Self-adaptive control method of multivariable nonlinear system

Abstract

The invention discloses a self-adaptive control method of a multivariable nonlinear system. The method comprises the following steps: constructing the multivariable nonlinear system comprising unknown parameters and an unknown high-frequency gain matrix; the model not only describes system behaviors through state, input and output vectors, but also introduces an unknown parameter matrix and a smooth nonlinear function to simulate complexity and nonlinear characteristics of the system. And further constructing an adaptive controller and a switching mechanism, and determining a control direction matrix through the adaptive controller and the switching mechanism, so that the output of the multivariable nonlinear system can accurately track the reference signal. According to the method, by introducing the self-adaptive tracking control law design, the limiting condition of a high-frequency gain matrix is relaxed, it is ensured that the system performance is good when the direction matrix is controlled to be switched, and high-precision tracking of a multivariable nonlinear system reference signal is achieved.

Description

Technical Field

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

[0002] The control of multivariable nonlinear systems is a crucial aspect in modern industry and engineering technology. Such systems involve multidimensional signals and complex data processing. They achieve precise control of multiple outputs by real-time regulation of multiple inputs to achieve more efficient, optimized and intelligent process management. Such systems are widely used in traditional and new fields such as chemical production, intelligent power systems, intelligent braking of new energy vehicles, intelligent traffic flow, multidimensional force command, large-scale cluster command, etc.

[0003] However, although artificial intelligence algorithms such as neural networks and fuzzy functions can quickly fit the unknown functions and parameters of the system when solving the control of multivariable nonlinear systems and can solve the control problems of multivariable nonlinear systems, such methods have high requirements for training data and processor computing power, which limits 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 to directly apply traditional adaptive control methods, which usually rely on accurate estimation of the high-frequency gain matrix. When the high-frequency gain matrix is ​​unknown, the choice of system control direction becomes complex and uncertain, which may lead to control failure, instability of the system, and greatly reduced tracking performance.

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

[0006] Finally, the existing technology is not ideal for handling the complex coupling relationship of multivariable nonlinear systems. Multivariable nonlinear systems usually exhibit complex interactions between multiple inputs and multiple outputs. This coupling relationship makes the control of the system particularly complex. When dealing with such complex coupling relationships, existing methods often fail to fully consider the influence of various factors, resulting in the design of control strategies that are not sophisticated enough and it is difficult to achieve precise control of the system.

[0007] Therefore, how to design an adaptive control method for multivariable nonlinear systems, and quickly achieve effective control of complex multivariable nonlinear systems by building a system model and designing corresponding control strategies is an urgent problem that technicians in this field need to solve. Summary of the invention

[0008] In view of this, the present invention provides an adaptive control method for a multivariable nonlinear system, which quickly realizes effective control of a complex multivariable nonlinear system by 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, ensuring stable operation of the system while optimizing the control performance, and is suitable for a variety of application scenarios that require precise control.

[0009] In order to achieve the above object, the present invention adopts the following technical solution:

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

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

[0012]

[0013] y=x 1

[0014] in, Represents the state vector of a multivariable nonlinear system. The state vector x consists of n subvectors, each of which is n The dimension is M, Represents the subvector x n The time derivative of 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 the unknown parameter matrix; B∈R M×M represents the unknown high-frequency gain matrix; i=1,…,ν, j=1,…,n, ν, n, M represent known positive constants;

[0016] Introduce the matrices Θ and

[0017] θ=[A 1 ,…,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 exist compact convex sets Π Θ and Π B :

[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] Among them, Θ S Denotes a compact convex set Π Θ The matrix elements of dimension M×Mν in B S Denotes a compact convex set Π B The matrix element with dimension M×M in , Ρ Θ and P B represents a smooth convex function, and c 1 ≤||B -1 ||≤c 2 , c 1 and c 2 is a positive constant;

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

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

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

[0026] Furthermore, in S2, an adaptive controller and a switching mechanism are constructed, including:

[0027] S21, constructing a preset error performance function; the constructing a preset error performance function includes:

[0028] Define the system tracking error z 1 and the error variable z i :

[0029] z 1 =yy r

[0030] z i =x i -α i-1

[0031] Among them, α i-1 represents the virtual control law to be designed;

[0032] For the error variable z i , define the error variable z i The default performance function is:

[0033]

[0034] in, represents the error variable z i The transposed matrix, K i Represents the preset constant, t 0 represents the initial time point, and t represents the time variable;

