Spacecraft orbit safety adaptive output feedback tracking control method based on observer

Abstract

The invention belongs to the technical field of spacecraft approaching orbit safety control, and particularly relates to a spacecraft orbit safety self-adaptive output feedback tracking control method based on an observer. A spacecraft orbit safety controller is established by using a virtual controller, an actual control law and a parameter adaptive law, and the spacecraft approaching orbit tracking system is controlled by using the safety controller, so that the problem of output feedback control when the system is attacked by false data injection of an actuator is effectively solved, and the stability of the system is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft approaching orbit safety control, and in particular relates to an observer-based spacecraft orbit safety adaptive output feedback tracking control method. Background Art

[0002] With the continuous development of aerospace technology, the research on spacecraft orbit control in related fields has become increasingly in-depth. The spacecraft approach orbit control system can achieve the approach tracking of the controlled spacecraft to the target, thereby meeting the requirements of various tasks. However, in practical applications, subject to the complex environment and actuator performance, the control system often faces the situation where the system state is unknown. When the spacecraft orbit control system is working, its communication network may be attacked by false data injection, causing the actuator to be paralyzed, thereby affecting the normal operation of the spacecraft and even causing serious losses. Therefore, it is particularly important to study the safe output feedback control method of the spacecraft approaching the orbit.

[0003] Chinese patent publication number CN117262252B discloses a spacecraft autonomous rendezvous and docking control method that can achieve fuel optimization. Based on the CW equation, a relative motion dynamics model of the tracking spacecraft in a near-circular orbit is established. Considering the slow full transmission of the target spacecraft, a target port motion model is established. According to the mission requirements of autonomous rendezvous and docking of the spacecraft, multiple constraints including thrust constraints, soft docking constraints and line of sight cone constraints are established. The optimal controller for rendezvous and docking based on variable range model predictive control is designed, and the optimal control problem solution strategy is obtained. However, this invention is only for the case where the system state is known. For spacecraft orbit systems with unknown states, this method is not applicable. At the same time, this method does not consider the security control problem of the system being attacked by a network.

[0004] Chinese patent publication number CN114995150B discloses an adaptive output feedback control method for spacecraft rendezvous under thrust limitation. This method uses a reference trajectory generator to give a system dynamic tracking model, combines anti-saturation technology to design a passivity-based adaptive state feedback controller, and uses a filter to generate a pseudo-velocity signal to propose an adaptive output feedback control law. This method can solve the output feedback tracking control problem of the control system, but does not consider the response strategy of the spacecraft orbit tracking system when it is attacked by a network, and cannot solve the system's security control problem.

[0005] In summary, the existing technology has made some progress in the control of spacecraft approaching orbit, but there are still challenges in security and stability when facing unknown system status and false data injection attacks. Therefore, developing an output feedback control method that can effectively resist false data injection attacks and ensure the safe and stable operation of the spacecraft approaching orbit system is a problem to be solved in the current aerospace technology field. Summary of the invention

[0006] The purpose of the present invention is to provide an observer-based spacecraft orbit safety adaptive output feedback tracking control method, which effectively solves the output feedback control problem of the spacecraft approaching orbit system facing false data injection attacks and ensures the safety and stability of the system.

[0007] The technical solution adopted by the present invention is as follows:

[0008] An observer-based spacecraft orbit safety adaptive output feedback tracking control method, characterized in that it includes the following steps:

[0009] Step 1: Use the line-of-sight coordinate system to establish a spacecraft approaching orbit dynamics model, and consider the actuator false data injection attack to establish a trajectory tracking error mathematical model;

[0010] Step 2: Use the state observer to estimate the unknown system state through the system output;

[0011] Step 3: Use the tracking error and estimated state to construct a virtual controller and actual control law, and design a parameter adaptive law to estimate the upper bound of the attack signal to complete the adaptive safety control of the spacecraft orbit of the observer under the attack of unknown state and unknown false data injection.

