A marine robot cluster tracking optimization control method for non-cooperative targets

Abstract

The application discloses a kind of marine robot cluster tracking optimization control methods for non-cooperative target, first for the marine robot system working in water surface environment, respectively establish linearization marine robot cluster dynamics model and the dynamics model of non-cooperative target;Then construct state tracking error system;Design finite time sliding mode control protocol, simultaneously solve the equivalent state tracking error system that moves on sliding surface;Next define the performance index function of marine robot cluster system, design distributed state feedback nominal optimization control protocol, ensure that performance index function meets global Nash equilibrium;Finally, using Hurwitz stability theory proves that distributed state feedback nominal optimization control protocol can ensure the asymptotic stability of equivalent state tracking error system.The method of the application can realize the optimization tracking control of marine robot cluster system to non-cooperative target with uncertain control strategy under the interference of complex marine environment water surface wind wave.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of robots, and particularly relates to a marine robot cluster tracking optimization control method for non-cooperative targets. BACKGROUND

[0002] Marine robots have the characteristics of flexible deployment and high maneuverability, and have become one of the key equipment widely used in the marine field. Compared with a single marine robot, a marine robot cluster system has many advantages such as wide operation area, strong survivability and high robustness, and is more suitable for complex marine environments. When the marine robot cluster system performs a tracking task for a non-cooperative target with a dynamic and uncertain motion trend, the unknown control strategy of the non-cooperative target and the surface wind and wave of the complex marine environment cause the control system to inevitably have disturbance components. Improper handling of the above disturbances will affect the stability and convergence of the control algorithm, and even cause the task to fail. SUMMARY

[0003] In order to overcome the shortcomings of the prior art, the application provides a marine robot cluster tracking optimization control method for non-cooperative targets. First, for a marine robot system working in a surface environment, a linearized marine robot cluster dynamics model and a non-cooperative target dynamics model are respectively established. Then, a state tracking error system is constructed. A finite-time sliding mode control protocol is designed for the state tracking error system, and an equivalent state tracking error system moving on a sliding surface is solved. Next, a performance index function of the marine robot cluster system is defined, a distributed state feedback nominal optimization control protocol is designed, and it is ensured that the performance index function satisfies global Nash equilibrium. Finally, the Hurwitz stability theory is used to prove that the distributed state feedback nominal optimization control protocol can ensure the asymptotic stability of the equivalent state tracking error system. The method can realize the optimization tracking control of the marine robot cluster system on the non-cooperative target with an uncertain control strategy under the disturbance of the surface wind and wave of the complex marine environment.

[0004] The technical scheme adopted by the application to solve the technical problems is as follows:

[0005] Step 1: For a marine robot system working in a surface environment, a linearized marine robot cluster dynamics model and a non-cooperative target dynamics model are respectively established.

[0006] Step 2: For the marine robot cluster dynamics model and the non-cooperative target dynamics model constructed in step 1, a state tracking error system is constructed. A finite-time sliding mode control protocol is designed for the state tracking error system, and an equivalent state tracking error system moving on a sliding surface is solved.

[0007] Step 3: Defining a performance index function of the swarm system of marine robots, designing a distributed state feedback nominal optimal control protocol, and ensuring that the performance index function satisfies global Nash equilibrium for the equivalent state tracking error system obtained in Step 1;

[0008] Step 4: Using Hurwitz stability theory to prove that the distributed state feedback nominal optimal control protocol designed in Step 3 can ensure the asymptotic stability of the equivalent state tracking error system.

[0009] Further, the step 1 is specifically:

[0010] Step 1-1: The following six-degree-of-freedom swarm dynamics model of marine robots is given:

[0011]

[0012] wherein η i =[η ix ,η iy ,φ i ] T represents the position and angle components of the marine robot, η ix ,η iy ,φ i respectively represent the x-axis coordinate, y-axis coordinate and heading angle of the marine robot in the earth coordinate system; v i =[v ix ,v iy ,ω i ] T represents the velocity component of the marine robot, v ix ,v iy ,ω i respectively represent the x-axis direction velocity, y-axis direction velocity and heading angle velocity of the marine robot in the earth coordinate system; u i represents the control input, f i represents an uncertain water surface wave disturbance input and satisfies ||f i ||≤γ, γ is a positive number greater than 0; and are respectively the inertia matrix, fluid damping matrix and mooring force matrix of the system; N represents the number of marine robots; is a coordinate conversion matrix, which is represented as follows:

[0013]

[0014] Step 1-2: Let be a time-invariant constant, and the six-degree-of-freedom swarm dynamics model of marine robots described in equation (1) is constructed as the following linearized swarm dynamics model of marine robots:

[0015]

[0016] wherein,

[0017]

[0018] Step 1-3: The following six-degree-of-freedom non-cooperative target dynamics model is given:

[0019]

[0020] wherein, x0 = [η0, v0] Τ denotes the state component of the non-cooperative target, η0, v0denote the pose component and the velocity component of the non-cooperative target respectively; u0denotes the uncertain control input of the non-cooperative target and satisfies ||u0||≤α, α is a positive number greater than 0; f0denotes the uncertain water surface wave disturbance input of the non-cooperative target and satisfies ||f0||≤γ.

[0021] Further, the step 2 is specifically:

[0022] Step 2-1: The state tracking error system is constructed as follows:

[0023]

[0024] wherein, a ij denotes the communication relationship between the i-th ocean robot and the j-th ocean robot, when the i-th ocean robot can obtain the state information of the j-th ocean robot, a ij = 1, otherwise a ij = 0; x j denotes the state information of the j-th ocean robot;

[0025] Step 2-2: A directed graph G is selected denotes the communication relationship between the ocean robot cluster and the non-cooperative target, and contains a directed spanning tree with the non-cooperative target as the root node, then the directed graph G The corresponding Laplacian matrix is represented as follows:

[0026]

[0027] wherein, is a non-singular M matrix, denotes the matrix component;

[0028] Step 2-3: Based on the Kronecker product, the global form of formula (4) is represented as:

[0029]

[0030] where 1 N denotes an N-dimensional column vector with all elements equal to 1, I p denotes an identity matrix with appropriate dimension; X denotes the global form of the marine robot swarm system state components;

[0031] Step 2-4: Since is a nonsingular M-matrix, the state tracking error system is equivalent to the multi-marine robot swarm system achieving the tracking of the non-cooperative target, i.e.

[0032] Taking the derivative of both sides of equation (6) gives

[0033]

[0034] where

[0035]

[0036] Let h i = f i (u0+ f0), then equation (7) is rewritten as

[0037]

[0038] where denotes the equivalent disturbance component;

[0039] Step 2-5: The integral-type sliding mode variable is designed as follows:

[0040]

[0041] where ∈ i (0) denotes the variable ∈ i at the initial time t = 0, M is a constant matrix and satisfies the matrix MBis a full rank matrix, is the distributed state feedback nominal optimal control protocol to be designed; a i0 denotes the communication relationship between the i-th marine robot and the non-cooperative target, a i0 = 1 indicates that the i-th marine robot can directly obtain the state information of the non-cooperative target;

[0042] Taking the derivative of both sides of equation (9) gives

[0043]

[0044] Based on the Kronecker product, the global form of equation (10) is represented as

[0045]

[0046] where

[0047]

[0048] Step 2-6: For the system given in formula (10), the finite time sliding mode control protocol is designed as follows:

[0049]

[0050] In the formula, sgn(s i ) = [sgn(s i1 ),..., sgn(s ip )] T represents the sign function of variable s i , and β represents the sliding mode gain parameter to be designed;

[0051] Substituting formula (12) into formula (11) has:

[0052]

[0053] The sliding mode gain parameter β1 is a positive number greater than 0; the Lyapunov function V sm related to formula (11) is selected as T S, then according to the fixed time stability theory, it can be obtained that the finite time sliding mode control protocol designed in formula (12) guarantees that the integral sliding mode variable s i = 0 is realized in a finite time; according to formula (11), s i = 0 is equivalent to U-U mm +H = 0, so the equivalent state tracking error system on the sliding surface is represented as:

[0054]

[0055] Further, the step 3 is specifically:

[0056] Step 3-1: For the equivalent state tracking error system (14), the performance index function is defined as follows:

[0057]

[0058] In the formula, ∈ ij = [∈ i , ∈ j ] Τ , represents the incidence of the i-th marine robot; represents the weighted matrix of the tracking error; is a positive definite symmetric matrix and satisfies and respectively represent the matrix and The minimum eigenvalue of Representation matrix The maximum eigenvalue of and is a symmetric positive definite matrix, c is a coupling parameter and satisfies Representation matrix The smallest singular value of ; is a positive definite solution to the following algebraic Riccati equation:

[0059]

[0060] Step 3-2: Based on the equivalent state tracking error system (14) and the performance index function (15), a distributed state feedback nominal optimization control protocol is designed as follows:

[0061]

[0062] According to equations (14) and (15), the following Hamiltonian function is selected:

[0063]

[0064] Where, Represents a value function;

[0065] According to optimization theory, it can be proved that under the action of the distributed state feedback nominal optimization control protocol (17), the performance indicator function (15) can satisfy the global Nash equilibrium.

[0066] Furthermore, the step 4 is specifically as follows:

[0067] Step 4-1: Substitute the distributed state feedback nominal optimization control protocol (17) into the equivalent state tracking error system (14) to obtain:

[0068]

[0069] Where,

[0070] Step 4-2: Define the matrix The equivalent standard form is where Ξ is an invertible matrix of suitable dimensions, so the matrix A ∈ is the Hurwitz equivalent of the matrix is Hurwitz's; from the algebraic Riccati equation (16) we can infer that:

[0071]

[0072] The matrix A can be obtained ∈is Hurwitz's;

[0073] According to Hurwitz stability theory, it is inferred that the equivalent state tracking error system (14) is asymptotically stable.

[0074] The beneficial effects of the present application are as follows:

[0075] By using the marine robot cluster tracking optimization control method for non-cooperative targets provided in the present application, the tracking error norm of each state component gradually converges to zero at about 30 seconds, and has good stability. Therefore, the control protocol provided in the present application can realize the optimization tracking control of the marine robot cluster system on the non-cooperative target with uncertain control strategy under the disturbance of the wind and wave on the water surface in the complex marine environment. BRIEF DESCRIPTION OF DRAWINGS

[0076] Figure 1 Fig. 1 is a schematic diagram of the communication topology structure between the non-cooperative target (marked as 0) and the four marine robots (marked as 1 to 4) in the embodiment of the present application;

[0077] Figure 2 Fig. 2 is a tracking error norm curve of the state components of the four marine robots under the control protocol provided in the present application in the embodiment of the present application;

[0078] Figure 3 Fig. 3 is a tracking error norm curve of the state components of the four marine robots under the control protocol provided in the present application in the embodiment of the present application;

[0079] Figure 4 Fig. 4 is a tracking error norm curve of the state components of the four marine robots under the control protocol provided in the present application in the embodiment of the present application. DETAILED DESCRIPTION

[0080] The present application is further illustrated below in combination with the drawings and embodiments.

[0081] The application provides a marine robot cluster tracking control method for non-cooperative targets.

[0082] A marine robot cluster tracking optimization control method for non-cooperative targets, and the technical solution is as follows:

[0083] Step one: considering a kind of marine robot system working in the water surface environment, linear marine robot cluster dynamics model and non-cooperative target dynamics model are respectively established.

[0084]

[0085] In the formula, η i =[η ix ,η iy ,φ i ] T Indicate the position and angle components of the marine robot, v i =[v ix ,v iy ,ω i ] T Indicate the speed components of the marine robot; u i Indicate the control input, f i Indicate the uncertain water surface wind disturbance input and satisfy ||f i ||≤γ, γ is a normal number greater than 0; And Respectively, the inertia matrix, fluid damping matrix and mooring matrix of the system, The coordinate conversion matrix is as follows:

[0086] The application can realize the tracking control of the marine robot cluster system on the non-cooperative target, and the system can realize the expected control performance with the optimal control input.

