Local key state constrained unmanned helicopter anti-interference tracking control method

Abstract

The invention discloses an unmanned helicopter anti-interference tracking control method based on local key state constraint, and the method comprises the steps: firstly introducing interference estimation for an unmanned helicopter six-degree-of-freedom system model through an input and output feedback linearization method, and obtaining an unmanned helicopter error tracking system; secondly, designing a simplified nonlinear disturbance observer, and estimating disturbance force and disturbance torque borne by the unmanned helicopter; and finally, designing a partial state constraint anti-interference flight tracking controller for the unmanned helicopter error tracking system by using a backstepping control method, introducing a barrier Lyapunov function to constrain a local key intermediate variable, and compensating the influence of system interference based on estimation of a nonlinear interference observer. Interference estimation is introduced into the feedback linearization process, the design of the controller is simplified, and it is guaranteed that the unmanned helicopter has good flight control performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of anti-interference control for the state constraints of unmanned helicopters, and specifically relates to an anti-interference tracking control method for unmanned helicopters with local key state constraints. Background Art

[0002] An unmanned helicopter is an unmanned aerial vehicle (UAV) based on a helicopter, which uses rotors to achieve vertical takeoff, landing, and hovering capabilities. With the rapid development of UAV technology, unmanned helicopters are increasingly widely used in military, civilian, and scientific research fields. However, due to the complex nonlinear, strongly coupled, and multivariable characteristics of unmanned helicopters, their attitude control, trajectory tracking, and anti-interference capabilities pose high requirements for the control system. To ensure its safe and stable operation in complex environments, the control system must have robustness and adaptability. This means that the control algorithm not only needs to consider the state constraints of the unmanned helicopter but also be able to effectively suppress interference and adjust the control strategy in real time.

[0003] Since the key attitude angles of an unmanned helicopter, such as the pitch angle and roll angle, have an important impact on the flight attitude safety, to ensure flight safety, the state variables need to meet certain constraint conditions to limit the attitude angle range, which makes it difficult for traditional control methods to effectively address these challenges. In addition, in the actual flight environment of an unmanned helicopter, it is often full of uncertainties and may be affected by external interferences such as airflow and load fluctuations, further increasing the control difficulty. To ensure that it can perform tasks safely and stably in complex environments, fully considering these factors in the design of the flight controller will directly enhance the robustness of the helicopter control system. Therefore, effectively constraining the local key states of the unmanned helicopter flight and designing an anti-interference controller will ensure the flight safety of the unmanned helicopter, improve the system's adaptability, and better complete the flight mission. Summary of the Invention

[0004] The purpose of the present invention is to provide an anti-interference tracking control method for unmanned helicopters with local key state constraints, which estimates a class of bounded interferences using an interference observer and introduces the interference estimation into the feedback linearization process, simplifies the design of the controller, and ensures that the unmanned helicopter has good flight control performance.

[0005] The technical solution adopted by the present invention is an anti-interference tracking control method for unmanned helicopters with local key state constraints, which is specifically implemented according to the following steps:

[0006] Step 1: Apply the input-output feedback linearization method to the six-degree-of-freedom system model of the unmanned helicopter, introduce the estimation of interference, and obtain the error tracking system of the unmanned helicopter;

[0007] Step 2: Design a simplified non-linear disturbance observer to estimate the disturbance forces and torques acting on the unmanned helicopter;

[0008] Step 3: Use the backstepping control method to design a partial state-constrained anti-disturbance flight tracking controller for the unmanned helicopter error tracking system. At the same time, introduce a barrier Lyapunov function to constrain the local key intermediate variables, and compensate for the influence of system disturbances based on the estimation of the non-linear disturbance observer.

[0009] The features of the present invention also lie in that,

[0010] Step 1 is specifically implemented according to the following steps:

[0011] The following notations involved in the formula are explained as follows:

[0012] Denotes the first derivative of A(t); Denotes the second derivative of A(t); Denotes the third derivative of A(t); A (4) (t) denotes the fourth derivative of A(t); B T Denotes the transpose matrix of matrix B; C -1 Denotes the inverse matrix of matrix C;

[0013] The following unmanned helicopter system is obtained according to the Newton-Euler equation:

[0014]

[0015] Among them, P(t) = (P x (t) P y (t) P z (t)) T and V(t) = (V x (t) V y (t) V z (t)) T respectively represent the position and velocity in the inertial coordinate system. P x (t), P y (t), P z (t) and V x (t), V y (t), V z (t) respectively represent the components on the x, y, and z coordinate axes. Denotes the derivative of velocity, i.e., acceleration. g is the acceleration due to gravity. e 3 =(0 0 1) T , m represents the mass of the unmanned helicopter, R(t) represents the rotational inertia matrix from the body coordinate to the inertial coordinate, f(t) represents the resultant external force on the centroid of the unmanned helicopter, d 1(t) represents the acceleration of the interference force of the system, and Ω(t) = (φ(t) θ(t) ψ(t)) T represents the attitude angles of the helicopter, represents the attitude angular acceleration, where φ(t) represents the roll angle, θ(t) is the pitch angle, ψ(t) is the yaw angle, H(t) represents the attitude motion matrix, and W(t) = (p(t) q(t) r(t)) T are the three attitude angular velocities relative to the ground coordinate system, and p(t), q(t), and r(t) represent the roll angular velocity, pitch angular velocity, and yaw angular velocity respectively. J = diag{J xx J yy J zz} represents the inertia matrix of the unmanned helicopter, and J xx 、J yy and J zz represent the roll moment of inertia, pitch moment of inertia, and yaw moment of inertia respectively, represents the attitude angular acceleration, τ(t) represents the resultant external moment on the center of mass of the unmanned helicopter, and d 2 (t) represents the interference moment of the system,

[0016]

[0017] where c * and s * represent cos(*) and sin(*) in trigonometric functions respectively, and * represents φ(t), θ(t), and ψ(t). The attitude motion matrix:

[0018]

[0019] W(t) × is the cross product operator matrix:

[0020]

[0021] Add new system variables f 1 (t) and f 2 (t), and expand the system into a new system:

[0022]

[0023] At this time, the relative order of formula (2) is the same as the system dimension. Select the following variables as the new system variables:

[0024]

[0025] where, x 1 (t), x 2 (t), x 3 (t), x4 (t) represent the position tracking error, velocity tracking error, acceleration generated by the controllable resultant force of the unmanned helicopter, and the rate of change of the force generated by the controllable resultant force of the helicopter; x 5 (t), x 6 (t) represent the yaw angle tracking error and yaw angle rate tracking error of the unmanned helicopter, P r (t) represents the actual position trajectory of the unmanned helicopter, represents the actual speed and acceleration of the unmanned helicopter, represents the estimated value of the disturbing force acceleration, represents the derivative of the actual acceleration, β 1 (t) = (0 sinφ(t)secθ(t) cosφ(t)secθ(t)), is the yaw angular acceleration.

