A data-driven optimization control method for mass-spring-damper system

Abstract

The present invention discloses an optimization control method for a mass-spring-shock absorber system based on data drive. The method first obtains a compact data model of the mass-spring-shock absorber system, and uses an optimization criterion based on the model to approximate unknown pseudo-partial derivative parameters; presets an optimization index, and then uses a neural network to approximate the preset index function at the future moment; uses adaptive dynamic programming technology to design an optimal controller under the preset index to control the mass-spring-shock absorber system, effectively improving the control performance.

Description

Technical Field

[0001] The present invention relates to a control method for a mass-spring-shock absorber system, and in particular to an optimization control method for a mass-spring-shock absorber system based on data driving. Background Art

[0002] Mass-spring-damper is widely used in nuclear power plants, thermal power plants, chemical industry and other important industries. However, due to the inherent unmodeled dynamic characteristics, it is difficult or even impossible to get an accurate model of the system. How to design a controller using only measured state and input data is a very meaningful work. Based on this idea, researchers have carried out 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 case where the preset indicator is quadratic. Under the quadratic indicator, the local optimal controller is obtained, which has certain limitations. In order to reduce the limitations, it is necessary to study the method of designing the controller under the global indicator. Summary of the invention

[0004] The purpose of the present invention is to propose an optimization control method for a mass-spring-damper system based on data-driven, which can effectively solve the optimization control problem of a mass-spring-damper system that cannot be modeled.

[0005] The specific technical solution of the present invention is as follows: A data-driven optimization control method for a mass-spring-damper system comprises the following steps:

[0006] A compact data model is given using the quantized state signal, and then an optimization criterion is used to approximate the unknown pseudo-partial derivative parameters in the model.

[0007] Preset the optimization index, and then use the neural network to approximate the preset index function at the future moment;

[0008] Using adaptive dynamic programming technology, the optimal controller under the preset indicators is designed to control the mass-spring-damper system.

[0009] Furthermore, the discrete mathematical expression of the mass-spring-damper system is as follows:

[0010]

[0011] In the formula, Indicates the system status. represents the system input, m represents the system dimension, which is a known integer, k∈{0, 1, ...} represents the sampling time, f(·) represents the unknown nonlinear function, c x and c uRepresents the unknown system order.

[0012] Furthermore, the specific steps of using adaptive dynamic programming technology to design an optimal controller under preset indicators include: obtaining a compact data model of the mass-spring-shock absorber system, and using optimization criteria based on this model to approximate unknown pseudo-partial derivative parameters; presetting the optimization indicator, and then using a neural network to approximate the indicator function of the preset future moment; using adaptive dynamic programming technology to design an optimal controller under the preset indicator to control the mass-spring-shock absorber system.

[0013] Furthermore, the specific steps of designing the optimal controller under the preset index by using the adaptive dynamic programming technology include: obtaining a compact data model of the mass-spring-shock absorber system, and using the optimization criterion based on the model to approximate the unknown pseudo-partial derivative parameters; presetting the optimization index, and then using the neural network to approximate the index function of the preset future moment; using the adaptive dynamic programming technology, designing the optimal controller under the preset index to control the mass-spring-shock absorber system, specifically including:

[0014] Using dynamic linearization techniques, a compact data model of the mass-spring-damper system is obtained as follows:

[0015] Δx k+1 =Φ k Δu k

[0016] In the formula, It is called the pseudo partial derivative, Δx k+1 =x k+1 -x k , Δu k =u k -u k-1 ;

[0017] Introduce a uniform quantizer as follows:

[0018]

[0019] In the formula, q(u k ) represents the quantized u k ,

[0020] Preset an infinite-dimensional indicator function as follows:

[0021]

[0022] Solve the equation The optimal controller under this indicator is obtained as follows:

[0023]

[0024] Using the optimal criterion function, design pseudo partial derivatives using quantized input data Update algorithm; select the following cost function:

[0025]

[0026] Solve the equation Get the pseudo partial derivative The update algorithm is as follows:

[0027]

[0028] Where 0<ρ<2, λ>0 are the selected parameters. The algorithm can ensure the pseudo partial derivative The estimation error is bounded, and the proof process is as follows:

[0029] definition get:

[0030]

[0031] definition The estimated error Subtract both sides of the above equation The following formula is obtained:

[0032]

[0033] use replace The following formula is obtained:

[0034]

[0035] According to the compact format model, Taking the two-norm operation on the above formula, we get the following formula:

[0036]

