An event-triggered robust adaptive saturation guidance method based on fuzzy model

Abstract

The present invention belongs to the field of guidance and control technology, and specifically relates to an event-triggered robust adaptive saturation guidance method based on a fuzzy model, the steps of which include providing the relative motion equation and the center of mass motion equation of a missile and a target; constructing the guidance system into a nonlinear differential game system; converting the missile interception problem into an optimal control problem of a nonlinear system with uncertainties and finite time domain constraints; designing a finite time domain input saturation optimal control strategy; introducing a periodic event trigger mechanism, constructing an input saturation optimal control strategy that intercepts the missile depending on the trigger state and an event-triggered optimal control input of a maneuvering target; constructing an evaluation network using an adaptive dynamic programming technology based on a generalized fuzzy hyperbolic tangent model, and constructing a finite time domain optimal cost function, a terminal state constraint, and an event-triggered control input based on the evaluation network. The present invention solves the problem that a missile is affected by system uncertainty and input constraints when intercepting a maneuvering target.

Description

Technical Field

[0001] The invention belongs to the technical field of guidance control, and in particular relates to an event-triggered robust adaptive saturation guidance method based on a fuzzy model. Background Art

[0002] In recent years, the interceptor missile and the target are the two parties in the missile interception and guidance problem. Their goals conflict with each other. The control is independent and only requires the current state information of the other party. The result of the control will cause one party to benefit while the other party will inevitably suffer losses. This is a typical zero-sum differential game problem. Therefore, applying differential game theory to the missile interception and guidance problem can fully consider the dynamic zero-sum game characteristics of the "missile-target" parties in the process of designing the guidance law, and obtain the guidance strategy of the interceptor and escape aircraft, thereby solving the problem of the impact of unknown target maneuvers on the interception and guidance performance in the guidance problem.

[0003] At present, many achievements have been made in the research of differential game guidance law. However, most of the existing guidance methods based on differential game are derived from linear guidance dynamics models. With the continuous development of high-speed flight weapon technology, the motion state of today's intelligent maneuvering targets changes dramatically and has strong nonlinearity and strong uncertainty, and the phenomenon of excessive terminal overload occurs from time to time, which seriously limits the terminal guidance effect. However, the current differential game guidance method based on nonlinear interception guidance system is not yet mature. On the one hand, the research on nonlinear optimal problems based on differential game involves the problem of solving coupled nonlinear partial differential equations. Continuing to use dynamic programming algorithms will cause the "curse of dimensionality" problem as the amount of calculation and storage increases. On the other hand, in the process of "pursuit" between missiles and targets, designing guidance laws without considering overload constraints and uncertainties may lead to instability of guidance instructions. To this end, it is necessary to study the solution method of coupled nonlinear partial differential equations for nonlinear differential game systems, and develop robust differential game interception guidance technology that can achieve precise interception of intelligent maneuverable targets under overload constraints, so as to improve the guidance performance of interceptor missiles and complete the precision guidance mission against highly maneuverable targets.

[0004] With the development of machine learning technology, scholars have proposed many effective methods to estimate unknown nonlinear functions, such as ADP technology, fuzzy approximation technology, etc. Compared with the Takagi-Sugeno model, the generalized fuzzy hyperbolic tangent model (GFHM) has fewer unknown parameters. In addition, when using ADP technology to approximate unknown functions, GFHM can be used to design an evaluation network, because GFHM is also a technology that uses neural networks to approximate unknown functions. Due to its significant advantages in value function approximation, GFHM is widely used to deal with infinite time domain optimal control problems of continuous-time nonlinear systems and multi-agent systems. However, most practical systems require effective control within a finite time. For example, in a guidance system, the missile must hit the target within a finite time. But so far, GFHM has rarely been used to approximate the finite time domain optimal value function of a nonlinear differential game guidance system. Secondly, information transmission has become a key technology for guidance systems. Faced with the large amount of data generated during the guidance process, traditional time-based sampling methods almost inevitably lead to a lot of computational and communication costs. Summary of the invention

[0005] In view of the above deficiencies in the prior art, the purpose of the present invention is to provide an event-triggered robust adaptive saturation guidance method based on a fuzzy model, which solves the problem that the missile is affected by system uncertainty and input constraints when intercepting a maneuvering target. The generalized fuzzy hyperbolic tangent model is used to approximate the finite time domain optimal value function of the nonlinear differential game guidance system. At the same time, an event-triggered sampling method is introduced, which can save communication costs.

[0006] To achieve the above object, the technical solution adopted by the present invention is an event-triggered robust adaptive saturation guidance method based on a fuzzy model, comprising the following steps:

[0007] S1. Based on the two-dimensional plane guidance model, the relative motion equation of the missile and the target and the center of mass motion equation are given;

[0008] S2. According to the parallel guidance principle, the guidance system is constructed as a nonlinear differential game system;

[0009] S3. Based on differential game theory, the missile interception problem is transformed into an optimal control problem of a nonlinear system with uncertainties and finite time domain constraints;

[0010] S4. Design the optimal control strategy for finite-time input saturation based on the nominal system and non-quadratic utility function;

[0011] S5. Introduce a periodic event trigger mechanism to construct an input saturation optimal control strategy for intercepting missiles that depends on the trigger state and an event-triggered optimal control input for maneuvering targets;

[0012] S6. Use the adaptive dynamic programming technology based on the generalized fuzzy hyperbolic tangent model to build an evaluation network. Based on the evaluation network, construct the finite time domain optimal cost function, terminal state constraints and event-triggered control input to realize the robust adaptive saturation guidance strategy based on the event-triggered sampling scheme.

