Multi-missile self-learning differential game cooperative guidance method based on disturbance feed-forward compensation

Abstract

The invention discloses a multi-missile self-learning differential game cooperative guidance method based on disturbance feed-forward compensation, and the method comprises the steps: providing a finite-time convergence sliding-mode nonlinear expansion state observer for solving the problems of unknown partial parameters and external disturbance in a multi-missile cooperative guidance system; a sliding mode control method is combined with an extended state observer, a novel fixed-time convergence sliding mode surface and a sliding mode reaching law are constructed, and real-time estimation and efficient compensation of unknown disturbance in a system are achieved. Strictly proving the fixed convergence time of the observer by using a Lyapunov function, and analyzing a disturbance estimation error; compared with a traditional ESO, the method has the advantages that the speed and precision of state tracking are remarkably improved, and the anti-interference capability of the multi-missile cluster in a complex interference environment is effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of aircraft guidance, and in particular to a multi-missile self-learning differential game collaborative guidance method based on disturbance feedforward compensation. Background Art

[0002] Multiple-missile swarm systems are a crucial component of modern weapon systems. In actual combat environments, environmental changes, modeling errors, and uncertainty in internal system parameters can all interfere with the system. Furthermore, the enemy can use electronic jamming, signal shielding, or anti-missile measures to disrupt communication, navigation, and attack accuracy between munitions, thereby reducing combat efficiency and even causing mission failure. Therefore, robust anti-interference capabilities are crucial to ensuring the efficient and precise strike capability of multiple-missile swarm systems, making improving their anti-interference capabilities particularly important.

[0003] As a powerful disturbance estimation tool, ESO is widely used in control systems. By treating disturbances as state variables and expanding the system's state space, ESO can handle external disturbances and internal uncertainties, ensuring that the system maintains efficient operation in a dynamically changing environment. It has low dependence on the model of the observed system and its parameters are easy to adjust. It can estimate disturbances in the system in real time and compensate for them, thereby improving the robustness and stability of the system. If the ESO is not accurate enough and responds slowly when tracking external disturbances, it may cause oscillations in the control system, large output deviations, and even system instability. Therefore, it is necessary to develop an ESO with better performance to meet the growing control needs.

[0004] Based on the above analysis, in order to address the problems of phase delay, slow tracking speed and low tracking accuracy existing in traditional ESO, it is necessary to construct a sliding mode nonlinear extended state observer with fixed-time convergence capability to quickly and accurately estimate and compensate for system disturbances, and integrate differential game and adaptive dynamic programming methods to generate collaborative control inputs in real time, thereby effectively improving the collaborative guidance accuracy and anti-interference capability of the missile cluster system. Summary of the Invention

[0005] The purpose of the present invention is to propose a multi-missile self-learning differential game cooperative guidance method based on disturbance feedforward compensation. In view of the problems of unknown parameters, external interference and model uncertainty in the actual operation of the multi-missile cooperative guidance system, a nonlinear sliding mode expansion state observer with fixed-time convergence characteristics is designed to achieve real-time, accurate estimation and rapid compensation of unknown disturbances. In addition, by combining differential game theory with adaptive dynamic programming technology, the optimal cooperative guidance control input in the pursuit and escape game process of missile clusters is solved online in real time, effectively suppressing the negative impact of external disturbances on the system, thereby significantly improving the cooperative guidance accuracy, anti-disturbance performance and overall mission execution efficiency of the missile cluster system in complex combat environments.

[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0007] A multi-missile self-learning differential game collaborative guidance method based on disturbance feedforward compensation includes the following steps:

[0008] S1, establish the relative motion model of the projectile and target, select the relative distance between the projectile and target as the state variable, and obtain the multi-agent nonlinear differential game system;

[0009] S2, for the unknown parameters and external disturbances that appear in the multi-missile coordinated guidance process, a sliding mode nonlinear extended state observer with finite time convergence is constructed;

[0010] S3, combining the sliding mode control method with the extended state observer to construct the sliding mode surface and sliding mode reaching rate with fixed time convergence;

[0011] S4, Lyapunov function is used to verify the fixed convergence time of the sliding mode nonlinear extended state observer and analyze the disturbance estimation error.

