A nonlinear hybrid H2 / H2 based observer for flexible satellites ∞ Control Methods

Abstract

The present invention relates to an observer-based nonlinear hybrid control method for a flexible satellite, comprising the following steps: S1, establishing a state space model of a flexible satellite attitude system with external disturbance and partial unmeasurable states; S2, designing a nonlinear dimension reduction observer and a state feedback controller to obtain a closed-loop system based on the nonlinear dimension reduction observer and the state feedback controller with external disturbance and partial unmeasurable states; S3, generating a nonlinear hybrid control problem of the flexible satellite attitude system through the closed-loop system, and converting the nonlinear hybrid control problem into a SOS convex optimization problem; S4, solving the SOS convex optimization problem by using Matlab / SOSTOOLS to obtain a solution of a nonlinear dimension reduction observer and a state feedback controller for the flexible satellite attitude system and satisfying the nonlinear hybrid control problem, and controlling the flexible satellite through the solution of the nonlinear dimension reduction observer and the state feedback controller.

Description

Technical Field

[0001] The present invention relates to the field of flexible satellite control, and in particular to a flexible satellite nonlinear hybrid H2 / H2 based on an observer. ∞ Control method. Background Art

[0002] In order to achieve various tasks such as meteorological observation, navigation and information detection, satellites need to have high-precision attitude maneuvering capabilities and rapid attitude tracking and response capabilities. In this context, satellite attitude control with flexible attachments has gradually become a hot topic in academic research. When a satellite performs rapid and large-angle attitude maneuvers, coupled motion will occur between the satellite and the flexible attachment, posing a serious threat to its attitude stability and operational safety. In addition, the space environment is complex, changeable and full of unknowns. Flexible satellites will be affected by various external interferences during their in-orbit operation, which undoubtedly greatly increases the difficulty and complexity of attitude control.

[0003] For satellites with external interference, H is usually used. ∞ control strategy, but this method is difficult to take into account the system regulation performance. ∞ The control method combines H2 and H ∞ The dual advantages of H2 / H2 control are considered to be a better solution, but the existing technology ∞ Control research is mainly limited to the state feedback method of linear systems. This is because the physical structure of modern satellites is unique, and their state parameters are often difficult to measure directly or the measurement cost is too high to adopt the state feedback method. In addition, due to the mixed H2 / H ∞ The control method in nonlinear systems requires a complex iterative process and has technical difficulties such as the complexity of overall control, which makes the hybrid H2 / H ∞ Control methods are difficult to implement in nonlinear systems.

[0004] Aiming at the above problems in the prior art, a nonlinear hybrid H2 / H2 based flexible satellite observer is designed. ∞ The control method is the purpose of this invention. Summary of the invention

[0005] In view of the problems existing in the above-mentioned prior art, the present invention provides a flexible satellite nonlinear hybrid H2 / H ∞ The control method can effectively solve at least one problem existing in the above-mentioned prior art.

[0006] The technical solution of the present invention is:

[0007] A nonlinear hybrid H2 / H2 based observer for flexible satellites ∞ The control method comprises the following steps:

[0008] S1, establish the state space model of the flexible satellite attitude system with external disturbances and unmeasurable states;

[0009] S2, designing a nonlinear dimension reduction observer and a state feedback controller to obtain a closed-loop system based on the nonlinear dimension reduction observer and the state feedback controller with external disturbances and unmeasurable states;

[0010] S3, generating a nonlinear hybrid H2 / H2 of the flexible satellite attitude system through the closed-loop system ∞ The control problem is to convert the nonlinear mixed H2 / H ∞ The control problem is transformed into an SOS convex optimization problem;

[0011] S4, using Matlab / SOSTOOLS to solve the SOS convex optimization problem, we obtain the nonlinear mixed H2 / H ∞ A nonlinear dimension reduction observer and a state feedback controller are provided for the control problem, and the flexible satellite is controlled by the nonlinear dimension reduction observer and the state feedback controller.

[0012] Furthermore, the state space model of the flexible satellite attitude system with external disturbances and unmeasurable states is established, including:

[0013] Auxiliary variables are introduced into the flexible satellite attitude kinematics and dynamics equations, and the flexible satellite attitude kinematics and the dynamics equations are expressed as the state space model.