[0026] According to (2) and (3), the transformed new system is obtained, and the expression is:

[0027]

[0028] Among them, is the estimation error, L 1 is the disturbance observer gain to be designed, F 1 (t), F 2 (t) are the control inputs,

[0029] Through the above input-output feedback linearization construction, the tracking error formula (4) of the unmanned helicopter is obtained, where the new control input:

[0030]

[0031] The expressions of θ(t) and φ(t) are as follows:

[0032]

[0033] Step 2 is specifically implemented according to the following steps:

[0034] First, introduce the following assumptions:

[0035] Assumption 1: There exist unknown boundaries D 1 and D 2 , such that the disturbing aerodynamic force and aerodynamic moment satisfy and

[0036] When estimating the disturbance according to formula (4), d 1 (t) The design of the disturbance observer is as follows:

[0037]

[0038] Among them, is the interference estimation value, and L 1 represents the interference observer gain, and δ 1 (t) is the auxiliary function, represents the first derivative of the auxiliary function. Define the estimation error as The dynamic description of the interference estimation error is:

[0039]

[0040] Design an interference observer according to the dynamic equation of the attitude angle in formula (4):

[0041]

[0042] Among them, is the interference estimation value, and L 2 represents the interference observer gain, and δ 2 (t) is the auxiliary function, represents the first derivative of the auxiliary function. Define the estimation error as The dynamic description of the interference estimation error is:

[0043]

[0044] Step 3 is specifically implemented according to the following steps:

[0045] Introduce the following lemma:

[0046] Lemma 1: For a matrix X or vector Y of a certain dimension, and for any constant ε > 0, the following inequality holds:

[0047] X T Y + Y T X ≤ εX T X + ε -1 Y T Y

[0048] Lemma 2: For any positive constant k b and the real variable z(t), when the condition z(t) < k b is satisfied, the following inequality holds:

[0049]

[0050] Step 3.1: Define the tracking errors e 1 (t), e 2 (t), and design the Lyapunov function V 1 (t);

[0051] Step 3.2. Define the tracking error \(e(t)\) and design the Lyapunov function \(V(t)\); 3 (t), and design the Lyapunov function \(V\) 2 (t);

[0052] Step 3.3. Define the tracking error \(e(t)\) and design the Lyapunov function \(V(t)\); 4 (t), and design the Lyapunov function \(V\) 3 (t);

[0053] Step 3.4. Design the controller \(F(t)\) and design the Lyapunov function \(V(t)\); 1 (t), and design the Lyapunov function \(V\) 4 (t);

[0054] Step 3.5. Define the tracking errors \(e(t)\) and \(e(t)\) and design the Lyapunov function \(V(t)\); 5 (t), \(e\) 6 (t), and design the Lyapunov function \(V\) 5 (t);

[0055] Step 3.6. Design the controller \(F(t)\) and design the Lyapunov function \(V(t)\). 2 (t), and design the Lyapunov function \(V\) 6 (t).

[0056] The definition of the tracking error in Step 3.1 is as follows:

[0057] e 1 (t)=x 1 (t)(9)

[0058] e 2 (t)=x 2 (t)-χ 1 (t)(10)

[0059] where \(\chi(t)\) is the virtual control law defined as: 1 (t) is the virtual control law, defined as:

[0060] χ 1 (t)=-k 1 e 1 (t)(11)

[0061] where \(k\) 1 >0 is the parameter to be designed, and the dynamics of \(e(t)\) are: 1 (t)

[0062]

[0063] where \(X(t)=-k\) 1 (t)+e 1 e 1 (t)+e 2 (t).

[0064] Define the candidate Lyapunov function \(V\) 1(t) is as follows:

[0065]

[0066] Deriving the derivative of (13) gives:

[0067]

[0068] The tracking error defined in step 3.2 is specifically as follows:

[0069] e 3 (t) = x 3 (t) - χ 2 (t) (15)

[0070] where χ 2 (t) is the virtual control law, defined as:

[0071] χ 2 (t) = -k 2 e 2 (t) (16)

[0072] where k 2 > 0 is a parameter to be designed. The dynamics of e 2 (t) are:

[0073]

[0074] where . Define the candidate Lyapunov function V 2 (t) as:

[0075]

[0076] Deriving the derivative of (18) gives:

[0077]

[0078] The tracking error defined in step 3.3 is specifically as follows:

[0079] e 4 (t) = x 4 (t) - χ 3 (t) (20)

[0080] where χ 3 (t) is the virtual control law, defined as:

[0081]

[0082] where e 3 (t) = (e 31 (t)e 32 (t)e33 (t)) T , k 3 >0, ε 3 >0, ρ 1 >0 are all parameters to be designed. According to formula (4), the dynamics of e 3 (t) are:

[0083]

[0084] Among them, Define the candidate Lyapunov function V 3 (t) as:

[0085]

[0086] Taking the derivative of (23), we can obtain:

[0087]

[0088] In step 3.4, design the controller F 1 (t), the dynamics of e 4 (t) are:

[0089]

[0090] To ensure the negative definiteness of , design the controller F 1 (t) as:

[0091]

[0092] Among them, F 1a (t) is the additional controller designed in the subsequent steps. At this time, the dynamics of e 4 (t) are:

[0093]

[0094] Among them,

[0095]

[0096] The additional controller F 1a (t) is designed as:

[0097]

[0098] Among them, ε 4 >0, ε 5 >0, k 4 >0.