[0012] Preferably, the step S1 specifically includes the following steps:

[0013] S11, suppose the missile and the target are both point masses, and the speed of the i-th missile is and are the track angle and its derivative of the i-th missile, γ MiT and are the sight angle and its derivative of the i-th missile respectively, and the speed of the target is V T , γ T and are the target track angle and its derivative, u i and v T are the normal control inputs of the missile and the target respectively, and by adjusting u i and v T The size of the missile changes its direction of movement, r i and are the relative distance between the missile and the target and its derivative respectively, then the relative kinematic equation between the i-th missile and the target is:

[0014]

[0015] S12, select state variables The state equation of the guidance system is:

[0016]

[0017] The feasible region of the system is N is the number of multiple bullets, is x i1 The derivative of is x i2 The derivative of

[0018] S13, further describe the state equation of step S12 as a multi-agent nonlinear differential system:

[0019]

[0020] in, u i and v T is the normal control input of the missile and the target, f(x i ),g(x i ) and k(x i ) is a locally Lipschitz continuous nonlinear function, where f(0) = 0;

[0021] In order to solve the uncertainty of the internal parameters of the cluster system and to solve the external disturbances caused by environmental changes and enemy electronic interference, the state equation of the guidance system is rewritten as:

[0022]

[0023] Where t is the time symbol h i (t) is an equivalent nonlinear term that comprehensively reflects the changes of geometric variables such as sight angle and track angle in the time domain. i (t) is an unknown term, is the control gain, d i (t) is the external disturbance of the system. The above quantities are explicitly written as ·(t) to highlight their time-varying properties. In control law design and Lyapunov convergence analysis, they are regarded as functions that can continuously change with time, rather than constants.

[0024] The unknown item o i and the external disturbance d of the system i Combined into a composite disturbance term containing parameter uncertainty and interference Will Expand to new state variables and design an extended state observer Make an estimate, define x i1 、x i2 and Estimate of , let:

[0025]

[0026] in, Represents the error between the observed relative position state and the true relative position, Represents the error between the observed relative velocity state and the true relative velocity, represents the extended observer for the integrated disturbance term The estimation error of

[0027] B0=[β 01 ,β 02 ,β 03 ] T is the gain vector of the extended state observer, by choosing the parameter β 01 ,β 02 ,β 03 , so that the observer can estimate the disturbance of the object in real time;

[0028] S14, Definition p is an equivalent disturbance function that couples the target motion state, the relative geometric relationship between the projectile and the target, and the nonlinear control input of the system, and comprehensively reflects the target velocity v T Incoming disturbances to the system, relative speed The changing trend of the control input u i The impact on missile trajectory change, the distance between the missile and the target r i Scaling of the above effects;

[0029] The extended state observer is designed as:

[0030]

[0031] in, is satisfied The nonlinear convergence function is:

[0032]

[0033] Wherein, sign(·) represents the sign function; i (·) is the power-type feedback function used for nonlinear convergence in the sliding mode extended state observer, is the linear feedback term, is a nonlinear feedback term of square root order, and so on. These functions are collectively referred to as , is a unified expression set of all the above nonlinear functions, and It represents the i-th item in this set; Ξ1 to Ξ n is the nonlinear convergence function of the controller at different orders.

[0034] Preferably, step S2 specifically includes the following steps:

[0035] S21, transform the extended state observer in S14 into a continuous power function with a linear segment near the origin to alleviate chattering:

[0036]

[0037] in, is a smaller filter factor;

[0038] S22, construct a sliding mode nonlinear extended state observer:

[0039]

[0040] in:

[0041]

[0042] Γ(·) is the nonlinear error compensation function in the sliding mode expansion observer, which enhances the system's error tolerance through multiple feedback forms. The rapid convergence ability and robustness of the algorithm; S is the auxiliary sliding mode variable; is the modulation factor in disturbance estimation, which controls the adaptability of the system to the nonlinear growth of error; χ is the intermediate compensation variable of the disturbance channel;

[0043]

[0044]

[0045] Introducing saturation function to reduce the The oscillation caused by excessive oscillation, the sat function satisfies:

[0046]

[0047] Among them, l 01 >0,l 02 >1 is the observer gain coefficient, by adjusting l 01 ,l 02The value of can improve the overshoot, chattering and tracking accuracy of the sliding mode nonlinear extended state observer. a1, a2, a3, a4> 0 are proportional gain coefficients, m1, n1> 1, m2< 1, n2> 0 are power term coefficients. By adjusting the values ​​of a1~a4, m1, m2, n1, n2, the error can be stabilized within the preset time. η E >0 is a constant, ω i is the composite disturbance term in the system, The sliding mode extended state observer is used to observe ω i The estimated value of is a positive number, indicating that the estimated error is stable after |z i3 |Estimation of the maximum value.

