Nonlinear adaptive control system design method and device based on pseudo-inverse matrix

Abstract

The invention discloses a nonlinear adaptive control system design method and device based on a pseudo-inverse matrix, and relates to the field of adaptive control, and the method comprises the steps: S1, constructing a controlled object state-space equation comprising matching uncertainty and non-matching uncertainty; non-matching uncertainty is converted into matching uncertainty through pseudo-inverse transformation; s2, introducing the state vector into a regression vector to obtain an expansion regression vector, and obtaining an uncertainty function based on the expansion regression vector; s3, constructing a state observer, and obtaining a state observation value of the controlled object; s4, taking the difference between the state observation value and the state actual value as the excitation of the adaptive law, and updating the parameters of the uncertain function; s5, constructing a self-adaptive control law by taking the estimated value of the uncertain function as input; and S6, filtering an output signal of the adaptive control law through L1 to obtain a final control law. Through the expansion regression vector comprising the state vector, accurate compensation of the uncertain function is realized, and the self-adaptive efficiency is improved.

Description

Technical Field

[0001] This invention relates to adaptive control, and more particularly to a design method and apparatus for a nonlinear adaptive control system based on a pseudo-inverse matrix. Background Technology

[0002] Unmanned aerial vehicles (UAVs) are complex systems exhibiting nonlinearity, time-varying characteristics, and parameter fuzziness. They often operate in challenging external environments such as strong winds, atmospheric turbulence, foreign object impacts, and sensor drift. Military UAVs have even been designed for takeoff and landing in extreme environments like sandstorms, high altitudes, typhoons, and torrential rain. Robust control of UAVs is both a key focus and a major challenge in their widespread application. Among these challenges, attitude control is the core element determining flight stability and safety.

[0003] Faced with the severe challenges posed by UAVs in diverse application scenarios to control systems, classic proportional-integral-derivative (PI-DE) flight control strategies are no longer sufficient to meet the requirements for control accuracy and stability margin. Domestic and international scholars have begun to apply numerous advanced control technologies to the field of UAV control. Typical control methods can be categorized into four types: nonlinear control, adaptive control, robust control, and intelligent control. The design of advanced control systems often relies on high-precision mathematical models of the controlled object. However, due to the complex dynamic characteristics and dynamic changes in the environment of UAVs, these control methods often fail to achieve the expected performance when applied to UAVs. Adaptive control is an effective solution; it can dynamically identify, reconstruct, and offset unpredictable system uncertainties such as model mutations, sudden faults, and external disturbances in real time, significantly improving the control performance and robustness of UAVs. While existing adaptive control suffers from losses in robustness and adaptive efficiency, some adaptive capabilities remain to be developed.

[0004] In adaptive control, Model Reference Adaptive Control (MRA) is the most mature method in both theoretical research and practical application. MRA exhibits strong robustness and performance advantages when handling systems with unknown parameters, nonlinear characteristics, or dynamically changing models. However, this method is prone to system oscillations when the learning rate is too large, requiring extensive simulation experiments to determine the optimal learning rate. To address this issue, Hovakimyan and Cao introduced the L1 filter, proposing the L1 adaptive control theory. The L1 filter smooths the adaptively adjusted control signal, suppressing high-frequency interference signals while balancing system robustness and control performance. The advantages of L1 adaptive control lie in its high design flexibility, clear parameter meaning, and strong engineering feasibility, solving the engineering application difficulties of traditional adaptive control and gradually becoming the primary choice for adaptive control in engineering applications. L1 adaptive control theory has been successfully applied to NASA's Airstar aircraft, achieving excellent flight test performance. However, research on the theoretical analysis of L1 adaptive control is still incomplete, leading to the closed-loop performance of the control system failing to meet expectations, and the designed nonlinear adaptive system exhibiting performance similar to a linear time-invariant system.

