CN102749852A

CN102749852A - Fault-tolerant anti-interference control method for multisource interference system

Info

Publication number: CN102749852A
Application number: CN2012102586742A
Authority: CN
Inventors: 郭雷; 乔建忠; 李小凤; 曹松银; 雷燕婕
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2012-07-24
Filing date: 2012-07-24
Publication date: 2012-10-24
Anticipated expiration: 2032-07-24
Also published as: CN102749852B

Abstract

Fault-tolerant and anti-jamming control method for multi-source jamming systems, for multi-source jamming systems with time-varying faults, modelable disturbances and unmodelable random disturbances, a fault-tolerant and anti-jamming controller is designed; first, a fault diagnosis observer is designed to estimate And offset the time-varying faults in the system; secondly, design a disturbance observer to estimate and offset the modelable disturbance in the multi-source disturbance system; thirdly, design a robust H _∞ state feedback controller to suppress the unmodelable disturbance in the multi-source disturbance system Random disturbance, fault estimation error and disturbance estimation error; finally, based on fault diagnosis observer, disturbance observer and robust H _∞ state feedback controller, a fault-tolerant and anti-disturbance controller is designed; this method has strong anti-disturbance and remarkable fault-tolerant performance , High reliability, etc., can be used in the attitude control subsystem in the field of aviation and aerospace.

Description

Fault Tolerance and Anti-jamming Control Method for Multi-source Jamming System

技术领域 technical field

本发明涉及一种容错抗干扰控制方法，特别是一种多源干扰系统的容错抗干扰控制方法，该方法可用于多源干扰系统的故障诊断与容错抗干扰控制，如卫星、导弹和飞机等航空航天系统的姿态控制子系统。The invention relates to a fault-tolerant and anti-jamming control method, in particular to a fault-tolerant and anti-jamming control method for a multi-source jamming system. The method can be used for fault diagnosis and fault-tolerant anti-jamming control of a multi-source jamming system, such as satellites, missiles and aircraft, etc. Attitude control subsystem for aerospace systems.

背景技术 Background technique

近年来，随着航空航天技术的发展，飞行器的结构和任务需求日益复杂，对控制精度和稳定度的要求也越来越高，导致飞行器的故障发生概率也愈来愈高。例如，有学者通过对1990-2001年间国内外成功发射的764个航天器进行了统计和分析，结果发现121个出现故障，占航天器总数的15.8%。飞行器工作的可靠性、在轨飞行的可维护性和有效性成为了航空航天领域的一个研究重点。而容错控制及故障检测与诊断为提高系统的可靠性、可维护性和有效性开辟了一条新途径。另外，伴随着飞行器结构和任务需求的日益复杂，影响飞行器姿态控制精度和稳定度的因素越来越多，主要归纳为以下几点：外部环境干扰力矩、星体内部执行机构飞轮的振动、飞轮的摩擦、喷气动量卸载、敏感器测量噪声及系统模型的不确定性等。In recent years, with the development of aerospace technology, the structure and task requirements of aircraft have become increasingly complex, and the requirements for control accuracy and stability have become higher and higher, resulting in an increasing probability of aircraft failure. For example, some scholars have conducted statistics and analysis on 764 spacecraft successfully launched at home and abroad during 1990-2001, and found that 121 of them had malfunctioned, accounting for 15.8% of the total number of spacecraft. The reliability of aircraft work, the maintainability and effectiveness of on-orbit flight have become a research focus in the field of aerospace. Fault-tolerant control and fault detection and diagnosis open up a new way to improve the reliability, maintainability and effectiveness of the system. In addition, with the increasing complexity of aircraft structure and mission requirements, there are more and more factors affecting the accuracy and stability of aircraft attitude control, which are mainly summarized as the following points: external environmental disturbance torque, vibration of the flywheel of the actuator inside the star body, and the vibration of the flywheel. Friction, jet momentum unloading, sensor measurement noise and uncertainty of the system model, etc.

针对上述一系列问题，当系统中存在时变能量有界故障但是没有干扰时，国内外学者提出了很多有效的方法并取得了一定的效果。但是考虑到实际系统中干扰无时不在、无处不在，单一的考虑故障就会带来一系列的问题，特别是不能保证系统的姿态控制精度和稳定度。在此基础上，系统中同时存在时变故障和干扰的情况成为了一个研究方向，国内外学者提出了一系列的解决方法，例如H_∞优化技术、基于内模结构的H_∞控制器等。但是现有方法在设计观测器估计故障的基础上，将干扰看作范数有界量进行抑制，这样的处理方法有以下两方面的劣势：第一，将系统中的所有干扰看作范数有界量进行抑制，即将系统中存在的干扰看作一个整体进行处理，忽略了系统内部分可建模干扰的信息或者通过物理测量手段能获得的干扰信息，没有充分利用系统资源，难以实现高精度的姿态控制；第二，将系统中的所有干扰看作范数有界量进行抑制，势必会增加系统的保守性，同样难以实现高精度的姿态控制。For the above series of problems, when there are time-varying energy bounded faults in the system but no interference, domestic and foreign scholars have proposed many effective methods and achieved certain results. However, considering that interference is present everywhere and everywhere in the actual system, a single consideration of failure will bring a series of problems, especially the attitude control accuracy and stability of the system cannot be guaranteed. On this basis, the simultaneous existence of time-varying faults and disturbances in the system has become a research direction. Scholars at home and abroad have proposed a series of solutions, such as H _∞ optimization technology, H _∞ controller based on internal model structure, etc. However, based on the design of the observer to estimate the fault, the existing method treats the disturbance as a norm bounded quantity for suppression. This processing method has the following two disadvantages: First, all disturbances in the system are regarded as a norm Bounded quantities are suppressed, that is, the interference existing in the system is treated as a whole, and the interference information that can be modeled in the system or the interference information that can be obtained through physical measurement methods are ignored. The system resources are not fully utilized, and it is difficult to achieve high Accurate attitude control; Second, treating all disturbances in the system as norm-bounded quantities for suppression will inevitably increase the conservatism of the system, and it is also difficult to achieve high-precision attitude control.

发明内容 Contents of the invention

本发明的技术解决问题是：针对多源干扰系统，克服现有技术的不足，提供一种具有干扰抵消和抑制性能的容错抗干扰控制方法，解决多源干扰系统的干扰抵消、干扰抑制和故障诊断及容错控制问题，提高系统的控制精度与稳定度。The technical problem of the present invention is: aiming at the multi-source interference system, overcoming the deficiencies of the prior art, providing a fault-tolerant anti-interference control method with interference cancellation and suppression performance, and solving the interference cancellation, interference suppression and failure of the multi-source interference system Diagnose and fault-tolerant control problems, improve the control accuracy and stability of the system.