[0013] As a preferred embodiment of the present invention, in said S1, the method for providing the relative motion equation and the center of mass motion equation of the missile and the target is specifically:

[0014] S1.1, the two-dimensional plane guidance model is a particle model considering the missile and the target. The two-dimensional plane includes the intercepted missile and the maneuvering target. M represents the missile and A represents the target. The missile M seeks the optimal control strategy to intercept the target A, while the target A tries to avoid the attack of the missile M.

[0015] S1.2. In the final guidance phase, assuming that the flight speeds of the missile M and the target A are both constant, the relative motion relationship between the missile and the target is expressed as:

[0016] (1);

[0017] In the formula, , They represent the speeds of missile M and target A respectively; , They represent the normal control inputs of the missile M and target A in the velocity direction, which are used to generate the lateral acceleration of the missile and target in the autopilot; r is the relative distance between the missile and the target, is the derivative of r with respect to time t; , They represent the track angles of missile M and target A respectively; Indicates the sight angle; , , They are , , The derivative with respect to time t;

[0018] S1.3. Assuming that the autopilots of missile M and target A are both first-order systems, the center-of-mass motion equations of missile M and target A are:

[0019] (2);

[0020] (3);

[0021] In the formula, , Respectively represent the position coordinates of missile M and target A in the two-dimensional plane; , They represent the lateral acceleration of the missile M and the target A respectively; , , , , , They are , , , , , Derivative with respect to time; , is the autopilot time constant.

[0022] As a preferred solution of the present invention, in S2, the process of constructing the guidance system into a nonlinear differential game system is:

[0023] S2.1. When the missile M and the target A are no longer maneuvering, the minimum distance between them is the zero control miss distance. , expressed as:

[0024] (4);

[0025] S2.2. Based on equation (4), the condition for missile M to successfully capture the target in the final guidance phase is: tends to zero, and Less than zero, that is ;

[0026] S2.3, according to the parallel guidance principle, by controlling the normal acceleration of the missile tends to zero, the missile M can successfully intercept the target A. At this time, it is considered that , In the terminal guidance stage, the size remains unchanged; in order to zero the line-of-sight angular rate, the state variable is defined , taking the derivative of the state variables, we get the state equation of the guidance system:

[0027] (5);

[0028] In the formula, for The derivative with respect to time t; for The derivative with respect to time t;

[0029] S2.4. Formula (5) is further described as a nonlinear differential game system:

[0030] (6);

[0031] In the formula, Represents the state of the differential game system The derivative with respect to time t, , , is a 2-dimensional real vector space, and the rest Similarly; is a locally Lipschitz continuous function, , is a nonlinear function, , , Represent the nonlinear dynamics of differential game systems; , is the control input of the differential game system.

[0032] As a preferred embodiment of the present invention, in S2.4, , , .

[0033] As a preferred embodiment of the present invention, in S3, the conversion method is:

[0034] Define the remaining flight time , define a new state variable , thus obtaining the state equation of the new guidance system:

[0035] (7);

[0036] In the formula, , are the new control inputs for missile M and target A respectively; is the distance variable, ,in is the initial distance between missile M and target A, is the distance between the missile M and the target A at time t; the guidance target is to adjust , so that r converges to zero, thereby achieving effective interception of target A.

[0037] As a preferred solution of the present invention, in said S4, the step of designing a finite time domain input saturation optimal control strategy is:

[0038] S4.1. Considering the dynamic game characteristics between missile M and target A, the uncertainty of differential game system in the guidance process and input constraints, a nonlinear zero-sum differential game system is used to describe the one-to-one guidance system, which can be expressed as:

[0039] (8);

[0040] In the formula, , They represent the two parties in the game, namely the control inputs of the missile M and the target A at time t, and The module satisfies the inequality , is a positive constant; a nonlinear function , is norm-bounded, that is, it satisfies the inequality and ,in and is a positive constant; is a locally Lipschitz continuous function, and ; Matching uncertainty function , is norm-bounded, that is, it satisfies the inequality and ,in and is a positive constant that satisfies ;

[0041] S4.2. When there is no uncertainty in equation (8), the following nominal system is obtained:

[0042] (9);

[0043] The finite time domain cost function of the nominal system is defined as:

[0044] (10);

[0045] In the formula, is a finite-time domain cost function; It’s the final moment; is the state of the differential game system at the final moment; u and v are the control inputs, which are , , x is ; is a term related to the uncertainty of the differential game system; Represents terminal state constraints; To characterize the function, From time t to The characterization of the system state and control input during is a positive definite function, represents a non-quadratic functional, is a first-order matrix, and the superscript T indicates transpose;