[0005] Adaptive control achieves dynamic reconfiguration of the system by compensating for uncertainties in real time. The effectiveness of adaptation is affected by the accuracy and speed of identification. However, existing L1 adaptive control structures suffer from robustness and loss of adaptive capability utilization, and the dynamic performance of L1 adaptive control cannot perfectly match the desired performance. Summary of the Invention

[0006] To address the above problems, this invention proposes a design method and apparatus for a nonlinear adaptive control system based on a pseudo-inverse matrix. This method incorporates the state vector of the controlled object into the extended regression vector, thereby introducing an extension of the nonlinear state quantity into the state observer, adaptive law, and adaptive control law. This enables the adaptive control system to accurately estimate and converge to the true value of the system uncertainty, and then enter the closed-loop system through the adaptive control signal of the adaptive control law. Ultimately, this achieves accurate compensation for the uncertain function and improves the adaptive performance.

[0007] On the one hand, the design method for nonlinear adaptive control systems based on pseudo-inverse matrices involves the following steps:

[0008] 1. A design method for a nonlinear adaptive control system based on a pseudo-inverse matrix, characterized by comprising the following steps:

[0009] S1, construct the state-space equation of the controlled object including matched uncertainty and unmatched uncertainty; transform the unmatched uncertainty into matched uncertainty through pseudo-inverse transformation to obtain the state-space equation containing uncertainty;

[0010] S2, parameterize the uncertain function in the state-space equation containing uncertainty into the product of the uncertain parameter matrix and the extended regression vector; the extended regression vector includes the state vector of the controlled object;

[0011] S3, Construct a state observer based on the state space equation of the controlled object; The state observer is excited by the control input and the estimated value of the uncertain function, and outputs the state observation value of the controlled object.

[0012] S4, the difference between the observed state value and the actual state value is used as the state observation error, and an adaptive law is constructed with the state observation error as the excitation; the adaptive law updates the parameters of the uncertain function and outputs the estimated value of the uncertain function.

[0013] S5, using the estimated value of the uncertain function as input, constructs an adaptive control law to counteract the uncertainty;

[0014] S6 filters the control signal output by the adaptive control law through L1 to obtain the final control law of the controlled object.

[0015] Preferably, the state-space equation of the controlled object is expressed as:

[0016] ;

[0017] in, State vector The derivative; Represents the state vector; Represents the control vector; Represents the state matrix, Represents the input matrix; This indicates uncertainty in the matching process; This indicates non-matching uncertainty; Represents a constant matrix;

[0018] The state-space equation containing uncertainty is expressed as:

[0019] ;

[0020] in, express The pseudo-inverse matrix.

[0021] Preferably, the uncertain function is expressed as:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] in, Represents an uncertain function; This represents a bounded regression function; Represents an uncertain parameter matrix, express The inverse matrix; Represents a constant matrix; Indicates the definition symbol; State vector transpose; and These represent the state vector parameter matrices for matching uncertainty and non-matching uncertainty, respectively. and Let represent the linear parameter matrices representing matching uncertainty and non-matching uncertainty, respectively; This indicates uncertainty in the matching process; This indicates non-match uncertainty.

[0027] Preferably, the adaptive law updates the parameters of the uncertain function and outputs an estimated value of the uncertain function. Specifically, the adaptive law update uses a piecewise constant method and iteratively updates the estimated value of the uncertain parameter matrix by introducing error information from past sampling times, as expressed as:

[0028] ;

[0029] ;

[0030] ;

[0031] in, Represents the uncertain parameter matrix The estimated value; Indicates in The estimated value of the state vector parameter matrix after the time-limited update matches the uncertainty; Indicates in The estimated value of the linear parameter matrix matching uncertainty after the time-time update. Indicates in The estimated value of the state vector parameter matrix of the unmatched uncertainty after the time-time update; Indicates in The estimated value of the linear parameter matrix of the non-matching uncertainty after the time-time update; Indicates the sampling index; Indicates the sampling time for adaptive updates; This represents the gain matrix that is adaptively updated. , and They represent the times respectively. , and The cumulative amount of uncertainty estimation information within the historical time step; State matrix Matrix exponent; express Error of state quantity at time; Represents the regression vector The pseudo-inverse matrix.

[0032] Preferably, the adaptive control law is expressed as:

[0033] ;

[0034] in, This represents an adaptive control law; Indicates matching uncertainty estimation Laplace transform; Indicates reference input; Indicates unmatched uncertainty estimation Laplace transform The form after transformation to match uncertainty.

