Novel circuit system data driving optimization control method

Abstract

The invention discloses a novel circuit system data driving optimization control method. According to the method, a novel multivariable output error state space method based on an estimated initial state matrix is established, then a self-adaptive dynamic programming algorithm based on the novel multivariable output error state space is designed, finally the optimality of the proposed algorithm is demonstrated, and the problem of dependence on circuit system model data driving optimization control is effectively relieved.

Description

Technical Field

[0001] The present invention relates to a control method for a circuit system, and in particular to a novel data-driven optimization control method for a circuit system. Background Art

[0002] Circuit systems are widely used in important industries such as automobiles, robots, and intelligent manufacturing. However, due to the inherent unmodeled dynamic characteristics, it is difficult or even impossible to obtain an accurate model of the system. How to design a controller using only measured input and output data is a very meaningful task. Based on this idea, researchers have conducted a lot of research on data-driven controller design and achieved a series of results.

[0003] However, the above research work mainly focuses on the feasible control methods of circuit systems without considering performance optimization, which has certain limitations. In order to reduce the limitations, it is necessary to study the optimization of data-driven control methods. Summary of the invention

[0004] The purpose of the present invention is to propose a novel circuit system data-driven optimization control method, which can effectively solve the circuit system optimization data-driven control problem that cannot be modeled.

[0005] The specific technical solution of the present invention is as follows: A novel circuit system data-driven optimization control method comprises the following steps:

[0006] A novel multivariable output error state space method based on estimating the initial state matrix is ​​established;

[0007] An adaptive dynamic programming algorithm based on a novel multivariable output error state space is designed;

[0008] The optimality of the proposed algorithm is demonstrated;

[0009] Furthermore, for the RLC parallel circuit system, its characteristics are:

[0010] Where U C is the capacitor voltage, I L is the inductor current, R1 and R2 are resistors, C is the capacitor, L is the inductor, and U is the power supply voltage;

[0011] Let the capacitor voltage U C =ξ1(ω), inductor current I L =ξ2(ω), resistor R2 voltage σ(ω), power supply voltage U=δ(ω), using the above characteristics, the state space model of the RLC parallel circuit system is established as:

[0012] In the formula,

[0013] The state space model of the RLC parallel circuit system is discretized as

[0014] In the formula, is the identity matrix;

[0015] For the unknown system matrices Ξ, Y, Ω, Θ in the model, a novel multivariable output error state space method based on estimating the initial state matrix is ​​established to identify them. First, two Hankel matrices U are constructed using the input and output data. 0|τ and Y 0|τ for

[0016] Wherein, τ (τ>2) and N are positive integers;

[0017] Using system characteristics, U 0|τ and Y 0|τ satisfy Y 0|τ =O τ X0+Ψ τ U 0|τ

[0018] In the formula, X0=[ξ(1) ξ(2) … ξ(N)],

[0019] For the Hankel matrix The state dimension n=rank(L 22 )

[0020] In the formula,

[0021] According to the above formula, we can deduce and Combined with Y 0|τ =O τ X0+Ψ τ U 0|τ We can get:

[0022] Since Q1 and Q2 are positive definite matrices, multiplying both sides of the above equation by Q2 yields O τ X0Q2=L 22 , further obtained To this end, the X0 estimation rate is designed to drive Oτ The updates are as follows:

[0023] Where 0<α<1, i=1, 2, … are iteration indices,

[0024] At this point, a novel multivariable output error state space method based on estimating the initial state matrix has been established. The system matrix identified under this method is as follows:

[0025] In the formula,

[0026] Furthermore, an adaptive dynamic programming algorithm based on a novel multivariable output error state space is designed. The specific steps are as follows:

[0027] Select the performance index J[ξ(ω)]=ξ T (ω)Eξ(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γJ[ξ(ω+1)], where J[·] is the indicator function, and are two positive definite matrices, 0<γ≤1;

[0028] The optimal control rate obtained by minimizing the index is as follows:

[0029] The above formula is a theoretical solution, which is actually difficult to solve. Therefore, an iterative solution method is designed as follows: Φ i+1 [ξ(ω)]=ξ T (ω)Eξ(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γΦ i [ξ(ω+1)]

[0030] Where Φ(·) is the selected function and ξ(ω+1) is the system matrix estimated using the multivariable output error state space method;

[0031] At this point, the design of the adaptive dynamic programming algorithm based on the novel multivariable output error state space is completed.