[0046] S4.3. Considering the input constraints, It is expressed as:

[0047] (11);

[0048] In the formula, is a first-order matrix; is an intermediate variable;

[0049] S4.4. According to differential game theory, the Hamiltonian function It is expressed as:

[0050] (12);

[0051] In the formula, yes The partial derivative with respect to time is ; yes The partial derivative with respect to x is ;

[0052] S4.5. According to the Nash-Pontryagin maximum-minimum principle, Nash equilibrium solution The necessary condition for existence is ,in, , They represent the optimal control inputs of missile M and target A respectively, is the optimal cost function and satisfies the following relationship:

[0053] ,and ;

[0054] When the value of v is the largest and the value of u is the smallest, The value of is the optimal cost function, express;

[0055] Based on optimal control theory, , Respectively expressed as:

[0056] (13);

[0057] (14);

[0058] In the formula, the symbol express ,Right now ; yes The partial derivative with respect to x is ;

[0059] S4.6. According to equations (11) and (13), we obtain the optimal non-quadratic functional :

[0060] (15);

[0061] S4.7. Substituting equations (13), (14) and (15) into equation (12), we obtain the HJI equation of the nonlinear differential game system in the finite time domain, which is expressed as:

[0062] (16);

[0063] In the formula, yes The partial derivative with respect to t; , The control input , The optimal value of .

[0064] As a preferred embodiment of the present invention, in S4.2, , , This indicates the uncertainty-related parameters.

[0065] As a preferred solution of the present invention, in said S5, the process of constructing the input saturation optimal control strategy of the interceptor missile dependent on the trigger state and the event-triggered optimal control input of the maneuvering target is:

[0066] S5.1. State of nonlinear differential game system Perform periodic sampling, the sampling period is h seconds, and the system state after sampling is recorded as , is the index of the sampling period, indicating the Sub-cycle sampling, Indicates Sub-periodic sampling time;

[0067] S5.2. Introduce an event-based sampling strategy. When the trigger condition is violated, it is transmitted to the controller; if the trigger condition is not violated, the control input maintains the value at the last trigger moment, and the zero-order holder is used to maintain the continuity of the control input; the state transmitted to the control input use Indicates that the optimal control input triggered by the corresponding event use Indicates that is transmitted only when the trigger condition is violated, represents the i-th triggering time, Indicates the i-th trigger (a marker for the number of triggers);

[0068] S5.3. Define the current cycle sampling status The difference between the last trigger state is , expressed as:

[0069] (17);

[0070] In the formula, It means equivalent to; Indicates that after the i-th trigger, The time of sub-periodic sampling; is the set of natural numbers;

[0071] when When the event trigger condition is violated, the new trigger time Generated, which means the i+1th triggering moment;

[0072] S5.4. By introducing an event triggering scheme, equations (13) to (15) are made dependent on the triggering state, thereby obtaining the optimal control input for the missile M and target A event triggering: , :

[0073] (18);

[0074] (19);

[0075] In the formula, The corresponding cost function ; , express Corresponding , ; At this time, for time t, .

[0076] As a preferred solution of the present invention, in said S6, the process of constructing the finite time domain optimal cost function, terminal state constraints and event-triggered control input is:

[0077] S6.1, for time t and Time and its corresponding system status , , its optimal cost function , It is expressed as:

[0078] (20);

[0079] (twenty one);

[0080] In the formula, is the offset; is a generalized fuzzy input, , represents the Kronecker product, is a j-dimensional column vector, yes exist The value of the moment; and is the ideal weight, j is the system state The number of linear transformations of each component; is the approximate error;

[0081] S6.2. Since all ideal weights are unknown, the ideal weights are estimated using the output of the neural network. The specific expression is:

[0082] (twenty two);

[0083] (twenty three);

[0084] In the formula, , Respectively , An estimated value of , Respectively , The estimated value of , , yes An estimated value of , They are , An estimated value of

[0085] S6.3. Derivation of the optimal control input for the missile M triggered by the approximate saturation event and the approximate event triggering optimal control input of target A , respectively expressed as:

[0086] (twenty four);

[0087] (25);

[0088] In the formula, and They are and The estimated value of Recorded as , Recorded as ; Recorded as ,Right now ,function exist The partial derivative with respect to x is Indicates that ;

[0089] S6.4. Substituting equation (24) into equation (11), we obtain the non-quadratic functional based on event-triggered sampling: :

[0090] (26);

[0091] S6.5. and Substituting into the Hamiltonian function, that is, formula (12), we get the approximation error function:

[0092] (27);

[0093] In the formula, is the approximation error of the Hamiltonian function; is a function The partial derivative with respect to x, yes The partial derivative with respect to t is , ;

[0094] S6.5, correspondingly, the terminal constraint estimation error for:

[0095] (28);

[0096] In the formula, is the ideal weight The approximation error of Recorded as ,Right now ;

[0097] S6.6. In order to make the residual Without the need to give the minimum initial stable control, the gradient descent method is used to design the following weight update law with additional function:

[0098] (29);

[0099] (30);

[0100] In the formula, , They are and Derivative with respect to time; yes The partial derivative with respect to x, is a continuously differentiable Lyapunov candidate function; , , is the set learning rate, represents the Hadamard product of the matrix; express ,Right now ;function The expression is:

[0101] (31);

[0102] In the formula, for , there exists a positive definite matrix ,satisfy:

[0103] (32);

[0104] In the formula, is a function The derivative with respect to time t;

[0105] S6.7. The triggering conditions are as follows:

[0106] (33);

[0107] In the formula, , is a constant; is a function The Lipschitz constant.