本发明的技术解决方案为：一种多源干扰系统的容错抗干扰控制方法，其特征在于包括以下步骤：The technical solution of the present invention is: a fault-tolerant and anti-interference control method for a multi-source interference system, which is characterized in that it includes the following steps:

首先，设计故障诊断观测器估计并抵消系统中的时变故障；其次，设计干扰观测器估计并抵消多源干扰系统中的可建模干扰；再次，设计鲁棒H_∞状态反馈控制器抑制多源干扰系统中的不可建模随机干扰、故障估计误差和干扰估计误差；最后，基于故障诊断观测器、干扰观测器和鲁棒H_∞状态反馈控制器，设计容错抗干扰控制器；具体步骤如下：First, a fault diagnosis observer is designed to estimate and offset time-varying faults in the system; second, a disturbance observer is designed to estimate and offset modelable disturbances in a multi-source interference system; third, a robust H _∞ state feedback controller is designed to suppress multiple Unmodelable random disturbances, fault estimation errors and disturbance estimation errors in the source-interference system; finally, based on the fault diagnosis observer, disturbance observer and robust H _∞ state feedback controller, a fault-tolerant and anti-disturbance controller is designed; the specific steps are as follows :

第一步，搭建含有多源干扰系统的动力学模型，并写成状态空间表达式The first step is to build a dynamic model of the system with multi-source interference and write it as a state space expression

针对含有时变故障、可建模干扰和不可建模随机干扰的多源干扰系统，搭建其系统动力学模型，并写成状态空间表达式如下：For a multi-source disturbance system with time-varying faults, modelable disturbances and non-modelable random disturbances, a system dynamics model is built, and the state space expression is written as follows:

$\overset{\cdot &Center Dot;}{x x} ((t t)) + + Ef Ef ((\overset{\cdot &Center Dot;}{x x},, t t)) = = Ax Ax ((t t)) + + {B B}_{11} ((u u ((t t)) + + {d d}_{11} ((t t)) + + F f ((t t)))) + + {B B}_{22} {d d}_{22} ((t t))$

其中，x(t)为多源干扰系统状态变量，u(t)为控制输入，d₁(t)为可建模干扰，F(t)为时变故障，d₂(t)为不可建模随机干扰，A,E,B₁和B₂为已知维数的矩阵，

为系统非线性项且满足Lipschitz条件，外部模型描述干扰d₁(t)由下列外部干扰模型∑₁表示：Among them, x(t) is the state variable of the multi-source disturbance system, u(t) is the control input, d ₁ (t) is the disturbance that can be modeled, F(t) is the time-varying fault, and d ₂ (t) is the non-buildable Modular random interference, A, E, B ₁ and B ₂ are matrices of known dimensions,

is a nonlinear item of the system and satisfies the Lipschitz condition, the external model describes the disturbance d ₁ (t) by the following external disturbance model Σ ₁ :

${Σ Σ}_{11} : : \{\begin{matrix} {d d}_{11} ((t t)) = = Vw Vw ((t t)) \\ \overset{\cdot &Center Dot;}{w w} ((t t)) = = Ww w ((t t)) + + {B B}_{33} δ δ ((t t)) \end{matrix}$

其中，w(t)为可建模干扰模型的状态变量，V为可建模干扰模型的输出矩阵，W表示可建模干扰模型的系统阵，δ(t)为能量有界的不可建模随机干扰，B₃为不可建模随机干扰的增益阵。where w(t) is the state variable of the modelable disturbance model, V is the output matrix of the modelable disturbance model, W represents the system matrix of the modelable disturbance model, and δ(t) is the non-modelable Random interference, B ₃ is the gain array of random interference that cannot be modeled.

第二步，设计故障诊断观测器The second step is to design the fault diagnosis observer

针对多源干扰系统中的时变故障F(t)，设计故障诊断观测器对其进行实时估计，并求得估计值

进而得到故障估计误差

Aiming at the time-varying fault F(t) in the multi-source interference system, a fault diagnosis observer is designed to estimate it in real time and obtain the estimated value

Then get the fault estimation error

第三步，设计干扰观测器The third step is to design the disturbance observer

针对多源干扰系统中的可建模干扰d₁(t)，设计干扰观测器对其进行实时估计，并求得估计值

进而得到干扰估计误差为w(t)的估计值。For the modelable interference d ₁ (t) in the multi-source interference system, design an interference observer to estimate it in real time, and obtain the estimated value

Then get the interference estimation error is the estimated value of w(t).

第四步，设计鲁棒H_∞状态反馈控制器The fourth step is to design a robust H _∞ state feedback controller

针对多源干扰系统中的不可建模随机干扰d₂(t)、故障估计误差e_F(t)和干扰估计误差e_w(t)，设计鲁棒H_∞状态反馈控制器对其进行抑制，控制器结构如下：Aiming at the unmodelable random disturbance d ₂ (t), fault estimation error e _F (t) and disturbance estimation error e _w (t) in the multi-source interference system, a robust H _∞ state feedback controller is designed to suppress it, The controller structure is as follows:

u_f(t)＝Mx(t)u _f (t) = Mx (t)

其中，u_f(t)为鲁棒H_∞状态反馈控制输入，M为待定状态反馈控制器增益阵。Among them, u _f (t) is the robust H _∞ state feedback control input, and M is the undetermined state feedback controller gain matrix.

第五步，设计容错抗干扰控制器The fifth step is to design a fault-tolerant and anti-jamming controller

设计容错抗干扰控制器，对系统中的时变故障F(t)和可建模干扰d₁(t)进行抵消，不可建模随机干扰d₂(t)、故障估计误差e_F(t)和干扰估计误差e_w(t)进行抑制，容错抗干扰控制器结构如下：Design a fault-tolerant anti-disturbance controller to offset the time-varying fault F(t) in the system and the modelable disturbance d ₁ (t), while the random disturbance d ₂ (t) and the fault estimation error e _F (t) cannot be modeled and interference estimation error e _w (t) to suppress, the fault-tolerant anti-interference controller structure is as follows:

$u u ((t t)) = = {u u}_{f f} ((t t)) - - \overset{^^}{F f} ((t t)) - - {\overset{^^}{d d}}_{11} ((t t))$

则多源干扰系统可表示为：Then the multi-source interference system can be expressed as:

$\overset{\cdot &Center Dot;}{x x} ((t t)) + + Ef Ef ((\overset{\cdot &Center Dot;}{x x},, t t)) = = ((A A + + {B B}_{11} M m)) x x ((t t)) + + {B B}_{11} V V {e e}_{w w} ((t t)) + + {B B}_{11} {e e}_{F f} ((t t)) + + {B B}_{22} {d d}_{22} ((t t))$

整理可建模干扰模型的系统估计误差方程和时变故障的系统估计误差方程如下：The system estimation error equation of the modelable disturbance model and the system estimation error equation of time-varying fault are sorted out as follows:

${\overset{\cdot \cdot}{e e}}_{w w} ((t t)) = = ((W W + + {LB LB}_{11} V V)) {e e}_{w w} ((t t)) + + {LB LB}_{11} {e e}_{F f} ((t t)) + + {LB LB}_{22} {d d}_{22} ((t t)) + + {B B}_{33} δ δ ((t t))$

${\overset{\cdot \cdot}{e e}}_{F f} ((t t)) = = {KB KB}_{11} V V {e e}_{w w} ((t t)) + + {KB KB}_{11} {e e}_{F f} ((t t)) + + {KB KB}_{22} {d d}_{22} ((t t)) + + \overset{\cdot &Center Dot;}{F f} ((t t))$

联列上述多源干扰系统、时变故障的系统估计误差方程和可建模干扰的系统估计误差方程得到闭环系统：Combine the above multi-source interference system, the system estimation error equation of time-varying fault and the system estimation error equation of modelable interference to obtain the closed-loop system:

$\{\begin{matrix} (\begin{matrix} \overset{\cdot &Center Dot;}{x x} ((t t)) \\ {\overset{\cdot &Center Dot;}{e e}}_{w w} ((t t)) \\ {\overset{\cdot \cdot}{e e}}_{F f} ((t t)) \end{matrix}) = = (\begin{matrix} A A + + {B B}_{11} M m & {B B}_{11} V V & {B B}_{11} \\ 00 & W W + + {LB LB}_{11} V V & {LB LB}_{11} \\ 00 & {KB KB}_{11} V V & {KB KB}_{11} \end{matrix}) (\begin{matrix} x x ((t t)) \\ {e e}_{w w} ((t t)) \\ {e e}_{F f} ((t t)) \end{matrix}) + + (\begin{matrix} {B B}_{22} \\ {LB LB}_{22} \\ {KB KB}_{22} \end{matrix}) {d d}_{22} ((t t)) + + (\begin{matrix} 00 \\ {B B}_{33} \\ 00 \end{matrix}) δ δ ((t t)) + + (\begin{matrix} 00 \\ 00 \\ 11 \end{matrix}) \overset{\cdot \cdot}{F f} ((t t)) - - (\begin{matrix} E E. \\ 00 \\ 00 \end{matrix}) f f ((\overset{\cdot \cdot}{x x} ((t t)))) \\ {z z}_{\infty \infty} ((t t)) = = [\begin{matrix} {C C}_{00} & {C C}_{11} & {C C}_{22} \end{matrix}] (\begin{matrix} x x ((t t)) \\ {e e}_{w w} ((t t)) \\ {e e}_{F f} ((t t)) \end{matrix}) \end{matrix}$

其中，z_∞(t)为H_∞性能参考输出，[C₀C₁C₂]为H_∞性能可调输出矩阵。Among them, z _∞ (t) is the H _∞ performance reference output, [C ₀ C ₁ C ₂ ] is the H _∞ performance adjustable output matrix.

第六步，增益矩阵求解The sixth step is to solve the gain matrix

利用凸优化算法求解多源干扰系统的容错抗干扰控制器增益阵；给定初始值x(0)、e_w(0)和e_F(0)，可调输出矩阵[C₀C₁C₂]，非线性权重参数λ，干扰抑制度γ₁、γ₂和γ₃，求解以下凸优化问题：Using the convex optimization algorithm to solve the gain matrix of the fault-tolerant anti-jamming controller of the multi-source jamming system; given the initial values x(0), e _w (0) and e _F (0), the adjustable output matrix [C ₀ C ₁ C ₂ ], nonlinear weight parameter λ, interference suppression degree γ ₁ , γ ₂ and γ ₃ , to solve the following convex optimization problem:

$min min (\begin{matrix} (\begin{matrix} {x x}^{T T} ((00)) & {e e}^{T T} ((00)) \end{matrix}) & (\begin{matrix} {P P}_{11} \\ {P P}_{22} \end{matrix}) & {(\begin{matrix} {x x}^{T T} ((00)) & {e e}^{T T} ((00)) \end{matrix})}^{T T} \end{matrix})$

$Φ Φ = = [\begin{matrix} {Φ Φ}_{1111} & {B B}_{11} G G & - - E E. & 00 & {B B}_{22} & 00 & {Φ Φ}_{1818} & {P P}_{11} {C C}_{00}^{T T} \\ * * & {Φ Φ}_{22 twenty two} & 00 & {P P}_{22} {H h}_{11} & {R R}_{22} {B B}_{22} & {P P}_{22} {H h}_{22} & λ λ {((U u {B B}_{11} G G))}^{T T} & {C C}^{T T} \\ * * & * * & - - {λ λ}^{22} I I & 00 & 00 & 00 & λ λ {((UE UE))}^{T T} & 00 \\ * * & * * & * * & - - {γ γ}_{11}^{22} & 00 & 00 & 00 & 00 \\ * * & * * & * * & * * & - - {γ γ}_{22}^{22} & 00 & λ λ {(({UB UB}_{22}))}^{T T} & 00 \\ * * & * * & * * & * * & * * & - - {γ γ}_{33}^{22} I I & 00 & 00 \\ * * & * * & * * & * * & * * & * * & - - I I & 00 \\ * * & * * & * * & * * & * * & * * & * * & - - I I \end{matrix}]$

其中:e(0)＝[e_w(0)e_F(0)]^T,Φ₁₁＝(AP₁+B₁R₁)+(AP₁+B₁R₁)^T,Φ₂₂＝(P₂W₁+R₂B₁G)+(P₂W₁+R₂B₁G)^T,Φ₁₈＝λ(AP₁+B₁R₁)^T,C＝[C₁C₂],G＝[EI],H₁＝[B₃ 0]^T，H₂＝[0 1]^T；符号*表示对称矩阵中相应部分的对称块，求解得P₁、P₂、R₁和R₂，则干扰观测器和故障诊断观测器增益阵为 $[\begin{matrix} L \\ K \end{matrix}] = P_{2}^{- 1} R_{2},$ 状态反馈控制器增益阵为 Among them: e(0)＝[e _w (0)e _F (0)] ^T ,Φ ₁₁ ＝(AP ₁ +B ₁ R ₁ )+(AP ₁ +B ₁ R ₁ ) ^T ,Φ ₂₂ ＝(P ₂ W ₁ +R ₂ B ₁ G)+(P ₂ W ₁ +R ₂ B ₁ G) ^T ,Φ ₁₈ ＝λ(AP ₁ +B ₁ R ₁ ) ^T ,C＝[C ₁ C ₂ ],G =[EI], H ₁ =[B ₃ 0] ^T , H ₂ =[0 1] ^T ; the symbol * represents the symmetric block of the corresponding part in the symmetric matrix, and P ₁ , P ₂ , R ₁ and R ₂ can be obtained by solving, Then the gain matrix of disturbance observer and fault diagnosis observer is $[\begin{matrix} L \\ K \end{matrix}] = P_{2}^{- 1} R_{2},$ The state feedback controller gain matrix is

所述步骤2中的故障诊断观测器结构如下：The structure of the fault diagnosis observer in the step 2 is as follows:

$\{\begin{matrix} \overset{^^}{F f} ((t t)) = = τ τ - - p p ((x x)) \\ \overset{\cdot &Center Dot;}{τ τ} = = {KB KB}_{11} ((τ τ - - p p ((x x)))) + + K K [[Ax Ax ((t t)) + + {B B}_{11} u u ((t t)) + + {B B}_{11} {\overset{^^}{d d}}_{11} ((t t)) - - Ef Ef ((\overset{\cdot &Center Dot;}{x x} ((t t))))]] \end{matrix}$

其中，K为待定的故障诊断观测器增益矩阵，ε(t)为辅助变量。in, K is the undetermined gain matrix of the fault diagnosis observer, and ε(t) is the auxiliary variable.