[0032] Furthermore, the proposed algorithm can ensure the optimality of the control rate. The demonstration process is as follows:

[0033] A001: According to the definition of performance indicators, we can get G i+1 [ξ(ω)]=ξT (ω)Eξ(ω)+η T [ξ(ω)]Fη[ξ(ω)]+γΓ i [ξ(ω+1)]

[0034] Where η[ξ(ω)] is any stable input, Г0(·)=Φ0(·)=0;

[0035] A002: Subtract Г from both sides of A001 i [ξ(ω)],

[0036] A003: Rewrite A002 to get

[0037] A004: Rewrite A003,

[0038] A005: When i→∞, we can get

[0039] A006: Integrates A004 and A005,

[0040] A007: Since η[ξ(ω)] is an arbitrarily stable input, ξ(∞)=0. Under this premise, A006 gives

[0041] Where, ε>0;

[0042] A008: Combining the defined index with A007, we can get Φ i+1 [ξ(ω)], which indicates that Φ i+1 [ξ(ω)]≤Γ i+1 [ξ(ω)]≤ε is bounded;

[0043] A009: Select function Λ i [ξ(ω)]Full Where Λ0(·)=Φ0(·)=0;

[0044] A010: For i = 0,

[0045] A011: A010 indicates that Λ0[ξ(ω)]≤Φ1[ξ(ω)];

[0046] A012: Based on A011 and assuming Λ i-1 [ξ(ω)]≤Φi [ξ(ω)] holds, we can get Φ i+1 [ξ(ω)]-Λ i [ξ(ω)] =γ(Φ i [ξ(ω+1)]-Λ i-1 [ξ(ω+1)]) ≥0

[0047] A013: Using mathematical induction, A012 can deduce Λ i [ξ(ω)]≤Φ i+1 [ξ(ω)], combining this conclusion with A009, we have Φ i [ξ(ω)]≤Φ i+1 [ξ(ω)], which indicates a monotonic non-decreasing function;

[0048] A014: According to the definition of performance indicators, we can get Φ i [ξ(ω)] ≤ξ T (ω)Eξ(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γФ i-1 [ξ(ω+1)]

[0049] Where ε>0 represents an arbitrarily stable input;

[0050] A015: When i→∞, according to A013, we can get Φ i [ξ(ω)]≤Φ ∞ [ξ(ω)];

[0051] A016: Combined with A014 and A015, Φ i [ξ(ω)]≤ξ T (ω)Eξ(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γΦ ∞ [ξ(ω+1)]

[0052] A017: When i→∞, A016 gives Φ ∞ [ξ(ω)] ≤ξ T (ω)Eξ(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γΦ ∞ [ξ(ω+1)]

[0053] A018: Since i→∞ is an arbitrary stable input, we can get

[0054] A019: According to the definition of performance indicators, we can get

[0055] A020: Combined with A019 and A015,

[0056] A021: When i→∞, A020 ​​gives

[0057] A022: Combined with A021 and A018,

[0058] A023: A022 indicates Φ ∞ [ξ(ω)] is optimal, and the δ obtained based on the function is * [ξ(ω)]=v ∞ (ω) is also optimal, and the argument is complete. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0060] Figure 2 This is a comparison diagram of model outputs identified using the novel multivariable output error state space method proposed by the present invention;

[0061] Figure 3 The state curve diagram of the method proposed by the present invention is adopted in the embodiment; DETAILED DESCRIPTION

[0062] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments 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.

[0063] like Figure 1 As shown, a novel circuit system data-driven optimization control method comprises the following steps:

[0064] Step 1: Let δ(ω) = rand(1) enter the system and collect data offline, that is, U 0|τ , Y 0|τ ;

[0065] Step 2: Identify the system matrices A, B, C, and D using the established novel multivariable output error state space method based on estimating the initial state matrix;

[0066] Step 3: Use the identified system matrix to drive the adaptive dynamic programming algorithm to calculate the optimal control rate;

[0067] Step 4: Update the control input δ(ω) online;

[0068] Step 5: Use the online updated input δ(ω) to control the circuit system;

[0069] Step 6: Repeat step 4 to enter the next cycle.

[0070] An embodiment of the present invention is described below:

[0071] Considering the optimization data-driven control problem of the RLC parallel circuit system, its discretized state space model is:

[0072] in,

[0073] Figure 1 is a flow chart of the method of the embodiment of the present invention; applying the proposed method, the output of the identified model is as follows Figure 2 As shown, it can be seen that the circuit system model parameters can be effectively identified: Figure 3 The state curve diagrams after the proposed method is applied to the system are shown. From these three figures, it can be seen that the proposed method can not only effectively identify the parameters, but also obtain a satisfactory control performance.

[0074] References

[0075] [1]Dc Persis C, Tesi P.Formulas for data-driven control: Stabilization, optimality, and robustness[J]. IEEE Transactions on Automatic Control, 2019, 65(3): 909-924.

[0076] [2] Berberich J, J, Müller MA, et al. Data-driven model predictive control with stability and robustness guarantees[J]. IEEE Transactions on Automatic Control, 2020, 66(4): 1702-1717.

Claims

1. A novel circuit system data-driven optimization control method, characterized in that: The following steps are involved: A novel multivariable output error state space method based on estimating the initial state matrix is ​​established; An adaptive dynamic programming algorithm based on a novel multivariable output error state space is designed: The optimality of the proposed algorithm is demonstrated.

