A multi-unmanned system fuzzy pre-defined time optimization formation control method

Abstract

The application discloses a multi-unmanned system fuzzy pre-defined time optimization formation control method and belongs to the field of automation and control. In view of the multi-unmanned system with unknown dynamics and input saturation constraints, the method approaches the unknown dynamics of the system online through a fuzzy logic system, designs a cost function with a pre-defined time convergence characteristic, and constructs a single evaluation network to adaptively solve a Hamilton-Jacobi-Bellman equation to obtain an approximate optimal control law. The application does not need prior knowledge of the system dynamics, can realize accurate formation control within a pre-defined time set by a user, effectively handles control input saturation, optimizes system control energy consumption, and is suitable for cluster collaborative control tasks of unmanned aerial vehicles, unmanned vehicles and the like.

Description

Technical Field

[0001] This invention belongs to the field of automation and control, specifically relating to a fuzzy predefined time-optimized formation control method for multi-unmanned systems. This method can achieve formation control of multi-unmanned systems with input saturation and unknown dynamics while optimizing energy consumption and formation control performance. Background Technology

[0002] Autonomous unmanned platform systems integrate environmental perception, intelligent decision-making, and autonomous execution capabilities, enabling them to independently undertake diverse tasks. Their forms include unmanned ground vehicles, unmanned surface vessels, autonomous underwater vehicles, and aerial drones. With breakthroughs in the integration of artificial intelligence, big data communication, and advanced robotics technologies, unmanned systems have been deeply integrated into many key areas such as smart city management, emergency rescue, ecological monitoring, resource exploration, and intelligent manufacturing, demonstrating their unique value in enhancing operational efficiency and ensuring personnel safety.

[0003] Formation cooperative control, as a core enabling technology for achieving intelligent swarm collaboration, has been extensively studied. In practical deployments, each unmanned platform, in addition to being subject to external environmental disturbances, also faces physical limits in its drive mechanism, i.e., control input saturation. If this constraint is not fully considered in the controller design, it may lead to a decline in cooperative performance or even system instability. Therefore, input saturation is a critical issue that must be addressed in swarm cooperative control. Meanwhile, the dynamics of unmanned systems often include parameter uncertainties, unmodeled dynamics, and external disturbances, making it difficult for traditional control methods to guarantee robust performance. Fuzzy systems, with their powerful nonlinear approximation capabilities, provide an effective approach to solving the modeling and control challenges of such uncertain systems. It is noteworthy that most unmanned platforms rely on battery power, resulting in limited energy resources. To achieve long-term continuous operation, energy optimization must be fully considered in formation control. Optimal control theory provides an important methodological foundation for solving energy management in swarm collaboration. Summary of the Invention

[0004] The problem this invention aims to solve is to provide a cooperative predefined time control method for multi-unmanned systems that can simultaneously handle input saturation, model unknowns, and energy consumption optimization. To this end, this invention proposes a fuzzy optimization formation control method for multi-unmanned systems with predetermined time convergence characteristics. For multi-unmanned system clusters with unknown dynamics and input saturation constraints, an optimal cooperative formation control architecture is designed. This method uses a continuously differentiable saturation function to smooth and limit the control command, utilizes a fuzzy logic system to approximate the unknown system dynamics online, and constructs a single evaluation network to adaptively solve the Hamilton-Jacobi-Bellman equations, thereby obtaining the optimal control law.

[0005] The present invention provides an optimized formation control method for a multi-unmanned system, comprising the following steps: Step 1: Obtain the location information of neighboring unmanned systems, and combine it with the location information of the unmanned system itself to calculate the time-varying relative position vector. ; Step 2: Design a fuzzy approximation-based identifier, and then use the fuzzy identifier to identify the unknown dynamic parameters of the system based on the position and velocity information of the unmanned system. and A dynamic model of the unmanned system based on the unknown dynamic parameters is constructed. Step 3: Based on the location information of the neighboring unmanned systems, the location information of the unmanned system itself, and the time-varying relative position vector obtained in Step 1... Calculate the formation position error vector and velocity error vector for each unmanned system. ; Step 4, based on the formation position error vector and velocity error vector Optimal cost function approximation The approximate optimal control law is calculated. ; Step 5, according to the approximate optimal control law gradient of cost function and unknown dynamic parameters and Calculate the approximate Hamiltonian function error and historical error; Step 6: Adjust the cost function using the fuzzy parameter update law based on the approximate Hamiltonian function error and historical error. The weight vector in; Step 7, apply the approximate optimal control law Input the unmanned system dynamics model described in step 2, and update the position and velocity state of the unmanned system.