[0012] Preferably, in step 1, a line-of-sight coordinate system is used to establish a dynamic model of the spacecraft approaching the orbit, and a mathematical model of the trajectory tracking error is established by considering the actuator false data injection attack; for the line-of-sight coordinate system, its x-axis points from the center of mass of the controlled spacecraft to the target, which can be obtained by rotating the non-rotating system fixed to the controlled spacecraft with a rotation angle β and a rotation angle ε in a 2-3 rotation sequence; let the distance between the controlled spacecraft and the target be ρ, and only consider ρ>0 and In the case of spacecraft approaching orbit control, the target has no power, and the disturbance and gravity acceleration difference between the target and the controlled spacecraft are ignored. In the line of sight coordinate system, there are:

[0013]

[0014] where ρ s =[ρ00] T is the relative position vector in the line of sight coordinate system, a s is the control acceleration of the controlled spacecraft expressed in the line-of-sight coordinate system, ω∈R 3×1 is the angular velocity vector in the line of sight, is the angular acceleration vector in the line of sight.

[0015] In step 1, for the angular velocity vector in the line of sight system and the angular acceleration vector in the line of sight system:

[0016]

[0017] where ω × ∈R 3×1 and They are the cross product matrices of the angular velocity vector in the line of sight and the angular acceleration vector in the line of sight, respectively, and are defined as:

[0018]

[0019] in Then the dynamic equation in the line of sight system can be obtained:

[0020]

[0021] The control law is a s =u=[u 1 u 2 u 3 ] T ∈R 3×1 Suffering from bounded false data injection attackη=[η 1 η 2 η 3 ] T ∈R 3×1 , whose upper bound is η m =[η m1 η m2 η m3 ] T ∈R 3×1 .

[0022] The dynamic equation of the spacecraft approaching orbit with actuator false data injection attack in the line of sight system is:

[0023]

[0024] Let the spacecraft be controlled to track the expected trajectory and define ρ r , ε r and β r are the expected values ​​of relative distance ρ, line of sight inclination ε and line of sight deflection β respectively, let y r =[ρ r ε r β r ] T and μ = [ρεβ] T , then the orbit tracking error is:

[0025]

[0026] From the above formula, the orbit tracking error equation can be obtained as:

[0027]

[0028] Let the system state be x 1 =μ, Then we can get:

[0029]

[0030] Where y is the system output, and the nonlinear term Satisfies the Lipschitz condition Where δ>0 is the Lipschitz constant; the time-varying matrix The second norm satisfies in It is its upper bound.

[0031] Preferably, in step 2: using a state observer to estimate the unknown system state through the system output;

[0032] First, the state space form of the system is as follows:

[0033]

[0034] where x = [x 1 T x 2 T ] T ∈R 6×1 ,

[0035] where k 1 >0,k 2 >0,k 3 >0,k 4 >0,k 5 >0,k 6 >0 is the design parameter;

[0036] Design the state observer as follows:

[0037]

[0038] in is an estimate of x, and the gain matrix K is selected so that the matrix A is Hurwitz, that is, for a given positive definite matrix Q∈R 6×6 There exists a positive definite matrix P∈R 6×6 Satisfies the following equation:

[0039] A T P+PA=-Q; To estimate the error, choose the Lyapunov function: The derivative of the Lyapunov function is obtained as:

[0040]

[0041] where λ min (Q) is the smallest eigenvalue of the matrix Q, ||PB|| is the bi-norm of PB, ||η m || is η m The mold length.

[0042] Preferably, the step three comprises:

[0043] The virtual controller and actual control law are constructed using the tracking error and estimated state, and the parameter adaptive law is designed to estimate the upper bound of the attack signal.

[0044] According to the backstepping method, the design coordinate changes are as follows:

[0045]

[0046] Among them, α∈R 3×1 It is a virtual controller;

[0047] The first step of the backstepping method: by selecting the Lyapunov function:

[0048]

[0049] Design the virtual control law α as:

[0050] where c 1 >0 is the design parameter; the derivative of the Lyapunov function is:

[0051]

[0052] The second step of the backstepping method: Derivation yields:

[0053]

[0054] in The Lyapunov function is selected as follows:

[0055]

[0056] Where γ>0 is a design parameter, is the estimated error of the attack upper bound, is the attack upper bound η m The actual control law and parameter adaptive law are designed as follows:

[0057]

[0058] in, where c 2 >0 is the design parameter, (g(x 1 ))-1 is g(x 1 ), The derivative of the Lyapunov function of the closed-loop system is obtained as:

[0059]

[0060] in

[0061] And meet Then the closed-loop system is eventually uniformly bounded; and by choosing the parameter k 1 , k 2 , k 3 , k 4 , k 5 , k 6 , c 1 , c 2 , γ is a suitable value, and the adaptive safety control of the spacecraft orbit of the observer under the attack of unknown state and unknown false data injection is completed.

