An adaptive control method for a multivariable nonlinear system

Abstract

The application discloses a kind of adaptive control methods of multivariable nonlinear system, comprising the following steps: constructing multivariable nonlinear system including unknown parameter and unknown high-frequency gain matrix;The model not only describes the system behavior by state, input and output vector, but also introduces unknown parameter matrix and smooth nonlinear function to simulate the complexity and nonlinear characteristics of system.Further construct adaptive controller and switching mechanism, determine the control direction matrix through adaptive controller and switching mechanism, so that the output of multivariable nonlinear system can accurately track reference signal.This method relaxes the restriction condition of high-frequency gain matrix by introducing adaptive tracking control law design, ensures good system performance when the control direction matrix switches, and realizes high-precision tracking of multivariable nonlinear system reference signal.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of multivariable nonlinear systems, and more particularly to an adaptive control method for multivariable nonlinear systems. BACKGROUND

[0002] The control of multivariable nonlinear systems is a crucial aspect in modern industry and engineering technology. Such systems involve multiple-dimensional signals and complex data processing. Through real-time regulation of multiple inputs, precise control of multiple outputs is achieved to achieve more efficient, optimized, and intelligent process management. These systems have wide applications in traditional and new fields such as chemical production, intelligent power systems, new energy vehicle intelligent braking, intelligent traffic flow, multi-dimensional force command, large-scale cluster command, etc.

[0003] However, although artificial intelligence algorithms such as neural networks and fuzzy functions can quickly fit unknown functions and parameters of the system when solving the control of multivariable nonlinear systems, they can solve the control problem of multivariable nonlinear systems. However, such methods have high requirements for training data and processor computing power, thus limiting the industrial application and promotion of such methods.

[0004] Secondly, existing control methods often cannot effectively determine the control direction when dealing with unknown high-frequency gain matrices. The uncertainty of the high-frequency gain matrix makes it difficult for traditional adaptive control methods to be directly applied. They usually rely on accurate estimation of the high-frequency gain matrix. When the high-frequency gain matrix is unknown, the selection of the system control direction becomes complex and uncertain, which may lead to control failure, unstable system operation, and poor tracking performance.

[0005] Thirdly, for the case where system parameters are unknown, the performance of existing control methods is often severely limited. Although many adaptive control methods can handle some degree of uncertainty, when the system parameters are completely unknown, these methods may not work effectively due to the lack of necessary prior information. The unknown system parameters increase the difficulty of control design, making it difficult for the controller to accurately adapt to system dynamics, thus affecting the overall control effect of the system.

[0006] Finally, existing technologies are not ideal for handling the complex coupling relationship of multivariable nonlinear systems. Multivariable nonlinear systems often exhibit complex interactions between multiple inputs and multiple outputs, making system control particularly complex. Existing methods often fail to fully consider the influence of various factors when dealing with such complex coupling relationships, resulting in a lack of refinement in control strategy design and difficulty in achieving precise control of the system.

[0007] Therefore, how to design an adaptive control method of a multivariable nonlinear system, through constructing a system model and designing a corresponding control strategy, quickly realizing effective control of a complex multivariable nonlinear system is a problem to be solved by the person skilled in the art. SUMMARY

[0008] Therefore, the present application provides an adaptive control method of a multivariable nonlinear system, which quickly realizes effective control of a complex multivariable nonlinear system through constructing a system model and designing a corresponding control strategy. It can automatically adjust the control parameters according to the dynamic characteristics of the system, ensure the stable operation of the system, and optimize the control performance, and is suitable for various application scenarios that require accurate control.

