Uncertain nonlinear system stabilization control method for quantizing input and output constraints

Abstract

The invention provides an uncertain nonlinear system stabilization control method for quantizing input and output constraints, and the method comprises the steps: carrying out the filtering of an output, converting the output into a state equation, and constructing an extension system; adopting fuzzy logic to approach an unknown nonlinear term; estimating unknown external disturbance by adopting a disturbance estimator; a non-fragile robust fuzzy adaptive observer is constructed in order to estimate an uncertain nonlinear system state; due to the existence of various uncertainties, the output of the system is constrained through a constraint equation, and the robustness of the system is improved; a hyperbolic tangent type self-adaptive quantization controller is provided, so that the nonlinear system can achieve the stabilization purpose, and the output is restrained in a preset curve; and finally, the effectiveness and the applicability of the proposed control scheme are verified through a single-connecting-rod manipulator. According to the method, the robustness of the multi-source disturbance nonlinear system is improved, and the influence of various uncertainties on the controlled system can be effectively weakened and compensated.

Description

Technical Field

[0001] The invention relates to the field of advanced control theory, and in particular to an uncertain nonlinear system stabilization control method with quantized input and output constraints. Background Art

[0002] As control systems expand, control signals need to be transmitted remotely over the network. However, the bandwidth and data transmission rate of communication channels are usually limited, which may make real-time transmission impossible. In order to solve the problem of signal congestion, many scholars have conducted research on quantizing continuous signals before transmission, aiming to improve the efficiency and reliability of the system. Although quantization technology provides many benefits in networked control systems, it also introduces important nonlinear factors.

[0003] For complex control systems such as robotic arms, smart vehicles, quadcopter drones, and underwater robots, there are many unknown mismatched nonlinear functions, which becomes one of the main challenges in controlling these systems. To cope with this problem, fuzzy logic systems are widely used to address this challenge, which have easy-to-understand concepts, excellent adaptive learning capabilities, fault tolerance, and robustness. Different activation functions can be used to approximate these complex nonlinear functions with high accuracy to achieve precise control objectives, and methods such as backstepping techniques, adaptive control, and neural networks can also be combined to estimate and compensate for these uncertainties.

[0004] However, we cannot ignore the influence of disturbance and noise introduced by the failure, nonlinearity and drift of electronic components on the system and measurement equipment. In system synthesis, if the existence of state disturbance or measurement noise is ignored, it may have a negative impact on the steady-state and transient performance of the system, and even cause system failure. At the same time, in the observer design process, the influence of gain disturbance caused by factors such as computer digital truncation or potential disturbance in the transmission process on the system must be considered. However, very few studies have considered this issue.

[0005] In summary, there are still some complex problems in the field of control, such as quantized input, nonlinear systems with uncertainties, disturbances and output constraints, measurement equipment with measurement noise, and gain disturbances in observers. So far, there has been little research on this topic. Summary of the invention

[0006] The main purpose of the present invention is to provide a stabilization control method for uncertain nonlinear systems with quantized input and output constraints, so as to solve the output feedback stabilization problem in the presence of measurement noise, observer gain disturbance, network quantization and inevitable external influences in actual complex environments.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is: a stabilization control method for an uncertain nonlinear system with quantized input and output constraints, comprising the following steps: Step 1: Construct a nonlinear system model with multiple uncertainties Step 2: Convert the output in step 1.1 into a state equation and construct an extended nonlinear system; Step 3: Use a hysteresis quantizer to eliminate quantization signal jitter; Step 4: Use fuzzy logic system to approximate the unknown smooth mismatched nonlinear function; Step 5: Design a non-fragile robust fuzzy adaptive observer to estimate the system state and parameters and suppress multiple disturbances; Step 6: Design the fuzzy logic weights and the adaptive rate of disturbance estimation; Step 7: Design constraint equations to constrain the system output and transform it into an unconstrained optimization problem; Step 8: Define the dynamic error and use the backstepping technique to gradually design the virtual control law to obtain a disturbance-resistant quantitative controller.