[0014] Furthermore, designing a nonlinear dimension reduction observer and a state feedback controller includes:

[0015] S2.1, establishing the nonlinear dimension reduction observer according to the input signal and the output signal of the state space model;

[0016] S2.2, establishing the state feedback controller according to the estimation information of the nonlinear dimensionality reduction observer.

[0017] Furthermore, a closed-loop system based on the nonlinear dimension reduction observer and the state feedback controller with external disturbances and unmeasurable states is obtained, including:

[0018] S2.3, applying the state feedback controller and the nonlinear dimension reduction observer to the state space model to obtain a closed-loop system with external disturbances and unmeasurable states.

[0019] Furthermore, the closed-loop system generates a nonlinear hybrid H2 / H ∞ Control issues include:

[0020] The state feedback controller based on the nonlinear dimension reduction observer satisfies the following conditions:

[0021] when When , the closed-loop system is asymptotically stable at the zero equilibrium point;

[0022] when hour, ,in is an upper bound of a performance indicator;

[0023] Given a constant ,when satisfy And the initial state When, from arrive of Gain ;

[0024] in, For external interference, is the controlled output, For time, It is the H2 control performance index, Gain is H ∞ Control performance indicators.

[0025] Furthermore, the nonlinear mixture H2 / H ∞ The control problem is transformed into an SOS convex optimization problem including:

[0026] According to the structural characteristics of the flexible satellite attitude, the Lyapunov stability theory is used to establish a nonlinear hybrid H2 / H based on the observer. ∞ The conditions for the posture control problem to exist;

[0027] The nonlinear mixed H2 / H ∞ The existence conditions of the attitude control problem are transformed into a SOS convex optimization problem.

[0028] Further, the nonlinear mixed H2 / H ∞ The existence conditions of the attitude control problem are transformed into the SOS convex optimization problem, including:

[0029] The nonlinear mixed H2 / H is derived by SOS and S-procedure methods. ∞ Solvability conditions for the attitude control problem.

[0030] Furthermore, Matlab / SOSTOOLS is used to solve the SOS convex optimization problem and obtain the nonlinear mixed H2 / H∞ The solutions of the nonlinear reduced-dimensionality observer and state feedback controller to the control problem include:

[0031] The kinematic and dynamic parameters of the flexible satellite attitude control process are determined, the given parameters required for solving the solvability conditions are determined, and the solvability conditions are solved by Matlab / SOSTOOLS.

[0032] Further, after step S4, the following steps are included:

[0033] S5, build a flexible satellite attitude control simulation platform through Matlab / Simulink to verify the flexible satellite attitude control effect of the obtained nonlinear dimensionality reduction observer and state feedback controller.

[0034] Therefore, the present invention provides the following effects and / or advantages:

[0035] This application focuses on the nonlinear hybrid H2 / H ∞ The output feedback control problem is solved by realizing the independent design of nonlinear observer and controller without complicated iterative process, which significantly reduces the complexity of the overall control design and realizes the nonlinear hybrid H2 / H2 that can be used to control flexible satellites. ∞ Control method.

[0036] In addition, the SOS convex solvability condition is established to facilitate computational processing, which effectively solves the common computational difficulties in constructing Lyapunov functions in nonlinear control research. Simulation results show that the proposed nonlinear hybrid H2 / H ∞ The attitude control method not only ensures the stability of the attitude system, but also improves the stability of the attitude system compared with the classical nonlinear H ∞ The method showed better control performance and stronger interference suppression ability.

[0037] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention are realized and obtained by the structures particularly pointed out in the description and the drawings.

[0038] It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic diagram of a flow chart provided for an embodiment of the present invention.

[0040] Figure 2It is a partial schematic diagram of the calculation results of solving the solvability conditions by Matlab / SOSTOOLS.

[0041] Figure 3 Schematic diagram of building a flexible satellite attitude control simulation platform for Matlab / Simulink.

[0042] Figure 4 Schematic diagram of external interference input to the flexible satellite attitude system.

[0043] Figure 5 for Schematic diagram of the trajectory.