所述步骤3中的干扰观测器结构如下：The interference observer structure in the step 3 is as follows:

$\{\begin{matrix} {\overset{^^}{d d}}_{11} ((t t)) = = V V \overset{^^}{w w} ((t t)) \\ \overset{^^}{w w} ((t t)) = = v v ((t t)) - - Lx Lx ((t t)) \\ \overset{\cdot \cdot}{v v} ((t t)) = = ((W W + + {LB LB}_{11} V V)) ((v v ((t t)) - - Lx Lx ((t t)))) + + L L [[Ax Ax ((t t)) + + {B B}_{11} u u ((t t)) + + {B B}_{11} \overset{^^}{F f} ((t t)) - - Ef Ef ((\overset{\cdot &Center Dot;}{x x},, t t))]] \end{matrix}$

其中，v(t)为辅助变量，L为待定的干扰观测器增益矩阵，V为可建模干扰模型的输出矩阵，W表示可建模干扰模型的系统阵。Among them, v(t) is an auxiliary variable, L is the undetermined interference observer gain matrix, V is the output matrix of the modelable interference model, and W represents the system matrix of the modelable interference model.

本发明与现有技术相比的优点在于：The advantage of the present invention compared with prior art is:

（1）本发明的多源干扰系统的容错抗干扰控制方法是一种复合分层抗干扰控制方法，控制器的前馈部分由故障诊断观测器和干扰观测器组成，用于估计和抵消系统中的时变故障和可建模干扰，控制器的反馈部分由鲁棒H_∞状态反馈控制器构成，设计的控制器使系统具有更为精细的故障诊断与容错控制能力。(1) The fault-tolerant and anti-interference control method of the multi-source interference system of the present invention is a compound layered anti-interference control method. The feed-forward part of the controller is composed of a fault diagnosis observer and a disturbance observer, which are used to estimate and offset the system For time-varying faults and modelable disturbances, the feedback part of the controller is composed of a robust H _∞ state feedback controller. The designed controller enables the system to have more sophisticated fault diagnosis and fault-tolerant control capabilities.

（2）本发明对干扰的鲁棒性强，在同时存在变化率有界的时变故障、可建模干扰和不可建模随机干扰等多源干扰的情况下，所述方法中的故障诊断观测器可以估计并抵消时变故障，干扰观测器可以估计并抵消可建模干扰，鲁棒H_∞状态反馈控制器抑制不可建模随机干扰、故障估计误差和干扰估计误差，克服了现有方法将干扰看作范数有界量进行抑制带来的保守性大的问题。(2) The present invention has strong robustness to interference. In the case of multi-source interference such as time-varying fault with bounded rate of change, modelable interference, and unmodelable random interference, the fault diagnosis in the method The observer can estimate and offset time-varying faults, the disturbance observer can estimate and offset modelable disturbances, and the robust H _∞ state feedback controller suppresses unmodelable random disturbances, fault estimation errors, and disturbance estimation errors, overcoming existing methods Consider the interference as a norm-bounded quantity to suppress the conservative problem.

附图说明 Description of drawings

图1为本发明一种基于多源干扰系统的容错抗干扰控制方法的设计流程图。Fig. 1 is a design flowchart of a fault-tolerant and anti-interference control method based on a multi-source interference system according to the present invention.

具体实施方式 Detailed ways

如图1所示，本发明具体实现步骤如下（以下以卫星姿态确定与控制系统为例来说明方法的具体实现）：As shown in Figure 1, the specific implementation steps of the present invention are as follows (the following takes the satellite attitude determination and control system as an example to illustrate the specific implementation of the method):

1、搭建含有多源干扰系统的动力学模型，并写成状态空间表达式1. Build a dynamic model containing multi-source interference system and write it as a state space expression

当微纳卫星本体坐标系和轨道坐标系之间的欧拉角很小时，可以得到如下的卫星线性化姿态动力学和运动学模型：When the Euler angle between the micro-nano-satellite body coordinate system and the orbital coordinate system is small, the following linearized attitude dynamics and kinematics model of the satellite can be obtained:

$\{\begin{matrix} {J J}_{11} \overset{\cdot \cdot \cdot &Center Dot;}{φ φ} - - n no (({J J}_{11} - - {J J}_{22} + + {J J}_{33})) \overset{\cdot &Center Dot;}{ψ ψ} + + 44 {n no}^{22} (({J J}_{22} - - {J J}_{33})) φ φ = = {u u}_{11} + + {T T}_{d d 11} \\ {J J}_{22} \overset{\cdot &Center Dot; \cdot &Center Dot;}{θ θ} + + 33 {n no}^{22} (({J J}_{11} - - {J J}_{33})) θ θ = = {u u}_{22} + + F f ((t t)) + + {T T}_{d d 22} \\ {J J}_{33} \overset{\cdot &Center Dot; \cdot \cdot}{ψ ψ} + + n no (({J J}_{11} - - {J J}_{22} + + {J J}_{33})) \overset{\cdot &Center Dot;}{φ φ} + + {n no}^{22} (({J J}_{22} - - {J J}_{11})) ψ ψ = = {u u}_{33} + + {T T}_{d d 33} \end{matrix}$

上式中，J₁,J₂,J₃分别为三轴的转动惯量，n为卫星轨道角速度，φ，θ，ψ分别为卫星本体坐标系和轨道坐标系之间的三轴欧拉角；

分别为三轴欧拉角速率；

分别为三轴欧拉角加速度；u₁,u₂,u₃分别为三轴控制力矩；F(t)为时变故障，T_d1,T_d2,T_d3分别为三轴的干扰力矩(包括由于敏感器或者执行机构故障带来的干扰力矩)；In the above formula, J ₁ , J ₂ , J ₃ are the moments of inertia of the three axes respectively, n is the orbital angular velocity of the satellite, φ, θ, ψ are the three-axis Euler angles between the satellite body coordinate system and the orbit coordinate system respectively;

are the three-axis Euler angle rates;

are three-axis Euler angular accelerations; u ₁ , u ₂ , u ₃ are three-axis control torques; F(t) is time-varying fault; T _d1 , T _d2 , T _d3 are three-axis disturbance torques (including Disturbance torque due to sensor or actuator failure);