[0099] Define the candidate Lyapunov function V 4(t) is as follows:

[0100]

[0101] Taking the derivative of (29), we can obtain:

[0102]

[0103] The tracking error defined in Step 3.5 is specifically as follows:

[0104] e 5 (t) = x 5 (t) (31)

[0105] e 6 (t) = x 6 (t) - χ 4 (t) (32)

[0106] where χ 4 (t) is the virtual control law, defined as:

[0107] χ 4 (t) = -k 5 e 5 (t) (33)

[0108] where k 5 > 0. The dynamics of e 5 (t) are:

[0109]

[0110] Define the candidate Lyapunov function V 5 (t) as:

[0111]

[0112] Taking the derivative of (35), we can obtain:

[0113]

[0114] Design the controller F 2 (t), and the dynamics of e 6 (t) are:

[0115]

[0116] To ensure is negative definite, design the controller F 2 (t) as:

[0117]

[0118] where F 2a(t) is an additional controller designed to:

[0119]

[0120] where ε 6 > 0;

[0121] Select the candidate Lyapunov function V 6 (t) as:

[0122]

[0123] Taking the derivative of (40) gives:

[0124]

[0125] Stability analysis:

[0126] Select the Lyapunov function V(t) as:

[0127]

[0128] Combining the above process, the derivative of V(t) is obtained:

[0129]

[0130] According to Lemma 1, there exists ε 1 > 0, ε 2 > 0, ε 3 > 0, ε 4 > 0, ε 5 > 0, ε 6 > 0, ε 7 > 0, ε 8 > 0 such that:

[0131]

[0132]

[0133] According to Lemma 2, there exists an inequality:

[0134]

[0135] Therefore, (43) is rewritten as:

[0136]

[0137] where

[0138]

[0139] Define (44) can be rewritten as:

[0140]

[0141] According to (42) and (45), under the action of the designed controller and disturbance observer, the state of formula (4) can converge to the required bounded range.

[0142] The beneficial effect of the present invention is that the anti-disturbance tracking control method for an unmanned helicopter with local key state constraints realizes precise tracking control of the preset position and yaw angle of the unmanned helicopter. Compared with the full-degree-of-freedom anti-disturbance control method, the controller designed in the present invention is effectively simplified. By using the feedback linearization method and introducing disturbance estimation, while reducing the complexity in the control process of the original system, the control design is simplified. The controller designed by combining the backstepping control method, the barrier Lyapunov function, and the nonlinear disturbance observer effectively weakens and cancels the influence of disturbances on the flight performance and maintains a safe flight attitude. Description of the Drawings

[0143] Figure 1 is the overall flowchart of the anti-disturbance tracking control method for an unmanned helicopter with local key state constraints of the present invention;

[0144] Figure 2 is the position tracking curve graph of the unmanned helicopter in the anti-disturbance tracking control method for an unmanned helicopter with local key state constraints of the present invention;

[0145] Figure 3 is the control input curve graph of the unmanned helicopter in the anti-disturbance tracking control method for an unmanned helicopter with local key state constraints of the present invention;

[0146] Figure 4 is the yaw angle curve graph of the unmanned helicopter in the anti-disturbance tracking control method for an unmanned helicopter with local key state constraints of the present invention;

[0147] Figure 5 is the pitch angle and yaw angle curve graph of the unmanned helicopter in the anti-disturbance tracking control method for an unmanned helicopter with local key state constraints of the present invention;

[0148] Figure 6 is the disturbance force and its estimated value curve graph of the unmanned helicopter in the anti-disturbance tracking control method for an unmanned helicopter with local key state constraints of the present invention;

[0149] Figure 7 is the disturbance torque and its estimated value curve graph of the unmanned helicopter in the anti-disturbance tracking control method for an unmanned helicopter with local key state constraints of the present invention;

[0150] Figure 8 is the pitch angle comparison graph of the unmanned helicopter in the anti-disturbance tracking control method for an unmanned helicopter with local key state constraints of the present invention;

[0151] Figure 9 It is the comparison diagram of the roll angle of the unmanned helicopter in the anti-interference tracking control method of the unmanned helicopter with local key state constraints of the present invention. Detailed implementation manners

[0152] The present invention will be described in detail below with reference to the accompanying drawings and specific implementation manners.

[0153] Since the unmanned aerial vehicle will be affected by disturbances such as airflow fluctuations, environmental vibrations, and mechanical resonances during actual flight, many harmonic disturbances will be generated during these periodic motion processes, seriously affecting the control performance of the unmanned helicopter. In addition, in order to ensure flight safety, the key attitude angles are usually subject to prerequisite constraints. Therefore, to solve these adverse effects, first, the forces and torques acting on the unmanned helicopter are analyzed in the present invention to obtain an abstracted six-degree-of-freedom unmanned helicopter system model. Based on this model, the feedback linearization method is used to obtain the error tracking system model of the unmanned helicopter while introducing the estimation of disturbances into the model; a nonlinear disturbance observer is used to estimate a class of bounded disturbances to improve the anti-interference ability of the unmanned helicopter system; then, some local key intermediate variables of the system after feedback linearization are constrained, and a suitable anti-interference controller is designed based on the backstepping control method; subsequently, the Lyapunov stability theory is used to analyze the stability of the error tracking closed-loop system of the unmanned helicopter; finally, the designed anti-interference control strategy with local key state constraints is applied to the unmanned helicopter system, and verification and comparison experiments are carried out on the proposed control scheme.

[0154] Embodiment 1

[0155] The anti-interference tracking control method of the unmanned helicopter with local key state constraints of the present invention has a flow chart as Figure 1 shown, and is specifically implemented according to the following steps:

[0156] Step 1: Apply the input-output feedback linearization method to the six-degree-of-freedom system model of the unmanned helicopter, introduce the estimation of disturbances, and obtain the error tracking system of the unmanned helicopter;

[0157] Some formulas in the present invention involve the following notations:

[0158] Denotes the first derivative of A(t); Denotes the second derivative of A(t); Denotes the third derivative of A(t); A (4) (t) denotes the fourth derivative of A(t); B T Denotes the transpose matrix of matrix B; C -1 Denotes the inverse matrix of matrix C.

[0159] Step 1 is specifically implemented according to the following steps:

[0160] Considering the possible harmonic interference, the following unmanned helicopter system is obtained according to the Newton-Euler equation:

[0161]

[0162] where P(t) = (P x (t) P y (t) P z (t)) T and V(t) = (V x (t) V y (t) V z (t)) T represent the position and velocity in the inertial coordinate system respectively, P x (t), P y (t), P z (t) and V x (t), V y (t), V z (t) represent the components on the three coordinate axes of x, y, and z respectively, represents the derivative of velocity, i.e., acceleration, g is the acceleration due to gravity, e 3 = (0 0 1) T , m represents the mass of the unmanned helicopter, R(t) represents the rotational inertia matrix from the body coordinate to the inertial coordinate rotation matrix, f(t) represents the resultant external force on the center of mass of the unmanned helicopter, d 1 (t) represents the acceleration of the interference force of the system, Ω(t) = (φ(t) θ(t) ψ(t)) T represents the attitude angle of the helicopter, represents the angular acceleration of the attitude angle, where φ(t) represents the roll angle, θ(t) is the pitch angle, ψ(t) is the yaw angle, H(t) represents the attitude motion matrix, W(t) = (p(t) q(t) r(t)) T is the three attitude angular velocities relative to the ground coordinate system, p(t), q(t), and r(t) represent the roll angular velocity, pitch angular velocity, and yaw angular velocity respectively, J = diag{J xx J yy J zz} represents the inertia matrix of the unmanned helicopter, J xx , J yy and J zz represent the roll moment of inertia, pitch moment of inertia, and yaw moment of inertia respectively, represents the angular acceleration of the attitude angle, τ(t) represents the resultant external torque on the center of mass of the unmanned helicopter, d 2 (t) represents the interference torque of the system,