[0062] The technical effects achieved by the present invention are:

[0063] The present invention provides an observer-based spacecraft orbit safety adaptive output feedback tracking control method, which uses an observer to estimate the unknown state of the system, uses a virtual controller and an actual control law as well as a parameter adaptive law to establish a spacecraft orbit safety controller, and uses the safety controller to control the spacecraft approaching orbit tracking system, thereby effectively solving the output feedback control problem of the system being attacked by false data injection from an actuator, and ensuring the stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is a flow chart of the observer-based spacecraft orbit safety adaptive output feedback tracking control method disclosed in an embodiment of the present invention.

[0065] Figure 2 This is a schematic diagram of the overall structure of the controller designed for the embodiment of the present invention.

[0066] Figure 3 is a tracking error curve diagram of an embodiment of the present invention;

[0067] Figure 4 4 is a parameter adaptive law curve diagram of an embodiment of the present invention.

[0068] Figure 5 It is a graph of the actual control law of an embodiment of the present invention. DETAILED DESCRIPTION

[0069] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0070] like Figure 1-Figure 5 As shown, an observer-based adaptive output feedback tracking control method for spacecraft orbit safety is presented. In the line-of-sight coordinate system, a spacecraft approaching orbit dynamics model with actuator false data injection attack is established using relative distance, line-of-sight deflection angle and line-of-sight inclination angle. The observer is used to estimate the unknown system state, the parameter adaptive law is used to estimate the upper bound of the attack signal, and the virtual controller and the actual control law are used to control the system, thus achieving adaptive safety control in the face of unknown states and unknown false data injection attacks.

[0071] like Figure 1 As shown in FIG. 1 , the observer-based spacecraft orbit safety adaptive output feedback tracking control method comprises the following steps:

[0072] Step 1: Use the line of sight coordinate system Ox s y s z s Establish a dynamic model of spacecraft approaching orbit, and consider the actuator false data injection attack to establish a mathematical model of trajectory tracking error;

[0073] The spacecraft approaches the orbit system to meet the following conditions:

[0074] Condition 1: The controlled spacecraft approaches the target at a close distance, the difference in gravitational acceleration between the two is negligible, and the target has no power;

[0075] Condition 2: The approaching orbit system meets the following boundary conditions:

[0076]

[0077] Where ρ is the relative distance between the controlled spacecraft and the target, ε is the line of sight inclination, and β is the line of sight deflection.

[0078] Condition 3: Expected trajectory y r ∈R 3×1 , its derivative and the second-order derivative Known, bounded and continuous;

[0079] Condition 4: The false data injection attack energy suffered by the spacecraft is limited, and the false data injection attack η=[η 1 η 2 η 3 ] T ∈R 3×1 The absolute value of each component of has an upper bound, which is ηm =[η m1 η m2 η m3 ] T ∈R 3×1 .

[0080] Condition 5: Nonlinear function f(x 1 ,x 2 ) satisfies the Lipschitz condition:

[0081]

[0082] where δ>0 is the Lipschitz constant.

[0083] Condition 6: Time-varying matrix g(x 1 )satisfy in It is its upper bound.

[0084] First, define the geocentric inertial coordinate system Ox i y i z i , whose origin is fixed to the center of mass of the Earth, Ox i The axis points to the vernal equinox, Oz i The axis points to the North Pole, Oy i The axis is determined by the right-hand rule. i y i z i In the example, let the position vectors of the controlled spacecraft and the target be r c ∈R 3×1 and r t ∈R 3×1 , and its orbital dynamics are modeled as:

[0085]

[0086] where ||r c || and ||r t || are r c and r t The modulus of the earth, κ is the gravitational constant, a c ∈R 3×1 is the control acceleration of the controlled spacecraft. In the body coordinate system Ox fixed to the center of mass of the controlled spacecraft b y b z b In the example, let its coordinate axis be parallel to Ox i y i z i , let the relative position vector be ρ b =r t -r c, the relative orbital dynamics model is obtained as:

[0087]

[0088] in It is the difference in gravitational acceleration between the controlled spacecraft and the target.