[0006] Furthermore, unknown dynamic parameters of the system are identified using a fuzzy identifier, and a dynamic model of the unmanned system based on these unknown dynamic parameters is constructed. The specific steps are as follows: Establish a mathematical model for the unmanned system; (3)

[0007] in, , , , , Indicates the first The inertial matrix of an unmanned system Indicates the first The Coriolis force-centrifugal force matrix of an unmanned system Indicates the first The gravity vector of an unmanned system express A real-valued column vector space, and , as well as It is unknown; Indicates the first The location of an unmanned system. Indicates the first The speed of an unmanned system Indicates the first The acceleration vector of an unmanned system Indicates the first Environmental disturbances of an unmanned system For the first A control input with input saturation for an unmanned system; Design a fuzzy approximation-based identifier and an update law for the fuzzy parameter matrix in the identifier, such that the ideal fuzzy parameter matrix in the identifier converges to a constant matrix. Reconstruct the mathematical model of the unmanned system based on the identification results.

[0008] Furthermore, in step 3, the formation position error vector and velocity error vector of the unmanned system... , is represented as: (10) In the formula, Indicates the first The and the first Communication connections between unmanned systems Indicates the first The and the first Time-varying relative position vectors between unmanned systems Indicates the first The unmanned system and the first The expected relative position vector between the unmanned systems.

[0009] Furthermore, the optimal cost function in step 4 It includes a predefined time and has the predefined time convergence property, expressed as: (13) in, ,exist middle, It is a positive definite function, defined as: (14) Selected as , It is a symmetric positive definite weighted matrix. Represents the integral variable; , Both are continuous functions; (15) In the formula, It is a predefined convergence time; ; in, It is the Gamma function. These are all design parameters. , , and ; (16) In the formula, , express Compared to gradient, ; Furthermore, in step 5, the approximate Hamiltonian function error and historical error are calculated and expressed as follows: Approximate Hamiltonian function error: (25) Record Historical error of time as follows: (26) Furthermore, step 6 involves designing a fuzzy parameter update law. as follows: (27) In the formula, , , and For design parameters, , , in It is a symbolic function.

[0010] Beneficial effects: This invention can ensure that multiple unmanned systems can achieve precise formation within a user-defined time without prior knowledge of system dynamics, effectively handle control input saturation constraints, and optimize system control energy consumption. It is suitable for collaborative control tasks of swarm systems such as UAVs and unmanned vehicles. Attached Figure Description

[0011] Figure 1This is a flowchart of the fuzzy predefined time optimization formation control method for multi-unmanned systems according to the present invention.

[0012] Figure 2 This is a flowchart of the formation control method of the present invention. Detailed Implementation

[0013] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0014] 1. Establish a mathematical model for the unmanned system. Consider a A formation system composed of several unmanned systems, the first of which An unmanned system can be described using the following Eulerian-Lagrange system: (1) In the formula, Indicating an index for an unmanned system, , Indicates the first The inertial matrix of an unmanned system Indicates the first The Coriolis force-centrifugal force matrix of an unmanned system Indicates the first The gravity vector of an unmanned system express A real-valued column vector space, and , as well as It is unknown; Indicates the first The location of an unmanned system. Indicates the first The speed of an unmanned system Indicates the first The acceleration vector of an unmanned system Indicates the first Environmental disturbances of an unmanned system For the first A control input with input saturation for an unmanned system, namely (2) In the formula, , express The One location, express dimensionality express The One portion, Indicates a control input without saturation The One portion, For symbolic functions, For the first The maximum value of the control input of an unmanned system.

[0015] To facilitate design control, , Therefore, the formation system is redescribed, that is, the mathematical model of the unmanned system (1) is re-expressed as: (3) (4) In the formula, and .

[0016] 2. Design a fuzzy identifier because and Given the unknown dynamic parameters, a fuzzy logic system will be used to design an identifier to reconstruct the unknown dynamic model of the system. Therefore, equation (4) is rewritten as follows: (5) In the formula , , For an ideal fuzzy parameter matrix, Indicates fitting The number of selected fuzzy rules, Indicates fitting The number of selected fuzzy rules, Let be a vector composed of fuzzy basis functions, and let its input vector be... , It is a matrix composed of fuzzy basis functions. This is the approximate error vector.