[0009] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:

[0010] The present application provides an adaptive control method of a multivariable nonlinear system, comprising the following steps:

[0011] S1, constructing a multivariable nonlinear system including unknown parameters and unknown high-frequency gain matrix; the multivariable nonlinear system model is expressed as:

[0012]

[0013] y=x1

[0014] wherein, x represents the state vector of the multivariable nonlinear system, the state vector x includes n sub-vectors, each sub-vector x n has a dimension of M, dx / dt represents the time derivative of the sub-vector x n , and u represents the input vector of the multivariable nonlinear system; y represents the output vector of the multivariable nonlinear system; represents a smooth nonlinear function;

[0015] A i ∈R M×M represents an unknown parameter matrix; B∈R M×M represents an unknown high-frequency gain matrix; i=1,…,ν,j=1,…,n,ν,n,M represent known normal numbers;

[0016] introducing matrix Θ and

[0017] Θ=[A1,…,A ν ]∈R M×Mν

[0018]

[0019] In the multivariable nonlinear system model, for the matrix Θ, the inverse matrix B of the matrix B -1 , there are the compact convex sets Π Θ and Π B respectively:

[0020] Π Θ ={Θ S ∈R M×Mν |Ρ Θ (Θ S )≤0}

[0021] Π B ={B S ∈R M×M |Ρ B (B S )≤0}

[0022] Wherein, Θ S represents the matrix element of the compact convex set Π Θ with the dimension of MxMv, B S represents the matrix element of the compact convex set Π B with the dimension of MxM, Ρ Θ and Ρ B represent smooth convex functions, and c1≤||B -1 ||≤c2, c1 and c2 are normal numbers;

[0023] For the matrix B, there is a matrix S q ∈R M×M , The matrix -BS q is a Hurwitz matrix under a bounded index q; wherein Ω represents a bounded index set, and Q is a positive integer;

[0024] And the reference signal y r ∈R M and its n-order derivative are known to be bounded;

[0025] S2, based on the multivariable nonlinear system model, an adaptive controller and a switching mechanism are constructed, and the control direction matrix S q is determined through the adaptive controller and the switching mechanism, so that the multivariable nonlinear system output y can accurately track the reference signal y r .

[0026] Further, in the S2, the adaptive controller and the switching mechanism are constructed, comprising:

[0027] S21, an error performance preset function is constructed; the construction of the error performance preset function comprises:

[0028] Define the system tracking error z1 and the error variable z i :

[0029] z1=y-y r

[0030] z i =x i -α i-1

[0031] wherein, α i-1 represents a virtual control law to be designed;

[0032] For an error variable z i , a preset performance function of the error variable z i is defined as:

[0033]

[0034] wherein, represents a transpose matrix of the error variable z i , K i represents a preset constant, t0 represents an initial time point, and t represents a time variable;

[0035] S22, based on the error performance preset function, a boundary Lyapunov function is constructed; the boundary Lyapunov function V(z i ) is expressed as:

[0036]

[0037] When z approaches z , the boundary Lyapunov function V(z i ) approaches infinity;

[0038] S23, an adaptive control law is constructed in combination with a backstepping algorithm; the adaptive control law constructed in combination with the backstepping algorithm comprises:

[0039] When i=1,

[0040]

[0041] When i=2,

[0042] V2=V(z2)+V1

[0043]

[0044] When 3≤i≤n-1,

[0045] V i =V(z i )+V i-1

[0046]

[0047] when i = n,

[0048]

[0049] where V n represents a Lyapunov function for assessing the stability of the system; a n represents a partial control input including a feedback term and an adaptive control term; τ n represents a partial control input including an adaptive control term; Γ represents a gain matrix; represents a regression vector; tr() represents the trace of a matrix; C i represents a feedback gain matrix; represents the derivative of the reference signal y r ; represents the j-th derivative of the reference signal y r ; represents a parameter estimation error, represents an estimate of the matrix Θ; represents a parameter estimation error, P = B -1 , represents an estimate of the matrix P; Proj represents a projection operator;

[0050]

[0051] Based on the adaptive control law, if the error variable z i satisfies the initial condition:

[0052]

[0053] then all signals in the system are bounded, and the error z i satisfies:

[0054]

[0055] can converge to zero:

[0056]

[0057] and there exists a positive number μ0such that the following is true:

[0058]

[0059] The value of the positive number μ0is:

[0060]

[0061] where λ Γ is the largest eigenvalue of the matrix Γ -1 , λS To control the direction matrix S q The largest eigenvalue, Θ M Let ε0 be the upper bound of the infinite norm of matrix Θ, and let ε0 be an arbitrarily small positive constant.