[0089] For the line of sight coordinate system Ox s y s z s , whose x-axis points from the center of mass of the controlled spacecraft to the target, can be obtained by rotating the system in the order of 2-3 with the line of sight deflection angle β and the line of sight inclination angle ε. b The axis is rotated by angle β to obtain the intermediate coordinate system Ox′y′z′:

[0090]

[0091] in Then rotate the angle ε around the Oz′ axis to obtain the sight coordinate system Ox s y s z s :

[0092]

[0093] The transformation equation can be obtained from the rotation process:

[0094]

[0095] in is the transformation matrix, and the line of sight Ox s y s z s The following kinetic equation:

[0096]

[0097] where a s =R bs a c is the acceleration of the controlled spacecraft in the line of sight. From the vector derivative law, we know that:

[0098]

[0099] where ρ s ∈R 3×1 is the relative position vector in the line of sight, ω∈R 3×1 is the angular velocity vector in the line of sight, is the angular acceleration vector in the line of sight, and they are defined as:

[0100]

[0101] where ω × ∈R 3×1 and are their cross product matrices, defined as:

[0102]

[0103] in Then the dynamic equation in the line of sight system can be obtained:

[0104]

[0105] Assume a g →0; acceleration is a s , that is, control law a s =u=[u 1 u 2 u 3 ] T ∈R 3×1 If the spacecraft is attacked by false data injection η, the dynamic equation of the spacecraft approaching the orbit in the line of sight system is:

[0106]

[0107] Let the spacecraft be controlled to track the expected trajectory and define ρ r , ε r and β r are the expected values ​​of relative distance ρ, line of sight inclination ε and line of sight deflection β respectively, let y r =[ρ r ε r β r ] T and μ = [ρεβ] T , then the orbit tracking error is:

[0108]

[0109] From the above formula, the orbit tracking error equation can be obtained as:

[0110]

[0111] Let the system state be x 1 =μ, Then we can get:

[0112]

[0113] Where y is the system output, and the nonlinear term Time-varying matrix

[0114]

[0115] Step 2: Use the state observer to estimate the unknown system state through the system output.

[0116] Combining (18), the state space form of the system is as follows:

[0117]

[0118] where x = [x 1 T x 2 T ] T ∈R 6×1 ,

[0119]

[0120] where k 1 >0,k 2 >0,k 3 >0,k 4 >0,k 5 >0,k 6 >0 is a design parameter.

[0121] Rewrite the system formula (19) as follows:

[0122]

[0123] in is an estimate of x,

[0124] Design the state observer as follows:

[0125]

[0126] Combining (8) and (9), the observation error equation is as follows:

[0127]

[0128] in is the observation error.

[0129] The gain matrix K is chosen so that the matrix A is Hurwitz, that is, for a given positive definite matrix Q∈R 6×6 There exists a positive definite matrix P∈R 6×6 Satisfies the following equation:

[0130] A T P+PA=-Q (24)

[0131] Select the Lyapunov function as follows:

[0132]

[0133] V 0 The derivative is:

[0134]

[0135] According to Young's inequality:

[0136]

[0137] Where ||PB|| is the second norm of PB. Substituting (14)-(15) into (13), we get:

[0138]

[0139] where λ min (Q) is the smallest eigenvalue of the matrix Q.

[0140] Step 3: Use the tracking error and estimated state to construct a virtual controller and actual control law, and design a parameter adaptive law to estimate the upper bound of the attack signal.

[0141] The design coordinates change as follows:

[0142]

[0143] Among them, α∈R 3×1 It is a virtual controller.

[0144] Step 1: Select the Lyapunov function as follows:

[0145]

[0146] where c 1 >0 is the design parameter. Combining (17) and (18), we can get:

[0147]

[0148] in, is the estimation error.

[0149] From Young's inequality we can get:

[0150]

[0151] Substituting (20) into (19) we obtain:

[0152]

[0153] Design the virtual control law α as:

[0154]

[0155] Among them, c1 >0 is a design parameter.

[0156] Substituting (22) into (21), we obtain:

[0157]

[0158] Step 2: From (17)(22), we can get:

[0159]

[0160] in The Lyapunov function is selected as follows:

[0161]

[0162] Where γ>0 is a design parameter, is the estimated error of the attack upper bound, is the attack upper bound η m The estimated value of .