[0163]

[0164] Among them, c * and s * respectively represent the cosine cos(*) and sine sin(*) in trigonometric functions, * represents φ(t), θ(t) and ψ(t), and the attitude motion matrix:

[0165]

[0166] W(t) × is the cross product operator matrix:

[0167]

[0168] Add new system variables f 1 (t) and f 2 (t), and expand the system into a new system:

[0169]

[0170] At this time, the relative order of formula (2) is the same as the system dimension. Select the following variables as the new system variables:

[0171] x 1 (t) = P(t) - P r (t),

[0172]

[0173] x 5 (t) = ψ(t) - ψ r (t),

[0174]

[0175] Among them, x 1 (t), x 2 (t), x 3 (t), x 4 (t) respectively represent the position tracking error, speed tracking error, acceleration generated by the controllable resultant force of the unmanned helicopter, and the rate of change of the force generated by the controllable resultant force of the helicopter; x 5 (t), x 6 (t) represent the yaw angle tracking error and yaw angle rate tracking error of the unmanned helicopter, P r (t) represents the actual position trajectory of the unmanned helicopter, represents the actual speed and acceleration of the unmanned helicopter, represents the estimated value of the disturbance force acceleration, represents the derivative of the actual acceleration, β 1\(\dot{\boldsymbol{\omega}}(t) = \begin{pmatrix} 0 \\ \sin\varphi(t)\sec\theta(t) \\ \cos\varphi(t)\sec\theta(t) \end{pmatrix}\), is the yaw angular acceleration.

[0176] According to (2) and (3), the transformed new system has the following expression:

[0177]

[0178] where, is the estimation error, \(L\) 1 is the disturbance observer gain to be designed, \(F\) 1 (t), \(F\) 2 (t) are the control inputs,

[0179] Through the above input-output feedback linearization construction, the tracking error formula (4) of the unmanned helicopter is obtained, where the new control input:

[0180]

[0181] It is usually assumed that the roll angle and pitch angle of the unmanned helicopter are within a limited range, generally This may lead to an insufficiently rigorous controller design process and imperfect aircraft attitude constraints. In the input-output feedback linearization process, the expressions of \(\theta(t)\) and \(\varphi(t)\) are obtained. According to \(\theta(t)\) and \(\varphi(t)\), it can be determined that the roll angle and pitch angle are constrained by the intermediate variable \(x\) 3 (t). Therefore, by restricting the state \(x\) 3 (t), the roll angle and pitch angle can be indirectly controlled within a certain range, thus achieving the goal of safe flight. The expressions of \(\theta(t)\) and \(\varphi(t)\) are as follows:

[0182]

[0183] Step 2: Design a simplified nonlinear disturbance observer to estimate the disturbance forces and torques acting on the unmanned helicopter and feedback them into the controller design;

[0184] Step 2 is specifically implemented according to the following steps:

[0185] First, introduce the following assumptions:

[0186] Assumption 1: There exist unknown bounds \(D\) 1 and \(D\) 2 , such that the disturbing aerodynamic forces and aerodynamic torques satisfy and

[0187] To suppress the impact of interference on the system, the system interference is estimated by an interference observer, and its estimated value is applied to the controller design. The system conversion process shows that equations (2) and (4) are equivalent, so the interference estimated values obtained from these two systems are also the same. When estimating the interference according to equation (4), d 1 (t) The design of the interference observer is as follows:

[0188]

[0189] where, is the interference estimated value, and L 1 represents the interference observer gain, and δ 1 (t) is the auxiliary function, represents the first derivative of the auxiliary function. Define the estimation error as The dynamic description of the interference estimation error is:

[0190]

[0191] Since the interference d 2 (t) only affects the dynamic change of the attitude angle in equation (2), an interference observer is designed according to the dynamic equation of the attitude angle in equation (4):

[0192]

[0193] where, is the interference estimated value, and L 2 represents the interference observer gain, and δ 2 (t) is the auxiliary function, represents the first derivative of the auxiliary function. Define the estimation error as The dynamic description of the interference estimation error is:

[0194]

[0195] Step 3: Use the backstepping control method to design a partial state-constrained anti-interference flight tracking controller for the unmanned helicopter error tracking system. At the same time, introduce a barrier Lyapunov function to constrain local key intermediate variables, and compensate for the impact of system interference based on the estimation of the nonlinear interference observer.

[0196] Step 3 is specifically implemented according to the following steps:

[0197] Based on the designed interference observer, the state-constrained anti-interference flight controller of the unmanned helicopter will be constructed next.

[0198] For the convenience of design, the following lemma is introduced:

[0199] Lemma 1: For a matrix X or vector Y of a certain dimension, and for any constant ε > 0, the following inequality holds:

[0200] X T Y + Y T X ≤ εX T X + ε -1 Y T Y

[0201] Lemma 2: For any positive constant k b and real variable z(t), when the condition z(t) < k b is satisfied, the following inequality holds:

[0202]

[0203] Step 3.1: Define the tracking errors e 1 (t), e 2 (t), and design the Lyapunov function V 1 (t);

[0204] Step 3.2: Define the tracking error e 3 (t), and design the Lyapunov function V 2 (t);

[0205] Step 3.3: Define the tracking error e 4 (t), and design the Lyapunov function V 3 (t);

[0206] Step 3.4: Design the controller F 1 (t), and design the Lyapunov function V 4 (t);

[0207] Step 3.5: Define the tracking errors e 5 (t), e 6 (t), and design the Lyapunov function V 5 (t);

[0208] Step 3.6: Design the controller F 2 (t), and design the Lyapunov function V 6 (t).

[0209] The specific definitions of the tracking errors in Step 3.1 are as follows:

[0210] e 1 (t) = x 1 (t) (54)

[0211] e 2 (t) = x 2 (t) - χ 1 (t) (55)

[0212] Among them, χ 1 (t) is the virtual control law, defined as:

[0213] χ 1 (t) = -k 1 e 1 (t) (56)

[0214] Among them, k 1 > 0 is the parameter to be designed, and the dynamics of e 1 (t) are:

[0215]

[0216] Among them, X 1 (t) = -k 1 e 1 (t) + e 2 (t).

