Multi-unmanned-system fixed-time fuzzy adaptive event triggering formation control method

Abstract

According to the multi-unmanned-system fixed-time fuzzy self-adaptive event triggering formation control method, an unmanned system mathematical model considering environment disturbance factors is rewritten into a state equation, a fuzzy state observer based on the unmanned system mathematical model is established, and speed vector estimation of the unmanned systems is achieved; the problem that the speed information of the unmanned system cannot be measured is solved, a fixed time fuzzy adaptive event trigger formation controller based on an event trigger mechanism is established through a virtual controller in combination with a fuzzy state observer and a filtering error, and fixed time fuzzy adaptive event trigger formation control of multiple unmanned systems is realized. Based on the established event triggering mechanism, the problems of communication redundancy and communication limitation caused by uninterrupted information transmission of the formation control target can be solved, the number of times of updating the actuator is reduced, and the waste of network communication resources is reduced. And the fixed time formation control of the multi-unmanned system with unknown dynamics and unmeasurable speed can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned system control, and in particular to a fixed-time fuzzy adaptive event-triggered formation control method for multiple unmanned systems. Background Art

[0002] Unmanned systems, including unmanned ground vehicles, unmanned underwater ships, unmanned underwater vehicles and drones, can rely on their own perception, decision-making and execution capabilities to complete specific tasks autonomously. Especially in recent years, with the rapid development of artificial intelligence, information technology and robotics, unmanned systems have shown great application prospects in the fields of intelligent transportation, industrial manufacturing, ocean exploration, aerospace and disaster relief.

[0003] With the continuous development of unmanned systems, the operating efficiency and flexibility of a single unmanned system can no longer meet the existing application requirements. Formation control, as one of the key technologies to achieve efficient and flexible operation of multiple unmanned systems, has received widespread attention from researchers and has become a research hotspot. Due to the parameter uncertainty, nonlinearity, unmodeled dynamics and external environmental disturbances in unmanned systems, it is difficult to establish an accurate dynamic model for them, which brings challenges to the design of traditional unmanned system formation control. Considering the limitations of the equipment carried by the unmanned system and factors such as equipment failure, the speed information of the unmanned system cannot be measured. At the same time, in order to achieve the formation control goal, information transmission is usually carried out uninterruptedly, which will cause communication redundancy and communication restrictions. The problem brings difficulties to the formation control design of multiple unmanned systems. Summary of the invention

[0004] The present invention discloses a fixed-time fuzzy adaptive event-triggered formation control method for multiple unmanned systems to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A fixed-time fuzzy adaptive event-triggered formation control method for multiple unmanned systems comprises the following steps:

[0007] S1: establishing a mathematical model of an unmanned system taking environmental disturbance factors into consideration; and rewriting the mathematical model of the unmanned system into a state equation to obtain a position vector under the state equation and a velocity vector under the state equation;

[0008] S2: According to the position vector under the state equation and the velocity vector under the state equation, a fuzzy state observer based on the mathematical model of the unmanned system is established to obtain an estimate of the velocity vector of the unmanned system;

[0009] S3: Based on the estimation of the unmanned system velocity vector, obtain the formation velocity error vector:

[0010] S4: According to the formation error vector and the formation speed error vector, based on the fuzzy state observer and the first-order filter, a filtering error is obtained to obtain a fixed-time virtual controller;

[0011] S5: According to the formation speed error vector, filtering error and fixed-time virtual controller, a fixed-time fuzzy adaptive event-triggered formation controller based on an event trigger mechanism is established to complete the fixed-time fuzzy adaptive event-triggered formation control of multiple unmanned systems.

[0012] Furthermore, the method for obtaining the fixed-time fuzzy adaptive event-triggered formation controller based on the event trigger mechanism is as follows:

[0013] S51: According to the fuzzy state observer and the formation speed error vector, we get

[0014]

[0015] Where: e 2,i represents the formation velocity error vector; Represents x 2,i The estimated inertia matrix; x 2,i represents the velocity vector under the state equation; Represents x 2,i An estimate of , that is, an estimate of the velocity vector of the unmanned system; express The inverse of i represents control input; express estimates; represents the fuzzy parameter matrix; express The transpose of represents the fuzzy basis function vector; Represents x 1,i estimates; Represents x 2,i The estimate of the velocity vector of the unmanned system; x 1,i represents the position vector under the state equation; k 2,i and k 3,i All are observation gains; represents the observation error; express The first derivative of ; for The first derivative of ; represents virtual control input; represents virtual control input;