[0035] Preferably, the control signal output by the adaptive control law is filtered by L1 to obtain the final control law of the controlled object, which is expressed as:

[0036] ;

[0037] ;

[0038] in, This indicates the final control law of the controlled object; This represents an adaptive control law; Represents the feedback gain matrix; Represents the transition matrix. Indicates an L1 filter; Represents the identity matrix.

[0039] On the other hand, the design device for a nonlinear adaptive control system based on a pseudo-inverse matrix includes the following:

[0040] The state-space equation construction module is used to construct the state-space equation of the controlled object, including matched and unmatched uncertainties; the unmatched uncertainty is converted into matched uncertainty through pseudo-inverse transformation, resulting in a state-space equation containing uncertainty.

[0041] The uncertain function nonlinearization module is used to parameterize the uncertain function in the state-space equation containing uncertainty into the product of the uncertain parameter matrix and the extended regression vector; the extended regression vector includes the state vector of the controlled object;

[0042] A state observer construction module is used to construct a state observer based on the state space equation of the controlled object; the state observer is excited by the control input and the estimated value of the uncertain function, and outputs the state observation value of the controlled object.

[0043] An adaptive law construction module is used to construct an adaptive law with the state observation error as the excitation by taking the difference between the state observation value and the actual state value as the state observation error; the adaptive law updates the parameters of the uncertain function and outputs the estimated value of the uncertain function.

[0044] The adaptive control law building module is used to construct an adaptive control law to counteract uncertainty by taking the estimated value of the uncertain function as input.

[0045] The L1 filter module is used to filter the control signal output by the adaptive control law to obtain the final control law of the controlled object.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] (1) The extended regression vector of the present invention includes the state vector of the controlled object, thereby constructing a novel adaptive control structure with augmented adaptive identification regression vector; the reasons for insufficient adaptive identification capability are analyzed from the perspective of adaptive control structure, and the potential capability of L1 adaptive control in real-time reconstructing control structure is further developed.

[0048] (2) The present invention constructs an adaptive law based on the piecewise constant method, and performs posterior iterative updates on the estimated value of the uncertain parameter matrix by introducing error information from past sampling times, thereby accelerating nonlinear posterior identification. It considers the cumulative benefits of adaptive estimation parameter state iteration, significantly improves the efficiency and accuracy of adaptive identification, and greatly increases the application value of L1 adaptive system in engineering practice. It also increases the nonlinearity of L1 adaptive control, improves the efficiency and capability of system adaptive real-time identification and dynamic reconstruction, and broadens the adaptive capability boundary. Attached Figure Description

[0049] The present invention will now be described in further detail with reference to the accompanying drawings;

[0050] Figure 1 This is a flowchart illustrating the design method of a nonlinear adaptive control system based on a pseudo-inverse matrix according to an embodiment of the present invention.

[0051] Figure 2This is a structural diagram of the nonlinear adaptive control system design method based on pseudo-inverse matrix according to an embodiment of the present invention;

[0052] Figure 3 The pitch angle response curve is shown in the diagram of the nonlinear adaptive control system design method based on pseudo-inverse matrix according to an embodiment of the present invention.

[0053] Figure 4 The elevator output curve is shown in the nonlinear adaptive control system design method based on pseudo-inverse matrix according to an embodiment of the present invention.

[0054] Figure 5 This is a structural block diagram of a nonlinear adaptive control system design device based on a pseudo-inverse matrix according to an embodiment of the present invention. Detailed Implementation

[0055] The present invention will be further described below through specific embodiments.

[0056] like Figure 1 As shown, the design method for a nonlinear adaptive control system based on a pseudo-inverse matrix includes the following specific steps:

[0057] S1. Construct the state-space equation of the controlled object, which includes matched uncertainty and unmatched uncertainty; transform the unmatched uncertainty into matched uncertainty through pseudo-inverse transformation to obtain the state-space equation containing uncertainty.

[0058] The controlled object is an arbitrary linear system, and its state-space equations can be described as follows:

[0059] (1);

[0060] In the formula, For state vectors, For control vectors, The state matrix, The input matrix is ​​denoted as .

[0061] In the nominal system shown in equation (1), if uncertainty is introduced, then:

[0062] (2);

[0063] In the formula, To match uncertainty, For non-matching uncertainty, Let be a constant matrix, which satisfies And matrix Full term.