[0017] Due to the ideal fuzzy parameter matrix , and Since it is unknown, according to (7), the identifier based on fuzzy approximation is designed as follows: (6) In the formula, for The estimate, , and These are the ideal fuzzy parameter matrices. , and The estimate, , Represents the input vector The estimate.

[0018] Estimated ideal fuzzy parameter matrix , and The update law is designed as follows: (7) In the formula, , and Positive design parameters For the first An unmanned system with control inputs that have input saturation. This indicates the estimation error. , and They can converge to constant matrices respectively , and , It can converge to a constant vector Equation (4) can be re-established as follows: (8) In the formula, and .

[0019] Combining equations (3) and (8), the mathematical model of the unmanned system, equation (1), can finally be expressed as: (9) in, , and

[0020] 3. Design a fuzzy predefined time-optimized formation controller Based on equation (9), the first... Formation position error vector and velocity error vector of an unmanned system as follows: (10) In the formula, Indicates the first The and the first Communication connections between unmanned systems Indicates the first The and the first Time-varying relative position vectors between unmanned systems Indicates the first The unmanned system and the first The expected relative position vector between the unmanned systems.

[0021] Step 1: According to equation (10), consider the following cooperative tracking error dynamic system with affine nonlinear form: (11) In the formula, and .

[0022] For equation (11), let a local cost function for (12) In the formula, , It is a symmetric positive definite weighted matrix. For the first The set of all neighboring nodes of an unmanned system.

[0023] The following is the first... The optimal cost function for each unmanned system is as follows: (13) exist middle, It is a positive definite function, defined as: (14) in, Selected as , It is a symmetric positive definite weighted matrix. This represents the integral variable.

[0024] It is a continuous function, defined as (15) In the formula, It is a predefined convergence time; ; in, It is the Gamma function. These are all design parameters. , , and .

[0025] It is a continuous function, defined as (16) In the formula, , express Compared to gradient,

[0026] To solve for the optimal control law, the Hamiltonian function is defined as follows: (17) Then, by solving The optimal control law can be obtained as follows: (18) In the formula, .

[0027] Substituting (18) into (17) yields the following Hamilton-Jacobi-Bellman equation:

[0028] (19)

[0029] In the formula, This is the ideal error equation under optimal control.

[0030] The following will employ an approximate optimal cost function for a fuzzy logic system. ,Right now

[0031] (20)

[0032] In the formula, For the ideal parameter vector, A vector composed of fuzzy basis functions. The number of fuzzy basis functions. This is the approximation error.

[0033] Then, we can obtain Compared to The gradient is as follows

[0034] (twenty one)

[0035] In the formula, and They are respectively and Compared to The gradient.

[0036] Substituting (21) into (18), the optimal control law is derived as follows:

[0037]

[0038] In the formula, .

[0039] definition For the ideal weight vector The estimate of the optimal cost function. approximation and about gradient as follows:

[0040] (twenty two)

[0041] (twenty three)

[0042] Therefore, based on (21) and (23), an approximate optimal control law can be obtained. The calculation is as follows:

[0043] (twenty four) In the formula, .

[0044] Substituting (23) and (24) into (17), we obtain the approximate Hamiltonian function error as follows: (25) And record Historical error of time as follows: (26) Next, a fuzzy parameter update law is designed. as follows: (27) In the formula, , , and For design parameters, , , in It is a symbolic function.

[0045] The present invention provides a fuzzy predefined time-optimized formation control method for multi-unmanned systems, such as... Figure 1 and 2 As shown, it includes the following steps: Step 1: Obtaining Status Information Receive location information from neighboring unmanned systems The location information of the unmanned system itself Calculate the first The and the first Time-varying relative position vectors between unmanned systems ; Step 2: Online Identification of Unknown Dynamics Position of the unmanned system itself With speed The state information is input into the fuzzy identifier (9) to calculate the unknown dynamic parameters. and It is used for real-time compensation of model uncertainty; Step 3, calculate formation error Calculate the first according to formula (10). Formation position error vector and velocity error vector of an unmanned system ; ,in ,

[0046] Step 4: Calculate the approximate optimal control law Based on formation position error vector and velocity error vector The fuzzy logic system is used to approximate the optimal cost function. The optimal cost function is calculated according to equations (22) and (23). approximation and approximate values about gradient According to equation (24), the approximate optimal control law is obtained. ; Step 5: Calculation of the approximate Hamiltonian function Approximate optimal control law gradient of cost function Unknown dynamic parameters and Substitute into formula (25) to calculate the error of the approximate Hamiltonian function. as well as Historical error of time It is used to evaluate the deviation between the current control strategy and the optimal strategy.