[0163] Combining (23)-(25) we can get:

[0164]

[0165] Combining (16), (23), (24), (26) we can obtain:

[0166]

[0167] According to Young's inequality:

[0168]

[0169] Combining (27) with (28) and (29) we can obtain:

[0170]

[0171] The actual control law and parameter adaptation law are designed as follows:

[0172]

[0173] where c 2 >0 is the design parameter, (g(x 1 )) -1 is g(x 1 ),

[0174] Combining (30)-(32) we can get:

[0175]

[0176] Combined with the attack signal, we can get an upper bound:

[0177]

[0178] Among them, Λ and g(x 1 ) are all diagonal matrices, and From the assumption, we know that |η i |≤η mi ,i=1,2,3

[0179] According to Young's inequality:

[0180]

[0181] Combining (33)-(35) we get

[0182]

[0183] in

[0184] And meet Then the closed-loop system is eventually uniformly bounded. And by choosing the parameter k 1 , k 2 , k 3 , k 4 , k 5 , k 6 , c 1 , c 2 , γ is a suitable value, which can make the system tracking error approach a small neighborhood of the origin, and the problem of safe adaptive output feedback control of spacecraft approaching orbit with actuator false data injection attack is solved.

[0185] In this case, if Figure 2 As shown in the overall schematic diagram consisting of a state observer, a parameter adaptive law, a virtual controller, an actual control law, and a spacecraft approaching orbit system with an actuator false data injection attack, the control process of the method of the present invention is as follows: the system output is sent to the state observer to obtain an estimated state, the estimated state is used to generate a state adaptive law, the tracking error signal is used to generate a virtual control law, the virtual control signal and the adaptive parameter are sent to the actual controller to generate an actual control signal, the spacecraft approaching orbit system with an actuator false data injection attack is controlled, and the system output is compared with a reference signal (expected trajectory) to generate a tracking error signal.

[0186] In order to verify the effectiveness of the solution proposed in this case, the system attack signal is given as

[0187] η=[0.2+0.1sin0.3t 0.1cos0.2t 0.1-0.1sin0.1t] T (50)

[0188] The expected trajectory is set as:

[0189] y r =[ρ r ε r β r ] T =[4+cos0.1t 0.6sin0.2t 0.6cos0.2t] T (51)

[0190] The initial state information of the system is

[0191] x 1 (0) = μ(0) = [8 - 0.9 - 1.8] T (52)

[0192]

[0193] Choosing the parameter k 1 =k 2 =k 3 =20,k 4 =k 5 =k 6 =600,c 1 =0.2,c 2 =0.8,γ=20,Q=5I 6×6 , calculated Right now If the parameter requirements are met, the spacecraft control effect diagram is as follows: Figure 3-5 shown. Figure 3 is the spacecraft tracking error trajectory diagram; z 1 =ρ-ρ r , z 2 =β-β r , z 3 =ε-ε r They are the three components of tracking error. Figure 3 It can be seen that the adaptive safety output feedback tracking control method of the present invention can control the spacecraft to track the desired trajectory, the tracking error converges within 20s, and the tracking effect is good; Figure 4 The curve diagram of the parameter adaptation law, They are the three components of the parameter adaptation law; Figure 5 is the true control law curve, u 1 ,u 2 ,u 3They are the three components of the real control law. It can be seen that the adaptive safety output feedback tracking control scheme proposed in the present invention can enable a spacecraft with unknown system state to track the target trajectory under the attack of actuator false data injection.

[0194] Through the above technical scheme, the present invention provides an observer-based spacecraft orbit safety adaptive output feedback tracking control method, which uses the observer to estimate the unknown state of the system, uses the virtual controller and the actual control law and the parameter adaptive law to establish the spacecraft orbit safety controller, and uses the safety controller to control the spacecraft approaching orbit tracking system, effectively solving the output feedback control problem of the system being attacked by false data injection from the actuator, and ensuring the stability of the system.

[0195] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. An observer-based spacecraft orbit safety adaptive output feedback tracking control method, characterized in that: The following steps are involved: Step 1: Use the line-of-sight coordinate system to establish a spacecraft approaching orbit dynamics model, and consider the actuator false data injection attack to establish a trajectory tracking error mathematical model; Step 2: Use the state observer to estimate the unknown system state through the system output; Step 3: Use the tracking error and estimated state to construct a virtual controller and actual control law, and design a parameter adaptive law to estimate the upper bound of the attack signal to complete the adaptive safety control of the spacecraft orbit of the observer under the attack of unknown state and unknown false data injection.