[0062] S24. Build a switching mechanism; the build switching mechanism includes:

[0063] Selecting the control direction matrix

[0064] Within the time interval [t0, t1),

[0065]

[0066] If t1 = +∞, then matrix S q No switching will occur; otherwise, the control direction matrix S q Depend on Switch to S q2 q2∈Ω-{q1}; define t1 as:

[0067]

[0068] In t k If 1 < k < Q-1, at least one inequality is false, and the inequality is expressed as:

[0069]

[0070] positive constant μ k-1 The range of values ​​is:

[0071]

[0072] Where, ε k-1 For any arbitrarily small positive constant, there exists:

[0073]

[0074] Define the switching time t k for:

[0075]

[0076] And the control direction matrix S q Depend on Switch to S qk+1 ,q k+1 ∈Ω-{q1,…,q k}

[0077] As can be seen from the above technical solutions, compared with the prior art, the technical solutions of the present invention have the following advantages:

[0078] Beneficial effects:

[0079] 1. The method introduces an adaptive tracking control law design for such systems, enabling the intelligent switching of control direction matrices to find appropriate control strategies even in the absence of prior knowledge of the high-frequency gain matrix. This greatly relaxes the restrictions on the high-frequency gain matrix, eliminating the need to assume that it is a diagonal matrix or satisfies specific positive definite conditions, thereby expanding the scope of application and improving the flexibility and robustness of the control system.

[0080] 2. The method ensures that the system maintains good performance even during the switching process of the control direction matrix, specifically ensuring the boundedness of all signals within the closed-loop system and the convergence of the system tracking error to zero or maintenance within a pre-set small range. This not only improves the stability of the system but also enhances the response speed and accuracy, which is crucial for dynamic adjustment in practical applications.

[0081] 3. When faced with multivariable nonlinear systems with unknown parameters and high-frequency gain matrices, it can effectively achieve high-precision tracking of reference signals, proving its reliability and practicality in complex environments. It has important significance for many fields such as chemical production, power system control, and vehicle braking, helping these industries improve efficiency, reduce resource consumption, and enhance safety, and promoting related technologies to more advanced levels. BRIEF DESCRIPTION OF DRAWINGS

[0082] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, a brief introduction of the drawings needed in the embodiment or prior art description will be given below. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without creative labor.

[0083] Figure 1 The adaptive control method flowchart of the multivariable nonlinear system provided for the embodiments of the present application;

[0084] Figure 2 The process schematic diagram of constructing an adaptive controller and switching mechanism provided for the embodiments of the present application;

[0085] Figure 3 The convergence error z1 provided for the embodiments of the present application T z1 change schematic diagram;

[0086] Figure 4 The convergence error z2 provided for the embodiments of the present application T z2 change schematic diagram;

[0087] Figure 5 a tracking schematic diagram of the reference signal y provided by an embodiment of the present application 1r a tracking schematic diagram of the reference signal y provided by an embodiment of the present application

[0088] Figure 6 a tracking schematic diagram of the reference signal y provided by an embodiment of the present application 2r a tracking schematic diagram of the reference signal y provided by an embodiment of the present application

[0089] Figure 7 a tracking schematic diagram of the reference signal y provided by an embodiment of the present application 11 a tracking schematic diagram of the reference signal y provided by an embodiment of the present application 12 a tracking schematic diagram of the reference signal y provided by an embodiment of the present application DETAILED DESCRIPTION

[0090] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0091] Embodiment 1

[0092] As shown in the accompanying drawings, the present embodiment provides an adaptive control method for a multivariable nonlinear system, comprising the following steps: Figure 1 S1, constructing a multivariable nonlinear system comprising unknown parameters and unknown high-frequency gain matrix; the multivariable nonlinear system model is expressed as:

[0093]

[0094]