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

[0036]

[0037] when Approaching When the boundary Lyapunov function V(z i ) tends to infinity;

[0038] S23, constructing an adaptive control law in combination with a backstepping algorithm; the constructing an adaptive control law in combination with a backstepping algorithm includes:

[0039] When i=1,

[0040]

[0041] When i=2,

[0042] V 2 =V(z 2 )+V 1

[0043]

[0044] When 3≤i≤n-1,

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

[0046]

[0047] When i=n,

[0048]

[0049] Among them, V n represents the Lyapunov function, which is used to evaluate the stability of the system; α n represents part of the control input, including feedback terms and adaptive control terms; τ n represents part of the control input, including the adaptive control term; Γ represents the gain matrix; represents the regression vector; tr() represents the trace of the matrix; C i represents the feedback gain matrix; represents the reference signal y r The derivative of represents the reference signal y r The j-order derivative of ; represents the parameter estimation error, represents the estimate of the matrix Θ; Represents parameter estimation error, P = B -1 , represents the estimation of the matrix P; Proj represents the projection operator;

[0050]

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

[0052]

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

[0054]

[0055] It can converge to zero:

[0056]

[0057] And there exists a positive constant μ 0 , the following holds true:

[0058]

[0059] The positive constant μ 0 The value of is:

[0060]

[0061] Among them, λ Γ is the matrix Γ -1 The maximum eigenvalue of S is the control direction matrix S q The maximum eigenvalue of M is the upper bound of the infinity norm of the matrix Θ, ε 0 is an arbitrarily small positive constant;

[0062] S24, constructing a switching mechanism; the constructing a switching mechanism includes:

[0063] Select the control direction matrix

[0064] In the time interval [t 0 ,t 1 )Down,

[0065]

[0066] If 1 =+∞, then the matrix S q No switching occurs; otherwise, the control direction matrix S q Depend on Switch to S q2 ,q 2 ∈Ω-{q 1}; define t 1 for:

[0067]

[0068] In t k Under this condition, 1<k<Q-1, at least one inequality does not hold, and the inequality is expressed as:

[0069]

[0070] Normal constant μ k-1 The value range is:

[0071]

[0072] Among them, ε k-1 is an 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-{q 1 ,…,q k}.

[0077] It can be seen from the above technical solution that compared with the prior art, the technical solution of the present invention has the following advantages:

[0078] Beneficial effects:

[0079] 1. This method introduces the design of adaptive tracking control law for such systems, so that even in the absence of prior knowledge of the high-frequency gain matrix, it is possible to find a suitable control strategy through intelligent switching of the control direction matrix. The restrictions on the high-frequency gain matrix are greatly relaxed, and it is no longer necessary to assume that the high-frequency gain matrix is ​​a diagonal matrix or satisfies specific positive definiteness conditions, thereby expanding the scope of application and improving the flexibility and robustness of the control system.

[0080] 2. This method ensures that the system can maintain good performance even when the control direction matrix is ​​switched. Specifically, it ensures the boundedness of all signals in the closed-loop system, and the system tracking error can converge to zero or remain within a preset small range. This not only improves the stability of the system, but also enhances the response speed and accuracy of the system, which is crucial for dynamic adjustment in practical applications.

[0081] 3. When facing a multivariable nonlinear system with unknown parameters and high-frequency gain matrix, it can effectively achieve high-precision tracking of the reference signal, proving its reliability and practicality in complex environments. It is of great significance to many fields such as chemical production, power system control, and vehicle braking, and can help these industries improve efficiency, reduce resource consumption, and enhance safety, and promote the development of related technologies to a more advanced level. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0083] Figure 1A flow chart of an adaptive control method for a multivariable nonlinear system provided by an embodiment of the present invention;

[0084] Figure 2 A schematic diagram of a process for constructing an adaptive controller and a switching mechanism provided by an embodiment of the present invention;

[0085] Figure 3 The convergence error z provided in the embodiment of the present invention is 1 T z 1 Schematic diagram of changes;

[0086] Figure 4 The convergence error z provided in the embodiment of the present invention is 2 T z 2 Schematic diagram of changes;

[0087] Figure 5 The reference signal y provided in the embodiment of the present invention 1r Tracking diagram of

[0088] Figure 6 The reference signal y provided in the embodiment of the present invention 2r Tracking diagram of

[0089] Figure 7 The input signal u provided by the embodiment of the present invention is 11 and u 12 Schematic diagram of changes. DETAILED DESCRIPTION