[0008] In the preferred solution, in step S1, consider a The order multiple uncertain nonlinear system model is as follows: ; (1) in, , and They represent the state variables, the control signals to be quantized, the system inputs with quantized values, and the measurement noise with unknown continuous bounded Output; , and They are unknown bounded disturbance, known smooth nonlinear function and unknown smooth mismatched nonlinear function respectively.

[0009] In the preferred solution, in step S2, the output is converted into a state equation, and an extended nonlinear system is constructed as follows: ; (2) in, Represents the output of the extended nonlinear system.

[0010] In the preferred solution, step S3 is to effectively eliminate the jitter of the quantized signal by using the following hysteresis quantizer: ; (3) in, ;function The value of is in the set ,and The value of represents the dead zone range of the quantizer.

[0011] In the preferred embodiment, step S4 is for the unknown continuous function , the fuzzy logic system is approximated and described as: ; (4) in, and denote the ideal weight vector, basis function vector, approximation error and the positive constant to be designed respectively; let (5) In the preferred solution, step S5 proposes the following non-fragile robust fuzzy adaptive observer for the multi-disturbance system in step S2: ; (6) in, and They represent the state variables, positive parameters, The estimate Estimates, high gains, and observer gain disturbances.

[0012] In the preferred embodiment, step S6 designs the fuzzy logic weights and the adaptive rate of disturbance estimation as follows: ; (7) ; (8) in, , , and is a positive parameter.

[0013] In the preferred embodiment, step S7 designs a constraint equation to constrain the output of the system; in order to make the system output Restricted to the interval In which and It is a continuous and differentiable function. The output of the extended nonlinear system is obtained by inverse transformation. Restricted to the range In which and ; The constraint equation is designed as follows: ; (9) The constrained nonlinear system is transformed into an unconstrained nonlinear system.

[0014] In the preferred solution, step S8 designs an anti-interference quantitative controller, first defining the following dynamic error: ; in, and is the error variable, It is obtained by using a first-order low-pass filter, designed as follows: ; (10) in, , and are the input (hereinafter referred to as the virtual control law) and output of the first-order low-pass filter and the designed normal constant; by definition: ; (11) get ; Through the backstepping technology, the virtual control law is obtained as follows: ; (12) ; (13) ; (14) in, ; According to the virtual control rate, the anti-interference quantitative controller is obtained as follows: ; (15) in, .

[0015] The present invention provides a stabilization control method for uncertain nonlinear systems with quantized input and output constraints. The present invention mainly studies the output feedback stabilization problem in the presence of measurement noise, observer gain disturbance, network quantization and inevitable external influence in a practical complex environment. Therefore, the method will be more effective in practical applications. In addition, the present invention adopts time-varying matrix inequality to deal with the multiplicative observer gain disturbance problem, so this method is more conducive to the selection of some suitable parameters.

[0016] The beneficial effects of the present invention are: 1) Perform output filtering transformation to obtain an extended system. The output with measurement noise is put into the state equation of the extended system.

[0017] 2) Apply fuzzy logic and estimators to estimate unknown mismatch uncertainties, measurement noise, and interference in the extended system.

[0018] 3) A non-fragile robust fuzzy adaptive observer is constructed and an output feedback stabilizer is proposed to ensure that the closed-loop system is ultimately uniformly bounded and the output is constrained by a predetermined performance curve. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The present invention will be further described below in conjunction with the accompanying drawings and embodiments: Figure 1 It is a flow chart of a stabilization control method for an uncertain nonlinear system with quantized input and output constraints of the present invention; Figure 2 is a mapping of the hysteresis quantizer of the present invention; Figure 3 It is a block diagram of the non-fragile robust fuzzy adaptive control strategy of the present invention; Figure 4 The system status of the present invention and its estimated status Trajectory; Figure 5 The system state of the present invention and its estimated status Trajectory; Figure 6 The system status of the present invention and its estimated status Trajectory; Figure 7 is the state estimation error of the present invention Trajectory; Figure 8 is the real input signal of the present invention Relative to the quantized input signal trajectories; Fig. 9 is the parameter estimation norm of the present invention trajectory. DETAILED DESCRIPTION