[0082] A marine robot cluster tracking optimization control method for non-cooperative targets, and the technical solution is as follows:

[0083] Step one: considering a kind of marine robot system working in the water surface environment, linear marine robot cluster dynamics model and non-cooperative target dynamics model are respectively established.

[0084]

[0085] In the formula, η i =[η ix ,η iy ,φ i ] T Indicate the position and angle components of the marine robot, v i =[v ix ,v iy ,ω i ] T Indicate the speed components of the marine robot; u i Indicate the control input, f i Indicate the uncertain water surface wind disturbance input and satisfy ||f i ||≤γ, γ is a normal number greater than 0; And Respectively, the inertia matrix, fluid damping matrix and mooring matrix of the system, The coordinate conversion matrix is as follows:

[0086] The application can realize the tracking control of the marine robot cluster system on the non-cooperative target, and the system can realize the expected control performance with the optimal control input.

[0087] Let For a time-invariant constant, the six-degree-of-freedom (6-DOF) dynamics model of the swarm of AUVs described in equation (1) is constructed as the following linearized dynamics model of the swarm of AUVs:

[0088]

[0089] where,

[0090]

[0091] Further, the following 6-DOF dynamics model of the non-cooperative target is given:

[0092]

[0093] where, x0=[η0,v0] Τ denotes the state components of the non-cooperative target; u0denotes the uncertain control input of the non-cooperative target and satisfies ||u0||≤α, α is a positive constant; f0denotes the uncertain water surface wind disturbance input and satisfies ||f0||≤γ.

[0094] Step two: In order to overcome the uncertain control strategy of the non-cooperative target and the water surface wind and other disturbance quantities existing in the complex ocean environment, a state tracking error system based on the leader-follower mechanism is constructed for the dynamics model of the swarm of AUVs and the dynamics model of the non-cooperative target constructed in step one, and a finite time sliding mode control protocol is designed for the above error system, and the equivalent state tracking error system moving on the sliding surface is solved. First, the state tracking error system is constructed as follows:

[0095]

[0096] A directed graph G is selected denotes the communication relationship between the swarm of AUVs and the non-cooperative target, and contains a directed spanning tree with the non-cooperative target as the root node, then the directed graph G The corresponding Laplacian matrix can be expressed as follows:

[0097]

[0098] where, is a non-singular M matrix.

[0099] Based on the Kronecker product, the global form of equation (4) can be expressed as:

[0100]

[0101] where, 1N N-dimensional column vector with all elements equal to 1, I p denotes the identity matrix with appropriate dimensions. According to equation (6), since is a nonsingular M-matrix, the state tracking error system is equivalent to the multi-aquatic robot swarm system to track the non-cooperative target, i.e. Taking the derivative of both sides of equation (6) gives

[0102]

[0103] where

[0104]

[0105] Let h i = f i (u0+ f0), i = 1, …, N, then equation (7) can be rewritten as

[0106]

[0107] where denotes the equivalent interference component.

[0108] For the system given in equation (8), the integral type sliding mode variable is designed as follows:

[0109]

[0110] where ∈ i (0) denotes the variable ∈ i at the initial time t = 0, M is a constant matrix and satisfies the matrix MBis a full rank matrix, is the distributed state feedback nominal optimal control protocol to be designed; a ij denotes the communication relationship between the i-th aquatic robot and the j-th aquatic robot, when the i-th aquatic robot can obtain the state information of the j-th aquatic robot, a ij = 1, otherwise a ij = 0; a i0 denotes the communication relationship between the i-th aquatic robot and the non-cooperative target, a i0 = 1 indicates that the i-th aquatic robot can directly obtain the state information of the non-cooperative target. Taking the derivative of both sides of equation (9) gives

[0111]

[0112] Based on the Kronecker product, the global form of equation (10) can be expressed as:

[0113]

[0114] where,

[0115]

[0116] For the system given in equation (10), the finite-time sliding mode control protocol is designed as follows:

[0117]

[0118] where sgn(s i ) = [sgn(s i1 ),..., sgn(s ip )] T is the sign function of variable s i , and β is the sliding mode gain parameter to be designed. Substituting equation (12) into equation (11) gives:

[0119]