[0016] S52: Construct the following second Lyapunov function:

[0017]

[0018] Where: V 2,i represents the second Lyapunov function; represents the error between the ideal parameters and the estimated parameters; e 2,i represents the formation velocity error vector; Indicates e 2,i The transpose of Represents the first-order filter output error; express The transpose of i Indicates w i Design parameters of the adaptive law; represents the error between the ideal parameters and the estimated parameters; express The transpose of

[0019] Get the second Lyapunov function V 2,i The time derivative of

[0020]

[0021] Where: φ i Expressed as a positive constant; α i Indicates virtual controller; B i (·) is a continuous function of the variable;

[0022] S53: According to the second Lyapunov function V 2,i The time derivative of , the formation controller is obtained as follows:

[0023]

[0024] sig 2ρ-1 (e z2,i )=sign(e z2,i )|e z2,i | 2ρ-1 ;

[0025] Among them, a i,d represents an intermediate variable; c 2,i , All represent the design parameters of the formation controller.

[0026] Furthermore, the mathematical model of the unmanned system is established as follows:

[0027]

[0028] Where: represents the inertia matrix of the unmanned system, represents the space of all n×n real matrices, where n represents a real number; represents the Coriolis force-centrifugal force matrix of the unmanned system, represents the gravity vector of the unmanned system, represents n-dimensional Euclidean space; q i represents the position vector of the unmanned system, represents the velocity vector of the unmanned system, represents the acceleration vector of the unmanned system, τ i represents the control input, σ i represents environmental disturbance,

[0029] Furthermore, the mathematical model of the unmanned system is rewritten as a state equation as follows:

[0030] Let x 1,i =q i and but

[0031]

[0032] Where: M i (x 2,i ) represents the inertia matrix under the state equation; M i (x 2,i ) -1 Indicates M i (x 2,i ) is the inverse of i (x 1,i ,x 2,i ) represents the Coriolis force-centrifugal force matrix under the state equation; g i (x 2,i ) represents the gravity vector under the state equation; x 1,i represents the position vector under the state equation; x 2,i represents the velocity vector under the state equation; Represents x 1,i The first derivative of ; Represents x 2,i The first derivative of .

[0033] Furthermore, the fuzzy state observer is established as follows:

[0034] Let f 2,i (x 1,i ,x 2,i )=-Mi (x 2,i ) -1 (C i (x 1,i ,x 2,i )x 2,i +g i (x 2,i ))

[0035] Using fuzzy logic system Approximation f 2,i (x 1,i ,x 2,i ), which is expressed as follows:

[0036]

[0037] Where: represents a fuzzy logic system; represents the fuzzy parameter matrix; express The transpose of represents the fuzzy basis function vector; ε i represents the approximation error; f 2,i (x 1,i ,x 2,i ) is an unknown nonlinear function;

[0038] Among them, there are unknown constants satisfy

[0039] Among them, ‖ε i ‖ represents ε i The 2-norm of ;

[0040] but,

[0041]

[0042] Where: y i0 Indicates system output;

[0043] Therefore, the fuzzy state observer is established as

[0044]

[0045] Where: express estimates; express estimates; Represents x 1,i estimates; Represents x 2,i An estimate of , that is, an estimate of the velocity vector of the unmanned system; represents the observation error; Represents x 2,i Estimated inertia matrix; express The estimation of , that is, the estimation of the fuzzy parameter matrix; express The first derivative of ; Represents y i0 Estimate of k 1,i , k 2,i and k 3,i Both are observation gains.

[0046] Furthermore, the formation speed error vector is obtained as follows:

[0047]

[0048] Where: e 1,i represents the formation error vector; j represents the index number of the neighboring unmanned system of the i-th unmanned system; I represents the total number of unmanned systems; a i,j represents the connection mark between the ith unmanned system and the jth neighbor unmanned system of the ith unmanned system; x 1d represents the desired position; x 1,j represents the position of the jth neighbor unmanned system of the ith unmanned system; represents the time-varying distance between the ith unmanned system and the pilot unmanned system; represents the time-varying distance between the jth neighbor unmanned system of the ith unmanned system and the pilot unmanned system; a i,0 represents the connection mark between the ith unmanned system and the pilot unmanned system; e 2,i represents the formation velocity error vector; represents virtual control input;

[0049] in, The first-order filter satisfies the following:

[0050]

[0051] Where: Represents the first-order filter output error; α i Represents a virtual controller; φ i is represented as a positive constant; for The first derivative of ; express The initial value of α i (0) indicates α i The initial value of .