[0044] Figure 6 is the attitude angular velocity Schematic diagram of the trajectory.

[0045] Figure 7 for and Schematic diagram of the trajectory.

[0046] Figure 8 For and Schematic diagram of the derivation trajectory. DETAILED DESCRIPTION

[0047] In order to facilitate understanding by those skilled in the art, the present invention is now described in further detail by way of examples:

[0048] refer to Figure 1 , a nonlinear hybrid H2 / H2 based observer for flexible satellites ∞ The control method comprises the following steps:

[0049] S1, establish the state space model of the flexible satellite attitude system with external disturbances and unmeasurable states;

[0050] S2, designing a nonlinear dimension reduction observer and a state feedback controller to obtain a closed-loop system based on the nonlinear dimension reduction observer and the state feedback controller with external disturbances and unmeasurable states;

[0051] S3, generating a nonlinear hybrid H2 / H2 of the flexible satellite attitude system through the closed-loop system ∞ The control problem is to convert the nonlinear mixed H2 / H ∞ The control problem is transformed into an SOS convex optimization problem;

[0052] S4, using Matlab / SOSTOOLS to solve the SOS convex optimization problem, we obtain the nonlinear mixed H2 / H ∞A nonlinear dimension reduction observer and a state feedback controller are provided for the control problem, and the flexible satellite is controlled by the nonlinear dimension reduction observer and the state feedback controller.

[0053] The state space model of the flexible satellite attitude system with external disturbances and unmeasurable states includes:

[0054] Auxiliary variables are introduced into the flexible satellite attitude kinematics and dynamics equations, and the flexible satellite attitude kinematics and the dynamics equations are expressed as the state space model.

[0055] Specifically, firstly, the flexible satellite attitude kinematics and dynamics equations in this embodiment can be directly adopted from the prior art, as follows:

[0056] Kinematics for (1);

[0057] The kinetic equation is (2);

[0058] in is the Rodrigues parameter vector, , is the moment of inertia matrix, is the attitude angular velocity vector, for The corresponding cross product matrix is, is the rigid-flex coupling coefficient matrix, is the flexible mode coordinate vector ( represents the truncated mode order), is the modal damping matrix, is the natural frequency matrix, and are the control and disturbance torques, respectively, is a zero matrix.

[0059] The kinematics and dynamics equations of attitude of flexible satellites are inherently subject to external interference and some states are unpredictable.

[0060] Then, auxiliary variables are introduced into the attitude kinematics and dynamics equations of the flexible satellite. and .

[0061] In this step, the auxiliary variable and It may be prior art.

[0062] The auxiliary variables are , .

[0063] After introducing auxiliary variables, the flexible satellite attitude kinematics and dynamics equations can be expressed as the following state space model:

[0064] (3),

[0065] in is the system status, and are the unmeasurable and measurable sub-states, respectively. ; and is the controlled output; , and They are external disturbance, control input and measurement output respectively; , , , , , , , , , is a matrix of appropriate dimension known; , ; ; and , ( ) is a known matrix of appropriate dimension; , , , , , , Respectively dimensional real vector set, dimensional real vector set, dimensional real vector set, 3-dimensional real vector set, 6-dimensional real vector set, dimensional real vector set, identity matrix of appropriate dimension; , , , are all known constants.

[0066] Furthermore, designing a nonlinear dimension reduction observer and a state feedback controller includes:

[0067] S2.1, establishing the nonlinear dimension reduction observer according to the input signal and the output signal of the state space model;

[0068] In this step, the input signal and output signal of the state space model are used to construct a nonlinear dimension reduction observer of the following form to estimate the flexible mode:

[0069] (4),

[0070] in for No. OK, is the observer state quantity, for The estimated value of is the observer gain matrix to be designed, yes The set of real matrices of dimension ;

[0071] S2.2, establishing the state feedback controller according to the estimation information of the nonlinear dimensionality reduction observer;

[0072] The state feedback controller obtained is as follows:

[0073] (5),

[0074] in , , is the observation error; is the controller gain matrix to be designed, yes The set of real matrices of dimension ;

[0075] Furthermore, a closed-loop system based on the nonlinear dimension reduction observer and the state feedback controller with external disturbances and unmeasurable states is obtained, including:

[0076] S2.3, applying the state feedback controller and the nonlinear dimension reduction observer to the state space model to obtain a closed-loop system with external disturbances and unmeasurable states.