微纳卫星模型的不确定性主要来自转动惯量的不确定性，考虑转动惯量不确定性，从姿态动力学模型中提取惯量矩阵，上式可以转化为如下形式：The uncertainty of the micro-nano satellite model mainly comes from the uncertainty of the moment of inertia. Considering the uncertainty of the moment of inertia, the inertia matrix is extracted from the attitude dynamics model. The above formula can be transformed into the following form:

$((M m + + ΔM ΔM)) \overset{\cdot \cdot \cdot \cdot}{p p} ((t t)) + + ((C C + + ΔC ΔC)) \overset{\cdot &Center Dot;}{p p} ((t t)) + + ((S S + + ΔS ΔS)) p p ((t t)) = = {B B}_{u u} ((u u ((t t)) + + {d d}_{11} ((t t)) + + F f ((t t)))) + + {B B}_{w w} {d d}_{22} ((t t))$

其中状态变量p(t)＝[φ，θ，ψ]^T为三轴欧拉角，

是三轴欧拉角速度，

是三轴欧拉角加速度，d₁(t)为可建模干扰，d₂(t)为能量有界的不可建模随机（即L₂范数

有界）干扰，B_u为控制输入分配矩阵，B_w为不可建模随机干扰输入分配矩阵，M，C，S为已知转动惯量，ΔM，ΔC，ΔS为由于扰动带来的不确定性转动惯量，

M = [\begin{matrix} I_{1} & 0 & 0 \\ 0 & I_{2} & 0 \\ 0 & 0 & I_{3} \end{matrix}],

C = [\begin{matrix} 0 & 0 & - ω (I_{1} - I_{2} + I_{3}) \\ 0 & 0 & 0 \\ ω (I_{1} - I_{2} + I_{3}) & 0 & 0 \end{matrix}],

S = [\begin{matrix} 4 ω^{2} (I_{2} - I_{3}) & 0 & 0 \\ 0 & 3 ω^{2} (I_{1} - I_{3}) & 0 \\ 0 & 0 & - ω^{2} (I_{1} - I_{2}) \end{matrix}]

B_{u} = B_{w} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}],

将上式进行整理转换为状态空间模型如下式所示：Among them, the state variable p(t)=[φ, θ, ψ] ^T is the three-axis Euler angle,

is the three-axis Euler angular velocity,

is the three-axis Euler angular acceleration, d ₁ (t) is a modelable disturbance, and d ₂ (t) is an energy-bounded non-modelable random (that is, the L ₂ norm

Bounded) disturbance, _Bu is the control input allocation matrix, B _w is the unmodelable random disturbance input allocation matrix, M, C, S are the known moments of inertia, ΔM, ΔC, ΔS are the uncertainties due to the disturbance Moment of inertia,

m = [\begin{matrix} I_{1} & 0 & 0 \\ 0 & I_{2} & 0 \\ 0 & 0 & I_{3} \end{matrix}],

C = [\begin{matrix} 0 & 0 & - ω (I_{1} - I_{2} + I_{3}) \\ 0 & 0 & 0 \\ ω (I_{1} - I_{2} + I_{3}) & 0 & 0 \end{matrix}],

S = [\begin{matrix} 4 ω^{2} (I_{2} - I_{3}) & 0 & 0 \\ 0 & 3 ω^{2} (I_{1} - I_{3}) & 0 \\ 0 & 0 & - ω^{2} (I_{1} - I_{2}) \end{matrix}]

B_{u} = B_{w} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}],

The above formula is sorted and transformed into a state space model as shown in the following formula:

$\overset{\cdot \cdot}{x x} ((t t)) + + Ef Ef ((\overset{\cdot \cdot}{x x},, t t)) = = Ax Ax ((t t)) + + {B B}_{11} ((u u ((t t)) + + {d d}_{11} ((t t)) + + F f ((t t)))) + + {B B}_{22} {d d}_{22} ((t t))$

其中，多源干扰系统状态变量 $x (t) = {[\begin{matrix} {&Integral;}_{0}^{t} e_{q} (τ) dτ & e_{q} (t) & {\overset{\cdot}{e}}_{q} \end{matrix}, (t)]}^{T},$ e_q(t)＝p(t)-p_p(t)，p_p(t)为参考轨迹信号，u(t)为控制输入，A,E,B₁和B₂为已知维数的矩阵， $A = [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & - M^{- 1} S & - M^{- 1} C \end{matrix}],$ $E = [\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ M^{- 1} ΔS & M^{- 1} ΔC & M^{- 1} ΔM \end{matrix}],$ $B_{1} = [\begin{matrix} 0 \\ 0 \\ M^{- 1} B_{u} \end{matrix}],$ $B_{2} = [\begin{matrix} 0 \\ 0 \\ M^{- 1} B_{w} \end{matrix}],$ 非线性项f(

(t))满足Lipschitz条件，即存在已知Lipschitz参数阵U∈R^3×3使得如下不等式成立：Among them, the multi-source interference system state variable

x (t) = {[\begin{matrix} {&Integral;}_{0}^{t} e_{q} (τ) dτ & e_{q} (t) & {\overset{\cdot}{e}}_{q} \end{matrix}, (t)]}^{T},

e _q (t)=p(t)-p _p (t), p _p (t) is the reference trajectory signal, u(t) is the control input, A, E, B ₁ and B ₂ are known dimensions matrix,

A = [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & - m^{- 1} S & - m^{- 1} C \end{matrix}],

E. = [\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ m^{- 1} ΔS & m^{- 1} ΔC & m^{- 1} ΔM \end{matrix}],

B_{1} = [\begin{matrix} 0 \\ 0 \\ m^{- 1} B_{u} \end{matrix}],

B_{2} = [\begin{matrix} 0 \\ 0 \\ m^{- 1} B_{w} \end{matrix}],

The non-linear term f(

(t)) satisfies the Lipschitz condition, that is, there is a known Lipschitz parameter matrix U∈R ^3×3 so that the following inequality holds:

$| | | | f f (({\overset{\cdot \cdot}{x x}}_{11} ((t t)))) - - f f (({\overset{\cdot \cdot}{x x}}_{22} ((t t)))) | | | | \leq \leq | | | | U u (({\overset{\cdot &Center Dot;}{x x}}_{11} ((t t)) - - {\overset{\cdot \cdot}{x x}}_{22} ((t t)))) | | | |$

其中，为系统状态集合中的任意两个状态，外部模型描述干扰d₁(t)由下列外部干扰模型∑₁表示：in, For any two states in the system state set, the external model describes the disturbance d ₁ (t) by the following external disturbance model ∑ ₁ :

其中，w(t)为可建模干扰模型的状态变量，V为可建模干扰模型的输出矩阵，W表示可建模干扰模型的系统阵，δ(t)为能量有界的不可建模随机（即L₂范数

有界）干扰，B₃为不可建模干扰模型的能量有界干扰增益阵。where w(t) is the state variable of the modelable disturbance model, V is the output matrix of the modelable disturbance model, W represents the system matrix of the modelable disturbance model, and δ(t) is the non-modelable random (i.e. _L2 norm

Bounded) interference, B ₃ is the energy bounded interference gain array of the unmodelable interference model.