[0052] Furthermore, the method for obtaining the virtual controller at a fixed time is as follows:

[0053] S41: Obtain the first-order derivative of the formation error vector to obtain a connection mark between the unmanned system and its neighboring system, as follows:

[0054]

[0055] in,

[0056]

[0057] Where: Indicates e 1,i The first derivative of i,d represents an intermediate variable; represents the deviation between the actual speed and the estimated speed of the i-th unmanned system; express The first derivative of ; Represents x 1d The first derivative of ; express The first derivative of ; represents the deviation between the actual speed and the estimated speed of the jth neighbor of the i-th unmanned system; represents the estimated speed of the jth neighbor unmanned system of the ith unmanned system; j is the index number of the neighbor unmanned system of the ith unmanned system;

[0058] S42: Construct the first Lyapunov function V as follows 1,i for

[0059]

[0060] Where: V 1,i represents the first Lyapunov function; Indicates e 1,i The transpose of

[0061] Get the first Lyapunov function V 1,i The derivative with respect to time is:

[0062]

[0063] According to the first Lyapunov function V 1,i The derivative with respect to time is:

[0064]

[0065] Where: c 1,j , are the design parameters of the virtual control law. q is a design parameter greater than 1, and ρ is a design parameter greater than 0 and less than 1;

[0066] in,

[0067]

[0068] sig 2ρ-1 (e z1,i )=sign(e z1,i )|e z1,i | 2ρ-1 ;

[0069] Where: e z1,i Indicates e 1,i The error of the zth element in ; z represents e 1,i The element number in; Z represents e 1,i The total number of elements in ; sign(·) represents the sign function;

[0070] S43: By And the first-order filter output error, get the virtual controller, the formula used is as follows,

[0071]

[0072] Where: Represents the first-order filter output error; Represents x 1d The second derivative of .

[0073] Furthermore, the event triggering mechanism is expressed as follows:

[0074] τ i (t) = ω i (t 2,h ),t∈[t 2,h ,t 2,h+1 )

[0075] t 2,h+1 = inf{t>t 2,h :|τ ki -ω ki |≥m τ}

[0076] Where: τ i (t) represents the actual control input; ω i represents the event triggering controller vector of the i-th unmanned system; t 2,h represents the sampling time; t represents time; inf{·} represents the lower bound function; τ ki represents the kth component of the control input vector of the ith unmanned system; ω ki represents the kth element of the event triggering controller vector of the i-th unmanned system; m τrepresents the trigger threshold; k represents the index number of the control input vector component in the unmanned system; m τ is a design parameter greater than 0.

[0077] Furthermore, the estimation of the event-triggered controller vector and the fuzzy parameter matrix The adaptive law is

[0078]

[0079] In the formula, express Estimates of 2,i Represents the first design parameter of the event-triggered controller; Represents the second design parameter of the event-triggered controller; represents the design parameters of the adaptive law.

[0080] Beneficial effects: The method for controlling a multi-unmanned system fixed-time fuzzy adaptive event-triggered formation of the present invention rewrites the mathematical model of the unmanned system taking into account environmental disturbance factors into a state equation, and establishes a fuzzy state observer based on the mathematical model of the unmanned system according to the position vector under the state equation and the velocity vector under the state equation, so as to estimate the velocity vector of the unmanned system; the problem that the velocity information of the unmanned system cannot be measured is solved, and at the same time, the velocity error vector of the formation is obtained according to the estimation of the velocity vector of the unmanned system, and a virtual controller is established by combining the fuzzy state observer and the filtering error, and finally a fixed-time fuzzy adaptive event-triggered formation controller based on the event trigger mechanism is established to realize the fixed-time fuzzy adaptive event-triggered formation control of the multi-unmanned system. Based on the established event trigger mechanism, the problems of communication redundancy and communication limitation caused by the uninterrupted information transmission of the formation control target can be solved, the number of actuator updates can be reduced, and the waste of network communication resources can be reduced. Fixed-time formation control of multi-unmanned systems with unknown dynamics and unmeasurable speed can be realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] 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 some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0082] Figure 1 It is a flow chart of the fixed-time fuzzy adaptive output feedback event-triggered formation control method for an unmanned system of the present invention;