[0217] Define the candidate Lyapunov function V 1 (t) as:

[0218]

[0219] Taking the derivative of (13), we get:

[0220]

[0221] The tracking error defined in Step 3.2 is specifically as follows:

[0222] e 3 (t) = x 3 (t) - χ 2 (t) (60)

[0223] Among them, χ 2 (t) is the virtual control law, defined as:

[0224] χ 2 (t) = -k 2 e 2 (t) (61)

[0225] Among them, k 2 > 0 is the parameter to be designed. The dynamics of e 2 (t) are:

[0226]

[0227] Among them, Define the candidate Lyapunov function V 2 (t) as:

[0228]

[0229] Deriving the derivative of (18) gives:

[0230]

[0231] The tracking error is defined in step 3.3 as follows:

[0232] e 4 (t) = x 4 (t) - χ 3 (t) (65)

[0233] where χ 3 (t) is the virtual control law, defined as:

[0234]

[0235] where e 3 (t) = (e 31 (t)e 32 (t)e 33 (t)) T , k 3 > 0, ε 3 > 0, ρ 1 > 0 are all parameters to be designed. According to formula (4), the dynamics of e 3 (t) are:

[0236]

[0237] where The candidate Lyapunov function V 3 (t) is defined as:

[0238]

[0239] Deriving the derivative of (23) gives:

[0240]

[0241] The controller F 1 (t) is designed in step 3.4, and the dynamics of e 4 (t) are:

[0242]

[0243] To ensure is negative definite, the controller F 1 (t) is designed as:

[0244]

[0245] Among them, F 1a (t) is an additional controller designed in subsequent steps. At this time, e 4 (t) has the following dynamics:

[0246]

[0247] Among them,

[0248]

[0249] The additional controller F 1a (t) is designed as:

[0250]

[0251] Among them, ε 4 >0, ε 5 >0, k 4 >0.

[0252] Define the candidate Lyapunov function V 4 (t) as:

[0253]

[0254] Taking the derivative of (29), it can be obtained that:

[0255]

[0256] The tracking error defined in step 3.5 is specifically as follows:

[0257] e 5 (t) = x 5 (t) (76)

[0258] e 6 (t) = x 6 (t) - χ 4 (t) (77)

[0259] Among them, χ 4 (t) is the virtual control law, defined as:

[0260] χ 4 (t) = -k 5 e 5 (t) (78)

[0261] Among them, k 5 >0. e 5 (t) has the following dynamics:

[0262]

[0263] Define the candidate Lyapunov function V5 (t) is:

[0264]

[0265] Taking the derivative of (35), we can obtain:

[0266]

[0267] Designing the controller F in step 3.6 2 (t), e 6 The dynamics of (t) are:

[0268]

[0269] To ensure is negative definite, design the controller F 2 (t) as:

[0270]

[0271] where F 2a (t) is the additional controller and is designed as:

[0272]

[0273] where ε 6 > 0;

[0274] Select the candidate Lyapunov function V 6 (t) as:

[0275]

[0276] Taking the derivative of (40) gives:

[0277]

[0278] Stability analysis:

[0279] Select the Lyapunov function V(t) as:

[0280]

[0281] Combining the above process, the derivative of V(t) is obtained:

[0282]

[0283] According to Lemma 1, there exist ε 1 > 0, ε 2 > 0, ε 3 > 0, ε 4 > 0, ε 5 > 0, ε 6> 0, ε 7 > 0, ε 8 > 0 such that:

[0284]

[0285]

[0286] According to Lemma 2, there exists an inequality:

[0287]

[0288] Therefore, (43) is rewritten as:

[0289]

[0290] where

[0291]

[0292] Define (44) can be rewritten as:

[0293]

[0294] According to (42) and (45), under the action of the designed controller and disturbance observer, the state of formula (4) can converge to the required bounded range.

[0295] Embodiment 2

[0296] The anti-interference tracking control method for an unmanned helicopter with local key state constraints of the present invention has a flowchart as Figure 1 shown, and is specifically implemented according to the following steps:

[0297] Step 1: Apply the input-output feedback linearization method to the six-degree-of-freedom system model of the unmanned helicopter, introduce the estimation of interference, and obtain the error tracking system of the unmanned helicopter;

[0298] Step 2: Design a simplified nonlinear disturbance observer to estimate the interference force and interference moment received by the unmanned helicopter and feedback it into the design of the controller;

[0299] Step 3: Use the backstepping control method to design a partial state constraint anti-interference flight tracking controller for the unmanned helicopter error tracking system, and at the same time introduce a barrier Lyapunov function to constrain the local key intermediate variables, and compensate for the influence of system interference based on the estimation of the nonlinear disturbance observer.

[0300] Embodiment 3

[0301] The anti-interference tracking control method for an unmanned helicopter with local key state constraints of the present invention has a flowchart as Figure 1As shown below, it is implemented specifically according to the following steps:

[0302] Step 1: Apply the input-output feedback linearization method to the six-degree-of-freedom system model of the unmanned helicopter, introduce the estimation of interference, and obtain the error tracking system of the unmanned helicopter.

[0303] Step 1 is specifically implemented according to the following steps:

[0304] Considering the possible harmonic interference, the following unmanned helicopter system is obtained according to the Newton-Euler equation:

[0305]

[0306] Among them, P(t) = (P x (t) P y (t) P z (t)) T and V(t) = (V x (t) V y (t) V z (t)) T respectively represent the position and velocity in the inertial coordinate system. P x (t), P y (t), P z (t) and V x (t), V y (t), V z (t) respectively represent the components on the three coordinate axes of x, y, and z. represents the derivative of velocity, i.e., acceleration. g is the acceleration due to gravity. e 3 = (0 0 1) T , m represents the mass of the unmanned helicopter. R(t) represents the rotational inertia matrix of the rotation from the body coordinate to the inertial coordinate. f(t) represents the resultant external force on the center of mass of the unmanned helicopter. d 1 (t) represents the acceleration of the interference force of the system. Ω(t) = (φ(t) θ(t) ψ(t)) T represents the attitude angle of the helicopter. represents the angular acceleration of the attitude angle, where φ(t) represents the roll angle, θ(t) is the pitch angle, ψ(t) is the yaw angle, H(t) represents the attitude motion matrix. W(t) = (p(t) q(t) r(t)) T is the three attitude angular velocities relative to the ground coordinate system. p(t), q(t), and r(t) respectively represent the roll angular velocity, pitch angular velocity, and yaw angular velocity. J = diag{J xx J yy J zz} represents the inertia matrix of the unmanned helicopter. J xx , J yyand J zz represent the roll moment of inertia, pitch moment of inertia, and yaw moment of inertia respectively, represents the angular acceleration of the attitude, τ(t) represents the resultant external moment on the center of mass of the unmanned helicopter, and d 2 (t) represents the disturbance moment of the system,