2、设计故障诊断观测器2. Design the fault diagnosis observer

针对多源干扰系统中的时变故障F(t)，设计故障诊断观测器为：For the time-varying fault F(t) in the multi-source interference system, the fault diagnosis observer is designed as:

$\{\begin{matrix} \overset{^^}{F f} ((t t)) = = τ τ - - p p ((x x)) \\ \overset{\cdot \cdot}{τ τ} = = {KB KB}_{11} ((τ τ - - p p ((x x)))) + + K K [[Ax Ax ((t t)) + + {B B}_{11} u u ((t t)) + + {B B}_{11} {\overset{^^}{d d}}_{11} ((t t)) - - Ef Ef ((\overset{\cdot \cdot}{x x} ((t t))))]] \end{matrix}$

其中，ε(t)为辅助变量,K为待定的故障诊断观测器增益矩阵，通过后续步骤6求得，进而得到故障估计误差

Among them, ε(t) is an auxiliary variable, K is the undetermined fault diagnosis observer gain matrix, obtained through the subsequent step 6, and then the fault estimation error

3、设计干扰观测器3. Design the disturbance observer

针对多源干扰系统中可建模干扰d₁(t)，设计干扰观测器为：For the modelable interference d ₁ (t) in the multi-source interference system, the designed interference observer is:

$\{\begin{matrix} {\overset{^^}{d d}}_{11} ((t t)) = = V V \overset{^^}{w w} ((t t)) \\ \overset{^^}{w w} ((t t)) = = v v ((t t)) - - Lx Lx ((t t)) \\ \overset{\cdot &Center Dot;}{v v} ((t t)) = = ((W W + + {LB LB}_{11} V V)) ((v v ((t t)) - - Lx Lx ((t t)))) + + L L [[Ax Ax ((t t)) + + {B B}_{11} u u ((t t)) + + {B B}_{11} \overset{^^}{F f} ((t t)) - - Ef Ef ((\overset{\cdot &Center Dot;}{x x},, t t))]] \end{matrix}$

其中，为可建模干扰d₁(t)的估计值，

为w(t)的估计值，v(t)为辅助变量，L为待定的干扰观测器增益矩阵，通过后续步骤6求得，进而得到故障估计误差

e_{w} (t) = w (t) - \hat{w} (t) .

in, is an estimate of the modelable disturbance d ₁ (t),

is the estimated value of w(t), v(t) is the auxiliary variable, L is the undetermined gain matrix of the disturbance observer, obtained through the subsequent step 6, and then the fault estimation error

e_{w} (t) = w (t) - \hat{w} (t) .

4、设计鲁棒H_∞状态反馈控制器4. Design a robust H _∞ state feedback controller

针对多源干扰系统中的不可建模随机干扰d₂(t)、故障估计误差e_F(t)和干扰估计误差e_w(t)设计鲁棒H_∞状态反馈控制器对其进行抑制，控制器结构如下：Aiming at the unmodelable random disturbance d ₂ (t), fault estimation error e _F (t) and disturbance estimation error e _w (t) in the multi-source interference system, a robust H _∞ state feedback controller is designed to suppress it, and control The device structure is as follows:

u_f(t)＝Mx(t)u _f (t) = Mx (t)

其中，u_f(t)为状态反馈控制器，M为待定状态反馈控制器增益阵。Among them, u _f (t) is the state feedback controller, and M is the undetermined state feedback controller gain matrix.

5、设计容错抗干扰控制器5. Design fault-tolerant and anti-jamming controller

基于干扰观测器、故障诊断观测器和鲁棒H_∞状态反馈控制器，设计容错抗干扰控制器如下：Based on the disturbance observer, fault diagnosis observer and robust H _∞ state feedback controller, the fault-tolerant and anti-disturbance controller is designed as follows:

$u u ((t t)) = = {u u}_{f f} ((t t)) - - {\overset{^^}{d d}}_{11} ((t t)) - - \overset{^^}{F f} ((t t))$

$\overset{\cdot \cdot}{x x} ((t t)) + + Ef Ef ((\overset{\cdot &Center Dot;}{x x},, t t)) = = ((A A + + {B B}_{11} M m)) x x ((t t)) + + {B B}_{11} V V {e e}_{w w} ((t t)) + + {B B}_{11} {e e}_{F f} ((t t)) + + {B B}_{22} {d d}_{22} ((t t))$

整理可建模干扰模型的系统估计误差方程和变化率有界的时变故障的系统估计误差方程如下：The system estimation error equation of the modelable disturbance model and the system estimation error equation of the time-varying fault with a bounded rate of change are sorted out as follows:

${\overset{\cdot &Center Dot;}{e e}}_{w w} ((t t)) = = ((W W + + {LB LB}_{11} V V)) {e e}_{w w} ((t t)) + + {LB LB}_{11} {e e}_{F f} ((t t)) + + {LB LB}_{22} {d d}_{22} ((t t)) + + {B B}_{33} δ δ ((t t))$

${\overset{\cdot &Center Dot;}{e e}}_{F f} ((t t)) = = {KB KB}_{11} V V {e e}_{w w} ((t t)) + + {KB KB}_{11} {e e}_{F f} ((t t)) + + {KB KB}_{22} {d d}_{22} ((t t)) + + \overset{\cdot &Center Dot;}{F f} ((t t))$

联列上述多源干扰系统、可建模干扰模型的系统估计误差和时变故障的系统估计误差方程得到闭环系统：The closed-loop system is obtained by combining the above multi-source interference system, the system estimation error of the modelable interference model, and the system estimation error equation of time-varying faults:

$\{\begin{matrix} (\begin{matrix} \overset{\cdot &Center Dot;}{x x} ((t t)) \\ {\overset{\cdot &Center Dot;}{e e}}_{w w} ((t t)) \\ {\overset{\cdot &Center Dot;}{e e}}_{F f} ((t t)) \end{matrix}) = = (\begin{matrix} A A + + {B B}_{11} M m & {B B}_{11} V V & {B B}_{11} \\ 00 & W W + + {LB LB}_{11} V V & {LB LB}_{11} \\ 00 & {KB KB}_{11} V V & {KB KB}_{11} \end{matrix}) (\begin{matrix} x x ((t t)) \\ {e e}_{w w} ((t t)) \\ {e e}_{F f} ((t t)) \end{matrix}) + + (\begin{matrix} {B B}_{22} \\ {LB LB}_{22} \\ {KB KB}_{22} \end{matrix}) {d d}_{22} ((t t)) + + (\begin{matrix} 00 \\ {B B}_{33} \\ 00 \end{matrix}) δ δ ((t t)) + + (\begin{matrix} 00 \\ 00 \\ 11 \end{matrix}) \overset{\cdot \cdot}{F f} ((t t)) - - (\begin{matrix} E E. \\ 00 \\ 00 \end{matrix}) f f ((\overset{\cdot &Center Dot;}{x x} ((t t)))) \\ {z z}_{\infty \infty} ((t t)) = = [\begin{matrix} {C C}_{00} & {C C}_{11} & {C C}_{22} \end{matrix}] (\begin{matrix} x x ((t t)) \\ {e e}_{w w} ((t t)) \\ {e e}_{F f} ((t t)) \end{matrix}) \end{matrix}$

6、增益矩阵求解6. Gain matrix solution

其中:e(0)＝[e_w(0)e_F(0)]^T,Φ₁₁＝(AP₁+B₁R₁)+(AP₁+B₁R₁)^T,Φ₂₂＝(P₂W₁+R₂B₁G)+(P₂W₁+R₂B₁G)^T,Φ₁₈＝λ(AP₁+B₁R₁)^T,C＝[C₁C₂],G＝[E I],H₁＝[B₃ 0]^T,H₂＝[0 1]^T；符号*表示对称矩阵中相应部分的对称块，求解得P₁、P₂、R₁和R₂，则干扰观测器和故障诊断观测器增益阵为 $[\begin{matrix} L \\ K \end{matrix}] = P_{2}^{- 1} R_{2},$ 状态反馈控制器增益阵为

Among them: e(0)＝[e _w (0)e _F (0)] ^T ,Φ ₁₁ ＝(AP ₁ +B ₁ R ₁ )+(AP ₁ +B ₁ R ₁ ) ^T ,Φ ₂₂ ＝(P ₂ W ₁ +R ₂ B ₁ G)+(P ₂ W ₁ +R ₂ B ₁ G) ^T ,Φ ₁₈ ＝λ(AP ₁ +B ₁ R ₁ ) ^T ,C＝[C ₁ C ₂ ],G ＝[E I], H ₁ ＝[B ₃ 0] ^T , H ₂ ＝[0 1] ^T ; the symbol * represents the symmetric block of the corresponding part in the symmetric matrix, P ₁ , P ₂ , R ₁ and R ₂ can be obtained by solving, Then the gain matrix of disturbance observer and fault diagnosis observer is

[\begin{matrix} L \\ K \end{matrix}] = P_{2}^{- 1} R_{2},

The state feedback controller gain matrix is

本发明说明书中未作详细描述的内容属于本领域专业技术人员公知的现有技术。The contents not described in detail in the description of the present invention belong to the prior art known to those skilled in the art.

Claims

1. A fault-tolerant and anti-jamming control method of a multi-source interference system is characterized in that it comprises the following steps: first, designing a fault diagnosis observer to estimate and offset the time-varying fault in the system; secondly, designing an interference observer to estimate and offset the multi-source Modelable disturbances in disturbance systems; thirdly, design a robust H _∞ state feedback controller to suppress unmodelable random disturbances, fault estimation errors and disturbance estimation errors in multi-source disturbance systems; finally, based on fault diagnosis observer, disturbance Observer and robust H _∞ state feedback controller, design fault-tolerant and anti-disturbance controller; the specific steps are as follows:

The first step is to build a dynamic model with multi-source interference system and write it as a state space expression

For a multi-source disturbance system with time-varying faults, modelable disturbances and non-modelable random disturbances, a system dynamics model is built, and the state space expression is written as follows:

\overset{\cdot &Center Dot;}{x x} ((t t)) + + Ef Ef ((\overset{\cdot &Center Dot;}{x x},, t t)) = = Ax Ax ((t t)) + + {B B}_{11} ((u u ((t t)) + + {d d}_{11} ((t t)) + + F f ((t t)))) + + {B B}_{22} {d d}_{22} ((t t))

Among them, x(t) is the state variable of the multi-source disturbance system, u(t) is the control input, d ₁ (t) is the disturbance that can be modeled, F(t) is the time-varying fault, and d ₂ (t) is the non-buildable Modular random interference, A, E, B ₁ and B ₂ are matrices of known dimensions, is a nonlinear item of the system and satisfies the Lipschitz condition, the external model describes the disturbance d ₁ (t) by the following external disturbance model Σ ₁ :

{Σ Σ}_{11} : : \{\begin{matrix} {d d}_{11} ((t t)) = = Vw Vw ((t t)) \\ \overset{\cdot &Center Dot;}{w w} ((t t)) = = Ww w ((t t)) + + {B B}_{33} δ δ ((t t)) \end{matrix}

where w(t) is the state variable of the modelable disturbance model, V is the output matrix of the modelable disturbance model, W represents the system matrix of the modelable disturbance model, and δ(t) is the non-modelable Random interference, B ₃ is the gain array of random interference that cannot be modeled;

The second step is to design the fault diagnosis observer

Then get the fault estimation error

The third step is to design the disturbance observer

For the modelable interference d ₁ (t) in the multi-source interference system, design an interference observer to estimate it in real time, and obtain the estimated value Then get the interference estimation error

is the estimated value of w(t);

The fourth step is to design a robust H _∞ state feedback controller

Aiming at the unmodelable random disturbance d ₂ (t), fault estimation error e _F (t) and disturbance estimation error e _w (t) in the multi-source interference system, a robust H _∞ state feedback controller is designed to suppress it, The controller structure is as follows:

u _f (t) = Mx (t)

Among them, u _f (t) is the robust H _∞ state feedback control input, and M is the undetermined state feedback controller gain matrix;

The fifth step is to design a fault-tolerant and anti-jamming controller

Design a fault-tolerant anti-disturbance controller to offset the time-varying fault F(t) in the system and the modelable disturbance d ₁ (t), while the random disturbance d ₂ (t) and the fault estimation error e _F (t) cannot be modeled and interference estimation error e _w (t) to suppress, the fault-tolerant anti-interference controller structure is as follows:

u u ((t t)) = = {u u}_{f f} ((t t)) - - \overset{^^}{F f} ((t t)) - - {\overset{^^}{d d}}_{11} ((t t))

Then the multi-source interference system can be expressed as:

\overset{\cdot &Center Dot;}{x x} ((t t)) + + Ef Ef ((\overset{\cdot &Center Dot;}{x x},, t t)) = = ((A A + + {B B}_{11} M m)) x x ((t t)) + + {B B}_{11} V V {e e}_{w w} ((t t)) + + {B B}_{11} {e e}_{F f} ((t t)) + + {B B}_{22} {d d}_{22} ((t t))