[0120] The sliding mode gain parameter β1is selected as a positive constant greater than 0. The Lyapunov function related to equation (11) is selected as V sm = 0.5S T S, then according to the fixed-time stability theory, the finite-time sliding mode control protocol designed in equation (12) guarantees that the integral sliding mode variable s i = 0 is achieved in finite time. According to equation (11), s i = 0 is equivalent to U-U mm + H = 0, thus the equivalent state tracking error system on the sliding surface for the system on the sliding surface can be expressed as:

[0121]

[0122] Step three: for the equivalent state tracking error system on the sliding surface obtained in step two, the performance index function of the marine robot swarm system is defined, and the distributed state feedback nominal optimal control protocol is designed to ensure that the performance index function satisfies the global Nash equilibrium; first, for the equivalent state tracking error system (14) in step two, the performance index function is defined as follows:

[0123]

[0124] where ∈ ij = [∈ i , ∈ j ] Τ , is the in-degree of the i-th marine robot; is the weighted matrix of the tracking error; is a positive definite symmetric matrix and satisfies denote the minimum eigenvalue of the matrix denote the maximum eigenvalue of the matrix are symmetric positive definite matrices, c is a coupling parameter and satisfies denote the minimum singular value of the matrix is the positive definite solution of the following algebraic Riccati equation:

[0125]

[0126] For the equivalent state tracking error system (14) and the performance index function (15), the distributed state feedback nominal optimal control protocol is designed as follows:

[0127]

[0128] According to the formula (14) and formula (15), the following Hamilton function is selected:

[0129]

[0130] In the formula, V denotes the value function. According to the optimization theory, it can be proved that under the action of the distributed state feedback nominal optimal control protocol (17), the performance index function (15) can satisfy the global Nash equilibrium.

[0131] Step four: using Hurwitz stability theory to prove that the distributed state feedback nominal optimal control protocol designed in step three can ensure the asymptotic stability of the equivalent state tracking error system in step two. First, substitute the distributed state feedback nominal optimal control protocol (17) into the equivalent state tracking error system (14) to have:

[0132]

[0133] In the formula, V

[0134] The Jordan canonical form of the matrix is defined as where Ξ is a reversible matrix with appropriate dimensions, so the matrix A ∈ is Hurwitz, which is equivalent to the matrix is Hurwitz. According to the algebraic Riccati equation (16), it can be deduced that:

[0135]

[0136] The matrix A​​​​​∈ Hurwitz. According to Hurwitz stability theory, it can be inferred that the equivalent state tracking error system (14) is asymptotically stable.

[0137] Embodiment:

[0138] Suppose there is a marine robot cluster system composed of 1 non-cooperative target and 4 marine robots, and the communication topology between each marine robot and the non-cooperative target is as shown in Figure 1 The Laplace matrix corresponding to the communication topology is represented as follows:

[0139]

[0140] The inertia matrix, fluid damping matrix, and mooring force matrix parameters of the system are selected as follows:

[0141]

[0142] Let the uncertain sea surface wind wave disturbance input acting on the non-cooperative target and the 4 marine robots be as follows:

[0143] f0=0.1[sin(0.1t),sin(0.1t),sin(0.1t)] T ,

[0144] f1=0.1[sin(0.1t),sin(0.1t),sin(0.1t)] T ,

[0145] f2=0.1[0.5sin(0.1t)-0.5,0.5sin(0.1t)-0.5,0.5sin(0.1t)-0.5] T ,

[0146] f3=0.1[0.5cos(0.1t)+0.5,0.5cos(0.1t)-0.5,0.5cos(0.1t)+0.5] T ,

[0147] f4=0.1[cos(0.1t),cos(0.1t),cos(0.1t)] T ,

[0148] The upper bound parameter of the uncertain sea surface wind wave disturbance input can be taken as The uncertain control input of the non-cooperative target is selected as u0=0.1[sin(0.1t),0.5sin(0.1t)+0.5,0.5cos(0.1t)+0.5] T , and its upper bound parameter can be taken as According to the finite time sliding mode control protocol designed for Equation (12), let the matrix M = [O 3× 3I3], the sliding mode gain parameter is selected as β=105.5482. Finally, let the matrix The coupling parameter c = 100, based on the algebraic Riccati equation (16), the control gain matrix in the distributed state feedback nominal optimization control protocol (17) can be calculated as for:

[0149]

[0150] Furthermore, let the initial states of the non-cooperative target and the four marine robots be:

[0151] x0(0)=[0.5,0.5,π / 3,0.1,0.1,0] T ,

[0152] x1(0)=[1,1.5,π / 6,0.1,0.15,0.1] T ,

[0153] x2(0)=[3,3.5,π / 8,0.3,0.35,0.3] T ,

[0154] x3(0)=[-1,-1.5,-π / 6,-0.1,-0.15,-0.1] T ,

[0155] x4(0)=[-2,-2.5,-π / 8,-0.2,-0.25,-0.2] T ,

[0156] Then, under the control protocol proposed in the present invention, the tracking error curves η of the four marine robot state components can be obtained. ix ,η iy and φ i The tracking error norm curve is as follows Figures 2 to 4 As shown in the figure, the simulation curves of the state component tracking error norms show that under the proposed control protocol, the tracking error norms of each state component gradually converge to zero in approximately 30 seconds, demonstrating good stability. Therefore, the control protocol proposed in this invention can achieve state tracking of non-cooperative targets with uncertain control strategies by a marine robot swarm system in complex marine environments with surface wind and wave interference.

Claims

1. A non-cooperative target-oriented marine robot swarm tracking optimization control method, characterized in that: The steps include: Step 1: For the marine robot system working in the water environment, establish a linearized marine robot cluster dynamics model and a non-cooperative target dynamics model respectively; Step 2: Construct a state tracking error system based on the dynamic model of the marine robot cluster and the dynamic model of the non-cooperative target constructed in step 1; A finite-time sliding mode control protocol is designed for the state tracking error system, and the equivalent state tracking error system moving on the sliding surface is solved. Step 3: Based on the equivalent state tracking error system obtained in step 2, define the performance index function of the marine robot cluster system and design a distributed state feedback nominal optimization control protocol to ensure that the performance index function satisfies the global Nash equilibrium. Step 4: Use Hurwitz stability theory to prove that the distributed state feedback nominal optimization control protocol designed in step 3 can ensure the asymptotic stability of the equivalent state tracking error system.

2. The method for tracking and optimizing the control of a marine robot cluster for non-cooperative targets according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1: Give the following six-DOF marine robot cluster dynamics model: Where η i =[η ix ,η iy ,φ i ] T represents the position and angle components of the marine robot, η ix ,η iy ,φ i They represent the x-axis coordinate, y-axis coordinate and heading angle of the marine robot around the z-axis in the earth coordinate system; v i =[v ix ,v iy ,ω i ] T represents the velocity component of the marine robot, v ix ,v iy ,ω i They represent the x-axis speed, y-axis speed and heading angular velocity of the marine robot in the earth coordinate system; u i represents the control input, f i Indicates the uncertain water surface wind and wave disturbance input and satisfies ||f i ||≤γ, γ is a positive constant greater than 0; and are the inertia matrix, fluid damping matrix and mooring force matrix of the system respectively; N represents the number of marine robots; is the coordinate transformation matrix, expressed as follows: Step 1-2: Make is a time-invariant constant, and the six-DOF marine robot swarm dynamics model described in Equation (1) is constructed as the following linearized marine robot swarm dynamics model: Where, Step 1-3: Give the following six-degree-of-freedom non-cooperative target dynamic model: Where x0 = [η0, v0] Τ represents the state component of the non-cooperative target, η0, v0 represent the posture component and velocity component of the non-cooperative target respectively; u0 represents the uncertain control input of the non-cooperative target and satisfies ||u0||≤α, α is a positive constant greater than 0; f0 represents the uncertain surface wind and wave interference input received by the non-cooperative target and satisfies ||f0||≤γ.