[0095] y=x1

[0096] wherein, x represents a state vector of the multivariable nonlinear system, the state vector x comprises n sub-vectors, each sub-vector x n has a dimension of M, x represents a time derivative of the sub-vector x n , and u represents an input vector of the multivariable nonlinear system; y represents an output vector of the multivariable nonlinear system; represents a smooth nonlinear function;

[0097] A i ∈R M×M represents an unknown parameter matrix; B∈R M×M represents an unknown high-frequency gain matrix; i=1,…,ν, j=1,…,n, ν, n, M represent known normal numbers;

[0098] introducing matrix Θ and ​

[0099] Θ=[A1,…,A ν ]∈R M×Mν

[0100]

[0101] In the multivariable nonlinear system model, for the matrix Θ, the inverse matrix B -1 of the matrix B Θ , there are a compact convex set Π B and Π Θ respectively:

[0102] Π S ={Θ M×Mν ∈R Θ |Ρ S (Θ B )≤0}

[0103] Π S ={B M×M ∈R B |Ρ S (B S )≤0}

[0104] Wherein, Θ Θ represents the matrix element with the dimension of MxMν in the compact convex set Π S , B B represents the matrix element with the dimension of MxM in the compact convex set Π Θ , Ρ B and Ρ -1 represent smooth convex functions, and c1≤||B q ||≤c2, c1 and c2 are normal numbers;

[0105] For the matrix B, there is a matrix S M×M ∈R q , The matrix -BS r is a Hurwitz matrix under a bounded index q; wherein Ω represents a bounded index set, and Q is a positive integer;

[0106] And the reference signal y M and its n-order derivative are known to be bounded;

[0107] S2, based on the multivariable nonlinear system model, an adaptive controller and a switching mechanism are constructed, and the control direction matrix S q is determined through the adaptive controller and the switching mechanism, so that the multivariable nonlinear system output y can accurately track the reference signal y r .

[0108] The method relaxes the restriction condition on the high-frequency gain matrix by introducing an adaptive tracking control law design, improves the flexibility and robustness of the control system, ensures good system performance when the control direction matrix switches, realizes high-precision tracking of the reference signal of the multivariable nonlinear system, has important significance in the fields of intelligent power system, new energy vehicle intelligent braking, multi-dimensional force command, etc., and can promote the development of related technologies and improve the efficiency and safety of the industry.

[0109] The above steps and related technical features are further described in detail as follows.

[0110] As shown in the following S2, the adaptive controller and the switching mechanism are constructed, including: Figure 2

[0111] S21, constructing an error performance preset function; the error performance preset function includes:

[0112] Defining the system tracking error z1 and the error variable z i :

[0113] z1=y-y r

[0114] z i =x i -α i-1

[0115] Wherein, α i-1 represents a virtual control law to be designed;

[0116] For the error variable z i , the preset performance function of the error variable z i is defined as:

[0117]

[0118] Wherein, represents the transpose matrix of the error variable z i , K i represents a preset constant, t0 represents an initial time point, and t represents a time variable;

[0119] S22, constructing a boundary Lyapunov function based on the error performance preset function; the boundary Lyapunov function V(z i ) is expressed as:

[0120]

[0121] When approaches , the boundary Lyapunov function V(z i ) tends to infinity; ​

[0122] S23, constructing an adaptive control law in combination with a backstepping algorithm; the constructing an adaptive control law in combination with a backstepping algorithm comprises:

[0123] When i = 1,

[0124]

[0125] When i = 2,

[0126] V2= V(z2) + V1

[0127]

[0128] When 3≤i≤n-1,

[0129] V i = V(z i )+ V i-1

[0130]

[0131]

[0132] When i = n,

[0133]

[0134] Wherein, V n represents a Lyapunov function for evaluating the stability of the system; α n represents a partial control input including a feedback term and an adaptive control term; τ n represents a partial control input including an adaptive control term; Γ represents a gain matrix; represents a regression vector; tr() represents the trace of a matrix; C i represents a feedback gain matrix; represents the derivative of a reference signal y r ; represents the j-th derivative of a reference signal y r ; represents a parameter estimation error, represents an estimate of the matrix Θ; represents a parameter estimation error, P = B -1 , represents an estimate of the matrix P; Proj represents a projection operator;