2. A novel circuit system data driven optimization control method according to claim 1, characterized in that A novel multivariable output error state space method based on estimating the initial state matrix is ​​established. The specific steps are as follows: For the RLC parallel circuit system, its characteristics are: Where U C is the capacitor voltage, I L is the inductor current, R1 and R2 are resistors, C is the capacitor, L is the inductor, and U is the power supply voltage; Let the capacitor voltage U C =ξ1(ω), inductor current I L =ξ2(ω), resistor R2 voltage σ(ω), power supply voltage U=δ(ω), using the above characteristics, the state space model of the RLC parallel circuit system is established as: In the formula, The state space model of the RLC parallel circuit system is discretized as In the formula, is the identity matrix; For the unknown system matrices Ξ, Y, Ω, Θ in the model, a novel multivariable output error state space method based on estimating the initial state matrix is ​​established to identify them. First, two Hankel matrices U are constructed using the input and output data. 0|τ and Y 0|τ for Wherein, τ (τ>2) and N are positive integers; Using system characteristics, U 0|τ and Y 0|τ satisfy Y 0|τ =O τ X0+Ψ τ U 0|τ X0: [ξ(1) ξ(2) … ξ(N)], For the Hankel matrix The state dimension n=rank(L 22 ) In the formula, According to the above formula, we can deduce and Combined with Y 0|τ =O τ X0+Ψ τ U 0|τ We can get: Since Q1 and Q2 are positive definite matrices, multiplying both sides of the above equation by Q2 yields O τ X0Q2=L 22 , further obtained To this end, the X0 estimation rate is designed to drive O τ The updates are as follows: Where 0<α<1, i=1, 2, … are iteration indices, At this point, a novel multivariable output error state space method based on estimating the initial state matrix has been established. The system matrix identified under this method is as follows: In the formula, 3. A novel circuit system data driven optimization control method according to claim 2, characterized in that An adaptive dynamic programming algorithm based on a novel multivariable output error state space is designed. The specific steps are as follows: Select the performance index J[ξ(ω)]=ξ T (ω)Eξ(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γJ[ξ(ω+1)], where J[·] is the indicator function, E>0 and F>0 are two positive definite matrices, 0<γ≤1; The optimal control rate obtained by minimizing the index is as follows: The above formula is a theoretical solution, which is actually difficult to solve. Therefore, an iterative solution method is designed as follows: F i+1 [ξ(ω)]=ξ T (ω)Ex(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γΦ i [ξ(ω+1)] Where Φ(·) is the selected function and ξ(ω+1) is the system matrix estimated using the multivariable output error state space method; At this point, the design of the adaptive dynamic programming algorithm based on the novel multivariable output error state space is completed.

4. A novel circuit system data driven optimization control method according to claim 3, characterized in that The optimality of the proposed algorithm is demonstrated. The proof process is as follows: A001: According to the definition of performance indicators, we can get G i+1 [ξ(ω)]=ξ T (ω)Ex(ω)+η T [ξ(ω)]Fη[ξ(ω)]+γΓ i [ξ(ω+1)] Where η[ξ(ω)] is any stable input and Г0(·)=Φ0(·)=0: A002: Subtract Г from both sides of A001 i [ξ(ω)], A003: Rewrite A002 to get A004: Rewrite A003, A005: When i→∞, we can get A006: Integrates A004 and A005, A007: Since η[ξ(ω)] is an arbitrarily stable input, ξ(∞)=0. Under this premise, A006 gives Where, ε>0; A008: Combining the defined index with A007, we can get Φ i+1 [ξ(ω)], which indicates that Φ i+1 [ξ(ω)]≤Г i+1 [ξ(ω)]≤ε is bounded; A009: Select function Λ i [ξ(ω)] satisfies Where Λ0(.)=Φ0(.)=0; A010: For i = 0, A011: A010 indicates that Λ0[ξ(ω)]≤Φ1[ξ(ω)]; A012: Based on A011 and assuming Λ i-1 [ξ(ω)]≤Φ i [ξ(ω)] holds, we can get A013: Using mathematical induction, A012 can deduce Λ i [ξ(ω)]≤Φ i+1 [ξ(ω)], combining this conclusion with A009, we have Φ i [ξ(ω)]≤Φ i+1 [ξ(ω)], which indicates a monotonic non-decreasing function; A014: According to the definition of performance indicators, we can get F i [x(ω)] ≤ξ T (ω)Ex(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γΦ i-1 [ξ(ω+1)] Where ε>0 represents an arbitrarily stable input; A015: When i→∞, according to A013, we can get Φ i [ξ(ω)]≤Φ ∞ [ξ(ω)]; A016: Combined with A014 and A015, F i [ξ(ω)]≤ξ T (ω)Ex(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γΦ ∞ [ξ(ω+1)] A017: When i→∞, A016 gives F ∞ [x(ω)] ≤ξ T (ω)Ex(ω)+δ T [ξ(ω)]Fδ[ξ(ω)]+γΦ ∞ [ξ(ω+1)] A018: Since i→∞ is an arbitrary stable input, we can get A019: According to the definition of performance indicators, we can get A020: Combined with A019 and A015, A021: When i→∞, A020 ​​gives A022: Combined with A021 and A018, A023: A022 indicates Φ ∞ [ξ(ω)] is optimal, and the δ obtained based on the function is * [ξ(ω)]=v ∞ (ω) is also optimal, and the argument is complete.

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