[0048] Preferably, the step 3 specifically includes the following steps:

[0049] S31, defines a new sliding surface with fixed time convergence:

[0050]

[0051] Among them, χ is used to speed up the convergence of the sliding surface. hour, when hour,

[0052] Taking the derivative of this formula, we can get:

[0053]

[0054] From S13 we can get:

[0055]

[0056] Substituting the derivative of the sliding surface, we can get:

[0057]

[0058] S32, design a new fixed-time convergence synovial reaching law:

[0059]

[0060] Rewritten as:

[0061]

[0062] in, It means that after the sliding mode observer reaches the steady state, Estimation of the maximum value; combined with this formula, we get the convergence function satisfy:

[0063]

[0064] Preferably, the step S4 specifically includes the following steps:

[0065] S41, there exists a continuous positive definite function V(t) whose derivative satisfies Where ζ1,ζ2>0, And q>1, then the system can converge to the equilibrium point in a finite time, and the convergence time satisfies

[0066] when Its steady-state error satisfies:

[0067]

[0068] When it is far away from the sliding surface, define the Lyapunov function:

[0069]

[0070] Taking the derivative of the Lyapunov function, we can get:

[0071]

[0072] It can be further simplified as:

[0073]

[0074] It can be seen that the observer can converge to the sliding surface within a fixed time, and the convergence time T1 satisfies:

[0075]

[0076] S42, after reaching the sliding surface, continue to move. satisfy

[0077] Define the Lyapunov function:

[0078]

[0079] when When , we can derive the formula:

[0080]

[0081] It can be further simplified as:

[0082]

[0083] The estimated error can converge to within a fixed time The convergence time T2 satisfies:

[0084]

[0085] when When:

[0086]

[0087] Estimation error It will eventually converge to 0;

[0088] The convergence time T satisfies:

[0089]

[0090] Combine We can get:

[0091]

[0092] When the sliding mode observer finally converges to a stable state, The steady-state error satisfies:

[0093]

[0094] Compared with the prior art, the present invention has the following beneficial effects:

[0095] First, the multi-missile self-learning differential game cooperative guidance method based on disturbance feedforward compensation of the present invention addresses the problems of unknown parameters, external interference and modeling uncertainty in the missile cluster cooperative guidance system. A nonlinear sliding mode expansion state observer with fixed-time convergence is designed, which can quickly and accurately estimate the unknown disturbance of the system within a limited fixed time, realize real-time feedforward compensation for external disturbances, and effectively improve the control accuracy and stability of the system in a complex disturbance environment.

[0096] Second, the multi-missile self-learning differential game collaborative guidance method based on disturbance feedforward compensation of the present invention combines sliding mode control theory with extended state observer technology. By constructing a new type of fixed-time convergence sliding mode surface and sliding mode convergence law, it significantly improves the tracking speed and accuracy of the state observer for system disturbances, overcoming the problems of slow convergence speed and insufficient tracking accuracy of traditional extended state observers.

[0097] Third, the multi-missile self-learning differential game collaborative guidance method based on disturbance feedforward compensation of the present invention fully combines differential game theory and adaptive dynamic programming technology to solve the optimal control strategy in the process of multi-missile collaborative pursuit of targets in real time online. It does not require prior knowledge of specific disturbance characteristics and can dynamically generate optimal control inputs in real time, thereby significantly improving the collaborative guidance performance of missile clusters and reducing the system's dependence on prior information.

[0098] Fourth, the multi-missile self-learning differential game collaborative guidance method based on disturbance feedforward compensation of the present invention, by comprehensively using disturbance feedforward compensation, differential game and adaptive dynamic programming technology, not only improves the robustness and stability of the missile cluster guidance system in a high interference environment, but also has better real-time and scalability when facing complex combat scenarios, significantly improving the overall task execution efficiency and anti-interference capability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0100] Figure 1 Schematic diagram of the relative motion model between projectile and target.