[0037] Because λ>0, we have:

[0038]

[0039] choose get:

[0040]

[0041] According to 0<ρ<2, λ>0, we get:

[0042]

[0043] Substituting the above formula into

[0022] , we get:

[0044]

[0045] Substituting the above equation and

[0021] into

[0020] yields:

[0046]

[0047] Taking the expectation operation on the above formula, we get:

[0048]

[0049] As the system runs, that is, k→∞, the above formula shows that the observation error Converge to this boundary End of proof;

[0050] With the help of neural network, the index function of the preset future moment is approximated. The approximate index function can be expressed as Then the goal of neural network weight adjustment is to minimize the error below

[0051]

[0052] Choosing a loss function Applying gradient descent to this function, we get the neural network weight update rate as follows:

[0053]

[0054]

[0055] In the formula, Θ k =σ[Y T x k+1 ]-σ[Y T x k ], 0<μ<1 is the selected parameter. Under the designed weight update rate, the approximate error of the indicator function is ultimately uniformly bounded. The proof process is as follows:

[0056] Select the following Lyapunov function

[0057]

[0058] Performing a backward difference operation on the above formula, we get

[0059]

[0060] Substituting the neural network weight update rate into the above formula, we get

[0061]

[0062] αk Substituting into the above formula, we get

[0063]

[0064] Since 0<μ<1, we have And because ||σ[·]||≤1, So there is Based on the above analysis, we can get

[0065]

[0066] The above formula shows that as long as It holds true, so the approximation error of the indicator function is eventually uniformly bounded, and the proof ends;

[0067] Using the approximate Φ k and J[x k+1 ], we can get the approximate solution of the optimal control, which is as follows:

[0068]

[0069] Using the approximate solution of optimal control, the state of the mass-spring-damper system can be guaranteed to converge consistently and boundedly. The proof process is as follows:

[0070] Select the Lyapunov function below;

[0071] V[x k ]=||x k || 2

[0072] Performing a backward difference operation on the above formula, we get:

[0073] ΔV[x k+1 ]=||x k+1 || 2 -||x k || 2

[0074] The Δu in the compact format model k use Substituting the descendants into the above formula, we get

[0075]

[0076] The Δu in the compact format model k use Substituting the descendants into the above formula, we get

[0077]

[0078] In the formula satisfy

[0079] According to the optimality principle, there exists a Make||x k +Φ k (1-θ k )Δu k || 2 ≤K||x k || 2 Based on this relationship, we can get

[0080]

[0081] The above formula shows that as long as It holds, so the state of the system is eventually uniformly bounded, and the proof ends. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0083] Figure 2 The state 1 curve diagram of the embodiment using the method of the present invention;

[0084] Figure 3 The state 2 curve diagram of the embodiment using the method of the present invention;

[0085] Figure 4 This is a sequence diagram of attacks suffered by the method proposed by the present invention in the embodiment; DETAILED DESCRIPTION

[0086] 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.

[0087] like Figure 1 As shown, a data-driven optimization control method for a mass-spring-damper system comprises the following steps:

[0088] Step 1: Set the initial value of the parameter;

[0089] Step 2: Update pseudo partial derivatives

[0090] Step 3: Update the indicator function

[0091] Step 4: Use the updated and Information, update control input

[0092] Step 6: Repeat step 2 to enter the next cycle.

[0093] An embodiment of the present invention is described below:

[0094] Consider the stabilization control problem of the mass-spring-damper system, and its system model is described as:

[0095]

[0096] Figure 1 is a flow chart of a method according to an embodiment of the present invention; applying the proposed method, the curve diagram of state 1 is as follows Figure 2 As shown, the curve diagram of state 2 is as follows Figure 3 As shown in the figure, the attack sequence diagram is as follows Figure 4 As shown in Figure 2, it can be seen that under attack and quantization, the state curve using the proposed method converges faster.

[0097] References

[0098] [1]

[0099] [2] W. Bai, Q. Zhou, T. Li, H. Li. Adaptive reinforcement learning neural network control for uncertain nonlinear system with input saturation. IEEETransactions on Cybernetics, vol.50, pp.3433-3443, 2019.