[0307]

[0308] where c * and s * represent cos(*) and sin(*) in trigonometric functions respectively, and * represents φ(t), θ(t), and ψ(t). The attitude motion matrix:

[0309]

[0310] W(t) × is the cross product operator matrix:

[0311]

[0312] Add new system variables f 1 (t) and f 2 (t), and expand the system into a new system:

[0313]

[0314] At this time, the relative order of formula (2) is the same as the system dimension. Select the following variables as the new system variables:

[0315] x 1 (t) = P(t) - P r (t),

[0316]

[0317] x 5 (t) = ψ(t) - ψ r (t),

[0318]

[0319] where x 1 (t), x 2 (t), x 3 (t), x 4 (t) represent the position tracking error, velocity tracking error, acceleration generated by the controllable resultant force of the unmanned helicopter, and the change rate of the force generated by the controllable resultant force of the helicopter respectively; x 5 (t), x 6 (t) represent the yaw angle tracking error and yaw angle rate tracking error of the unmanned helicopter, and Pr (t) represents the actual position trajectory of the unmanned helicopter, represents the actual speed and acceleration of the unmanned helicopter, represents the estimated value of the disturbing force acceleration, represents the derivative of the actual acceleration, β 1 (t) = (0 sinφ(t)secθ(t) cosφ(t)secθ(t)), is the yaw angular acceleration.

[0320] According to (2) and (3), the transformed new system is obtained, and the expression is:

[0321]

[0322] Among them, is the estimation error, L 1 is the disturbance observer gain to be designed, F 1 (t), F 2 (t) is the control input,

[0323] Through the above input-output feedback linearization construction, the tracking error formula (4) of the unmanned helicopter is obtained, where the new control input:

[0324]

[0325] It is usually assumed that the roll angle and pitch angle of the unmanned helicopter are within a limited range, generally This may lead to an insufficiently rigorous controller design process and imperfect aircraft attitude constraints. In the input-output feedback linearization process, the expressions of θ(t) and φ(t) are obtained. According to θ(t) and φ(t), it can be determined that the roll angle and pitch angle are constrained by the intermediate variable x 3 (t). Therefore, by restricting the state x 3 (t), the roll angle and pitch angle can be indirectly controlled within a certain range, so as to achieve the goal of safe flight. The expressions of θ(t) and φ(t) are as follows:

[0326]

[0327]

[0328] Step 2: Design a simplified nonlinear disturbance observer to estimate the disturbing force and disturbing moment acting on the unmanned helicopter and feedback them into the controller design;

[0329] Step 3: Use the backstepping control method to design a partial state-constrained anti-disturbance flight tracking controller for the UAV error tracking system. At the same time, introduce the barrier Lyapunov function to constrain the local key intermediate variables, and estimate and compensate for the influence of system disturbances based on the nonlinear disturbance observer.

[0330] Example 4

[0331] The anti-disturbance tracking control method for the UAV with local key state constraints of the present invention has a flowchart as Figure 1 shown, and is specifically implemented according to the following steps:

[0332] Step 1: Apply the input-output feedback linearization method to the six-degree-of-freedom system model of the UAV, introduce the estimation of disturbances, and obtain the UAV error tracking system;

[0333] Step 2: Design a simplified nonlinear disturbance observer to estimate the disturbance forces and moments acting on the UAV and feedback them into the controller design;

[0334] Step 2 is specifically implemented according to the following steps:

[0335] First, introduce the following assumptions:

[0336] Assumption 1: There exist unknown boundaries D 1 and D 2 such that the disturbing aerodynamic forces and moments satisfy and

[0337] To suppress the influence of disturbances on the system, the system disturbances are estimated by the disturbance observer and their estimated values are applied to the controller design. The system conversion process shows that Equations (2) and (4) are equivalent, so the disturbance estimated values obtained from these two systems are also the same. When estimating the disturbance according to Equation (4), the design of the disturbance observer for d 1 (t) is as follows:

[0338]

[0339] where is the disturbance estimated value, L 1 represents the disturbance observer gain, δ 1 (t) is the auxiliary function, represents the first derivative of the auxiliary function, and the estimation error is defined as The dynamic description of the disturbance estimation error is:

[0340]

[0341] Since the disturbance d 2(t) only affects the dynamic changes of the attitude angles in Equation (2). Therefore, a disturbance observer is designed according to the dynamic equation of the attitude angles in Equation (4):

[0342]

[0343] where is the estimated value of the disturbance, L 2 represents the disturbance observer gain, δ 2 (t) is the auxiliary function, represents the first derivative of the auxiliary function. Define the estimation error as The dynamic description of the disturbance estimation error is:

[0344]

[0345] Step 3: Use the backstepping control method to design a partial state-constrained anti-disturbance flight tracking controller for the UAV error tracking system. At the same time, introduce the barrier Lyapunov function to constrain the local key intermediate variables, and compensate for the influence of system disturbances based on the estimation of the nonlinear disturbance observer.

[0346] Example 5

[0347] The anti-disturbance tracking control method for a UAV with local key state constraints according to the present invention has a flowchart as Figure 1 shown, and is specifically implemented according to the following steps:

[0348] Step 1: Apply the input-output feedback linearization method to the six-degree-of-freedom system model of the UAV, introduce the estimation of the disturbance, and obtain the UAV error tracking system;

[0349] Step 2: Design a simplified nonlinear disturbance observer to estimate the disturbance force and disturbance moment acting on the UAV, and feedback them into the design of the controller;

[0350] Step 3 is specifically implemented according to the following steps:

[0351] Based on the designed disturbance observer, the state-constrained anti-disturbance flight controller of the UAV will be constructed next.