[0064] Unmatching uncertainty Not in the matrix Within the column space, this uncertainty cannot be eliminated by adaptive control of the input. Therefore, a pseudo-inverse transformation is used to convert the unmatched uncertainty into a matched uncertainty, i.e.:

[0065] (3);

[0066] In the formula, visible A full-rank, wide matrix The pseudo-reversal, satisfying and When the matrix When the matrix is ​​non-singular, the pseudo-inverse and the inverse are equal, i.e. .

[0067] Thus, the mathematical description of the controlled system with matching and non-matching uncertainties can be described by equation (2) or equation (3).

[0068] S2, parameterizes the uncertain function in the state-space equation containing uncertainty into the product of the uncertain parameter matrix and the extended regression vector; the extended regression vector includes the state vector of the controlled object.

[0069] System uncertainty function It can be described in the following form:

[0070] (4);

[0071] in, This is called the uncertain parameter matrix, which is an unknown constant matrix; It is called a bounded regression function, which is a known function with respect to time.

[0072] It is called a bounded regression function, which is a known function of the state variables.

[0073] To address the requirement of "accuracy" in adaptive law estimation, this embodiment proposes the concept of an extended regression vector, introducing a relevant description of the state vector x into the uncertainty function, and designing... This is called a known function of the state variable, i.e.:

[0074] (5);

[0075] In the formula, It is a constant matrix.

[0076] Substituting equation (5) into equation (4), the matching and non-matching uncertainty functions can be defined as shown in equations (6) and (7), respectively.

[0077] (6);

[0078] (7);

[0079] in, and These are respectively called the state vector parameter matrices for matched and unmatched uncertainties; and These are referred to as the linear parameter matrices of the matched and unmatched uncertainties, respectively.

[0080] If the uncertain parameter matrix is ​​defined as:

[0081] (8);

[0082] Then the matching is uncertain. Unmatching uncertainty and The relationship is:

[0083] (9);

[0084] In summary, the uncertainty function based on the extended regression vector can finally be defined by equations (4), (5), (8) and (9).

[0085] S3, construct a state observer based on the state space equation of the controlled object; the state observer is excited by the control input and the estimated value of the uncertain function, and outputs the state observation value that predicts the state of the controlled object.

[0086] A state observer is established based on a mathematical model of the nominal state of the controlled object and is used to estimate and predict the state and changes of the system. The state observer uses the system input and uncertain estimated values ​​as excitations to predict the state of the controlled system. As the estimation step size increases, the dynamic characteristics estimated by the state observer tend to be closer to the dynamics of the actual controlled object, and the estimation residuals gradually decrease and become uniformly bounded.

[0087] For the controlled object described by equation (2), the state observer is designed as follows:

[0088] (10);

[0089] In the formula, To match uncertain functions The estimate, Unmatched uncertain function The estimate, For observed state variables.

[0090] Combining the uncertainty function based on the extended regression vector described in equations (6) and (7), and It can be expanded as follows:

[0091] (11);

[0092] (12);

[0093] In the formula, For matrix parameters The adaptive estimate, For parameter matrix The adaptive estimate, For parameter matrix The adaptive estimate, For parameter matrix The adaptive estimate.

[0094] S4. The difference between the observed state value and the actual state value is taken as the state observation error, and an adaptive law is constructed with the state observation error as the excitation. The adaptive law updates the parameters of the uncertain function to obtain the estimated value of the uncertain function.

[0095] From the definition of the uncertainty parameter matrix based on the expanded regression vector in S2, we know that the adaptive parameter estimation matrix for the expanded regression vector is:

[0096] (13);

[0097] in, The adaptive parameter estimation matrix is ​​the uncertain parameter matrix. The estimated value.

[0098] The main function of the adaptive law is to adaptively realize the dynamic identification of the system uncertainty parameter matrix. This process is driven by the output deviation between the state observer described by equation (10) and the controlled object described by equation (2). The state variable error is defined as:

[0099] (14);

[0100] In the process of adaptive law identification, the estimated values ​​of the system uncertainty parameter matrix and other variables are all uniformly bounded. Considering the adaptive estimation parameter matrix for the extended regression vector as described in equation (13), and combining the state vector of the controlled object with the system uncertainty estimation information at past sampling times, the adaptive law based on the piecewise constant method can be designed as follows:

[0101] (15);

[0102] (16);

[0103] (17);

[0104] in, For the state quantity error, in the formula , Represents the regression vector The pseudo-inverse matrix, This represents the cumulative amount of information on system uncertainty estimation over the historical time step.