[0101] Figure 2 This is the system structure block diagram based on disturbance feedforward compensation.

[0102] Figure 3 This is a communication topology diagram.

[0103] Figure 4 This is a flow chart of the multi-missile self-learning differential game collaborative guidance method based on disturbance feedforward compensation. DETAILED DESCRIPTION

[0104] The embodiments of the present invention are described in further detail below with reference to the accompanying drawings.

[0105] like Figure 4 As shown, the present invention discloses a multi-missile self-learning differential game collaborative guidance method based on disturbance feedforward compensation, comprising the following steps:

[0106] Step 1: Establish a relative motion model between projectile and target, select the relative distance between projectile and target as the state variable, and obtain a nonlinear multi-agent differential game system;

[0107] Consider N missiles (M i ...M N ) to coordinate pursuit of maneuvering targets. The communication topology between missiles is as follows: Figure 3 It is represented by a directed graph G = (ν, E, A). i ...M N Seek the optimal control strategy to pursue the maneuvering target T, while the target T tries to seek the optimal control strategy to avoid the attack. Figure 1As shown, suppose the missile and the target are both point masses, and the speed of the i-th missile is , the track angle is , the sight angle is The target's velocity is V T , the track angle is γ T .u i and v T are the control inputs for the missile and the target respectively, and by adjusting u i and v T The size of the missile changes its direction of movement, r i and is the relative distance between the projectile and the target and its derivative.

[0108] Then the relative kinematic equation between the i-th missile and the target is:

[0109]

[0110] In order to satisfy the condition that each missile can hit the target at the same time, the state variable is selected Therefore, the state equation of the guidance system is as follows:

[0111]

[0112] Formula (2) is further described as a multi-agent nonlinear differential game system of the following form:

[0113]

[0114] Where: u i and v T It is the normal control input of our missile and target. i ),g(x i ) and k(x i ) is a locally Lipschitz continuous nonlinear function, where f(0) = 0. Obviously, the system (3) is controllable and x = 0 is an equilibrium point.

[0115] Note 1: According to formula (2), when |γ Mi -γ MiT |=0 and |γ T -γ MiT When |=0, the system is uncontrollable, which is the point that causes the system to be unstable. i →0, the state equation tends to infinity and the guidance process is destroyed. Therefore, the feasible region of the system is

[0116] However, in actual situations, there are uncertainties in the internal parameters of the cluster system, and changes in the environment and enemy electronic interference will also produce great external disturbances. Therefore, (2) can be rewritten as:

[0117]

[0118] Where t is the time symbol h i (t) is an equivalent nonlinear term that comprehensively reflects the changes of geometric variables such as sight angle and track angle in the time domain. i (t) is an unknown term, is the control gain, d i (t) is the external disturbance to the system. The above quantities are explicitly written as ·(t) to highlight their time-varying properties. In control law design and Lyapunov convergence analysis, they are considered as functions that can continuously change with time, rather than constants.

[0119] The unknown item o i and disturbance d i Combined into a composite disturbance term containing parameter uncertainty and interference It can be seen It is unknown to the aircraft and is expanded into a new state variable. Design ESO for Make an estimate, define x i1 、x i2 and An estimate of . Order:

[0120]

[0121] in, Represents the error between the observed relative position state and the true relative position, Represents the error between the observed relative velocity state and the true relative velocity, represents the extended observer for the integrated disturbance term The estimation error.

[0122] B0=[β 01 ,β 02 ,β 03 ] T is the gain vector of ESO. By choosing appropriate parameters β 01 ,β 02 ,β 03 , which enables the observer to estimate the disturbance of the object in real time.

[0123] definition p is an equivalent disturbance function that couples the target motion state, the relative geometric relationship between the projectile and the target, and the nonlinear control input of the system, and comprehensively reflects the target velocity v T Incoming disturbances to the system, relative speed The changing trend of the control input u i The impact on missile trajectory change, the distance between the missile and the target r i Scaling of the above effects.