[0352] For the convenience of design, the following lemma is introduced:

[0353] Lemma 1: For a matrix X or vector Y of a certain dimension, and for any constant ε > 0, the following inequality holds:

[0354] X T Y + Y T X ≤ εX T X + ε -1 Y T Y

[0355] Lemma 2: For any positive constant k b and real variable z(t), when the condition z(t) < k is satisfied b , the following inequality holds:

[0356]

[0357] Step 3.1: Define the tracking errors e 1 (t), e 2 (t), and design the Lyapunov function V 1 (t);

[0358] Step 3.2: Define the tracking error e 3 (t), and design the Lyapunov function V 2 (t);

[0359] Step 3.3: Define the tracking error e 4 (t), and design the Lyapunov function V 3 (t);

[0360] Step 3.4: Design the controller F 1 (t), and design the Lyapunov function V 4 (t);

[0361] Step 3.5: Define the tracking errors e 5 (t), e 6 (t), and design the Lyapunov function V 5 (t);

[0362] Step 3.6: Design the controller F 2 (t), and design the Lyapunov function V 6 (t).

[0363] Example 6

[0364] The present invention will be simulated in the MATLAB / Simlink environment to verify the designed controller. The experimental results are as Figures 2 - 9 shown. As Figure 2 shown, the position trajectory of the unmanned helicopter quickly tracks from the initial point to the preset position trajectory and maintains the tracking state. Figure 3 It includes four control inputs of the unmanned helicopter, including the pulling forces of the main rotor and the tail rotor, the lateral swing angle, and the longitudinal swing angle. The yaw angle is as Figure 4 shown, and the system can track the preset yaw angle in a relatively short time. The pitch angle and the roll angle are as Figure 5 shown. It can be seen from the results that the states of the unmanned helicopter are all maintained within an appropriate range. Figure 6 and Figure 7Curves representing the disturbance forces and torques and their estimated values, which can quickly track the disturbance forces and torques. Through the above experiments, the effectiveness of the proposed local key state constraint anti-disturbance backstepping control method is verified.

[0365] To demonstrate the superiority of the proposed local key state constraint anti-disturbance control scheme for a fully actuated unmanned helicopter, an experiment was designed and compared with the traditional non-linear controller method. This typical control method uses the backstepping control method and does not adopt the state constraint control strategy. The disturbance observer is the same as the one designed in the present invention. The simulation results are as Figures 8 - 9 shown. The key attitude angles of the unmanned aerial vehicle using the local key state constraint controller and the conventional anti-disturbance control are compared respectively. It can be seen that under the same conditions, the signal curve of the attitude angle of the unmanned helicopter using the local key state constraint anti-disturbance control has a smaller overshoot, indicating that the control strategy designed in the present invention has better dynamic performance compared with the conventional control scheme, and the safety and controllability of the helicopter during flight are better.

[0366] In the present invention, the relevant parameters of the simulated unmanned helicopter are as follows:

[0367] m = 800 kg, L y = 10 mm, L x = 50 mm, L z = 2100 mm, g = 9.8 m / s 2

[0368] J = diag{358.4 777.9 601.4} kg·m 2 , H x = 400 mm, H z = 70 mm

[0369]

[0370] The flight mission faced by the unmanned helicopter is to fly along the desired position trajectory and yaw angle. The required tracking signal is set as:

[0371]

[0372] The initial position and yaw angle of the unmanned helicopter are set as:

[0373] P(0) = [2 2 1.5] T , ψ(0) = 0 rad

[0374] The disturbance of the unmanned helicopter in the simulation experiment is preset as:

[0375] d 1= [0.4sin(0.3t) 0.6sin(0.4t) 0.2sin(0.3t)] T

[0376] d 2 = [1.3sin(0.4t) 1.4sin(0.3t) 1.6sin(0.5t)] T

Claims

1. An unmanned helicopter anti-interference tracking control method with local key state constraints, characterized in that: Follow the steps below to implement it: Step 1: Apply the input-output feedback linearization method to the unmanned helicopter six-degree-of-freedom system model, introduce interference estimation, and obtain the unmanned helicopter error tracking system; Step 2: Design a simplified nonlinear disturbance observer to estimate the disturbance force and disturbance torque on the unmanned helicopter; Step 3: Use the backstepping control method to design a partially state-constrained anti-interference flight tracking controller for the unmanned helicopter error tracking system. At the same time, introduce the obstacle Lyapunov function to constrain the local key intermediate variables, and estimate and compensate the influence of system interference based on the nonlinear disturbance observer.

2. The anti-interference tracking control method for an unmanned helicopter with local key state constraints according to claim 1 is characterized in that: The step 1 is specifically implemented according to the following steps: The following symbols involved in the formula are explained as follows: represents the first-order derivative of A(t); represents the second-order derivative of A(t); represents the third-order derivative of A(t); A (4) (t) represents the fourth-order derivative of A(t); B T represents the transposed matrix of matrix B; C -1 represents the inverse matrix of matrix C; According to the Newton-Euler equation, the following unmanned helicopter system is obtained: Where P(t)=(P x (t)P y (t)P z (t)) T and V(t)=(V x (t)V y (t)V z (t)) T Respectively represent the position and velocity in the inertial coordinate system, P x (t), P y (t), P z (t) and V x (t), V y (t), V z (t) represents the components on the x, y, and z axes respectively. The derivative of velocity is acceleration, g is the acceleration due to gravity, e3 = (001) T , m represents the mass of the unmanned helicopter, R(t) represents the rotational inertia of the rotation matrix from the fuselage coordinates to the inertial coordinates, f(t) represents the resultant external force on the center of mass of the unmanned helicopter, d1(t) represents the acceleration of the disturbance force of the system, Ω(t) = (φ(t)θ(t)ψ(t)) T represents the attitude angle of the helicopter, represents the attitude angular acceleration, where φ(t) represents the roll angle, θ(t) is the pitch angle, ψ(t) is the yaw angle, H(t) represents the attitude motion matrix, W(t) = (p(t)q(t)r(t)) T are the three attitude angular velocities relative to the ground coordinate system, p(t), q(t), r(t) represent the roll angular velocity, pitch angular velocity and yaw angular velocity respectively, J = diag{J xx J yy J zz } represents the inertia matrix of the unmanned helicopter, J xx , J yy and J zz They represent the rolling moment of inertia, the pitch moment of inertia and the yaw moment of inertia, represents the attitude angular acceleration, τ(t) represents the total external torque on the center of mass of the unmanned helicopter, d2(t) represents the disturbance torque of the system, Among them, c * and * They represent the cosine cos(*) and sine sin(*) in trigonometric functions respectively, * represents φ(t), θ(t) and ψ(t), and the attitude motion matrix is: W(t) × is the cross product operator matrix: Add new system variables f1(t) and f2(t) to expand the system into a new system: At this time, the relative order of formula (2) is the same as the system dimension, and the following variables are selected as new system variables: Among them, x1(t), x2(t), x3(t), and x4(t) represent the position tracking error, velocity tracking error, acceleration generated by the controllable result force of the unmanned helicopter, and the rate of change of the force generated by the controllable result force of the helicopter, respectively; x5(t) and x6(t) represent the yaw angle tracking error and yaw rate tracking error of the unmanned helicopter, P r (t) represents the actual position trajectory of the unmanned helicopter, Indicates the actual speed and acceleration of the unmanned helicopter. represents the estimated value of the acceleration of the disturbance force, represents the derivative of the actual acceleration, β1(t)=(0sinφ(t)secθ(t)cosφ(t)secθ(t)), is the yaw acceleration; According to (2) and (3), the transformed new system is obtained, which is expressed as: in, is the estimation error, L1 is the gain of the disturbance observer to be designed, F1(t) and F2(t) are the control inputs, The tracking error formula (4) of the unmanned helicopter is obtained through the above input-output feedback linearization construction, where the new control input is: The expressions of θ(t) and φ(t) are as follows:

3. The anti-interference tracking control method for an unmanned helicopter with local key state constraints according to claim 2 is characterized in that: The step 2 is specifically implemented according to the following steps: First, the following assumptions are introduced: Assumption 1: There are unknown boundaries D1 and D2 such that the aerodynamic force and aerodynamic moment satisfy and When estimating interference according to formula (4), the design of d1(t) interference observer is as follows: in, is the disturbance estimation value, L1 represents the disturbance observer gain, δ1(t) is the auxiliary function, Denotes the first-order derivative of the auxiliary function, and defines the estimation error as The dynamic description of the interference estimation error is: The disturbance observer is designed according to the dynamic equation of the attitude angle in formula (4): in, is the disturbance estimation value, L2 represents the disturbance observer gain, δ2(t) is the auxiliary function, Denotes the first-order derivative of the auxiliary function, and defines the estimation error as The dynamic description of the interference estimation error is:

4. The anti-interference tracking control method for an unmanned helicopter with local key state constraints according to claim 3 is characterized in that: The step 3 is specifically implemented according to the following steps: Introduce the following lemma: Lemma 1: For a matrix X or vector Y of a certain dimension, and for any constant ε>0, the following inequality holds: X T Y+Y T X≤εX T X+ε -1 AND T AND Lemma 2: For any positive constant k b and real variable z(t), when the condition z(t)<k ​​is satisfied b When , the following inequality holds: Step 3.1, define the tracking errors e1(t) and e2(t), and design the Lyapunov function V1(t); Step 3.2, define the tracking error e3(t) and design the Lyapunov function V2(t); Step 3.3, define the tracking error e4(t) and design the Lyapunov function V3(t); Step 3.4, design the controller F1(t), design the Lyapunov function V4(t); Step 3.5, define the tracking errors e5(t), e6(t), and design the Lyapunov function V5(t); Step 3.6, design the controller F2(t) and design the Lyapunov function V6(t).

5. The anti-interference tracking control method for an unmanned helicopter with local key state constraints according to claim 4 is characterized in that: The tracking error defined in step 3.1 is as follows: e1(t)=x1(t) (9) e2(t)=x2(t)-χ1(t) (10) Among them, χ1(t) is the virtual control law, which is defined as: χ1(t)=-k1e1(t) (11) Among them, k1>0 is the parameter to be designed, and the dynamics of e1(t) is: Where, X1(t)=-k1e1(t)+e2(t); Define the candidate Lyapunov function V1(t) as: Taking the derivative of (13), we get:

6. The anti-interference tracking control method for an unmanned helicopter with local key state constraints according to claim 5 is characterized in that: The tracking error is defined in step 3.2 as follows: e3(t)=x3(t)-χ2(t) (15) Among them, χ2(t) is the virtual control law, which is defined as: χ2(t)=-k2e2(t) (16) Among them, k2>0 is the parameter to be designed, and the dynamics of e2(t) is: in, Define the candidate Lyapunov function V2(t) as: By taking the derivative of (18), we can obtain:

7. The anti-interference tracking control method for an unmanned helicopter with local key state constraints according to claim 6 is characterized in that: The tracking error in step 3.3 is defined as follows: e4(t)=x4(t)-χ3(t) (20) Among them, χ3(t) is the virtual control law, which is defined as: Where, e3(t)=(e 31 (t)e 32 (t)e 33 (t)) T , k3>0, ε3>0, ρ1>0 are all parameters to be designed. According to formula (4), the dynamics of e3(t) is: in, Define the candidate Lyapunov function V3(t) as: By taking the derivative of (23), we can obtain:

8. The anti-interference tracking control method for an unmanned helicopter with local key state constraints according to claim 7 is characterized in that: The dynamics of the controllers F1(t), e4(t) designed in step 3.4 are: To ensure The negative definiteness of , the controller F1(t) is designed as: Among them, F 1a (t) is an additional controller designed in the subsequent step. At this time, the dynamics of e4(t) is: in, Additional controller F 1a (t) is designed to: Among them, ε4>0, ε5>0, k4>0; Define the candidate Lyapunov function V4(t) as: Taking the derivative of (29), we get:

9. The anti-interference tracking control method for an unmanned helicopter with local key state constraints according to claim 8 is characterized in that: The tracking error defined in step 3.5 is as follows: e5(t)=x5(t) (31) e6(t)=x6(t)-χ4(t) (32) Among them, χ4(t) is the virtual control law, defined as: χ4(t)=-k5e5(t) (33) Among them, k5>0, the dynamics of e5(t) is: Define the candidate Lyapunov function V5(t) as: Taking the derivative of (35), we get:

10. The anti-interference tracking control method for an unmanned helicopter with local key state constraints according to claim 9 is characterized in that: The dynamics of the controllers F2(t), e6(t) designed in step 3.6 are: To ensure The negative definiteness of , the controller F2(t) is designed as: Among them, F 2a (t) is an additional controller designed to: Among them, ε6>0; The candidate Lyapunov function V6(t) is selected as: Derivation of (40) yields: Stability analysis: Select the Lyapunov function V(t) as: Combining the above process, we get the derivative of V(t): According to Lemma 1, there exist ε1>0,ε2>0,ε3>0,ε4>0,ε5>0,ε6>0,ε7>0,ε8>0, such that: According to Lemma 2, there is an inequality: Therefore, (43) can be rewritten as: in, definition (44) can be rewritten as: According to (42) and (45), under the action of the designed controller and disturbance observer, the state of formula (4) can converge to the required bounded range.

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