[0020] Example 1 like Figures 1 to 9 As shown, a stabilization control method for an uncertain nonlinear system with quantized input and output constraints comprises the following steps: Step 1: Construct a nonlinear system model with multiple uncertainties Step 2: Convert the output in step 1.1 into a state equation and construct an extended nonlinear system; Step 3: Use a hysteresis quantizer to eliminate quantization signal jitter; Step 4: Use fuzzy logic system to approximate the unknown smooth mismatched nonlinear function; Step 5: Design a non-fragile robust fuzzy adaptive observer to estimate the system state and parameters and suppress multiple disturbances; Step 6: Design the fuzzy logic weights and the adaptive rate of disturbance estimation; Step 7: Design constraint equations to constrain the system output and transform it into an unconstrained optimization problem; Step 8: Define the dynamic error and use the backstepping technique to gradually design the virtual control law to obtain a disturbance-resistant quantitative controller.

[0021] In one embodiment, in step S1, consider a The order multiple uncertain nonlinear system model is as follows: ; (1) in, , and They represent the state variables, the control signals to be quantized, the system inputs with quantized values, and the measurement noise with unknown continuous bounded Output; , and They are unknown bounded disturbance, known smooth nonlinear function and unknown smooth mismatched nonlinear function respectively.

[0022] Nonlinear functions ,satisfy ; (1b) in, is a real number.

[0023] In one embodiment, in step S2, for the nonlinear system in step S1, a first-order output filtering strategy is proposed as follows: ; (2a) in, Represents a designed positive constant.

[0024] In one embodiment, in step S3, compared with the logarithmic quantizer, the hysteresis quantizer can effectively eliminate the jitter of the quantized signal, and the quantizer model is as follows: ; (3) In the formula, .function The value of is in the set ,and The value of represents the dead zone range of the quantizer. The mapping of the hysteresis quantizer is as follows Figure 2 shown.

[0025] In one embodiment, in step S4, for the unknown smoothing function It can be approximated by the following fuzzy logic: ; (4) In the formula, , , and represent the optimal weight vector, basis function vector, approximation error and designed positive parameters respectively.

[0026] ; (5) Then, by introducing the output filtering strategy (2a), fuzzy logic (4) and transformation (5), the system (1) can be rewritten as follows: ; (2) In the formula, represents the output of the extended nonlinear system (2). Function The following conditions are met: ; (2b) In the formula, are some normal numbers, functions satisfy ,Right now and They are and The upper bound of .

[0027] In one embodiment, in step S5, in order to suppress unknown multiple disturbances, a non-fragile robust fuzzy adaptive observer is proposed for the extended nonlinear system (2) with quantized input.

[0028] (6) In the formula, and They represent the state variables and positive parameters of the observer respectively. The estimate The estimate and observer gain perturbation of .

[0029] Combining equations (2) and (6), the following error system can be established:

[0030] In the formula, , , , , .

[0031] Consider the following coordinate transformation: ; (16) According to equations (2), (6) and (16), we can obtain: ; In the formula, ; ; ; ; .

[0032] In one embodiment, in step S6, and The adaptive rate is designed as follows: ; (7) ; (8) In the formula, , , and is a positive parameter.

[0033] In one embodiment, in step S7, in order for the system to output Restricted to the interval In which and is a continuous and differentiable function. The output of system (35) is obtained by inverse transformation Restricted to the range In which and The constraint equations are designed as follows: ; (9) Then, the constrained nonlinear system is transformed into an unconstrained nonlinear system. The derivative of can be obtained: ; In the formula, and .

