Ocean robot cluster tracking optimization control method for non-cooperative target

Abstract

The invention discloses a non-cooperative target-oriented ocean robot cluster tracking optimization control method, which comprises the following steps of: firstly, respectively establishing a linearized ocean robot cluster dynamic model and a non-cooperative target dynamic model for an ocean robot system working in a water surface environment; then constructing a state tracking error system; designing a finite time sliding mode control protocol, and solving an equivalent state tracking error system moving on a sliding mode surface; a performance index function of the ocean robot cluster system is defined, a distributed state feedback nominal optimization control protocol is designed, and it is ensured that the performance index function meets global Nash equilibrium; and finally proving that the distributed state feedback nominal optimization control protocol can ensure the asymptotic stability of the equivalent state tracking error system by utilizing a Hurwitz stability theory. According to the method disclosed by the invention, the optimal tracking control of the ocean robot cluster system on the non-cooperative target with an uncertain control strategy can be realized under the interference of water surface storm waves in a complex ocean environment.

Description

Technical Field

[0001] The invention belongs to the technical field of robots, and in particular relates to a marine robot cluster tracking optimization control method oriented to non-cooperative targets. Background Art

[0002] Marine robots have the characteristics of flexible deployment and high mobility, 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 a wide operating area, strong survivability, and high robustness, and is more suitable for complex and changeable marine environments. When a marine robot cluster performs tracking tasks facing a non-cooperative target with a dynamic and uncertain motion trend, the unknown control strategy of the non-cooperative target and the surface waves of the complex marine environment will inevitably cause interference components in its control system. Improper handling of the above interference will affect the stability and convergence of the control algorithm, and may even lead to mission failure. Summary of the invention

[0003] In order to overcome the shortcomings of the prior art, the present invention provides a marine robot cluster tracking optimization control method for non-cooperative targets. First, for the marine robot system working in the water surface environment, a linearized marine robot cluster dynamics model and a non-cooperative target dynamics model are established respectively; then a state tracking error system is constructed; 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 mode surface is solved at the same time; next, the performance index function of the marine robot cluster system is defined, and a distributed state feedback nominal optimization control protocol is designed to ensure that the performance index function satisfies the 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 of the present invention can realize the optimization tracking control of the marine robot cluster system for non-cooperative targets with uncertain control strategies under the interference of surface wind and waves in a complex marine environment.

[0004] The technical solution adopted by the present invention to solve the technical problem is as follows:

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

[0006] Step 2: Construct a state tracking error system for the marine robot cluster dynamics model and the non-cooperative target dynamics model constructed in step 1; design a finite-time sliding mode control protocol for the state tracking error system, and solve the equivalent state tracking error system moving on the sliding mode surface;

[0007] Step 3: For the equivalent state tracking error system obtained in step 1, define the performance index function of the marine robot cluster system, design a distributed state feedback nominal optimization control protocol, and ensure that the performance index function satisfies the global Nash equilibrium;

[0008] 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.

[0009] Furthermore, the step 1 is specifically as follows:

[0010] Step 1-1: Give the following six-DOF marine robot cluster dynamics model:

[0011]

[0012] 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 rotating 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 represents 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:

[0013]

[0014] Step 1-2: Order is a time-invariant constant, and the six-DOF marine robot cluster dynamics model described in equation (1) is constructed as the following linearized marine robot cluster dynamics model:

[0015]

[0016] In the formula,

[0017]

[0018] Step 1-3: Give the following six-degree-of-freedom non-cooperative target dynamics model:

[0019]

[0020] 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 water surface wind and wave disturbance input received by the non-cooperative target and satisfies ||f0||≤γ.

[0021] Furthermore, the step 2 is specifically as follows:

[0022] Step 2-1: Construct the state tracking error system as follows:

[0023]

[0024] In the formula, 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 jth marine robot;

[0025] 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 Laplacian matrix is ​​expressed as follows:

[0026]

[0027] In the formula, is a non-singular M matrix, represents matrix components;

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

[0029]

[0030] In the formula, 1 N Represents an N-dimensional column vector whose elements are all equal to 1, I p represents the identity matrix with appropriate dimensions; X represents the global form of the state component of the marine robot swarm system;

[0031] 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,

[0032] The derivatives of both sides of equation (6) are:

[0033]

[0034] In the formula,

[0035]

[0036] Let h i =f i -(u0+f0), then equation (7) can be rewritten as:

[0037]

[0038] In the formula, represents the equivalent interference component;

[0039] Step 2-5: Design the integral sliding mode variables as follows:

[0040]

[0041] In the formula, ∈ i (0) indicates 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 a 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;

[0042] Taking the derivatives of both sides of equation (9) we have:

[0043]

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

[0045]

[0046] In the formula,

[0047]

[0048] Step 2-6: For the system given in equation (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 variable s i The sign function of , β represents the sliding mode gain parameter to be designed;

[0051] Substituting formula (12) into formula (11), we have:

[0052]

[0053] 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 limited 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:

[0054]

[0055] Furthermore, the step 3 is specifically as follows:

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

[0057]

[0058] In the formula, ∈ 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 Respectively represent matrices 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: For 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] In the formula, represents the value function;

[0065] According to optimization theory, it can be proved that under 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):

[0068]

[0069] In the formula,

[0070] Step 4-2: Define the matrix The equivalent standard form is where Ξ is a reversible 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 ∈It was 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 invention are as follows:

[0075] By adopting the marine robot cluster tracking optimization control method for non-cooperative targets proposed in the present invention, the tracking error norm of each state component gradually converges to zero in about 30 seconds, with good stability. Therefore, the control protocol proposed in the present invention can realize the optimization tracking control of the marine robot cluster system for non-cooperative targets with uncertain control strategies under the interference of surface wind and waves in complex marine environments. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0077] Figure 2 is a tracking error norm curve of four marine robot state components under the control protocol proposed in the embodiment of the present invention;

[0078] Figure 3 is a tracking error norm curve of four marine robot state components under the control protocol proposed in the embodiment of the present invention;

[0079] Figure 4 It is a tracking error norm curve of four marine robot state components under the control protocol proposed in the embodiment of the present invention. DETAILED DESCRIPTION

[0080] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0081] The present invention provides a marine robot cluster tracking control method for non-cooperative targets. Considering a class of marine robot systems working in a water surface environment, a linearized marine robot cluster dynamics model and a non-cooperative target dynamics model are established respectively; in order to overcome the uncertain control strategy of the non-cooperative target and the disturbances such as surface wind and waves in the complex marine environment, a finite time sliding mode control protocol is designed for the constructed marine robot cluster dynamics model and the non-cooperative target dynamics model, and the equivalent tracking control system moving on the sliding surface is solved at the same time; for the equivalent tracking control system on the sliding surface, a state tracking error system based on the pilot-follower mechanism is constructed, and the performance index function of the marine robot cluster system is defined based on the error system, and a distributed state feedback nominal optimization control protocol is designed to ensure that the performance index function satisfies the global Nash equilibrium; the Hurwitz stability theory is used to prove that the designed distributed state feedback nominal optimization control protocol can ensure the asymptotic stability of the state tracking error system. The method provided by the present invention can realize the tracking control of the marine robot cluster system for non-cooperative targets, and the system can achieve the desired control performance with the optimal control input.

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

[0083] Step 1: Consider a class of marine robot systems working in a water environment, and establish a linearized marine robot cluster dynamics model and a non-cooperative target dynamics model. First, the following six-degree-of-freedom marine robot cluster dynamics model is given:

[0084]

[0085] Where η i =[η ix ,η iy ,φ i ] T represents the position and angle components of the marine robot, v i =[v ix ,v iy ,ω i ] T represents the velocity component of the marine robot; u i represents the control input, f i represents 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, The coordinate transformation matrix is ​​expressed as follows:

[0086]

[0087] make is a time-invariant constant, and the six-DOF marine robot cluster dynamics model described in equation (1) is constructed as the following linearized marine robot cluster dynamics model:

[0088]

[0089] In the formula,

[0090]

[0091] Furthermore, the following six-degree-of-freedom non-cooperative target dynamics model is given:

[0092]

[0093] Where x0 = [η0, v0] Τ Represents the state component of the non-cooperative target; 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 disturbance input and satisfies ||f0||≤γ.

[0094] Step 2: In order to overcome the uncertain control strategy of non-cooperative targets and the disturbances such as wind and waves on the surface in complex marine environments, a state tracking error system based on the pilot-follower mechanism is constructed for the marine robot cluster dynamics model and the non-cooperative target dynamics model constructed in step 1. 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 mode surface is solved. First, the state tracking error system is constructed as follows:

[0095]

[0096] Select 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 can be expressed as follows:

[0097]

[0098] In the formula, is a non-singular M matrix.

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

[0100]

[0101] In the formula, 1N Represents an N-dimensional column vector whose elements are all equal to 1, I p represents a unit matrix with appropriate dimensions. According to formula (6), since 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 equation (6) are:

[0102]

[0103] In the formula,

[0104]

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

[0106]

[0107] In the formula, Represents the equivalent interference component.