2. The observer-based spacecraft orbit safety adaptive output feedback tracking control method according to claim 1, characterized in that: In step 1, a line-of-sight coordinate system is used to establish a dynamic model of the spacecraft approaching the orbit, and a mathematical model of the trajectory tracking error is established by considering the actuator false data injection attack; for the line-of-sight coordinate system, its x-axis points from the center of mass of the controlled spacecraft to the target, which can be obtained by rotating the non-rotating system fixed to the controlled spacecraft with a rotation angle β and a rotation angle ε in a 2-3 rotation sequence; let the distance between the controlled spacecraft and the target be ρ, and only consider ρ>0 and In the case of spacecraft approaching orbit control, the target has no power, and the disturbance and gravity acceleration difference between the target and the controlled spacecraft are ignored. In the line of sight coordinate system, there are: where ρ s =[ρ 0 0] T is the relative position vector in the line of sight coordinate system, a s is the control acceleration of the controlled spacecraft expressed in the line-of-sight coordinate system, ω∈R 3×1 is the angular velocity vector in the line of sight, is the angular acceleration vector in the line of sight.

3. The observer-based spacecraft orbit safety adaptive output feedback tracking control method according to claim 2, characterized in that: In step 1, for the angular velocity vector in the line of sight system and the angular acceleration vector in the line of sight system:

4. The observer-based spacecraft orbit safety adaptive output feedback tracking control method according to claim 3, characterized in that: where ω × ∈R 3×1 and They are the cross product matrices of the angular velocity vector in the line of sight and the angular acceleration vector in the line of sight, respectively, and are defined as: in Then the dynamic equation in the line of sight system can be obtained: The control law is a s =u=[u1 u2 u3] T ∈R 3×1 Suffering from bounded false data injection attack η=[η1 η2 η3] T ∈R 3×1 , whose upper bound is η m =[η m1 η m2 η m3 ] T ∈R 3×1 .

5. The observer-based spacecraft orbit safety adaptive output feedback tracking control method according to claim 4, characterized in that: The dynamic equation of the spacecraft approaching orbit with actuator false data injection attack in the line of sight system is: Let the spacecraft be controlled to track the expected trajectory and define ρ r , ε r and β r are the expected values ​​of relative distance ρ, line of sight inclination ε and line of sight deflection β respectively, let y r =[ρ r ε r β r ] T and μ = [ρ ε β] T , then the orbit tracking error is: From the above formula, the orbit tracking error equation can be obtained as: Let the system state x1 = μ, Then we can get: Where y is the system output, and the nonlinear term Satisfies the Lipschitz condition Where δ>0 is the Lipschitz constant; the time-varying matrix The second norm satisfies in It is its upper bound.

6. The observer-based spacecraft orbit safety adaptive output feedback tracking control method according to claim 1, characterized in that: In the step 2: using a state observer to estimate the unknown system state through the system output; First, the state space form of the system is as follows: in Among them, k1>0, k2>0, k3>0, k4>0, k5>0, k6>0 are design parameters; Design the state observer as follows: in is an estimate of x, and the gain matrix K is selected so that the matrix A is Hurwitz, that is, for a given positive definite matrix Q∈R 6×6 There exists a positive definite matrix P∈R 6×6 Satisfies the following equation: A T P+PA=-Q; To estimate the error, choose the Lyapunov function: The derivative of the Lyapunov function is obtained as: where λ min (Q) is the smallest eigenvalue of the matrix Q, ||PB|| is the bi-norm of PB, |η m || is η m The mold length.

7. The observer-based spacecraft orbit safety adaptive output feedback tracking control method according to claim 1, characterized in that: The step three comprises: The virtual controller and actual control law are constructed using the tracking error and estimated state, and the parameter adaptive law is designed to estimate the upper bound of the attack signal. According to the backstepping method, the design coordinate changes are as follows: Among them, α∈R 3×1 It is a virtual controller; The first step of the backstepping method: by selecting the Lyapunov function: Design the virtual control law α as: Where c1>0 is the design parameter; the derivative of the Lyapunov function is: The second step of the backstepping method: Derivation yields: in The Lyapunov function is selected as follows: Where γ>0 is a design parameter, is the estimated error of the attack upper bound, is the attack upper bound η m The actual control law and parameter adaptive law are designed as follows: in, Where c2>0 is the design parameter, (g(x1)) -1 is the inverse matrix of g(x1), The derivative of the Lyapunov function of the closed-loop system is obtained as: in And meet Then the closed-loop system is eventually uniformly bounded; and by selecting parameters k1, k2, k3, k4, k5, k6, c1, c2, γ as appropriate values, the adaptive safety control of the spacecraft orbit of the observer under the attack of unknown state and unknown false data injection is completed.

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