[0108] As a preferred embodiment of the present invention, in S6.1, in order to satisfy the condition of the Lyapunov function, Set as ; In S6.2, is randomly selected in the stable region.

[0109] The algorithm involved in the present invention can be executed by an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the above algorithm calculation is implemented by executing the software by the processor.

[0110] The beneficial effects of the present invention are:

[0111] The invention transforms the missile interception problem into the optimal control problem of a nonlinear zero-sum differential game system with finite time domain constraints by establishing a plane interception mathematical model, thereby solving the problem of the influence of unknown target maneuver on the interception guidance performance in the guidance problem; replaces the traditional periodic sampling scheme with an event trigger mechanism, under which the guidance law state is transmitted only when the specified trigger condition is met, thereby improving the communication resource utilization rate of the system; and utilizes a generalized fuzzy hyperbolic evaluation network to approximate the optimal cost function, the terminal state constraint and the event-triggered robust optimal guidance strategy, so that the obtained guidance strategy has the advantages of high precision, low communication cost and good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0112] Figure 1 It is a schematic diagram of the process of the present invention;

[0113] Figure 2 is a schematic diagram of the relative motion between a missile and a target in an embodiment of the present invention;

[0114] Figure 3 It is a guidance flow chart in an embodiment of the present invention. DETAILED DESCRIPTION

[0115] The embodiments of the present invention are further described below in conjunction with the accompanying drawings:

[0116] like Figure 1 As shown, an event-triggered robust adaptive saturation guidance method based on a fuzzy model includes the following steps:

[0117] S1. Based on the two-dimensional plane guidance model, the relative motion equation of the missile and the target and the center of mass motion equation are given;

[0118] S2. According to the parallel guidance principle, the guidance system is constructed as a nonlinear differential game system;

[0119] S3. Based on differential game theory, the missile interception problem is transformed into an optimal control problem of a nonlinear system with uncertainties and finite time domain constraints;

[0120] S4. Design the optimal control strategy for finite-time input saturation based on the nominal system and non-quadratic utility function;

[0121] S5. Introduce a periodic event trigger mechanism to construct an input saturation optimal control strategy for intercepting missiles that depends on the trigger state and an event-triggered optimal control input for maneuvering targets;

[0122] S6. Use the adaptive dynamic programming technology based on the generalized fuzzy hyperbolic tangent model to build an evaluation network. Based on the evaluation network, construct the finite time domain optimal cost function, terminal state constraints and event-triggered control input to realize the robust adaptive saturation guidance strategy based on the event-triggered sampling scheme.

[0123] In S1, the method for giving the relative motion equation of the missile and the target and the center of mass motion equation is as follows:

[0124] S1.1, the two-dimensional plane guidance model is a particle model considering the missile and the target. The two-dimensional plane includes the intercepted missile and the maneuvering target. M represents the missile and A represents the target. The missile M seeks the optimal control strategy to intercept the target A, while the target A tries to avoid the attack of the missile M.

[0125] S1.2. In the final guidance phase, assuming that the flight speeds of the missile M and the target A are both constant, the relative motion relationship between the missile and the target is expressed as:

[0126] (1);

[0127] In the formula, , They represent the speeds of missile M and target A respectively; , They represent the normal control inputs of the missile M and target A in the velocity direction, which are used to generate the lateral acceleration of the missile and target in the autopilot; r is the relative distance between the missile and the target, is the derivative of r with respect to time t; , They represent the flight path angle (FPA) of the missile M and the target A respectively; Indicates the sight angle; , , They are , , The derivative with respect to time t; In the Cartesian coordinate system, the relative motion diagram of the missile and the target is as follows: Figure 2 shown.

[0128] S1.3. Assuming that the autopilots of missile M and target A are both first-order systems, the center-of-mass motion equations of missile M and target A are:

[0129] (2);

[0130] (3);

[0131] In the formula, , Respectively represent the position coordinates of missile M and target A in the two-dimensional plane; , They represent the lateral acceleration of the missile M and the target A respectively; , , , , , They are , , , , , Derivative with respect to time; , is the autopilot time constant.

[0132] In this embodiment, setting Second.