Claims

1. A data-driven optimization control method for a mass-spring-damper system, characterized in that: The following steps are involved: A compact data model is given using the quantized state signal, and then an optimization criterion is used to approximate the unknown pseudo-partial derivative parameters in the model. Preset the optimization index, and then use the neural network to approximate the preset index function at the future moment; Using adaptive dynamic programming technology, the optimal controller is designed under the preset indicators to control the mass-spring-damper system, including: (1) Using dynamic linearization technology, a compact data model of the mass-spring-damper system is obtained as follows: Δx k+1 =Φ k Thu k In the formula, Indicates the system status. represents the system input, m represents the system dimension, which is a known integer, k∈{0,1,...} represents the sampling time, It is called the pseudo partial derivative, Δx k+1 =x k+1 -x k , Δu k =u k -u k-1 ; (2) Introduce a uniform quantizer as follows: In the formula, q(u k ) represents the quantized u k , (3) Preset an infinite-dimensional index function as follows: Solve the equation The optimal controller under this indicator is obtained as follows: (4) Using the optimal criterion function, design pseudo partial derivatives using quantized input data Update algorithm; select the following cost function: Solve the equation Get the pseudo partial derivative The update algorithm is as follows: Where, 0<ρ<2,λ>0 are selected parameters.

2. The data-driven optimization control method of the mass-spring-damper system according to claim 1, characterized in that: The discrete mathematical expression of the mass-spring-damper system is as follows: In the formula, Indicates the system status. represents the system input, m represents the system dimension, which is a known integer, k∈{0,1,...} represents the sampling time, f(·) represents the unknown nonlinear function, c x and c u Represents the unknown system order.

3. The data-driven optimization control method for a mass-spring-damper system according to claim 1, characterized in that: The specific steps of using adaptive dynamic programming technology to design an optimal controller under preset indicators include: obtaining a compact data model of the mass-spring-shock absorber system, and using optimization criteria based on this model to approximate unknown pseudo-partial derivative parameters; presetting the optimization indicator, and then using a neural network to approximate the indicator function of the preset future moment; using adaptive dynamic programming technology to design an optimal controller under the preset indicator to control the mass-spring-shock absorber system.

4. The data-driven optimization control method for a mass-spring-damper system according to claim 1, characterized in that: The optimal controller under the preset index is used to control the mass-spring-damper system. The proof process is as follows: B001: Definition get: B002: Definition The estimated error Subtract both sides of the above equation The following formula is obtained: B003: replace The following formula is obtained: B004: According to the compact format model, Taking the two-norm operation on the above formula, we get the following formula: B005: Because λ>0, we have: B006:Select get: B007: According to 0<ρ<2,λ>0, we get: B008: Substitute the above formula into B006 to obtain: B009: Substitute the above formula and B005 into B004 to obtain: B010: Take the expected operation on the above formula and get: B011: As the system runs, that is, k→∞, the above formula shows that the observation error Converge to this boundary End of proof; (1) Using a neural network to approximate the index function of a preset future moment, the approximate index function can be expressed as Then the goal of neural network weight adjustment is to minimize the error below Choosing a loss function Applying gradient descent to this function, we get the neural network weight update rate as follows: a k =μ||I+Θ k I k T ||×(Θ k I k T ) + In the formula, Θ k =σ[Y T x k+1 ]-σ[Y T x k ], 0<μ<1 is the selected parameter. Under the designed weight update rate, the approximate error of the indicator function is ultimately uniformly bounded. The proof process is as follows: B012: Select the following Lyapunov function B013: Perform a backward difference operation on the above formula to obtain B014: Substitute the neural network weight update rate into the above formula to obtain B015: α k Substituting into the above formula, we get B016: Because 0<μ<1, so we have And because ||σ[·]||≤1, So there is Based on the above analysis, we can get B017: The above formula shows that as long as It holds true, so the approximation error of the indicator function is eventually uniformly bounded, and the proof ends; (2) Using the approximate Φ k and J[x k+1 ], we can get the approximate solution of the optimal control, which is as follows: Using the approximate solution of optimal control, the state of the mass-spring-damper system can be guaranteed to converge consistently and boundedly. The proof process is as follows: B018: Select the following Lyapunov function; V[x k ]=||x k || 2 B019: Perform a backward difference operation on the above formula to obtain: ΔV[x k+1 ]=||x k+1 || 2 -||x k || 2 B020: Convert Δu in the compact model k use Substituting the descendants into the above formula, we get B021: Convert Δu in the compact model k use Substituting the descendants into the above formula, we get In the formula satisfy B022: According to the optimal principle, there exists a Make||x k +Φ k (1-θ k )Δu k || 2 ≤K||x k || 2 Based on this relationship, we can get B023: The above formula shows that as long as It holds, so the state of the system is eventually uniformly bounded, and the proof ends.

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