[0124] Design ESO to:

[0125]

[0126] in, is satisfied The nonlinear convergence function is usually chosen as:

[0127]

[0128] Where, sign(·) represents the sign function; i (·) is the power-type feedback function used for nonlinear convergence in the sliding mode extended state observer, is the linear feedback term, is a nonlinear feedback term of square root order, and so on. These functions are collectively referred to as , is a unified expression set of all the above nonlinear functions, and It represents the i-th item in this set; Ξ1 to Ξ n is the nonlinear convergence function of the controller at different orders.

[0129] If the ESO's tracking accuracy for disturbances is insufficient and its speed is slow, it may lead to large output errors or even system instability. Therefore, it is necessary to develop a high-performance ESO to meet the growing control needs.

[0130] In order to facilitate the design of a new fixed-time convergence SMNESO, the following assumptions and lemmas are required:

[0131] Assumption 1: System composite disturbance term Derivative ω i exists and is bounded. That is, there exists a positive constant Satisfy the inequality

[0132] Lemma 1: Suppose there exists a continuous positive definite function V(t) whose derivative satisfies Where ζ1,ζ2>0, And q>1, then the system can converge to the equilibrium point in a finite time, and the convergence time satisfies

[0133] Step 2: To address the unknown parameters and external disturbances that occur during the multi-missile coordinated guidance process, and to improve the speed and accuracy of ESO state tracking, the following SMNESO is designed;

[0134] In order to avoid the occurrence of high-frequency chattering, (7) is transformed into a continuous power function with a linear segment near the origin to alleviate the chattering:

[0135]

[0136] in, is a smaller filter factor.

[0137] Compared with the traditional LESO, the selection of formula (8) can alleviate the chattering to a certain extent and has a faster tracking speed, but since it is an asymptotically convergent function, the terminal attraction factor It is not suitable for control far away from the origin, and the convergence speed at this time is slower than that of traditional LESO.

[0138] Therefore, it is necessary to design an ESO with fixed-time convergence and smaller tracking error.

[0139] The design is as follows SMNESO:

[0140] in:

[0141]

[0142] In the above formula, Γ(·) is the nonlinear error compensation function in the sliding mode expansion observer, which enhances the system's error compensation through multiple feedback forms. The rapid convergence ability and robustness of the algorithm; S is the auxiliary sliding mode variable; is the modulation factor in disturbance estimation, which controls the system's adaptability to nonlinear error growth; χ is the intermediate compensation variable of the disturbance channel.

[0143]

[0144]

[0145] Introducing saturation function to reduce the The oscillation caused by excessive oscillation, the sat function satisfies:

[0146]

[0147] Among them, l 01 >0,l 02 >1 is the observer gain coefficient, by adjusting l 01 ,l 02It can improve the overshoot, chattering and tracking accuracy of the observer (9). a1, a2, a3, a4> 0 are proportional gain coefficients, m1, n1> 1, m2< 1, n2> 0 are power term coefficients, and by adjusting the values ​​of a1~a4, m1, m2, n1, n2, the convergence time can be effectively shortened so that the error can be stabilized within the preset time. η E >0 is a very small constant, ω i is the composite disturbance term in the system, The sliding mode extended state observer is used to observe ω i The estimated value of is a positive number, indicating that the estimated error is stable after |z i3 |Estimation of the maximum value.

[0148] Step 3: Combine the sliding mode control method with ESO to design a new sliding mode surface and sliding mode reaching rate with fixed time convergence;

[0149] Define a new fixed-time convergence sliding surface:

[0150]

[0151] Note 2: The introduction of χ accelerates the convergence of the sliding surface. hour, This ensures the convergence speed of the observer when it is far away from the origin. hour, In the neighborhood of the origin, the sliding surface and its derivatives do not contain negative power terms, which can effectively avoid singular phenomena.

[0152] Taking the derivative of formula (15), we can get:

[0153]

[0154] From (5), we can get:

[0155]

[0156] Substitute (17) into (16):

[0157]

[0158] Design a new reaching law that converges in fixed time:

[0159]

[0160] because is unknown, so (19) is rewritten as:

[0161]

[0162] in, It means that after the sliding mode observer reaches the steady state, Estimate of the maximum value.