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

[0109]

[0110] In the formula, ∈ i (0) indicates 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 a distributed state feedback nominal optimization control protocol to be designed; 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; 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 state information of the non-cooperative target. The derivatives of both sides of equation (9) are:

[0111]

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

[0113]

[0114] In the formula,

[0115]

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

[0117]

[0118] In the formula, 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 equation (12) into equation (11), we have:

[0119]

[0120] Selecting the Sliding Mode Gain Parameters β1 is 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 formula (12) can be obtained to ensure the integral sliding mode variable s i = 0 is achieved 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 can be expressed as:

[0121]

[0122] Step 3: For the equivalent state tracking error system on the sliding surface obtained in step 2, define the performance index function of the marine robot cluster system, design a distributed state feedback nominal optimization control protocol, and ensure that the performance index function satisfies the global Nash equilibrium; First, for the equivalent state tracking error system (14) in step 2, define the performance index function as follows:

[0123]

[0124] In the formula, ∈ 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 Respectively represent matrices 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:

[0125]

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

[0127]

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

[0129]

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

[0131] 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 in step 2. First, substitute the distributed state feedback nominal optimization control protocol (17) into the equivalent state tracking error system (14):

[0132]

[0133] In the formula,

[0134] Defining the Matrix The equivalent standard form is where Ξ is a reversible matrix of suitable dimensions, so the matrix A ∈ is the Hurwitz equivalent of the matrix is Hurwitz's. According to the algebraic Riccati equation (16), it can be inferred that:

[0135]

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

[0137] Example:

[0138] Assume that there is a marine robot cluster system consisting of one non-cooperative target and four marine robots. The communication topology between each marine robot and the non-cooperative target is as follows: Figure 1 As shown, the Laplace matrix corresponding to the communication topology is expressed as follows:

[0139]

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

[0141]

[0142] The uncertain water surface wind and wave disturbance input acting on the non-cooperative target and the four marine robots is 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] Then the upper bound parameter of the uncertain water surface wind and wave disturbance input can be taken as The uncertain control input of the non-cooperative target is selected and satisfies u0=0.1[sin(0.1t),0.5sin(0.1t)+0.5,0.5cos(0.1t)+0.5] T , then its upper bound parameter can be taken as For 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: for:

[0149]

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

[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. It can be seen from the simulation curve of the state component tracking error norm that under the proposed control protocol, the tracking error norm of each state component gradually converges to zero in about 30 seconds, and it has good stability. Therefore, the control protocol proposed in the present invention can realize the state tracking of the marine robot cluster system for non-cooperative targets with uncertain control strategies under the interference of wind and waves on the water surface in a complex marine environment.

Claims

1. A marine robot cluster tracking optimization control method for non-cooperative targets, characterized in that: The steps include: Step 1: For the marine robot system working in the water surface environment, a linearized marine robot cluster dynamics model and a non-cooperative target dynamics model are established 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 at the same time; Step 3: For the equivalent state tracking error system obtained in step 1, define the performance index function of the marine robot cluster system, design a distributed state feedback nominal optimization control protocol, and 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 control of marine robot clusters 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 rotating 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 represents 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: Order is a time-invariant constant, and the six-DOF marine robot cluster dynamics model described in equation (1) is constructed as the following linearized marine robot cluster dynamics model: In the formula, Step 1-3: Give the following six-degree-of-freedom non-cooperative target dynamics 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 water surface wind and wave disturbance input received by the non-cooperative target and satisfies ||f0||≤γ.

3. The method for tracking and optimizing control of a 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: In the formula, 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 jth 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 Laplacian matrix is ​​expressed as follows: In the formula, is a non-singular M matrix, represents matrix components; Step 2-3: Based on the Kronecker product, the global form of equation (4) is expressed as: In the formula, 1 N Represents an N-dimensional column vector whose elements are all equal to 1, I p represents the 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 equation (6) are: In the formula, Let h i =f i -(u0+f0), then equation (7) can be rewritten as: In the formula, represents the equivalent interference component; Step 2-5: Design the integral sliding mode variables as follows: In the formula, ∈ i (0) indicates 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 a 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 equation (9) we have: Based on the Kronecker product, the global form of equation (10) is expressed as: In the formula, Step 2-6: For the system given in equation (10), the finite-time sliding mode control protocol is designed as follows: In the formula, 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 limited 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 control of marine robot clusters for non-cooperative targets according to claim 3 is 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: In the formula, ∈ 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 Respectively represent matrices 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: For 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: In the formula, represents the value function; According to optimization theory, it can be proved that under 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): In the formula, Step 4-2: Define the matrix The equivalent standard form is where Ξ is a reversible 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 was Hurwitz's; According to Hurwitz stability theory, it is inferred that the equivalent state tracking error system (14) is asymptotically stable.

Images