[0083] Figure 2It is a structural block diagram of a fuzzy adaptive output feedback fixed-time formation control method in an embodiment of the present invention;

[0084] Figure 3 It is a program flow chart of the formation control method in an embodiment of the present invention. DETAILED DESCRIPTION

[0085] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0086] This embodiment introduces a fixed-time fuzzy adaptive event-triggered formation control method for multiple unmanned systems. Figure 1-Figure 3 As shown, the following steps are included:

[0087] S1: Establish a mathematical model of the unmanned system taking into account environmental disturbances; and rewrite the mathematical model of the unmanned system into a state equation to obtain the position vector x under the state equation 1,i and the velocity vector x under the state equation 2,i ;

[0088] Specifically, consider a formation system consisting of I unmanned systems, where the i-th unmanned system is described by the following Euler-Lagrangian system (i = 1, 2, ..., I) to establish the unmanned system mathematical model as follows:

[0089]

[0090] Where: represents the inertia matrix of the unmanned system, represents the space of all n×n real matrices, where n represents a real number; represents the Coriolis force-centrifugal force matrix of the unmanned system, represents the gravity vector of the unmanned system, represents n-dimensional Euclidean space; q i represents the position vector of the unmanned system, represents the velocity vector of the unmanned system, represents the acceleration vector of the unmanned system, τ i represents the control input, σ i represents environmental disturbance,

[0091] In order to facilitate control design, the mathematical model of the unmanned system is rewritten as a state equation as follows:

[0092] Let x 1,i =q i and Then formula (1) is re-expressed as follows:

[0093]

[0094] Where: M i (x 2,i ) represents the inertia matrix under the state equation; M i (x 2,i ) -1 Indicates M i (x 2,i ) is the inverse of i (x 1,i ,x 2,i ) represents the Coriolis force-centrifugal force matrix under the state equation; g i (x 2,i ) represents the gravity vector under the state equation; x 1,i represents the position vector under the state equation; x 2,i represents the velocity vector under the state equation; Represents x 1,i The first derivative of ; Represents x 2,i The first derivative of ;

[0095] S2: According to the position vector under the state equation and the velocity vector under the state equation, a fuzzy state observer based on the mathematical model of the unmanned system is established to obtain an estimate of the velocity vector of the unmanned system;

[0096] Preferably, the fuzzy state observer is established as follows:

[0097] Let f 2,i (x 1,i ,x 2,i )=-M i (x 2,i ) -1 (C i (x 1,i ,x 2,i )x 2,i +g i (x 2,i ))

[0098] Because f 2,i (x 1,i ,x 2,i ) is an unknown nonlinear function, using the fuzzy logic system Approximation f 2,i (x 1,i ,x 2,i ), which is expressed as follows:

[0099]

[0100] Where: represents a fuzzy logic system; represents the fuzzy parameter matrix; express The transpose of represents the fuzzy basis function vector; ε i represents the approximation error; f 2,i (x 1,i ,x 2,i ) is an unknown nonlinear function;

[0101] Among them, there are unknown constants satisfy

[0102] Among them, ‖ε i ‖ represents ε i The 2-norm of ;

[0103] Then, by formula (3), (2) is expressed as follows:

[0104]

[0105] Where: y i0 Indicates system output;

[0106] Therefore, the fuzzy state observer is established as

[0107]

[0108]

[0109] Where: express estimates; express estimates; Represents x 1,i estimates; Represents x 2,i An estimate of , that is, an estimate of the velocity vector of the unmanned system; represents the observation error; Represents x 2,i Estimated inertia matrix; express The estimation of , that is, the estimation of the fuzzy parameter matrix; express The first derivative of ; Represents y i0 Estimate of k 1,i , k 2,i and k 3,i All are observation gains;

[0110] S3: Based on the estimation of the unmanned system velocity vector, obtain the formation velocity error vector:

[0111] Preferably, the formation speed error vector acquisition method is as follows:

[0112] Define the following coordinate transformation, based on the estimate of the unmanned system velocity vector Get the formation error vector and formation velocity error vector:

[0113]

[0114]

[0115] Where: e 1,i represents the formation error vector; j represents the index number of the neighboring unmanned system of the i-th unmanned system; I represents the total number of unmanned systems; a i,j represents the connection mark between the ith unmanned system and the jth neighbor unmanned system of the ith unmanned system; x 1d represents the desired position; x 1,j represents the position of the jth neighbor unmanned system of the ith unmanned system; represents the time-varying distance between the ith unmanned system and the pilot unmanned system; represents the time-varying distance between the jth neighbor unmanned system of the ith unmanned system and the pilot unmanned system; a i,0 represents the connection mark between the ith unmanned system and the pilot unmanned system; e 2,i represents the formation velocity error vector; represents virtual control input;

[0116] in, The first-order filter satisfies the following:

[0117]

[0118] Where: Represents the first-order filter output error; α i Represents a virtual controller; φ i is represented as a positive constant; for The first derivative of ; express The initial value of α i (0) indicates α i The initial value of .