[0133] In S2, the process of constructing the guidance system into a nonlinear differential game system is:

[0134] S2.1. When the missile M and the target A are no longer maneuvering, the minimum distance between them is the zero control miss distance. , expressed as:

[0135] (4);

[0136] S2.2. Based on equation (4), the condition for missile M to successfully capture the target in the final guidance phase is: tends to zero, and Less than zero, that is ;

[0137] S2.3, according to the parallel guidance principle, by controlling the normal acceleration of the missile tends to zero, the missile M can successfully intercept the target A. At this time, it is considered that , In the terminal guidance stage, the size remains unchanged; in order to zero the line-of-sight angular rate, the state variable is defined , taking the derivative of the state variables, we get the state equation of the guidance system:

[0138] (5);

[0139] In the formula, for The derivative with respect to time t; for The derivative with respect to time t;

[0140] S2.4. Formula (5) is further described as a nonlinear differential game system:

[0141] (6);

[0142] In the formula, Represents the state of the differential game system The derivative with respect to time t, , , is a 2-dimensional real vector space, and the rest Similarly; is a locally Lipschitz continuous function, , is a nonlinear function, , , Represent the nonlinear dynamics of differential game systems; , is the control input of the differential game system.

[0143] In S2.4, , , .

[0144] In S3, the conversion method is:

[0145] The guidance model based on finite-time differential games handles the finite-time constraints by performing a series of mathematical transformations to define the remaining flight time. , define a new state variable , thus obtaining the state equation of the new guidance system:

[0146] (7);

[0147] In the formula, , are the new control inputs for missile M and target A respectively; is the distance variable, ,in is the initial distance between missile M and target A, is the distance between the missile M and the target A at time t; the guidance target is to adjust , so that r converges to zero, thereby achieving effective interception of target A.

[0148] In S4, the steps for designing the optimal control strategy for finite-time input saturation are:

[0149] S4.1. Considering the dynamic game characteristics between missile M and target A, the uncertainty of differential game system in the guidance process and input constraints, a nonlinear zero-sum differential game system is used to describe the one-to-one guidance system, which can be expressed as:

[0150] (8);

[0151] In the formula, , They represent the two parties in the game, namely the control inputs of the missile M and the target A at time t, and The module satisfies the inequality , is a positive constant; a nonlinear function , is norm-bounded, that is, it satisfies the inequality and ,in and is a positive constant; is a locally Lipschitz continuous function, and ; Matching uncertainty function , is norm-bounded, that is, it satisfies the inequality and ,in and is a positive constant that satisfies ;

[0152] S4.2. When there is no uncertainty in equation (8), the following nominal system is obtained:

[0153] (9);

[0154] The finite time domain cost function of the nominal system is defined as:

[0155] (10);

[0156] when When , it is obvious that formula (10) is , because the integral interval is zero, the integral part in front is equal to 0 as a whole;

[0157] In the formula, is a finite-time domain cost function; It’s the final moment; is the state of the differential game system at the final moment; u and v are the control inputs, which are , , x is ; is a term related to the uncertainty of the differential game system; represents the terminal state constraint (i.e., the terminal state constraint constructed for S6); To characterize the function, From time t to The characterization of the system state and control input during is a positive definite function, represents a non-quadratic functional, is a first-order matrix, and the superscript T indicates transpose;

[0158] S4.3. Considering the input constraints, It is expressed as:

[0159] (11);

[0160] In the formula, is a first-order matrix; is an intermediate variable;

[0161] S4.4. According to differential game theory, the Hamiltonian function It is expressed as:

[0162] (12);

[0163] In the formula, yes The partial derivative with respect to time is ; yes The partial derivative with respect to x is ;

[0164] S4.5. According to the Nash-Pontryagin maximum-minimum principle, Nash equilibrium solution The necessary condition for existence is ,in, , They represent the optimal control inputs of missile M and target A respectively, is the optimal cost function and satisfies the following relationship:

[0165] ,and ;

[0166] No matter what the intermediate function is, the integral interval is 0, and the integral must be 0, so obviously ;

[0167] When the value of v is the largest and the value of u is the smallest, The value of is the optimal cost function, express;

[0168] Based on optimal control theory, , Respectively expressed as:

[0169] (13);

[0170] (14);

[0171] In the formula, the symbol express ,Right now ; yes The partial derivative with respect to x is ;

[0172] S4.6. According to equations (11) and (13), we obtain the optimal non-quadratic functional :

[0173] (15);

[0174] S4.7. Substituting equations (13), (14) and (15) into equation (12), we obtain the HJI equation of the nonlinear differential game system in the finite time domain, which is expressed as:

[0175] (16);

[0176] In the formula, yes The partial derivative with respect to t; , The control input , The optimal value of .

[0177] The Hamilton-Jacobi-Isaacs (HJI) equation is a partial differential equation in optimal control theory, used to describe optimal control problems in differential games. The Nash-Pontryagin Minimax Principle is a concept in optimal control theory that combines John Nash's game theory and LSPontryagin's maximum principle. This principle is used to solve differential game problems, that is, two or more participants in a dynamic system minimize or maximize a cost function by choosing a control strategy.

[0178] In S4.2, , , This indicates the uncertainty-related parameters.