[0163] Combining equations (18) and (19), we get the convergence function satisfy:

[0164]

[0165] Step 4: Use the Lyapunov function to verify the fixed convergence time of SMNESO;

[0166] The proof process is divided into two steps. The first part is the proof of fixed-time convergence, and the second part is the proof of steady-state error.

[0167] When it is far away from the sliding surface, the Lyapunov function is defined as:

[0168]

[0169] The derivative of formula (22) can be obtained:

[0170]

[0171] Since m1>1,0<m2<1, therefore Formula (23) can be further simplified as:

[0172]

[0173] Combined with Lemma 1, we can get that the observer can converge to the sliding surface in a fixed time, and the convergence time T1 satisfies:

[0174]

[0175] After reaching the sliding surface, the movement continues. At this time, Equation (15) satisfies:

[0176]

[0177] Define the Lyapunov function:

[0178]

[0179] when When , we can derive formula (27) as follows:

[0180]

[0181] Since n1>1,0<n2<1, therefore (28) can be further simplified as:

[0182]

[0183] Combined with Lemma 1, we can get the estimated error can converge to within a fixed time The convergence time T2 satisfies:

[0184]

[0185] Furthermore, when When:

[0186]

[0187] Therefore, the estimation error It will eventually converge to 0.

[0188] In summary, under the action of the proposed SMNESO, the state error can converge to a small neighborhood near the origin, and the convergence time T satisfies:

[0189]

[0190] Combining (4), (5) and (9), we can get:

[0191]

[0192] Since the sliding mode observer finally converges to a stable state, is 0, at this time Therefore, the steady-state error satisfies:

[0193]

[0194] By adjusting l 02 , which can significantly reduce the error.

[0195] In summary, the SMNESO based on disturbance feedforward compensation proposed in this section is a block diagram of the multi-missile self-learning differential game cooperative guidance system. Figure 2 shown.

[0196] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt 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.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal translation scripting language JavaScript, etc.

[0197] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes 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 steps in the process. 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.

[0198] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work 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 The function specified in one or more boxes.

[0199] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions for executing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0200] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional 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 application.

[0201] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A multi-missile self-learning differential game collaborative guidance method based on disturbance feedforward compensation, characterized in that: The method comprises the following steps: S1, establish the relative motion model of the projectile and target, select the relative distance between the projectile and target as the state variable, and obtain the multi-agent nonlinear differential game system; S2, for the unknown parameters and external disturbances that appear in the multi-missile coordinated guidance process, a sliding mode nonlinear extended state observer with finite time convergence is constructed; S3, combining the sliding mode control method with the extended state observer to construct the sliding mode surface and sliding mode reaching rate with fixed time convergence; S4, Lyapunov function is used to verify the fixed convergence time of the sliding mode nonlinear extended state observer and analyze the disturbance estimation error.

2. The multi-missile self-learning differential game collaborative guidance method based on disturbance feedforward compensation according to claim 1 is characterized in that: The step S1 specifically includes the following steps: S11, suppose the missile and the target are both point masses, and the speed of the i-th missile is and are the track angle and its derivative of the i-th missile, and are the sight angle and its derivative of the i-th missile respectively, and the speed of the target is V T , γ T and are the target track angle and its derivative, u i and v T are the normal control inputs of the missile and the target respectively, and by adjusting u i and v T The size of the missile changes its direction of motion, r i and are the relative distance between the missile and the target and its derivative respectively, then the relative kinematic equation between the i-th missile and the target is: S12, select state variables The state equation of the guidance system is: The feasible region of the system is N is the number of multiple bullets, is x i1 The derivative of is x i2 The derivative of S13, further describe the state equation of step S12 as a multi-agent nonlinear differential system: in, u i and v T is the normal control input of the missile and the target, f(x i ),g(x i ) and k(x i ) is a locally Lipschitz continuous nonlinear function, where f(0) = 0; In order to solve the uncertainty of the internal parameters of the cluster system and to solve the external disturbances caused by environmental changes and enemy electronic interference, the state equation of the guidance system is rewritten as: Where t is the time symbol h i (t) is the equivalent nonlinear term that comprehensively reflects the changes of geometric variables in the time domain, o i (t) is an unknown term, is the control gain, d i (t) is the external disturbance of the system. The above quantities are explicitly written as ·(t), which is used to represent functions that change continuously with time; The unknown item o i and the external disturbance d of the system i Combined into a composite disturbance term containing parameter uncertainty and interference Will Expand to new state variables and design an extended state observer Make an estimate, define x i1 、x i2 and Estimate of , let: in, Represents the error between the observed relative position state and the true relative position, Represents the error between the observed relative velocity state and the true relative velocity, represents the extended observer for the integrated disturbance term The estimation error of B0=[β 01 ,β 02 ,β 03 ] T is the gain vector of the extended state observer, by choosing the parameter β 01 ,β 02 ,β 03 , so that the observer can estimate the disturbance of the object in real time; S14, Definition p is an equivalent disturbance function that couples the target motion state, the relative geometric relationship between the projectile and the target, and the nonlinear control input of the system, and comprehensively reflects the target velocity v T Incoming disturbances to the system, relative speed The changing trend of the control input u i The impact on missile trajectory change, the distance between the missile and the target r i Scaling of the above effects. The extended state observer is designed as: Among them, Θ i To control the gain, is satisfied The nonlinear convergence function is: Wherein, sign(·) represents the sign function; i (·) is the power-type feedback function used for nonlinear convergence in the sliding mode extended state observer, is the linear feedback term, is a nonlinear feedback term of square root order, is a unified expression set of all the above nonlinear functions, represents the i-th item in the set, Ξ1 to Ξ n is the nonlinear convergence function of the controller at different orders.