[0119] S4: According to the formation error vector and the formation speed error vector, based on the fuzzy state observer and the first-order filter, a filtering error is obtained to obtain a fixed-time virtual controller;

[0120] S41: Obtain the first-order derivative of the formation error vector to obtain a connection mark between the unmanned system and its neighboring system, as follows:

[0121] According to the formation error formula (6), we can get

[0123]

[0124] in,

[0125]

[0126] Where: Indicates e 1,i The first derivative of i,d represents an intermediate variable; represents the deviation between the actual speed and the estimated speed of the i-th unmanned system; express The first derivative of ; Represents x 1d The first derivative of ; express The first derivative of ; represents the deviation between the actual speed and the estimated speed of the jth neighbor of the i-th unmanned system; represents the estimated speed of the jth neighbor unmanned system of the ith unmanned system; j is the index number of the neighbor unmanned system of the ith unmanned system;

[0127] S42: Construct the first Lyapunov function V as follows 1,i for

[0128]

[0129] Where: V 1,i represents the first Lyapunov function; Indicates e 1,i The transpose of

[0130] From formula (11), find the first Lyapunov function V 1,i The derivative with respect to time is:

[0131]

[0132] According to the first Lyapunov function V 1,iWith respect to the time derivative (12), the following virtual controller is designed, and we get:

[0133]

[0134] Where: c 1,j , are the design parameters of the virtual control law. q is a design parameter greater than 1, and ρ is a design parameter greater than 0 and less than 1;

[0135] in,

[0136]

[0137] sig 2ρ-1 (e z1,i )=sign(e z1,i )|e z1,i | 2ρ-1 ;

[0138] Where: e z1,i Indicates e 1,i The error of the zth element in ; z represents e 1,i The element number in; Z represents e 1,i The total number of elements in ; sign(·) represents the sign function;

[0139] Specifically, in a specific embodiment of the present invention, e 1,i There are 3 elements in , so,

[0140]

[0141] sig 2ρ-1 (e 11,i )=sign(e 11,i )|e 11, i| 2ρ-1 ;

[0142] sig 2ρ-1 (e 31, i)=sign(e 31,i )|e 31,i | 2ρ-1 ;

[0143] sig 2ρ-1 (e 21,i )=sign(e 21,i )|e 21,i | 2ρ-1

[0144] S43: By And the first-order filter output error formula (8), we get

[0145]

[0146] Where: Represents filtering error; B i (·) is about the variable A continuous function of Represents x 1d The second-order derivative of; S5: According to the formation speed error vector, filtering error and virtual controller, a fixed-time fuzzy adaptive event-triggered formation controller based on an event trigger mechanism is established; to complete the fixed-time fuzzy adaptive event-triggered formation control of multiple unmanned systems.

[0147] Preferably, the method for acquiring the fixed-time fuzzy adaptive event-triggered formation controller based on the event trigger mechanism is as follows:

[0148] S51: Based on the fuzzy state observer (5) and the formation speed error vector (7), e i2 Derivation, we get

[0149]

[0150] Where: e 2,i represents the formation velocity error vector; Represents x 2,i The estimated inertia matrix; x 2,i represents the velocity vector under the state equation; Represents x 2,i An estimate of , that is, an estimate of the velocity vector of the unmanned system; express The inverse of i represents control input; express estimates; represents the fuzzy parameter matrix; express The transpose of represents the fuzzy basis function vector; Represents x 1,i estimates; Represents x 2,i The estimate of the velocity vector of the unmanned system; x 1,i represents the position vector under the state equation; k 2,i and k 3,i All are observation gains; represents the observation error; express The first derivative of ; for The first derivative of ; represents virtual control input; represents virtual control input;

[0151] S52: Construct the following second Lyapunov function:

[0152]

[0153] Where: V 2,i represents the second Lyapunov function; represents the error between the ideal parameters and the estimated parameters; δ i Indicates w i Design parameters of the adaptive law;

[0154] From formula (15), we can get the second Lyapunov function V 2,i The time derivative of

[0155]

[0156] S53: According to the second Lyapunov function V 2,i The time derivative of (17) is used to obtain the formation controller as follows:

[0157]

[0158] in,

[0159]

[0160] Specifically, in this embodiment, e 1,i and e 2,i The number of elements in is the same. In one embodiment of the present invention, e 2,i There are 3 elements in , so,

[0161]

[0162] sig 2ρ-1 (e 12,i )=sign(e 12,i )|e 12,i | 2ρ-1 ;

[0163] sig 2ρ-1 (e 32,i )=sign(e 32,i )|e 32,i | 2ρ-1 ;

[0164] sig 2ρ-1 (e 22,i )=sign(e 22,i )|e 22,i | 2ρ-1

[0165] Where: e 12,i Indicates e 2,i The error of the first element in, e 22,i Indicates e 2,i The error of the second element in 32,i Indicates e 2,i The error of the third element in c 2,i , All represent the design parameters of the formation controller;

[0166] Among them, the virtual controller and the formation controller of this embodiment respectively introduce the intermediate calculation parameter sig 2 ρ-1 (e 1,i ) and sig 2ρ-1 (e 2,i ), so that the convergence speed of the control method of this embodiment can converge within a fixed time.

[0167] Preferably, the event triggering mechanism is expressed as follows:

[0168] In the traditional fuzzy adaptive formation control method, there are usually problems such as frequent updates of actuator signals and redundant transmission resources in the controller-actuator channel. To solve this problem, the following event trigger mechanism is designed:

[0169] τ i (t) = ω i (t 2,h ),t∈[t 2,h ,t 2,h+1 ) (19)

[0170] t 2,h+1 = inf{t>t 2,h :|τ ki -ω ki |≥m τ} (20)

[0171] Where: τ i (t) represents the actual control input; ω i represents the event triggering controller vector of the i-th unmanned system; t 2,h represents the sampling time; t represents time; inf{·} represents the lower bound function; τ ki represents the kth component of the control input vector of the ith unmanned system; ω ki represents the kth element of the event triggering controller vector of the i-th unmanned system; m τ represents the trigger threshold; k represents the index number of the component of the control input vector in the unmanned system, k = 1, 2, 3; m τ is a design parameter greater than 0,

[0172] ω i =[ω 1,i ,ω 2,i ,ω 3,i ] T At time t 2,h Updated when, h=1,2,…, h represents a positive integer; ω 1,i Represents ω i The first element of 2,i Represents ω i The second element of 3,i Represents ω i The third element of ;

[0173] Preferably, the event-triggered controller vector ω is designed by utilizing the event-triggered mechanism formulas (19) and (20). i and the fuzzy parameter matrix Estimates The adaptive law is

[0174]

[0175] In the formula, express Estimates of 2,i Represents the first design parameter of the event-triggered controller; Represents the second design parameter of the event-triggered controller; represents the design parameters of the adaptive law.

[0176] This embodiment has the following beneficial effects:

[0177] The unmanned system in this embodiment receives the position and speed information of neighboring nodes through the wireless communication equipment carried by it, and uses the approximation ability of the fuzzy logic system to estimate the speed vector of the unmanned system. At the same time, the event triggering technology of this embodiment enables the control signal of the unmanned system to be updated and transmitted only when the specified triggering conditions are met, thereby reducing the waste of network communication resources. In addition, the fixed time control method can achieve convergence within a fixed time in terms of convergence speed, and at the same time has more advantages in terms of convergence accuracy and initial state information limitation, which can make the unmanned system stable within a fixed time; therefore, the event-triggered formation control method of this embodiment has broad application value and research significance.