[0105] Finally, using equations (15) to (17), the estimated values ​​of the uncertain parameters are updated.

[0106] S5. Based on the estimated value of the uncertain function, construct an adaptive control law to counteract the uncertainty.

[0107] For the controlled object defined by equation (3) in S1, and combined with the adaptive estimation of the uncertainty function in S4, an adaptive control input is designed to offset the system uncertainty. Based on the above design idea, the adaptive control quantity consists of an adaptive parameter estimation matrix, a system state vector, and a reference input signal. Its main function is to estimate the system uncertainty in the control input and then compensate for the real uncertainty, ultimately maintaining the desired system performance. Therefore, the adaptive control law in this embodiment can be described as follows:

[0108] (18);

[0109] In the formula, System matching uncertainty estimation Laplace transform, For reference only. For system mismatch uncertainty estimation Laplace transform The system is matched to the form after uncertainty transformation, if defined and From equation (3), we can derive and It has the following form:

[0110] (19);

[0111] (20);

[0112] S6 filters the output of the adaptive control law through L1 to obtain the final control law of the controlled object.

[0113] definition for The final control law after L1 filtering is:

[0114] (twenty one);

[0115] (twenty two);

[0116] In the formula, For the feedback gain matrix, Let be the transition matrix. and Jointly determine the L1 filter Normally, Designed as a low-pass filter, it is a strictly regular transfer function with bounded input / bounded output stability and a steady-state gain of 1.

[0117] Finally, the nonlinear adaptive control system based on the pseudo-inverse matrix (or the nonlinear adaptive control system based on the extended regression vector) is defined by equations (10), (16), (18), and (21). Its structural diagram can be found in [reference needed]. Figure 2 As shown.

[0118] The advantage of adaptive control over other nonlinear systems lies in its ability to adaptively adjust controller parameters without relying on a high-precision model. The degree of adaptivity varies depending on the form of the L1 adaptive law. In existing technologies, the regression matrix of an L1 adaptive control system... Since all variables are 1, the L1 adaptive law can only estimate the state variables in the uncertainty of the system. The irrelevant linear component lacks the ability to observe nonlinear terms, which is the fundamental reason why its adaptive capability is limited and it approximates a linear time-invariant system when the sampling time is very small and the learning rate is very large.

[0119] The nonlinear adaptive control system based on the extended regression vector designed in this embodiment introduces the extension of nonlinear state variables into the state observer, adaptive law, and adaptive control law, thus its form differs from that of the classical L1 adaptive control system. The extended regression matrix, as described in equation (4), is obtained through... The addition of nonlinear estimation of state variables enables the adaptive control system to accurately estimate and converge to the true value of system uncertainty. This estimation process enters the closed-loop system through the adaptive control input terminal described in equation (18), ultimately achieving accurate compensation for the uncertain function and improving the adaptive performance of the system. On the other hand, in response to the requirement of "fast" convergence speed of the adaptive law, this embodiment records the posterior information of system uncertainty estimation at past sampling times in the L1 adaptive law to compensate for the future system uncertainty estimation effect, reducing the adaptive performance error and lowering the computation and measurement frequency requirements.

[0120] In a specific embodiment of a fixed-wing aircraft, the system obtained by the method of this embodiment is used as an automatic control system for the longitudinal loop of the aircraft. The controlled object is the pitch angle state variable, and the final control law calculated by the control system is the elevator actuator. The system calculates the required overall torque and force based on the desired pitch angle command, and maps it to a specific control surface deflection angle according to the aerodynamic characteristics and power structure of the aircraft. The servo drives the control surface deflection according to the command, and the changes in overall lift and drag work together to change the pitch attitude of the UAV, so as to accurately track the desired pitch angle command and effectively resist interference such as wind disturbance and model uncertainty.