[0135]

[0136]

[0137] Based on the adaptive control law, if the error variable zi satisfy the initial conditions:

[0138]

[0139] then all signals in the system are bounded, and the error z i satisfy:

[0140]

[0141] can converge to zero:

[0142]

[0143] and there exists a positive number μ0such that the following inequality holds:

[0144]

[0145] The value of the positive number μ0is:

[0146]

[0147] where λ Γ is the maximum eigenvalue of the matrix Γ -1 , λ S is the maximum eigenvalue of the control direction matrix S q , Θ M is the upper bound of the infinite norm of the matrix Θ, and ε0is an arbitrarily small positive number;

[0148] S24, a switching mechanism is constructed; the switching mechanism comprises:

[0149] a control direction matrix S

[0150] In the time interval [t0, t1), the control direction matrix S

[0151]

[0152] If t1= +∞, the control direction matrix S q will not switch; otherwise, the control direction matrix S q is switched from S to S q2 , q2∈Ω-{q1}; t1is defined as:

[0153]

[0154] In t k , 1 < k < Q-1, at least one of the inequalities does not hold, which is expressed as:

[0155]

[0156] normal number μ k-1 The value range is:

[0157]

[0158] Wherein, ε k-1 is an arbitrary small normal number; there is:

[0159]

[0160] The switching moment t k is defined as:

[0161]

[0162] And the control direction matrix S q is changed from to S qk+1 , q k+1 ∈Ω-{q1,…,q k}.

[0163] Combined with the preset performance function designed above, the adaptive control law and parameter update law of the system with known control direction designed by backstepping method, and the control direction matrix S q Switching criteria, we can get:

[0164] The switching number of the control direction matrix S q is at most k (1≤k≤Q) times;

[0165] All signals of the closed-loop system are bounded;

[0166] The system tracking error z1 can converge to zero or satisfy the following inequality:

[0167]

[0168] Wherein, μ k represents the decay rate;

[0169] Further, numerical simulation is carried out to verify it;

[0170] In this embodiment, simulation is carried out for a two-input two-output nonlinear system:

[0171] Specifically, in the process of unmanned vehicle braking, especially in the field of new energy vehicle intelligent braking system, accurate control of multivariable nonlinear system is an important guarantee for efficient and stable braking. In a two-input two-output nonlinear system, input 1 is set as brake pressure control, and the size of brake pressure directly affects the braking effect and braking distance of the vehicle, which is a key factor to ensure driving safety. Input 2 is vehicle speed control, and real-time adjustment of vehicle speed is of great significance to maintain the stability of the vehicle and prevent accidents in emergency braking or complex road conditions. Output 1 of the system is braking distance, which directly reflects the performance and effect of the braking system; output 2 is brake disc temperature, which needs to be strictly controlled because high brake disc temperature may lead to decreased braking performance or even brake failure. It can achieve accurate control of brake pressure and vehicle speed, thereby shortening braking distance, improving braking stability, reducing brake disc temperature, prolonging the service life of the braking system, and providing strong protection for active safety driving of vehicles.

[0172] In the process of multi-dimensional force command, complex multivariable nonlinear system control is the key to efficient and stable command. In a two-input two-output nonlinear system, input 1 and input 2 are set as the power intensity control of two groups of heterogeneous forces, which is the key factor affecting coordinated command in real-time command of multi-dimensional forces. At the same time, power intensity needs to be accurately controlled to ensure that the corresponding target is completed with the lowest power intensity. Output 1 and output 2 of the system are the real-time displacement of the two groups of heterogeneous forces, which directly reflects the command and scheduling of multi-dimensional forces and accurately realizes real-time regulation and control of multi-dimensional forces. Therefore, this adaptive control method is of great significance for improving the automation level and overall performance of the multi-dimensional force command process.