[0034] In one embodiment, in step S8, the following dynamic errors are defined: ; In the formula, and is the error variable, It is obtained by using a first-order low-pass filter, designed as follows: ; (10) In the formula, , and are the input (hereinafter referred to as the virtual control law) and output of the first-order low-pass filter and the designed positive constant. By definition: ; (11) Can get . Then use the backstepping technique to derive the virtual control law .

[0035] Step 0: Consider the first dynamic error Then, design the virtual control law : ; (12) In the formula, .Then ; (16) Using Young's inequality, we can get: ; (17) Substituting equations (12) and (17) into equation (16), we can obtain: ; (18) step :Consider the Dynamic Error , design virtual control law : ; (13) In the formula, .Then ; (19) According to Young's inequality, we can get: ; (20) Substituting (13) and (20) into (19), we can obtain: ;(twenty one) step :Consider the Dynamic Error ,Design Virtual Control Method and controller : ; (14) ; (15) In the formula, and .Then ;(twenty two) From the hysteresis quantizer proposed in step S3, we know that there are two functions and , so that the hysteresis quantizer can be expressed as: and

[0036] In the formula, .

[0037] By applying Young's inequality and the above hysteresis quantizer formula, we can obtain: ;(twenty three) In particular, for any positive number and any real constant , the following inequality holds: ;(twenty four) Through equations (14)-(15) and (22)-(24), we can obtain: ; (25) The control objective of the present invention is to make all signals in the closed-loop system bounded and the output of the system (29) constrained within a preset curve. In order to make the control strategy more readable, Figure 3 The block diagram of the non-fragile robust fuzzy adaptive control strategy is shown. Next, we will prove the feasibility of the control objective.

[0038] Consider the following Lyapunov function: ; (26) in, , , , , .

[0039] In particular, define the positive definite matrix and the time-varying matrix as follows:

[0040] In the formula, as well as The following conditions are met:

[0041] In the formula, and satisfy: and .

[0042] Then, the following inequality holds: ; (27) In the formula, ,and is the n-th order identity matrix.

[0043] Prove that According to (59), we can get the following inequality: ; because Therefore, the conclusion holds.

[0044] Redefine the matrix in ,and The following conditions are met: ; (28) Then, the following inequality holds: ; In the formula, .

[0045] From the above content, it can be deduced that The derivative of is: ; (29) According to Young's inequality, (1b) and (2b), we can obtain: ; (30) In the formula, Substituting (30) into (29), we can obtain ; (31) According to Young's inequality and the adaptive law of the estimator (7), The derivative of can be obtained: ; (32) According to Young's inequality and the adaptive law of the estimator (8), The derivative of can be obtained: ; (33) According to (16), (19) and (25), The derivative of can be obtained: ; (34) In the formula,

[0046] According to Young's inequality and (11), The derivative of can be obtained:

[0047] In the collection On the definition, for any , all have the following formula: .

[0048] therefore, In the collection The maximum value on , we can get: ; (35) From (31)-(35), we can obtain the following inequality: ; (36) In the formula, we have: and .

[0049] because With variables irrelevant, and by adjusting ,inequality Established, therefore, is an invariant set.

[0050] In particular, according to inequality (36), there exists a positive real number , so that Therefore, the signal is bounded. From (12), we can get is bounded. In addition, since therefore is also bounded. By considering It can be determined is bounded. This means is bounded because . Similar reasoning can be used to prove that and is also bounded. In addition, according to (15) and (3), we can ensure that the control input and quantized input Bounded.

[0051] From the above, we can see that all signals in the closed-loop system are bounded, and the output constraint range of the nonlinear system (29) is .