3. The method for tracking and optimizing the marine robot cluster for non-cooperative targets according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2-1: Construct the state tracking error system as follows: Where a ij Represents the communication relationship between the i-th marine robot and the j-th marine robot. When the i-th marine robot can obtain the status information of the j-th marine robot, a ij =1, otherwise a ij =0;x j Represents the status information of the j-th marine robot; Step 2-2: Select a directed graph represents the communication relationship between the marine robot cluster and the non-cooperative target, and Contains a directed spanning tree with the non-cooperative goal as the root node, then the directed graph The corresponding Laplace matrix is ​​expressed as follows: Where, is a non-singular M matrix, represents the matrix components; Step 2-3: Based on the Kronecker product, the global form of equation (4) is expressed as: Where, 1 N Represents an N-dimensional column vector whose elements are all equal to 1, I p represents an identity matrix with appropriate dimensions; X represents the global form of the state component of the marine robot swarm system; Step 2-4: Due to is a non-singular M matrix, so the state tracking error system It is equivalent to a multi-ocean robot swarm system to track non-cooperative targets, that is, The derivatives of both sides of formula (6) are: Where, Let h i =f i -(u0+f0), then equation (7) can be rewritten as: Where, represents the equivalent interference component; Step 2-5: Design the integral sliding mode variables as follows: Where,∈ i (0) represents the variable ∈ i At the initial value at time t=0, M is a constant matrix and the matrix MB is a full rank matrix. is the distributed state feedback nominal optimization control protocol to be designed; a i0 represents the communication relationship between the i-th marine robot and the non-cooperative target, a i0 =1 means that the i-th marine robot can directly obtain the status information of the non-cooperative target; Taking the derivatives of both sides of formula (9) we have: Based on the Kronecker product, the global form of Equation (10) is expressed as: Where, Step 2-6: For the system given in Equation (10), design a finite-time sliding mode control protocol as follows: Where, sgn(s i )=[sgn(s i1 ),...,sgn(s ip )] T Represents variable s i The sign function of , β represents the sliding mode gain parameter to be designed; Substituting formula (12) into formula (11), we have: Selecting the sliding mode gain parameters β1 is a positive constant greater than 0; the Lyapunov function related to formula (11) is selected as V sm =0.5S T S, then according to the fixed time stability theory, the finite time sliding mode control protocol designed in formula (12) can be obtained to ensure the integral sliding mode variable s i = 0 is realized in a finite time; According to formula (11), we know that s i =0 is equivalent to UU mm +H=0, so the equivalent state tracking error system moving on the sliding surface is expressed as:

4. The method for tracking and optimizing the control of a marine robot cluster for non-cooperative targets according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3-1: For the equivalent state tracking error system (14), define the performance index function as follows: Where,∈ ij =[∈ i ,∈ j ] Τ , represents the in-degree of the i-th marine robot; represents the weighting matrix of tracking error; is a positive symmetric matrix that satisfies and Represents matrices respectively and The minimum eigenvalue of Representation matrix The maximum eigenvalue of and is a symmetric positive definite matrix, c is a coupling parameter and satisfies Representation matrix The smallest singular value of ; is a positive definite solution to the following algebraic Riccati equation: Step 3-2: Based on the equivalent state tracking error system (14) and the performance index function (15), a distributed state feedback nominal optimization control protocol is designed as follows: According to equations (14) and (15), the following Hamiltonian function is selected: Where, represents the value function; According to optimization theory, it can be proved that under the action of the distributed state feedback nominal optimization control protocol (17), the performance indicator function (15) can satisfy the global Nash equilibrium.

5. The method for tracking and optimizing control of marine robot clusters for non-cooperative targets according to claim 4, characterized in that: The step 4 is specifically as follows: Step 4-1: Substitute the distributed state feedback nominal optimization control protocol (17) into the equivalent state tracking error system (14) to obtain: Where, Step 4-2: Define the matrix The equivalent standard form is where Ξ is an invertible matrix of suitable dimensions, so the matrix A ∈ is the Hurwitz equivalent of the matrix is Hurwitz's; from the algebraic Riccati equation (16) we can infer that: The matrix A can be obtained ∈ It's Hurwitz's; According to Hurwitz stability theory, it is inferred that the equivalent state tracking error system (14) is asymptotically stable.

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