 3: Generate control input u in real time based on updated algorithm parameters k (t);

[0051] Step 4: According to the control input u k (t) The tracking error generated is used to update the algorithm parameters synchronously;

[0052] Step 5: Repeat steps 3 and 4 until the current iteration ends and the next iteration begins;

[0053] Step 6: An embodiment of the present invention is described below: Consider an iterative learning control method for a circuit system that handles local Lipschitz nonlinearity under unknown states. The corresponding mathematical model is:

[0054]

[0055] The system parameters are: R1 = 1Ω, R2 = 1Ω is the circuit resistance, L1 = 0.36H, L2 = 0.5H is the inductor, M = 0.15H is the mutual inductor, θ(t)ξ(x k (t)) = x 2，k sin 3 t+0.8sin 2 tsinx 1，k ;

[0056] The expected reference input is: The ideal operating length T of the system is 3s, and the system output limit and observer output limit are β1=2 and β2=1.65 respectively;

[0057] Figure 1 is a flow chart of a method according to an embodiment of the present invention; applying the proposed method, Figure 2 , 3 denote the system output and observer output tracking diagrams respectively, Figure 4It can be seen from these three figures that the proposed method has a good application effect in the circuit system, and after the 10th iteration, a satisfactory tracking performance can be obtained.

[0058] References

[0059] [1]

[0060] [2] D.Shen, J.-X.Xu. Adaptive learning control for nonlinear systems with randomly varying iteration lengths. IEEE Transactions on Neural Networks and Learning Systems, vol.30, pp.1119-1132, 2019.

Claims

1. An iterative learning control method for a circuit system for processing local Lipschitz nonlinearity under unknown state, characterized in that: It includes the following steps: For the problem of unknown current in the circuit system, an adaptive gain state observer based on a reference model is constructed; An iterative length selection index is constructed to ensure that the outputs of the system and the observer do not violate the given limit range; An iterative learning controller is constructed to control the circuit system with locally Lipschitz nonlinearity.

2. The iterative learning control method for a circuit system for processing local Lipschitz nonlinearity under unknown state according to claim 1, characterized in that: For the problem of unknown state in the circuit system, an adaptive gain state observer based on a reference model is constructed: For the following circuit system: In the formula, x k (t) = [x 1，k (t)x 2，k (t)] T represents the loop current, x 1，k (t), x 2，k (t) is x k (t) is the sub-state, k is the number of iterations, R1, R2 are resistances, L1, L2, M are inductors, u k (t) represents the controller, θ(t) represents the unknown matrix time-varying function, ζ(x k (t)) represents the local Lipschitz nonlinear function related to the current. A and B are consistent with the coefficients in the circuit model. The system output is y k (t) = Cx k (t), where C is the system output matrix; The reference trajectory of the system is generated by the following reference model: In the formula, x r (t) represents the reference state, u r (t) represents the reference input, y r (t) represents the reference output; For the practical problem of unknown current in the circuit system, an adaptive gain state observer based on a reference model is constructed: In the formula, x r，k (t) represents the estimated current value, represents the bounded adaptive gain, y r，k (t) represents the observer output.

3. The iterative learning control method for a circuit system for processing local Lipschitz nonlinearity under unknown state according to claim 1, characterized in that: An iterative length selection index is constructed to ensure that the outputs of the system and the observer do not violate the given limit range: The iterative length selection index is constructed as follows: Where, T k represents the actual running time of each iteration of the system, t∈[0,T] represents the time variable, where T represents the ideal running length of each iteration of the system, are the constraints on the system output and the observer output, ||.|| represents the Euclidean norm, represents t∈[0,T] on ||y r The maximum value of (t)|| 4. The iterative learning control method for a circuit system for processing local Lipschitz nonlinearity under unknown state according to claim 1, characterized in that: An iterative learning controller is constructed to control the circuit system with locally Lipschitz nonlinearity: Construct the state estimation error e in the following form x，k (t) and tracking error e y，k (t): e x，k (t)=x k (t)-x r，k (t) e y，k (t)=y k (t)-y r，k (t) The constructed controller is as follows: In the formula, represents the estimated value of θ(t) and is bounded, ζ(x r,k (t)) represents the local Lipschitz nonlinear function associated with the current estimate; The following relationship exists for the current estimate: In the formula, ψ represents the transformation matrix, from which we can get x r，k (t) is bounded, and we can conclude that u k (t) is bounded; The following relationship exists between the loop current and the controller: In the formula, α1, α2 represent k-type functions, because u k (t) is bounded, so x k (t) is bounded; The following relationship exists for the locally Lipschitz nonlinearity: z k (t)=h(t)x k (t)+(1-h(t))x r，k (t) In the formula, represents the local Lipschitz function, α3 represents the k-type function, h(t) represents a function greater than zero and less than one, β α (t), γ α (t) is a function greater than or equal to zero, because x k (t), x r，k (t) is bounded, so z k (t) is bounded, and we can conclude that is bounded and satisfies where β z is an unknown constant greater than zero; The design parameter update law is in the following form: In the formula, proj θ (.),proj L (.) indicates parameter update projection, Indicates a gain greater than zero, (.) T Represents the transpose of a vector or matrix; In order to ensure the continuity of the analysis, the virtual estimation error ω is defined as follows: x，k (t): A composite energy function is constructed to analyze the convergence of the tracking error, and the proof process is as follows: B001: Select a composite energy function of the following form: B002: In the formula, where β θ ≥||θ(t)|| is an unknown constant greater than zero, λ1 is an eigenvalue greater than zero, and tr(.) represents the trace of the matrix; B003: Consider t≤T k Case E k (t) and E k-1 (t) The difference AE k (t), assuming PB = C, where P is a positive definite matrix, where: B004: According to B003, the following formula can be obtained: B005: Consider T k <When t ≤ T, E k (t) and E k-1 (t), the difference ΔE k (t), where: B006: According to B005, the following formula can be obtained: B007: According to B004 and B006, ΔE in the case of 0 < t ≤ T can be obtained k (t): B008: In the formula, B009: Consider t≤T k The boundedness of E1(t) in the case: B010: According to B009, E1(t) is obtained when t≤T k Boundedness of the case; B011: Consider T k Boundedness of E1(t) when <t≤T: B012: According to B011, E1(t) at T k Boundedness when <t≤T; B013: According to B009 and B011, the boundedness of E1(t) can be obtained for 0 < t ≤ T; B014: Give the convergence proof of the tracking error: B015: By E k The positive definiteness of (t) and the boundedness of E1(t) lead to the convergence form of the virtual estimation error as follows: B016: obtained from B015 Then we can get e y,k (t) at t∈[0,T k ] converges on t∈[0,T k ] on x r，k (t) = x r (t), y k (t) = y r，k (t) = y r (t), which means that in T k Time y k (t), y r，k (t) does not touch the boundary, which can be proved by contradiction. That is, the tracking error converges along the iteration axis.

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