[0179] In S5, the process of constructing the input saturation optimal control strategy of the interceptor missile dependent on the trigger state and the event-triggered optimal control input of the maneuvering target is:

[0180] S5.1. State of nonlinear differential game system Perform periodic sampling, the sampling period is h seconds, and the system state after sampling is recorded as , is the index of the sampling period, indicating the Sub-cycle sampling, Indicates Sub-periodic sampling time;

[0181] S5.2. Introduce an event-based sampling strategy. When the trigger condition is violated, it is transmitted to the controller (the controller refers to the state transmitted to the optimal control input ), the trigger condition is the subsequent formula (33); if the trigger condition is not violated, the control input maintains the value at the last trigger time. Here, the zero-order holder is used to maintain the continuity of the control input. The state transmitted to the control input use Indicates that the optimal control input triggered by the corresponding event use Indicates that is transmitted only when the trigger condition is violated, represents the i-th triggering moment; Indicates the i-th trigger;

[0182] S5.3. Define the current cycle sampling status The difference between the last trigger state is , expressed as:

[0183] (17);

[0184] In the formula, It means equivalent to; Indicates that after the i-th trigger, The time of sub-periodic sampling; is the set of natural numbers;

[0185] when When the event trigger condition is violated, the new trigger time Generated, which means the i+1th triggering moment;

[0186] S5.4. By introducing an event triggering scheme, equations (13) to (15) are made dependent on the triggering state, thereby obtaining the optimal control input for the missile M and target A event triggering: , :

[0187] (18);

[0188] (19);

[0189] In the formula, The corresponding cost function ; , express Corresponding , ; At this time, for time t, .

[0190] In S6, the process of constructing the finite-time optimal cost function, terminal state constraints, and event-triggered control input is:

[0191] S6.1, for time t and Time and its corresponding system status , , its optimal cost function , It is expressed as:

[0192] (20);

[0193] (twenty one);

[0194] In the formula, is the offset; is a generalized fuzzy input, , represents the Kronecker product, is a j-dimensional column vector, , yes exist The value of the moment; and is the ideal weight, j is the system state The number of linear transformations of each component; is the approximate error; ,so There are two components, x1 and x2, where the number of linear transformations of x1 and x2 is set to j;

[0195] S6.2. Since all ideal weights are unknown, the ideal weights are estimated using the output of the neural network. The specific expression is:

[0196] (twenty two);

[0197] (twenty three);

[0198] In the formula, , Respectively , An estimated value of , Respectively , The estimated value of , , yes An estimated value of , They are , An estimated value of

[0199] S6.3. Derivation of the optimal control input for the missile M triggered by the approximate saturation event and the approximate event triggering optimal control input of target A , respectively expressed as:

[0200] (twenty four);

[0201] (25);

[0202] In the formula, and They are and The estimated value of Recorded as , Recorded as ; Recorded as ,Right now ,function exist The partial derivative with respect to x is Indicates that ;

[0203] S6.4. Substituting equation (24) into equation (11), we obtain the non-quadratic functional based on event-triggered sampling: :

[0204] (26);

[0205] S6.5. and Substituting into the Hamiltonian function, that is, formula (12), we get the approximation error function:

[0206] (27);

[0207] In the formula, is the approximation error of the Hamiltonian function; is a function The partial derivative with respect to x, yes The partial derivative with respect to t is , ;

[0208] S6.5, correspondingly, the terminal constraint estimation error for:

[0209] (28);

[0210] In the formula, is the ideal weight The approximation error of Recorded as ,Right now ; mentioned earlier express So here is the estimated value of is an estimation error;

[0211] S6.6. In order to make the residual Without the need to give the minimum initial stable control, the gradient descent method is used to design the following weight update law with additional function:

[0212] (29);

[0213] (30);

[0214] In the formula, , They are and Derivative with respect to time; yes The partial derivative with respect to x, is a continuously differentiable Lyapunov candidate function; , , is the set learning rate, represents the Hadamard product of the matrix; express ,Right now ;function The expression is:

[0215] (31);

[0216] In the formula, for , there exists a positive definite matrix ,satisfy:

[0217] (32);

[0218] In the formula, is a function The derivative with respect to time t;

[0219] S6.7. The triggering conditions are as follows:

[0220] (33);

[0221] In the formula, , is a constant; is a function The Lipschitz constant.

[0222] In S6.1, to satisfy the conditions of the Lyapunov function, Set as ; In S6.2, is randomly selected in the stable region. The stable region is closely related to the stability of the control system. Stability refers to the property of the system being able to return to its equilibrium state or remain near the desired state after being disturbed. Combined with the above formulas and symbol settings, the guidance process of this embodiment is as follows Figure 3 shown.

[0223] The generalized fuzzy hyperbolic tangent model involved in S6 is a well-known technology, and the evaluation network can be constructed using the known model. The optimal cost function is the one in S6.1 , ;Terminal state constraints ; The event-triggered control input is and .