[0090] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0091] Embodiment 1;

[0092] like Figure 1 As shown, this embodiment provides an adaptive control method for a multivariable nonlinear system, comprising the following steps:

[0093] S1. Construct a multivariable nonlinear system including unknown parameters and unknown high-frequency gain matrix; the multivariable nonlinear system model is expressed as:

[0094]

[0095] y=x 1

[0096] in, Represents the state vector of a multivariable nonlinear system. The state vector x consists of n subvectors, each of which is n The dimension is M, Represents the subvector x n The time derivative of 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;

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

[0098] Introduce the matrices Θ and

[0099] θ=[A 1 ,…,A ν ]∈R M×Mν

[0100]

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

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

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

[0104] Among them, Θ S Denotes a compact convex set Π Θ The matrix elements of dimension M×Mν in B S Denotes a compact convex set Π B The matrix element with dimension M×M in , Ρ Θ and P B represents a smooth convex function, and c 1 ≤||B -1 ||≤c 2 , c 1 and c2 is a positive constant;

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

[0106] And the reference signal y r ∈R M and its nth-order derivative is known to be bounded;

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

[0108] This method relaxes the restrictions 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 is ​​switched, and achieves high-precision tracking of the reference signal of the multivariable nonlinear system. It is of great significance in the fields of intelligent power systems, intelligent braking of new energy vehicles, multi-dimensional force command, etc., and can promote the development of related technologies and improve industry efficiency and safety.

[0109] The above steps and related technical features are further described in detail below;

[0110] like Figure 2 As shown, an adaptive controller and a switching mechanism are constructed in S2, including:

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

[0112] Define the system tracking error z 1 and error variable z i :

[0113] z 1 =yy r

[0114] z i =x i -α i-1

[0115] Among them, α i-1 represents the virtual control law to be designed;

[0116] For the error variable z i, define the error variable z i The default performance function is:

[0117]

[0118] in, represents the error variable z i The transposed matrix, K i Represents the preset constant, t 0 represents the initial time point, and t represents the time variable;

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

[0120]

[0121] when Approaching When 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 includes:

[0123] When i=1,

[0124]

[0125] When i=2,

[0126] V 2 =V(z 2 )+V 1

[0127]

[0128] When 3≤i≤n-1,

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

[0130]

[0131]

[0132] When i=n,

[0133]

[0134] Among them, V nrepresents the Lyapunov function, which is used to evaluate the stability of the system; α n represents part of the control input, including feedback terms and adaptive control terms; τ n represents part of the control input, including the adaptive control term; Γ represents the gain matrix; represents the regression vector; tr() represents the trace of the matrix; C i represents the feedback gain matrix; represents the reference signal y r The derivative of represents the reference signal y r The j-order derivative of ; represents the parameter estimation error, represents the estimate of the matrix Θ; Represents parameter estimation error, P = B -1 , represents the estimation of the matrix P; Proj represents the projection operator;

[0135]

[0136]

[0137] Based on the adaptive control law, if the error variable z i Satisfy the initial conditions:

[0138]

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

[0140]

[0141] It can converge to zero:

[0142]

[0143] And there exists a positive constant μ 0 , the following holds true:

[0144]

[0145] The positive constant μ 0 The value of is:

[0146]

[0147] Among them, λ Γ is the matrix Γ -1 The maximum eigenvalue of S is the control direction matrix S q The maximum eigenvalue of Mis the upper bound of the infinity norm of the matrix Θ, ε 0 is an arbitrarily small positive constant;

[0148] S24, constructing a switching mechanism; the constructing a switching mechanism includes:

[0149] Select the control direction matrix

[0150] In the time interval [t 0 ,t 1 )Down,

[0151]

[0152] If t 1 =+∞, then the matrix S q No switching occurs; otherwise, the control direction matrix S q Depend on Switch to S q2 ,q 2 ∈Ω-{q 1}; define t 1 for:

[0153]

[0154] In t k Under this condition, 1<k<Q-1, at least one inequality does not hold, and the inequality is expressed as:

[0155]

[0156] Normal constant μ k-1 The value range is:

[0157]

[0158] Among them, ε k-1 is an arbitrarily small positive constant; there exists:

[0159]

[0160] Define the switching time t k for:

[0161]

[0162] And the control direction matrix S q Depend on Switch to S qk+1 ,q k+1 ∈Ω-{q 1 ,…,q k}.