[0077] In this step, the closed-loop system obtained by combining (3)-(5) is as follows:

[0078] (6),

[0079] in , , ,

[0080] , .

[0081] , , , , are matrices of appropriate dimension.

[0082] Furthermore, the nonlinear hybrid H2 / H∞ control problem of the flexible satellite attitude system generated by the closed-loop system includes:

[0083] The state feedback controller based on the nonlinear dimension reduction observer satisfies the following conditions:

[0084] (I) When When , the closed-loop system is asymptotically stable at the zero equilibrium point;

[0085] (II) When hour, ,in is an upper bound of a performance indicator;

[0086] (III) Given a constant ,when satisfy And the initial state When, from arrive of Gain ;

[0087] in, For external interference, is the controlled output, For time, It is the H2 control performance index, Gain is an indicator of H∞ control performance.

[0088] Based on the three conditions (I)-(III) above, the results obtained can be used to represent the nonlinear dimensionality reduction observer and the state feedback controller.

[0089] Furthermore, the nonlinear mixture H2 / H ∞ The control problem is transformed into an SOS convex optimization problem including:

[0090] According to the structural characteristics of the flexible satellite attitude, the Lyapunov stability theory is used to establish a nonlinear hybrid H2 / H based on the observer. ∞ The conditions for the posture control problem to exist;

[0091] The nonlinear mixed H2 / H ∞ The existence conditions of the attitude control problem are transformed into a SOS convex optimization problem.

[0092] Further, the nonlinear mixed H2 / H ∞ The existence conditions of the attitude control problem are transformed into the SOS convex optimization problem, including:

[0093] The nonlinear mixed H2 / H is derived by SOS and S-procedure methods. ∞ Solvability conditions for the attitude control problem.

[0094] This step is specifically to give a constant ,when When it is a bounded closed set, there exists First-order differentiable and continuous positive definite matrix And continuous function matrix and So that:

[0095] (7)

[0096] The necessary and sufficient condition for the existence of First-order differentiable and continuous positive definite matrix and , and the continuous function matrix and So that:

[0097] (8)

[0098] (9)

[0099] in ,

[0100] , , .

[0101] If equations (8) and (9) hold, the observer-based nonlinear hybrid H2 / H ∞ The attitude control problem conditions are all met, and the corresponding controller and observer gain matrices are:

[0102] (10)

[0103] Next, the specific steps of transforming to the SOS convex optimization problem are as follows.

[0104] Define the following collections:

[0105] ,

[0106] in , is a known constant, , They are (i=1, 2, 3) and (i=1, 2, 3) initial values.

[0107] when When, for a given constant , , and , if the following two conditions (i) and (ii) are met, then the observer-based nonlinear hybrid H2 / H ∞ The attitude control problem is solvable.

[0108] i) Existence constant , and , the polynomial matrix and satisfy:

[0109] ;

[0110] ;

[0111] in , , for The three elements in for The 6 elements in . , is a real vector, Represents the set of SOS polynomials.

[0112] ii) Existence of constants , and , the polynomial matrix and satisfy:

[0113] ;

[0114] ;

[0115] in , , for The three elements in for The 6 elements in . , is a real vector.

[0116] Furthermore, Matlab / SOSTOOLS is used to solve the SOS convex optimization problem, and the solutions of the nonlinear dimension reduction observer and state feedback controller for the flexible satellite attitude system that satisfies the nonlinear mixed H2 / H∞ control problem are obtained, including:

[0117] The kinematic and dynamic parameters of the flexible satellite attitude control process are determined, the given parameters required for solving the solvability conditions are determined, and the solvability conditions are solved by Matlab / SOSTOOLS.

[0118] In this embodiment, the kinematic and dynamic parameters in the attitude control process of the flexible satellite are directly adopted from the existing technology.

[0119] The kinematic and dynamic parameters during the attitude control of the flexible satellite are as follows:

[0120] , , , , , , , , , .