Claims

1. An event-triggered robust adaptive saturation guidance method based on fuzzy model, characterized in that The following steps are involved: S1. Based on the two-dimensional plane guidance model, the relative motion equation of the missile and the target and the center of mass motion equation are given; S2. According to the parallel guidance principle, the guidance system is constructed as a nonlinear differential game system; S3. Based on differential game theory, the missile interception problem is transformed into an optimal control problem of a nonlinear system with uncertainties and finite time domain constraints; S4. Design the optimal control strategy for finite-time input saturation based on the nominal system and non-quadratic utility function; S5. Introduce a periodic event trigger mechanism to construct an input saturation optimal control strategy for intercepting missiles that depends on the trigger state and an event-triggered optimal control input for maneuvering targets; S6. Use the adaptive dynamic programming technology based on the generalized fuzzy hyperbolic tangent model to build an evaluation network, construct the finite time domain optimal cost function, terminal state constraints and event-triggered control input based on the evaluation network, and realize the robust adaptive saturation guidance strategy based on the event-triggered sampling scheme; In the above S1, the method for giving the relative motion equation between the missile and the target is specifically: S1.1, the two-dimensional plane guidance model is a particle model considering the missile and the target. The two-dimensional plane includes the intercepted missile and the maneuvering target. M represents the missile and A represents the target. The missile M seeks the optimal control strategy to intercept the target A, while the target A tries to avoid the attack of the missile M. S1.

2. In the final guidance phase, assuming that the flight speeds of the missile M and the target A are both constant, the relative motion relationship between the missile and the target is expressed as: （1）； In the formula, , They represent the speeds of missile M and target A respectively; , They represent the normal control inputs of the missile M and target A in the velocity direction, which are used to generate the lateral acceleration of the missile and target in the autopilot; r is the relative distance between the missile and the target, is the derivative of r with respect to time t; , They represent the track angles of missile M and target A respectively; Indicates the sight angle; , , They are , , The derivative with respect to time t; In S2, the process of constructing the guidance system into a nonlinear differential game system is: S2.

1. When the missile M and the target A are no longer maneuvering, the minimum distance between them is the zero control miss distance. , expressed as: （4）； S2.

2. Based on equation (4), the condition for missile M to successfully capture the target in the final guidance phase is: tends to zero, and Less than zero, that is ; S2.3, according to the parallel guidance principle, by controlling the normal acceleration of the missile tends to zero, the missile M can successfully intercept the target A. At this time, it is considered that , In the terminal guidance stage, the size remains unchanged; in order to zero the line-of-sight angular rate, the state variable is defined , taking the derivative of the state variables, we get the state equation of the guidance system: （5）； In the formula, for The derivative with respect to time t; for The derivative with respect to time t; S2.

4. Formula (5) is further described as a nonlinear differential game system: （6）； In the formula, Represents the state of the differential game system The derivative with respect to time t, , , is a 2-dimensional real vector space, and the rest Similarly; is a locally Lipschitz continuous function, , is a nonlinear function, , , Represent the nonlinear dynamics of differential game systems; , is the control input of the differential game system; In the above S4, the steps of designing the finite time domain input saturation optimal control strategy are: S4.

1. Considering the dynamic game characteristics between missile M and target A, the uncertainty of differential game system in the guidance process and input constraints, a nonlinear zero-sum differential game system is used to describe the one-to-one guidance system, which can be expressed as: （8）； In the formula, , They represent the two parties in the game, namely the control inputs of the missile M and the target A at time t, and The module satisfies the inequality , is a positive constant; Nonlinear functions , is norm-bounded, that is, it satisfies the inequality and ,in and is a positive constant; is a locally Lipschitz continuous function, and ; Matching uncertainty function , is norm-bounded, that is, it satisfies the inequality and ,in and is a positive constant that satisfies ; S4.

2. When there is no uncertainty in equation (8), the following nominal system is obtained: （9）； The finite time domain cost function of the nominal system is defined as: （10）； In the formula, is a finite-time domain cost function; It’s the final moment; is the state of the differential game system at the final moment; u and v are control inputs, which are , , x is ; is a term related to the uncertainty of the differential game system; Represents terminal state constraints; To characterize the function, From time t to The characterization of the system state and control input during is a positive definite function, represents a non-quadratic functional, is a first-order matrix, and the superscript T indicates transpose; S4.

3. Considering the input constraints, It is expressed as: （11）； In the formula, is a first-order matrix; is an intermediate variable; S4.

4. According to differential game theory, the Hamiltonian function It is expressed as: （12）； In the formula, yes The partial derivative with respect to time is ; yes The partial derivative with respect to x is ; S4.

5. According to the Nash-Pontryagin maximum-minimum principle, Nash equilibrium solution The necessary condition for existence is ,in, , They represent the optimal control inputs of missile M and target A respectively, is the optimal cost function and satisfies the following relationship: ,and ; When the value of v is the largest and the value of u is the smallest, The value of is the optimal cost function, express; Based on optimal control theory, , Respectively expressed as: （13）； （14）； In the formula, the symbol express ,Right now ; yes The partial derivative with respect to x is ; S4.

6. According to equations (11) and (13), we obtain the optimal non-quadratic functional : （15）； S4.

7. Substituting equations (13), (14) and (15) into equation (12), we obtain the HJI equation of the nonlinear differential game system in the finite time domain, which is expressed as: （16）； In the formula, yes The partial derivative with respect to t; , The control input , The optimal value of .

2. The event-triggered robust adaptive saturation guidance method based on fuzzy model according to claim 1, characterized in that: In S1, the method for giving the center of mass motion equation is specifically: S1.