3. The multi-missile self-learning differential game cooperative guidance method based on disturbance feedforward compensation according to claim 2 is characterized in that: The step S2 specifically includes the following steps: S21, transform the extended state observer in S14 into a continuous power function with a linear segment near the origin to alleviate chattering: Among them, l∈(0,1), is the filtering factor; S22, construct a sliding mode nonlinear extended state observer: in: Γ(·) is the nonlinear error compensation function in the sliding mode expansion observer; S is the auxiliary sliding mode variable; is the modulation factor in disturbance estimation, which controls the adaptability of the system to the nonlinear growth of error; χ is the intermediate compensation variable of the disturbance channel; Introducing saturation function to reduce the The oscillation caused by excessive oscillation satisfies the following equation: max and b min Indicates independent variables: Among them, l 01 >0,l 02 >1 is the observer gain coefficient, by adjusting l 01 ,l 02 The value of a1~a4, m1, m2, n1, n2 is adjusted to make the error stable within the preset time, η E >0 is a constant, ω i is the composite disturbance term in the system, To calculate ω by sliding mode extended state observer i The estimated value of is a positive number, indicating that the estimated error is stable after |z i3 |Estimation of the maximum value.

4. The multi-missile self-learning differential game cooperative guidance method based on disturbance feedforward compensation according to claim 3 is characterized in that: The step 3 specifically includes the following steps: S31, defines a new sliding surface with fixed time convergence: Among them, χ is used to speed up the convergence of the sliding surface. hour, when hour, Taking the derivative of this formula, we can get: From S13 we can get: Substituting the derivative of the sliding surface, we can get: S32, design a new fixed-time convergence synovial reaching law: Rewritten as: in, It means that after the sliding mode observer reaches the steady state, Estimation of the maximum value; combined with this formula, we get the convergence function satisfy:

5. The multi-missile self-learning differential game cooperative guidance method based on disturbance feedforward compensation according to claim 4 is characterized in that: The step S4 specifically includes the following steps: S41, there exists a continuous positive definite function V(t) whose derivative satisfies Where ζ1,ζ2>0, And q>1, then the system can converge to the equilibrium point in a finite time, and the convergence time satisfies When l 02 >1, Its steady-state error satisfies: When the sliding surface is not reached, the Lyapunov function is defined as: Taking the derivative of the Lyapunov function, we can get: Further simplified to: It can be seen that the observer can converge to the sliding surface within a fixed time, and the convergence time T1 satisfies: S42, after reaching the sliding surface, continue to move. satisfy Define the Lyapunov function: when When , the derivative of this formula can be obtained: Further simplified to: The estimated error can converge to within a fixed time The convergence time T2 satisfies: when When: Estimation error It will eventually converge to 0; The convergence time T satisfies: Combine We can get: When the sliding mode observer finally converges to a stable state, The steady-state error satisfies:

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