[0173] Specifically, the above two-input two-output nonlinear system can be represented as:

[0174]

[0175] where all signals x 11 ,x 12 ,x 21 ,x 22 ,y 11 ,y 12 ,u 11 ,u 12 are scalars, and matrices A 11 ,A 12 ,B 11 are unknown constant parameter matrices. The candidate matrix of the control direction matrix S q of the controlled system can be determined as follows:

[0176]

[0177] In the above adaptive controller, the parameter matrix C1 = C2 = [1 1] T , Γ is the identity matrix. The preset parameters are set as

[0178] Assume the matrix A 11 , A 12 , B 11 are

[0179] The initial conditions are x 11 = 0.3, x 12 = -0.3, x 21 = 0, x 22 = 0, y 1r = y 2r = sin(t / 4), and the specific simulation results are obtained.

[0180] As shown in Figure 3 , the convergence error z1 T z1 rapidly decreases in the initial stage, and the system quickly approaches the desired value. Subsequently, the error gradually stabilizes and approaches zero, indicating that the adopted control strategy effectively makes the system output converge to the target value, ensuring the stability and accuracy of the system.

[0181] As shown in Figure 4 , the convergence error z2 T z2 rapidly decreases in the initial stage, and the system quickly approaches the desired value. Subsequently, the error gradually stabilizes and approaches zero, indicating that the adopted control strategy effectively makes the system output converge to the target value, ensuring the stability and accuracy of the system.

[0182] As shown in Figure 5 , the system state x 11 rapidly adjusts in the initial stage to track the reference signal y 1r . Over time, the tracking error between the system state and the reference signal gradually decreases, indicating that the controller effectively makes the system output approach and remain on the desired reference signal trajectory, showing good tracking performance and stability of the system.

[0183] As shown in Figure 6 , the system state x 12 rapidly adjusts in the initial stage to track the reference signal y 2r . Over time, the tracking error between the system state and the reference signal gradually decreases, indicating that the controller effectively makes the system output approach and remain on the desired reference signal trajectory, showing good tracking performance and stability of the system.

[0184] As shown in Figure 7 , the input signals u 11 and u12 In the initial stage, it is relatively stable, and the control signal quickly falls to near zero value at about 0.4s. This shows that the controller has small control strength in the initial stage, and with the passage of time, the control strength is obviously enhanced due to the inappropriate initial control direction. At about 0.4s, the system state is quickly adjusted with the switching of the control direction, and then enters the stable control stage, ensuring that the system output can accurately track the reference signal.

[0185] The embodiment proposes an adaptive control method for a multivariable nonlinear system. The method designs an adaptive controller and a switching mechanism capable of accurately tracking the reference signal by constructing a system model containing unknown parameters and high-frequency gain matrix. The method combines the preset performance function, backstepping algorithm and Lyapunov stability theory, ensures that the system can maintain good performance when the control direction is switched, and realizes high-precision tracking control of the complex dynamic system.

[0186] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same or similar parts of each embodiment can be referred to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0187] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method of adaptive control of a multivariable nonlinear system, characterized by, The method comprises the following steps: S1, constructing a multivariable nonlinear system comprising unknown parameters and unknown high-frequency gain matrix; the multivariable nonlinear system model is expressed as: y = x1 wherein denotes a state vector of the multivariable nonlinear system, the state vector x comprises n sub-vectors, each sub-vector x n has a dimension of M, denotes a time derivative of the sub-vector x n , and u denotes an input vector of the multivariable nonlinear system; y denotes an output vector of the multivariable nonlinear system; denotes a smooth nonlinear function; A i ∈R M×M denotes an unknown parameter matrix; B∈R M×M denotes an unknown high frequency gain matrix; i = 1,..., v, j = 1,..., n, v, n, M denote known constants; Introducing the matrix Θ and Θ = [A1,..., A ν ] ∈ R M×Mν In the multivariable nonlinear system model, for the matrix Θ, the inverse matrix B -1 of the matrix B Θ and Π B : respectively exist a compact convex set Π Θ and Π B : Π Θ = { Θ S ∈ R M×Mν | P Θ ( Θ S ) ≤ 0} Π B = {B S ∈ R M×M | P B (B S ) ≤ 0} Where, Θ S Represents the compact convex set Π Θ The elements of a matrix with dimensions M×Mν, B S Indicates the compact convex set Π B A matrix element of dimension M×M, P Θ and P B Let c1 denote a smooth convex function, and c1 ≤ ||B|. -1 ||≤c2, where c1 and c2 are positive constants; For matrix B, there exists matrix S q ∈R M×M , Under the bounded index q, matrix -BS q is a Hurwitz matrix; wherein Ω represents a bounded index set, and Q is a positive integer; and the reference signal y r ∈ R M and its n-th derivative are known to be bounded; S2, constructing an adaptive controller and a switching mechanism based on the multivariable nonlinear system model, and determining the control direction matrix S through the adaptive controller and the switching mechanism q such that the multivariable nonlinear system output y can accurately track the reference signal y r .