[0121] The given parameters required to solve the solvability conditions are as follows:

[0122] set up and is a 2nd order polynomial matrix, and are all constant matrices, and given , , , , , and , the nonlinear mixed H2 / H∞ attitude control problem based on the observer can be solved by Matlab / SOSTOOLS toolbox.

[0123] After that, the nonlinear hybrid H2 / H∞ attitude control problem based on the observer can be solved by Matlab / SOSTOOLS toolbox. The solvability conditions can be solved by Matlab / SOSTOOLS. Figure 2 The calculation result of .

[0124] Further, after step S4, the following steps are included:

[0125] S5, build a flexible satellite attitude control simulation platform through Matlab / Simulink to verify the flexible satellite attitude control effect of the obtained nonlinear dimensionality reduction observer and state feedback controller.

[0126] In this step, a flexible satellite attitude control simulation platform is built through Matlab / Simulink. Figure 3 shown.

[0127] Experimental data

[0128] In order to verify the feasibility and effectiveness of the obtained method, this embodiment takes an existing flexible satellite attitude system as an example to perform numerical simulation research and analysis, and the relevant parameters are shown in S4 above.

[0129] Finally, consider the satellite needs to perform a certain task For fast attitude maneuvers, the corresponding initial values ​​are:

[0130]

[0131] And the flexible satellite attitude system is also subject to the following Figure 4 The disturbance shown Impact:

[0132] .

[0133] The flexible satellite nonlinear hybrid H2 / H ∞ Control methods and nonlinear H of existing flexible satellites ∞ The control methods were compared.

[0134] refer to Figure 5 , Figure 5 is the Rodrigues parameter vector From the trajectory, it can be seen that the method provided by the present application tends to be stable faster. Figure 5 The extreme value in trajectory 1 is smaller, Figure 5 Trajectory 3 in the figure can become stable in about 200s.

[0135] refer to Figure 6 , Figure 6 is the attitude angular velocity From the trajectory, it can be seen that the method provided by the present application tends to be stable faster, and the extreme values ​​of the three curves obtained by the method provided by the present application are smaller and tend to be stable faster.

[0136] refer to Figure 7-8 , Figure 7 for and The trajectory of Figure 8 For and The trajectory of the derivation, in formula (2), the value of m in this embodiment is 2, so There are two values, for It can be seen that the curve extreme value obtained by the method provided in this application is smaller and converges faster, converging in about 100 seconds.

[0137] In summary, compared with the nonlinear H ∞ The control method provided in this embodiment is a nonlinear mixed H2 / H ∞ The control method achieves smaller overshoot and faster convergence speed when completing attitude maneuvers, and also performs better in suppressing flexible appendage vibration and external disturbances.

[0138] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0139] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0140] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0141] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0142] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms should not be understood as necessarily being directed to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

Claims

1. A nonlinear hybrid H2 / H2 based on an observer for flexible satellites ∞ The control method is characterized by: The following steps are involved: S1, establish the state space model of the flexible satellite attitude system with external disturbances and unmeasurable states; The kinematic and dynamic equations of the flexible satellite attitude are as follows: Kinematics for ; The kinetic equation is ; in is the Rodrigues parameter vector, , is the moment of inertia matrix, is the attitude angular velocity vector, for The corresponding cross product matrix is, is the rigid-flex coupling coefficient matrix, is the flexible mode coordinate vector ( represents the truncated mode order), is the modal damping matrix, is the natural frequency matrix, and are the control and disturbance torques, respectively, is a zero matrix; Introducing auxiliary variables into the attitude kinematics and dynamics equations of flexible satellites and , , , The state space model is: ， in is the system status, and are the unmeasurable and measurable sub-states, respectively. ; and is the controlled output; , and They are external disturbance, control input and measurement output respectively; , , , , , , , , , is a known matrix; , ; ; and , ( ) is a known matrix; , , , , , , Respectively dimensional real vector set, dimensional real vector set, dimensional real vector set, 3-dimensional real vector set, 6-dimensional real vector set, dimensional real vector set, identity matrix; , , , are all known constants; S2, designing a nonlinear dimension reduction observer and a state feedback controller to obtain a closed-loop system based on the nonlinear dimension reduction observer and the state feedback controller with external disturbances and unmeasurable states; Designing the nonlinear dimension reduction observer and state feedback controller involves: S2.1, establishing the nonlinear dimension reduction observer according to the input signal and the output signal of the state space model; S2.2, establishing the state feedback controller according to the estimation information of the nonlinear dimensionality reduction observer; S3, generating a nonlinear hybrid H2 / H2 of the flexible satellite attitude system through the closed-loop system ∞ The control problem is to convert the nonlinear mixed H2 / H ∞ The control problem is transformed into an SOS convex optimization problem; S4, using Matlab / SOSTOOLS to solve the SOS convex optimization problem, we obtain the nonlinear mixed H2 / H ∞ A nonlinear dimension reduction observer and a state feedback controller are provided for the control problem, and the flexible satellite is controlled by the nonlinear dimension reduction observer and the state feedback controller.