3. Assuming that the autopilots of missile M and target A are both first-order systems, the center-of-mass motion equations of missile M and target A are: （2）； （3）； In the formula, , Respectively represent the position coordinates of missile M and target A in the two-dimensional plane; , They represent the lateral acceleration of the missile M and the target A respectively; , , , , , They are , , , , , Derivative with respect to time; , is the autopilot time constant.

3. The event-triggered robust adaptive saturation guidance method based on fuzzy model according to claim 1, characterized in that: In S2.4, , , .

4. The event-triggered robust adaptive saturation guidance method based on fuzzy model according to claim 1, characterized in that: In the S3, the conversion method is: Define the remaining flight time , define a new state variable , thus obtaining the state equation of the new guidance system: （7）； In the formula, , are the new control inputs for missile M and target A respectively; is the distance variable, ,in is the initial distance between missile M and target A, is the distance between the missile M and the target A at time t; the guidance target is to adjust , so that r converges to zero, thereby achieving effective interception of target A.

5. The event-triggered robust adaptive saturation guidance method based on fuzzy model according to claim 1, characterized in that: In S4.2, , , This indicates the uncertainty-related parameters.

6. The event-triggered robust adaptive saturation guidance method based on fuzzy model according to claim 1, characterized in that: In the above S5, the process of constructing the input saturation optimal control strategy of the interceptor missile dependent on the trigger state and the event-triggered optimal control input of the maneuvering target is as follows: S5.

1. State of nonlinear differential game system Perform periodic sampling, the sampling period is h seconds, and the system state after sampling is recorded as , is the index of the sampling period, indicating the Sub-cycle sampling, Indicates Sub-periodic sampling time; S5.

2. Introduce an event-based sampling strategy. When the trigger condition is violated, it is transmitted to the controller; if the trigger condition is not violated, the control input maintains the value at the last trigger moment, and the zero-order holder is used to maintain the continuity of the control input; the state transmitted to the control input use Indicates that the optimal control input triggered by the corresponding event use Indicates that is transmitted only when the trigger condition is violated, represents the i-th triggering time, Indicates the i-th trigger; S5.

3. Define the current cycle sampling status The difference between the last trigger state is , expressed as: （17）； In the formula, It means equivalent to; Indicates that after the i-th trigger, The time of sub-periodic sampling; is the set of natural numbers; when When the event trigger condition is violated, the new trigger time Generated, which means the i+1th triggering moment; S5.

4. By introducing an event triggering scheme, equations (13) to (15) are made dependent on the triggering state, thereby obtaining the optimal control input for the missile M and target A event triggering: , : （18）； （19）； In the formula, The corresponding cost function ; , express Corresponding , ; At this time, for time t, .

7. The event-triggered robust adaptive saturation guidance method based on fuzzy model according to claim 6, characterized in that: In the above S6, the process of constructing the finite time domain optimal cost function, terminal state constraints and event-triggered control input is: S6.1, for time t and Time and its corresponding system status , , its optimal cost function , It is expressed as: （20）； （21）； In the formula, is the offset; is a generalized fuzzy input, , represents the Kronecker product, is a j-dimensional column vector, yes exist The value of the moment; and is the ideal weight, j is the system state The number of linear transformations of each component; is the approximate error; S6.

2. Since all ideal weights are unknown, the ideal weights are estimated using the output of the neural network. The specific expression is: （22）； （23）； In the formula, , Respectively , An estimated value of , Respectively , The estimated value of , , yes An estimated value of , They are , An estimated value of S6.

3. Derivation of the optimal control input for the missile M triggered by the approximate saturation event and the approximate event triggering optimal control input of target A , respectively expressed as: （24）； （25）； In the formula, and They are and The estimated value of Recorded as , Recorded as ; Recorded as ,Right now ,function exist The partial derivative with respect to x is Indicates that ; S6.

4. Substituting equation (24) into equation (11), we obtain the non-quadratic functional based on event-triggered sampling: : （26）； S6.

5. and Substituting into the Hamiltonian function, that is, formula (12), we get the approximation error function: （27）； In the formula, is the approximation error of the Hamiltonian function; is a function The partial derivative with respect to x, yes The partial derivative with respect to t is , ; S6.5, correspondingly, the terminal constraint estimation error for: （28）； In the formula, is the ideal weight The approximation error of Recorded as ,Right now ; S6.

6. In order to make the residual Without the need to give the minimum initial stable control, the gradient descent method is used to design the following weight update law with additional function: （29）； （30）； In the formula, , They are and Derivative with respect to time; yes The partial derivative with respect to x, is a continuously differentiable Lyapunov candidate function; , , is the set learning rate, represents the Hadamard product of the matrix; express ,Right now ;function The expression is: （31）； In the formula, for , there exists a positive definite matrix ,satisfy: （32）； In the formula, is a function The derivative with respect to time t; S6.

7. The triggering conditions are as follows: （33）； In the formula, , is a constant; is a function The Lipschitz constant.

8. The event-triggered robust adaptive saturation guidance method based on fuzzy model according to claim 7, characterized in that: In S6.1, in order to satisfy the conditions of the Lyapunov function, Set as ; In S6.2, is randomly selected in the stable region.

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