[0163] Combining 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 designed by Lyapunov function q The switching criteria are:

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

[0165] All signals in a closed-loop system are bounded;

[0166] System tracking error z 1 Can converge to zero or satisfy the following inequality:

[0167]

[0168] Among them, μ k represents the decay rate;

[0169] Furthermore, numerical simulation verification is carried out;

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

[0171] Specifically, in the braking process of unmanned vehicles, especially in the field of intelligent braking systems for new energy vehicles, precise control of multivariable nonlinear systems is an important guarantee for achieving efficient and stable braking. In a nonlinear system with two inputs and two outputs, input 1 is set as brake pressure control. The size of the brake pressure directly affects the braking effect and braking distance of the vehicle, and is a key factor in ensuring driving safety. Input 2 is vehicle speed control. In emergency braking or complex road conditions, real-time adjustment of vehicle speed is of great significance for maintaining vehicle stability and preventing accidents. Output 1 of the system is the braking distance, which directly reflects the performance and effect of the braking system; output 2 is the brake disc temperature. Excessive brake disc temperature may lead to reduced braking performance or even brake failure, so it needs to be strictly controlled. It can achieve precise control of brake pressure and vehicle speed, thereby shortening the braking distance, improving braking stability, while reducing brake disc temperature, extending the service life of the brake system, and providing strong guarantees for active and safe driving of vehicles.

[0172] In the process of multi-dimensional force command, complex multi-variable nonlinear system control is the key to achieve efficient and stable command. In a two-input and two-output nonlinear system, input 1 and input 2 are set as the power intensity control of two groups of heterogeneous forces respectively. In the real-time command of multi-dimensional forces, power intensity is a key factor affecting coordinated command. At the same time, power intensity needs to be precisely controlled to ensure that the corresponding goals are achieved with the lowest power intensity. The output 1 and output 2 of the system are the real-time displacements of the two groups of heterogeneous forces, which directly reflect the command and dispatch of multi-dimensional forces and accurately realize the real-time regulation of multi-dimensional forces. Therefore, the use of this adaptive control method is of great significance to improving the automation level and overall performance of the multi-dimensional force command process.

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

[0174]

[0175] Among them, all signals x 11 ,x 12 ,x 21 ,x 22 ,y 11 ,y 12 ,u 11 ,u 12 are all scalars, matrix A 11 ,A 12 ,B 11 are all unknown constant parameter matrices. The control direction matrix S of the controlled system can be determined q There are four alternative matrices:

[0176]

[0177] In the above adaptive controller, the parameter matrix C 1 =C 2 =

[11] T , Γ is the identity matrix. The preset parameters are set to

[0178] Assume that the matrix A 11 ,A 12 ,B 11 for

[0179] The initial condition is x 11 =0.3,x 12 =-0.3,x 21 =0,x 22 =0,y 1r =y 2r =sin(t / 4) to obtain specific simulation results.

[0180] like Figure 3 As shown, the convergence error z 1 T z 1 It drops rapidly in the initial stage and the system quickly approaches the expected value. Then, the error gradually stabilizes and approaches zero, which shows that the adopted control strategy can effectively make the system output converge to the target value, ensuring the stability and accuracy of the system.

[0181] like Figure 4 As shown, the convergence error z 2 T z 2 In the initial stage, the error drops rapidly and the system quickly approaches the expected value. Then, the error gradually stabilizes and approaches zero, which shows that the adopted control strategy can effectively make the system output converge to the target value, ensuring the stability and accuracy of the system.

[0182] like Figure 5 As shown, the system status x 11 Rapidly adjust in the initial stage to track the reference signal y 1r As time goes by, the tracking error between the system state and the reference signal gradually decreases, indicating that the controller effectively makes the system output close to and maintains it on the desired reference signal trajectory, showing good tracking performance and system stability.

[0183] like Figure 6 As shown, the system status x 12 Rapidly adjust in the initial stage to track the reference signal y 2r As time goes by, the tracking error between the system state and the reference signal gradually decreases, indicating that the controller effectively makes the system output close to and maintains it on the desired reference signal trajectory, showing good tracking performance and system stability.

[0184] like Figure 7 As shown, the input signal u 11 and u 12 It is relatively stable in the initial stage, and the control signal quickly falls back to a stable value around 0.4s, close to zero. This shows that the controller has a small control force in the initial stage. As time goes by, the control force increases significantly due to the inappropriate initial control direction. Around 0.4s, as the control direction switches, the system state is quickly adjusted, and then enters the stable control stage, ensuring that the system output can accurately track the reference signal.