The system estimation error equation of the modelable disturbance model and the system estimation error equation of time-varying fault are sorted out as follows:

{\overset{\cdot &Center Dot;}{e e}}_{w w} ((t t)) = = ((W W + + {LB LB}_{11} V V)) {e e}_{w w} ((t t)) + + {LB LB}_{11} {e e}_{F f} ((t t)) + + {LB LB}_{22} {d d}_{22} ((t t)) + + {B B}_{33} δ δ ((t t))

{\overset{\cdot &Center Dot;}{e e}}_{F f} ((t t)) = = {KB KB}_{11} V V {e e}_{w w} ((t t)) + + {KB KB}_{11} {e e}_{F f} ((t t)) + + {KB KB}_{22} {d d}_{22} ((t t)) + + \overset{\cdot &Center Dot;}{F f} ((t t))

Combine the above multi-source interference system, the system estimation error equation of time-varying fault and the system estimation error equation of modelable interference to obtain the closed-loop system:

\{\begin{matrix} (\begin{matrix} \overset{\cdot &Center Dot;}{x x} ((t t)) \\ {\overset{\cdot &Center Dot;}{e e}}_{w w} ((t t)) \\ {\overset{\cdot &Center Dot;}{e e}}_{F f} ((t t)) \end{matrix}) = = (\begin{matrix} A A + + {B B}_{11} M m & {B B}_{11} V V & {B B}_{11} \\ 00 & W W + + {LB LB}_{11} V V & {LB LB}_{11} \\ 00 & {KB KB}_{11} V V & {KB KB}_{11} \end{matrix}) (\begin{matrix} x x ((t t)) \\ {e e}_{w w} ((t t)) \\ {e e}_{F f} ((t t)) \end{matrix}) + + (\begin{matrix} {B B}_{22} \\ {LB LB}_{22} \\ {KB KB}_{22} \end{matrix}) {d d}_{22} ((t t)) + + (\begin{matrix} 00 \\ {B B}_{33} \\ 00 \end{matrix}) δ δ ((t t)) + + (\begin{matrix} 00 \\ 00 \\ 11 \end{matrix}) \overset{\cdot &Center Dot;}{F f} ((t t)) - - (\begin{matrix} E E. \\ 00 \\ 00 \end{matrix}) f f ((\overset{\cdot &Center Dot;}{x x} ((t t)))) \\ {z z}_{\infty \infty} ((t t)) = = [\begin{matrix} {C C}_{00} & {C C}_{11} & {C C}_{22} \end{matrix}] (\begin{matrix} x x ((t t)) \\ {e e}_{w w} ((t t)) \\ {e e}_{F f} ((t t)) \end{matrix}) \end{matrix}

Among them, z _∞ (t) is H _∞ performance reference output, [C ₀ C ₁ C ₂ ] is H _∞ performance adjustable output matrix;

The sixth step is to solve the gain matrix

Using the convex optimization algorithm to solve the gain matrix of the fault-tolerant anti-jamming controller of the multi-source jamming system; given the initial values x(0), e _w (0) and e _F (0), the adjustable output matrix [C ₀ C ₁ C ₂ ], nonlinear weight parameter λ, interference suppression degree γ ₁ , γ ₂ and γ ₃ , to solve the following convex optimization problem:

min min (\begin{matrix} (\begin{matrix} {x x}^{T T} ((00)) & {e e}^{T T} ((00)) \end{matrix}) & (\begin{matrix} {P P}_{11} \\ {P P}_{22} \end{matrix}) & {(\begin{matrix} {x x}^{T T} ((00)) & {e e}^{T T} ((00)) \end{matrix})}^{T T} \end{matrix})

Φ Φ = = [\begin{matrix} {Φ Φ}_{1111} & {B B}_{11} G G & - - E E. & 00 & {B B}_{22} & 00 & {Φ Φ}_{1818} & {P P}_{11} {C C}_{00}^{T T} \\ * * & {Φ Φ}_{22 twenty two} & 00 & {P P}_{22} {H h}_{11} & {R R}_{22} {B B}_{22} & {P P}_{22} {H h}_{22} & λ λ {((U u {B B}_{11} G G))}^{T T} & {C C}^{T T} \\ * * & * * & - - {λ λ}^{22} I I & 00 & 00 & 00 & λ λ {((UE UE))}^{T T} & 00 \\ * * & * * & * * & - - {γ γ}_{11}^{22} & 00 & 00 & 00 & 00 \\ * * & * * & * * & * * & - - {γ γ}_{22}^{22} & 00 & λ λ {(({UB UB}_{22}))}^{T T} & 00 \\ * * & * * & * * & * * & * * & - - {γ γ}_{33}^{22} I I & 00 & 00 \\ * * & * * & * * & * * & * * & * * & - - I I & 00 \\ * * & * * & * * & * * & * * & * * & * * & - - I I \end{matrix}]

[\begin{matrix} L \\ K \end{matrix}] = P_{2}^{- 1} R_{2},

The state feedback controller gain matrix is

2. the fault-tolerant and anti-interference control method of a kind of multi-source interference system according to claim 1, is characterized in that: the fault diagnosis observer structure in the described step 2 is as follows:

\{\begin{matrix} \overset{^^}{F f} ((t t)) = = τ τ - - p p ((x x)) \\ \overset{\cdot &Center Dot;}{τ τ} = = {KB KB}_{11} ((τ τ - - p p ((x x)))) + + K K [[Ax Ax ((t t)) + + {B B}_{11} u u ((t t)) + + {B B}_{11} {\overset{^^}{d d}}_{11} ((t t)) - - Ef Ef ((\overset{\cdot &Center Dot;}{x x} ((t t))))]] \end{matrix}

in,

K is the undetermined gain matrix of the fault diagnosis observer, and ε(t) is the auxiliary variable.

3. The fault-tolerant anti-jamming control method of a kind of multi-source jamming system according to claim 1, is characterized in that: the disturbance observer structure in described step 3 is as follows:

\{\begin{matrix} {\overset{^^}{d d}}_{11} ((t t)) = = V V \overset{^^}{w w} ((t t)) \\ \overset{^^}{w w} ((t t)) = = v v ((t t)) - - Lx Lx ((t t)) \\ \overset{\cdot &Center Dot;}{v v} ((t t)) = = ((W W + + {LB LB}_{11} V V)) ((v v ((t t)) - - Lx Lx ((t t)))) + + L L [[Ax Ax ((t t)) + + {B B}_{11} u u ((t t)) + + {B B}_{11} \overset{^^}{F f} ((t t)) - - Ef Ef ((\overset{\cdot \cdot}{x x},, t t))]] \end{matrix}

Among them, v(t) is an auxiliary variable, L is the undetermined interference observer gain matrix, V is the output matrix of the modelable interference model, and W represents the system matrix of the modelable interference model.