[0178] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fixed-time fuzzy adaptive event-triggered formation control method for multiple unmanned systems, characterized in that: The steps include: S1: establishing a mathematical model of an unmanned system taking environmental disturbance factors into consideration; and rewriting the mathematical model of the unmanned system into a state equation to obtain a position vector under the state equation and a velocity vector under the state equation; S2: According to the position vector under the state equation and the velocity vector under the state equation, a fuzzy state observer based on the mathematical model of the unmanned system is established to obtain an estimate of the velocity vector of the unmanned system; S3: Based on the estimation of the unmanned system velocity vector, obtain the formation velocity error vector: S4: According to the formation error vector and the formation speed error vector, based on the fuzzy state observer and the first-order filter, a filtering error is obtained to obtain a fixed-time virtual controller; S5: establishing a fixed-time fuzzy adaptive event-triggered formation controller based on an event-triggered mechanism according to the formation speed error vector, the filtering error and the fixed-time virtual controller; To complete the fixed-time fuzzy adaptive event-triggered formation control of multiple unmanned systems.

2. A fixed-time fuzzy adaptive event-triggered formation control method for multiple unmanned systems according to claim 1, characterized in that: The method for obtaining the fixed-time fuzzy adaptive event-triggered formation controller based on the event trigger mechanism is as follows: S51: According to the fuzzy state observer and the formation speed error vector, we get Where: e 2,i represents the formation velocity error vector; Represents x 2,i The estimated inertia matrix; x 2,i represents the velocity vector under the state equation; Represents x 2,i An estimate of , that is, an estimate of the velocity vector of the unmanned system; express The inverse of i represents control input; express estimates; represents the fuzzy parameter matrix; express The transpose of represents the fuzzy basis function vector; Represents x 1,i estimates; Represents x 2,i The estimate of the velocity vector of the unmanned system; x 1,i represents the position vector under the state equation; k 2,i and k 3,i All are observation gains; represents the observation error; express The first derivative of ; for The first derivative of ; represents virtual control input; represents virtual control input; S52: Construct the following second Lyapunov function: Where: V 2,i represents the second Lyapunov function; represents the error between the ideal parameters and the estimated parameters; e 2,i represents the formation velocity error vector; Indicates e 2,i The transpose of Represents the first-order filter output error; express The transpose of i Indicates w i Design parameters of the adaptive law; represents the error between the ideal parameters and the estimated parameters; express The transpose of Get the second Lyapunov function V 2,i The time derivative of Where: φ i Expressed as a positive constant; α i Indicates a virtual controller; B i (·) is a continuous function of the variable; S53: According to the second Lyapunov function V 2,i The time derivative of , the formation controller is obtained as follows: Among them, a i,d represents an intermediate variable; c 2,i , Both represent the design parameters of the formation controller.

3. The method for controlling a multi-unmanned system fixed-time fuzzy adaptive event-triggered formation according to claim 1, characterized in that: The mathematical model of the unmanned system is established as follows: Where: represents the inertia matrix of the unmanned system, represents the space of all n×n real matrices, where n represents a real number; represents the Coriolis force-centrifugal force matrix of the unmanned system, represents the gravity vector of the unmanned system, represents n-dimensional Euclidean space; q i represents the position vector of the unmanned system, represents the velocity vector of the unmanned system, represents the acceleration vector of the unmanned system, τ i represents the control input, σ i represents environmental disturbance, 4. The method for controlling a multi-unmanned system fixed-time fuzzy adaptive event-triggered formation according to claim 1, characterized in that: The mathematical model of the unmanned system is rewritten as a state equation as follows: Let x 1,i =q i and but Where: M i (x 2,i ) represents the inertia matrix under the state equation; M i (x 2,i ) -1 Indicates M i (x 2,i ) is the inverse of i (x 1,i ,x 2,i ) represents the Coriolis force-centrifugal force matrix under the state equation; g i (x 2,i ) represents the gravity vector under the state equation; x 1,i represents the position vector under the state equation; x 2,i represents the velocity vector under the state equation; Represents x 1,i The first derivative of ; Represents x 2,i The first derivative of .

5. The method for controlling a multi-unmanned system fixed-time fuzzy adaptive event-triggered formation according to claim 1, characterized in that: The fuzzy state observer is established as follows: Let f 2,i (x 1,i ,x 2,i )=-M i (x 2,i ) -1 (C i (x 1,i ,x 2,i )x 2,i +g i (x 2,i )) Using fuzzy logic system Approximation f 2,i (x 1,i ,x 2,i ), which is expressed as follows: Where: represents a fuzzy logic system; represents the fuzzy parameter matrix; express The transpose of represents the fuzzy basis function vector; ε i represents the approximation error; f 2,i (x 1,i ,x 2,i ) is an unknown nonlinear function; Among them, there are unknown constants satisfy Among them, ‖ε i ‖ represents ε i The 2-norm of ; but, Where: y i0 Indicates system output; Therefore, the fuzzy state observer is established as Where: express estimates; express estimates; Represents x 1,i estimates; Represents x 2,i An estimate of , that is, an estimate of the velocity vector of the unmanned system; represents the observation error; Represents x 2,i Estimated inertia matrix; express The estimation of , that is, the estimation of the fuzzy parameter matrix; express The first derivative of ; Represents y i0 Estimate of k 1,i , k 2,i and k 3,i Both are observation gains.