[0047] Step 6: Update fuzzy parameters online Based on the update law shown in formula (27) in the instruction manual, and combined with step 5, the approximate Hamiltonian function error is calculated. as well as Historical error of time Used to adjust the estimated weight vector This makes the local cost function Closer to the optimal cost function The value of is used to achieve adaptive optimization learning; Step 7: Send control signal The approximate optimal control law calculated in step 4 Substitute into the mathematical model of the unmanned system (4) to update the position information of the unmanned system itself. and speed information ; Step 8: Loop and check Determine whether the loop termination condition is met, wherein the loop termination condition is reaching a predefined time Tc or the formation error converges to an allowable range; If the loop termination condition is not met, return to step 1 and proceed to the next control cycle; If the loop termination condition is met, the process ends.

Claims

1. An optimized formation control method for a multi-unmanned system, characterized in that, Includes the following steps: Step 1: Obtain the location information of the neighboring unmanned system, and combine it with the location information of the unmanned system itself to calculate the time-varying relative position vector; Step 2: Design an identifier based on fuzzy approximation, and then, based on the position and velocity information of the unmanned system, use the fuzzy identifier to identify the unknown dynamic parameters of the system and construct a dynamic model of the unmanned system based on the unknown dynamic parameters. Step 3: Based on the location information of neighboring unmanned systems, the location information of the unmanned system itself, and the time-varying relative position vector obtained in Step 1, calculate the formation position error vector and velocity error vector of each unmanned system. Step 4: Based on the formation position error vector, velocity error vector, and approximate value of the optimal cost function, calculate the approximate optimal control law; Step 5: Calculate the approximate Hamiltonian function error and historical error based on the approximate optimal control law, the gradient of the cost function, and the unknown dynamic parameters. Step 6: Based on the approximate Hamiltonian function error and historical error, adjust the weight vector in the cost function using the fuzzy parameter update law; Step 7: Input the approximate optimal control law into the unmanned system dynamics model described in Step 2 to update the position and velocity state of the unmanned system.

2. The method according to claim 1, characterized in that, The unknown dynamic parameters of the system are identified by a fuzzy identifier, and a dynamic model of the unmanned system based on the unknown dynamic parameters is constructed. The specific steps are as follows: Establish a mathematical model for the unmanned system; (3) in, , , , , Indicates the first The inertial matrix of an unmanned system Indicates the first The Coriolis force-centrifugal force matrix of an unmanned system Indicates the first The gravity vector of an unmanned system express A real-valued column vector space, and , as well as It is unknown; Indicates the first The location of an unmanned system. Indicates the first The speed of an unmanned system Indicates the first The acceleration vector of an unmanned system Indicates the first Environmental disturbances of an unmanned system For the first A control input with input saturation for an unmanned system; Design a fuzzy approximation-based identifier and an update law for the fuzzy parameter matrix in the identifier, such that the ideal fuzzy parameter matrix in the identifier converges to a constant matrix. Reconstruct the mathematical model of the unmanned system based on the identification results.

3. The method according to claim 1, characterized in that, In step 3, the formation position error vector and velocity error vector of the unmanned system , is represented as: (10) In the formula, Indicates the first The and the first Communication connections between unmanned systems Indicates the first The and the first Time-varying relative position vectors between unmanned systems Indicates the first The unmanned system and the first The expected relative position vector between the unmanned systems.

4. The method according to claim 1, characterized in that, Optimal cost function in step 4 It includes a predefined time and has the predefined time convergence property, expressed as: (13) in, ,exist middle, It is a positive definite function, defined as: (14) Selected as , It is a symmetric positive definite weighted matrix. Represents the integral variable; , Both are continuous functions; (15) In the formula, It is a predefined convergence time; ； in, It is the Gamma function. These are all design parameters. , , and ; (16) In the formula, , express Compared to gradient, .

5. The method according to claim 1, characterized in that, In step 5, the approximate Hamiltonian function error and the history error are calculated and expressed as follows: Approximate Hamiltonian function error: (25) Record Historical error of time as follows: (26)。 6. The method according to claim 1, characterized in that, Step 6: Design the fuzzy parameter update law as follows: (27) In the formula, , , and For design parameters, , , in It is a symbolic function.

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