[0052] The above embodiments are only preferred technical solutions of the present invention and should not be regarded as limiting the present invention. The protection scope of the present invention shall be the technical solutions recorded in the claims, including equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A stabilization control method for uncertain nonlinear systems with quantized input and output constraints, characterized in that: The following steps are involved: Step 1: Construct a nonlinear system model with multiple uncertainties Step 2: Convert the output in step 1.1 into a state equation and construct an extended nonlinear system; Step 3: Use a hysteresis quantizer to eliminate quantization signal jitter; Step 4: Use fuzzy logic system to approximate the unknown smooth mismatched nonlinear function; Step 5: Design a non-fragile robust fuzzy adaptive observer to estimate the system state and parameters and suppress multiple disturbances; Step 6: Design the fuzzy logic weights and the adaptive rate of disturbance estimation; Step 7: Design constraint equations to constrain the system output and transform it into an unconstrained optimization problem; Step 8: Define the dynamic error and use the backstepping technique to gradually design the virtual control law to obtain a disturbance-resistant quantitative controller.

2. The stabilization control method for uncertain nonlinear systems with quantized input and output constraints according to claim 1, characterized in that: In step S1, consider a The order multiple uncertain nonlinear system model is as follows: ；(1) in, , and They represent the state variables, the control signals to be quantized, the system inputs with quantized values, and the measurement noise with unknown continuous bounded Output; , and They are the unknown bounded disturbance, the known smooth nonlinear function and the unknown smooth mismatched nonlinear function respectively.

3. The stabilization control method for uncertain nonlinear systems with quantized input and output constraints according to claim 1, characterized in that: In step S2, the output is converted into a state equation and an extended nonlinear system is constructed as: ；(2) in, Represents the output of the extended nonlinear system.

4. The stabilization control method for uncertain nonlinear systems with quantized input and output constraints according to claim 1, characterized in that: Step S3 uses the following hysteresis quantizer to effectively eliminate the jitter of the quantized signal: ；(3) in, ;function The value of is in the set ,and The value of represents the dead zone range of the quantizer.

5. The stabilization control method for uncertain nonlinear systems with quantized input and output constraints according to claim 1, characterized in that: Step S4: for unknown continuous function , the fuzzy logic system is approximated and described as: ；(4) in, and denote the ideal weight vector, basis function vector, approximation error and the positive constant to be designed respectively; let 。(5)。 6. The stabilization control method for uncertain nonlinear systems with quantized input and output constraints according to claim 1, characterized in that: Step S5 proposes the following non-fragile robust fuzzy adaptive observer for the multi-disturbance system in step S2: ；(6) in, and They represent the state variables, positive parameters, The estimate Estimates, high gains, and observer gain disturbances.

7. The stabilization control method for uncertain nonlinear systems with quantized input and output constraints according to claim 1, characterized in that: Step S6 designs the fuzzy logic weights and the adaptive rate of disturbance estimation as follows: ；(7) ； (8) in, , , and is a positive parameter.

8. The method for stabilizing uncertain nonlinear systems with quantized input and output constraints according to claim 1, characterized in that: Step S7 designs a constraint equation to constrain the output of the system; in order to make the system output Restricted to the interval In which and It is a continuous and differentiable function. The output of the extended nonlinear system is obtained by inverse transformation. Restricted to the range In which and ; The constraint equation is designed as follows: ；(9) The constrained nonlinear system is transformed into an unconstrained nonlinear system.

9. The stabilization control method for uncertain nonlinear systems with quantized input and output constraints according to claim 1, characterized in that: Step S8 designs an anti-interference quantitative controller, first defining the following dynamic error: ； in, and is the error variable, It is obtained by using a first-order low-pass filter, designed as follows: ；(10) in, , and are the input (hereinafter referred to as the virtual control law) and output of the first-order low-pass filter and the designed normal constant; by definition: ；(11) get ; Through the backstepping technology, the virtual control law is obtained as follows: ；(12) ；(13) ；(14) in, ; According to the virtual control rate, the anti-interference quantitative controller is obtained as follows: ；(15) in, .

Images