6. The method for controlling a multi-unmanned system fixed-time fuzzy adaptive event-triggered formation according to claim 1, characterized in that: The formation velocity error vector is obtained as follows: Where: e 1,i represents the formation error vector; j represents the index number of the neighboring unmanned system of the i-th unmanned system; I represents the total number of unmanned systems; a i,j represents the connection mark between the ith unmanned system and the jth neighbor unmanned system of the ith unmanned system; x 1d represents the desired position; x 1,j represents the position of the jth neighbor unmanned system of the ith unmanned system; represents the time-varying distance between the ith unmanned system and the pilot unmanned system; represents the time-varying distance between the jth neighbor unmanned system of the ith unmanned system and the pilot unmanned system; a i,0 represents the connection mark between the ith unmanned system and the pilot unmanned system; e 2,i represents the formation velocity error vector; represents virtual control input; in, The first-order filter satisfies the following: Where: Represents the first-order filter output error; α i Represents a virtual controller; φ i is represented as a positive constant; for The first derivative of ; express The initial value of α i (0) indicates α i The initial value of .

7. The method for controlling a multi-unmanned system fixed-time fuzzy adaptive event-triggered formation according to claim 1, characterized in that: The method for obtaining the virtual controller at a fixed time is as follows: S41: Obtain the first-order derivative of the formation error vector to obtain a connection mark between the unmanned system and its neighboring system, as follows: in, Where: Indicates e 1,i The first derivative of i,d represents an intermediate variable; represents the deviation between the actual speed and the estimated speed of the i-th unmanned system; express The first derivative of ; Represents x 1d The first derivative of ; express The first derivative of ; represents the deviation between the actual speed and the estimated speed of the jth neighbor of the i-th unmanned system; represents the estimated speed of the jth neighbor unmanned system of the ith unmanned system; j is the index number of the neighbor unmanned system of the ith unmanned system; S42: Construct the first Lyapunov function V as follows 1,i for Where: V 1,i represents the first Lyapunov function; Indicates e 1,i The transpose of Get the first Lyapunov function V 1,i The derivative with respect to time is: According to the first Lyapunov function V 1,i The derivative with respect to time is: Where: c 1,j , are the design parameters of the virtual control law. q is a design parameter greater than 1, and ρ is a design parameter greater than 0 and less than 1; in, Mr 2ρ-1 (And z1,i )=sign(e z1,i )|and z1, i| 2ρ-1 ; Where: e z1,i Indicates e 1,i The error of the zth element in ; z represents e 1,i The element number in; Z represents e 1,i The total number of elements in ; sign(·) represents the sign function; S43: By And the first-order filter output error, get the virtual controller, the formula used is as follows, Where: Represents the first-order filter output error; Represents x 1d The second derivative of .

8. The method for controlling a multi-unmanned system fixed-time fuzzy adaptive event-triggered formation according to claim 5, characterized in that: The event triggering mechanism is as follows: τ i (t)=ω i (t 2,h ),t∈[t 2,h ,t 2,h+1 ) t 2,h+1 =inf{t>t 2,h :|τ ki -ω ki |≥m τ } Where: τ i (t) represents the actual control input; ω i represents the event triggering controller vector of the i-th unmanned system; t 2,h represents the sampling time; t represents time; inf{·} represents the lower bound function; τ ki represents the kth component of the control input vector of the ith unmanned system; ω ki represents the kth element of the event triggering controller vector of the i-th unmanned system; m τ represents the trigger threshold; k represents the index number of the control input vector component in the unmanned system; m τ is a design parameter greater than 0.

9. A fixed-time fuzzy adaptive event-triggered formation control method for multiple unmanned systems according to claim 8, characterized in that: Estimation of event-triggered controller vector and fuzzy parameter matrix The adaptive law is In the formula, express Estimates of 2,i Represents the first design parameter of the event-triggered controller; Represents the second design parameter of the event-triggered controller; represents the design parameters of the adaptive law.

Images