2. A nonlinear hybrid H2 / H2 based flexible satellite according to claim 1 ∞ The control method is characterized by: The state space model of the flexible satellite attitude system with external disturbances and unmeasurable states includes: Auxiliary variables are introduced into the flexible satellite attitude kinematics and dynamics equations, and the flexible satellite attitude kinematics and the dynamics equations are expressed as the state space model.

3. A nonlinear hybrid H2 / H2 based flexible satellite according to claim 1 ∞ The control method is characterized by: The closed-loop system based on the nonlinear dimension reduction observer and the state feedback controller with external disturbance and unmeasurable partial states includes: S2.3, applying the state feedback controller and the nonlinear dimension reduction observer to the state space model to obtain a closed-loop system with external disturbances and unmeasurable states.

4. A nonlinear hybrid H2 / H2 based flexible satellite observer according to claim 1 ∞ The control method is characterized by: The nonlinear hybrid H2 / H2 of the flexible satellite attitude system is generated by the closed-loop system. ∞ Control issues include: The state feedback controller based on the nonlinear dimension reduction observer satisfies the following conditions: when When , the closed-loop system is asymptotically stable at the zero equilibrium point; when hour, ,in is an upper bound of a performance indicator; Given a constant ,when satisfy And the initial state When, from arrive of Gain ; in, For external interference, is the controlled output, For time, It is the H2 control performance index, Gain is H ∞ Control performance indicators.

5. A nonlinear hybrid H2 / H2 based flexible satellite observer according to claim 1 ∞ The control method is characterized by: The nonlinear mixture H2 / H ∞ The control problem is transformed into an SOS convex optimization problem including: According to the structural characteristics of the flexible satellite attitude, the Lyapunov stability theory is used to establish a nonlinear hybrid H2 / H based on the observer. ∞ The conditions for the posture control problem to exist; The nonlinear mixed H2 / H ∞ The existence conditions of the attitude control problem are transformed into a SOS convex optimization problem.

6. A nonlinear hybrid H2 / H2 based flexible satellite observer according to claim 5 ∞ The control method is characterized by: The nonlinear mixed H2 / H ∞ The existence conditions of the attitude control problem are transformed into the SOS convex optimization problem, including: The nonlinear mixed H2 / H is derived by SOS and S-procedure methods. ∞ Solvability conditions for the attitude control problem.

7. A nonlinear hybrid H2 / H2 based flexible satellite according to claim 6 ∞ The control method is characterized by: Matlab / SOSTOOLS is used to solve the SOS convex optimization problem and obtains the nonlinear mixed H2 / H ∞ The solutions of the nonlinear reduced-dimensionality observer and state feedback controller to the control problem include: The kinematic and dynamic parameters of the flexible satellite attitude control process are determined, the given parameters required for solving the solvability conditions are determined, and the solvability conditions are solved by Matlab / SOSTOOLS.

8. The observer-based flexible satellite nonlinear hybrid H2 / H2 according to claim 1 ∞ The control method is characterized by: After step S4, the following steps are included: S5, build a flexible satellite attitude control simulation platform through Matlab / Simulink to verify the flexible satellite attitude control effect of the obtained nonlinear dimensionality reduction observer and state feedback controller.

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