[0121] Taking a longitudinal model system of an aircraft as an example, the time delay margin of the controlled object under nominal conditions is 0.1354 s. The experiment design adds a pure time delay of 0.18 s to its control input, adjusting the initial state of the system to an unstable state. Under simulation conditions, using a unit step signal as the reference input, the dynamic response curves of the proposed nonlinear adaptive control based on extended regression vector (System I), the classical L1 adaptive control (System II), and the system under nominal conditions (System III) are shown below. Figure 3 and Figure 4 As shown.

[0122] Depend on Figure 3 and Figure 4 It can be seen that when the nominal system is in an unstable state, the pitch angle and elevator of closed-loop system I can stabilize and track the corresponding command well under a unit step reference input. Under the same reference input signal, the pitch angle and elevator of closed-loop system II exhibit divergent behavior, but the divergence trend is weaker than that of system III. Obviously, both systems I and II have a certain degree of adaptive capability, which can identify system uncertainties online and increase the stability margin of the system. Compared with system II, system I extends the nonlinear adaptive identification capability, which can cancel system uncertainties faster and with higher accuracy, and can increase the stability performance of the controlled system to a greater extent.

[0123] Therefore, the nonlinear adaptive control system based on extended regression vector in this embodiment has stronger robustness than the traditional L1 adaptive control, can provide a stronger stability margin for the controlled object, and maintain good adaptive performance and dynamic tracking performance.

[0124] like Figure 5 As shown, the present invention also discloses a design device for a nonlinear adaptive control system based on a pseudo-inverse matrix, comprising:

[0125] The state-space equation construction module 501 is used to construct the state-space equation of the controlled object, which includes matched uncertainty and unmatched uncertainty; the unmatched uncertainty is converted into matched uncertainty through pseudo-inverse transformation, thus obtaining the state-space equation containing uncertainty;

[0126] The uncertain function nonlinearization module 502 is used to parameterize the uncertain function in the state-space equation containing uncertainty into the product of the uncertain parameter matrix and the extended regression vector; the extended regression vector includes the state vector of the controlled object;

[0127] The state observer construction module 503 is used to construct a state observer based on the state space equation of the controlled object; the state observer is excited by the control input and the estimated value of the uncertain function, and outputs the state observation value of the controlled object.

[0128] The adaptive law construction module 504 is used to construct an adaptive law with the state observation error as the excitation by taking the difference between the state observation value and the actual state value as the state observation error; the adaptive law updates the parameters of the uncertain function and outputs the estimated value of the uncertain function.

[0129] The adaptive control law construction module 505 is used to construct an adaptive control law to counteract uncertainty by taking the estimated value of the uncertain function as input.

[0130] The L1 filter module 506 is used to filter the control signal output by the adaptive control law to obtain the final control law of the controlled object.

[0131] The specific implementation of the nonlinear adaptive control system design device based on the pseudo-inverse matrix is ​​the same as the nonlinear adaptive control system design method based on the pseudo-inverse matrix, and will not be described again in this embodiment.

[0132] The above are merely specific embodiments of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention using this concept shall be considered as infringing upon the protection scope of the present invention.

Claims

1. A design method for a nonlinear adaptive control system based on a pseudo-inverse matrix, characterized in that, Includes the following steps: S1, construct the state-space equation of the controlled object including matched uncertainty and unmatched uncertainty; transform the unmatched uncertainty into matched uncertainty through pseudo-inverse transformation to obtain the state-space equation containing uncertainty; S2, parameterize the uncertain function in the state-space equation containing uncertainty into the product of the uncertain parameter matrix and the extended regression vector; the extended regression vector includes the state vector of the controlled object; S3, Construct a state observer based on the state space equation of the controlled object; The state observer is excited by the control input and the estimated value of the uncertain function, and outputs the state observation value of the controlled object. S4, the difference between the observed state value and the actual state value is used as the state observation error, and an adaptive law is constructed with the state observation error as the excitation; the adaptive law updates the parameters of the uncertain function and outputs the estimated value of the uncertain function. S5, using the estimated value of the uncertain function as input, constructs an adaptive control law to counteract the uncertainty; S6 filters the control signal output by the adaptive control law through L1 to obtain the final control law of the controlled object.