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

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

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

Claims

1. An adaptive control method for a multivariable nonlinear system, characterized in that: The following steps are involved: S1. Construct a multivariable nonlinear system including unknown parameters and unknown high-frequency gain matrix; the multivariable nonlinear system model is expressed as: y=x1 in, Represents the state vector of a multivariable nonlinear system. The state vector x consists of n subvectors, each of which is n The dimension is M, Represents the subvector x n The time derivative of 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; A i ∈R M×M Represents the unknown parameter matrix; B∈R M×M represents the unknown high-frequency gain matrix; i=1,…,ν, j=1,…,n, ν, n, M represent known positive constants; Introduce the matrices Θ and Θ=[A1,…,A ν ]∈R M×Mν In the multivariable nonlinear system model, for the matrix Θ, the inverse matrix B of the matrix B -1 , there exist compact convex sets Π Θ and Π B : P Θ ={Θ S ∈R M×Mν |P Θ (I S )≤0} P B ={B S ∈R M×M |P B (B S )≤0} Among them, Θ S Denotes a compact convex set Π Θ The matrix elements of dimension M×Mν in B S Denotes a compact convex set Π B The matrix element with dimension M×M in , Ρ Θ and P B represents a smooth convex function, and c1≤||B -1 ||≤c2, c1 and c2 are positive constants; For a matrix B, there exists a matrix S q ∈R M×M , Under bounded index q, the matrix -BS q is a Hurwitz matrix; where Ω represents a bounded index set and Q is a positive integer; And the reference signal y r ∈R M and its nth-order derivative is known to be bounded; S2. Based on the multivariable nonlinear system model, an adaptive controller and a switching mechanism are constructed, and a control direction matrix S is determined by the adaptive controller and the switching mechanism. q , so that the multivariable nonlinear system output y can accurately track the reference signal y r .

2. The adaptive control method for a multivariable nonlinear system according to claim 1, characterized in that: In S2, an adaptive controller and a switching mechanism are constructed, including: S21, constructing a preset error performance function; the constructing a preset error performance function includes: Define the system tracking error z1 and error variable z i : z1=y-y r z i =x i -α i-1 Among them, α i-1 represents the virtual control law to be designed; For the error variable z i , define the error variable z i The default performance function is: in, represents the error variable z i The transposed matrix, K i represents the preset constant, t0 represents the initial time point, and t represents the time variable; S22, based on the error performance preset function, construct a boundary Lyapunov function; the boundary Lyapunov function V(z i ) is expressed as: when Approaching When the boundary Lyapunov function V(z i ) tends to 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 includes: When i=1, When i=2, V2=V(z2)+V1 When 3≤i≤n-1, In i =V(with i )+V i-1 When i=n, Among them, V n represents the Lyapunov function, which is used to evaluate the stability of the system; α n represents part of the control input, including feedback terms and adaptive control terms; τ n represents part of the control input, including the adaptive control term; Γ represents the gain matrix; represents the regression vector; tr() represents the trace of the matrix; C i represents the feedback gain matrix; represents the reference signal y r The derivative of represents the reference signal y r The j-order derivative of ; represents the parameter estimation error, represents the estimate of the matrix Θ; Represents parameter estimation error, P = B -1 , represents the estimation of the matrix P; Proj represents the projection operator; Based on the adaptive control law, if the error variable z i Satisfy the initial conditions: Then all signals in the system are bounded, and the error z i satisfy: It can converge to zero: And there exists a positive constant μ0 for which the following holds: The value of the positive constant μ0 is: Among them, λ Γ is the matrix Γ -1 The maximum eigenvalue of S is the control direction matrix S q The maximum eigenvalue of M is the upper bound of the infinity norm of the matrix Θ, and ε0 is an arbitrarily small positive constant; S24, constructing a switching mechanism; the constructing a switching mechanism includes: Select the 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 Depend on Switch to S q2 , q2∈Ω-{q1}; define t1 as: In t k Under this condition, 1<k<Q-1, at least one inequality does not hold, and the inequality is expressed as: Normal constant μ k-1 The value range is: Among them, ε k-1 is an arbitrarily small positive constant; there exists: Define the switching time t k for: And the control direction matrix S q Depend on Switch to S qk+1 ,q k+1 ∈Ω-{q1,…,q k }.

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