2. The adaptive control method of a multivariable nonlinear system according to claim 1, characterized by, In S2, an adaptive controller and a switching mechanism are constructed, comprising: S21, constructing an error performance preset function; the constructing an error performance preset function comprises: Define system tracking error z1 and error variable z i : z1 = y - y r z i = x i - a i-1 wherein a i-1 represents the virtual control law to be designed; For the error variable z i , a preset performance function of the error variable z i is defined as: wherein, denotes an error variable z i denotes a transpose matrix of K i denotes a preset constant, t0 denotes an initial time point, and t denotes a time variable S22, constructing a boundary Lyapunov function based on the error performance preset function; the boundary Lyapunov function V(z i ) is expressed as: When approaches , the boundary Lyapunov function V(z i ) approaches infinity; S23, constructing an adaptive control law in combination with a backstepping algorithm; the constructing an adaptive control law in combination with a backstepping algorithm comprises: When i = 1, When i = 2, V2 = V(z2) + V1 When 3 ≤ i ≤ n-1, V i = V(z i )+ V i-1 When i = n, where V n represents a Lyapunov function for assessing the stability of the system; a n represents a partial control input, including a feedback term and an adaptive control term; τ n represents a partial control input, including an adaptive control term; Γ represents a gain matrix; represents a regression vector; tr() represents the trace of a matrix; C i represents a feedback gain matrix; represents the derivative of the reference signal y r ; represents the j-th derivative of the reference signal y r ; represents a parameter estimation error, represents an estimate of the matrix Θ; represents a parameter estimation error, P = B -1 , represents an estimate of the matrix P; Proj represents a projection operator; Based on the adaptive control law, if the error variable z i satisfies the initial condition: Then all signals in the system are bounded, the error z i satisfies: Converge to zero point: And there is a normal number μ0, for the following formula is true: The value of the normal number μ0 is: where λ Γ is the maximum eigenvalue of the matrix Γ -1 , λ S is the maximum eigenvalue of the control direction matrix S q , Θ M is an upper bound of the infinity norm of the matrix Θ, and ε0 is an arbitrarily small positive number. where λ Γ is the maximum eigenvalue of the matrix Γ -1 , λ S is the maximum eigenvalue of the control direction matrix S q , Θ M is an upper bound of the infinity norm of the matrix Θ, and ε0 is an arbitrarily small positive number. S24, constructing a switching mechanism; the constructing a switching mechanism comprises: select control direction matrix In the time interval [t0, t1), If t1 = +∞, then the matrix S q No switching occurs; otherwise, the control direction matrix S q is given by Switching to S q2 , q2∈Ω-{q1}; define t1 as: At t k Below, 1 < k < Q - 1, at least one of the inequalities does not hold, which is expressed as: Normal number μ k-1 Has a value in the range: where ε k-1 is an arbitrarily small positive number; there exists: Definition of switching time t k is: and control direction matrix S q By Switch to S qk+1 q k+1 ∈ Ω - {q1,..., q k}.

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