2. The design method for a nonlinear adaptive control system based on a pseudo-inverse matrix according to claim 1, characterized in that, The state-space equation of the controlled object is expressed as: ； in, Represents the state vector The derivative; Represents the state vector; Represents the control vector; Represents the state matrix, Represents the input matrix; This indicates uncertainty in the matching process; Indicates non-matching uncertainty; Represents a constant matrix; The state-space equation containing uncertainty is expressed as: ； in, express The pseudo-inverse matrix.

3. The design method for a nonlinear adaptive control system based on a pseudo-inverse matrix according to claim 1, characterized in that, The uncertain function is expressed as: ； ； ； ； in, Represents an uncertain function; This represents a bounded regression function; Represents an uncertain parameter matrix, express The inverse matrix; Represents a constant matrix; Indicates the definition symbol; Represents the state vector Transpose of; and These represent the state vector parameter matrices for matching uncertainty and non-matching uncertainty, respectively. and Let represent the linear parameter matrices representing matching uncertainty and non-matching uncertainty, respectively; This indicates uncertainty in the matching process; This indicates non-match uncertainty.

4. The design method for a nonlinear adaptive control system based on a pseudo-inverse matrix according to claim 1, characterized in that, The adaptive law updates the parameters of the uncertain function and outputs an estimated value of the uncertain function. Specifically, the adaptive law updates using a piecewise constant method and iteratively updates the estimated value of the uncertain parameter matrix by introducing error information from past sampling times, as expressed as: ； ； ； in, Represents the uncertain parameter matrix The estimated value; Indicates in The estimated value of the state vector parameter matrix after the time-limited update matches the uncertainty; Indicates in The estimated value of the linear parameter matrix matching uncertainty after the time-time update. Indicates in The estimated value of the state vector parameter matrix of the unmatched uncertainty after the time-time update; Indicates in The estimated value of the linear parameter matrix of the non-matching uncertainty after the time-time update; Indicates the sampling index; Indicates the sampling time for adaptive updates; This represents the gain matrix that is adaptively updated. , and They represent the times at time 1 and 2 respectively. , and The cumulative amount of uncertainty estimation information within the historical time step; State matrix Matrix exponent; express Error of state quantity at time; Represents the regression vector The pseudo-inverse matrix.

5. The design method for a nonlinear adaptive control system based on a pseudo-inverse matrix according to claim 1, characterized in that, The adaptive control law is expressed as: ； in, This represents an adaptive control law; Indicates matching uncertainty estimation Laplace transform; Indicates reference input; Indicates unmatched uncertainty estimation Laplace transform The form after transformation to match uncertainty.

6. The design method for a nonlinear adaptive control system based on a pseudo-inverse matrix according to claim 1, characterized in that, The control signal output by the adaptive control law is filtered by L1 to obtain the final control law of the controlled object, which is expressed as: ； ； in, This indicates the final control law of the controlled object; This represents an adaptive control law; Represents the feedback gain matrix; Represents the transition matrix. Indicates an L1 filter; Represents the identity matrix.

7. A design device for a nonlinear adaptive control system based on a pseudo-inverse matrix, characterized in that, Including the following: The state-space equation construction module is used to construct the state-space equation of the controlled object, including matched and unmatched uncertainties; the unmatched uncertainty is converted into matched uncertainty through pseudo-inverse transformation, resulting in a state-space equation containing uncertainty. The uncertain function nonlinearization module is used to parameterize the uncertain function in the state-space equation containing uncertainty into the product of the uncertain parameter matrix and the extended regression vector; the extended regression vector includes the state vector of the controlled object; A state observer construction module is used to construct a state observer based on the state space equation of the controlled object; the state observer is excited by the control input and the estimated value of the uncertain function, and outputs the state observation value of the controlled object. An adaptive law construction module is used to construct an adaptive law with the state observation error as the excitation by taking the difference between the observed state value and the actual state value as the state observation error; the adaptive law updates the parameters of the uncertain function and outputs the estimated value of the uncertain function. The adaptive control law building module is used to construct an adaptive control law to counteract uncertainty by taking the estimated value of the uncertain function as input. The L1 filter module is used to filter the control signal output by the adaptive control law to obtain the final control law of the controlled object.

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