Bridge crane game model-free optimal control method based on event triggering

Abstract

The invention relates to a bridge crane game model-free optimal control method based on event triggering, and the method comprises the steps: collecting a state vector of a bridge crane in real time, and building a nonlinear multi-player system model of the bridge crane; estimating an unknown dynamic function and an input gain matrix on line in the input identifier neural network; according to an event triggering mechanism, whether triggering is conducted or not is judged based on the error between the current state vector and the state vector of the recently-triggered sampling; if so, triggering a dynamic updating instruction; under a non-zero sum game framework, obtaining an optimal value function gradient based on an estimation result and a current state vector through a self-adaptive evaluator network, and generating an event triggering optimal control law of each player based on a sampled state vector; and the event triggering optimal control law is processed by a zero-order retainer and then is output as a physical driving signal to control the operation of the bridge crane. Compared with the prior art, the method has the advantages of high applicability, high disturbance resistance, high accuracy and the like.

Description

Technical Field

[0001] This invention relates to the field of automation control technology, and in particular to a game-theoretic model-free optimal control method for bridge cranes based on event triggering. Background Technology

[0002] In industrial settings such as large ports and heavy equipment manufacturing workshops, bridge cranes are widely used for handling large loads. These operations require high-precision control of the crane during operation to effectively suppress load swaying, prevent tilting or falling, while also optimizing operational efficiency and energy consumption. Due to the complex dynamic characteristics of crane systems, including strong nonlinearity and multivariable coupling, their control problem is typically modeled as a multi-agent cooperative control problem.

[0003] Currently, most control strategies for bridge cranes rely on precise system dynamics models. However, in real industrial environments, crane systems often contain numerous dynamic characteristics that are difficult to model accurately, such as complex friction effects, flexible vibrations of wire ropes, and nonlinear saturation of motor drives. These unmodeled dynamics make it extremely difficult to establish high-fidelity mathematical models. Controllers designed based on inaccurate or simplified models often experience performance degradation and insufficient robustness in practical applications, making it difficult to guarantee the safety and stability of the lifting process. Furthermore, existing control systems typically employ continuous or timed sampling communication methods, requiring continuous acquisition of system status information for real-time control. Under long-term, high-intensity operating conditions, this continuous communication mode not only places stringent requirements on the reliability and low latency of the communication link but also introduces significant bandwidth pressure and energy consumption, increasing system deployment and maintenance costs. Simultaneously, bridge cranes are frequently subjected to continuous external disturbances such as wind resistance and track irregularities during operation, further increasing the design complexity and operational risks of the control system.

[0004] While intelligent control methods such as adaptive dynamic programming provide effective approaches to solving optimal control problems in nonlinear systems, most existing studies assume a completely known system model or employ resource-intensive periodic update strategies. This makes it difficult to achieve integrated solutions under real-world conditions where model information is lacking, communication resources are limited, and external disturbances coexist. Therefore, designing an intelligent control method capable of autonomous learning, collaborative optimization, and disturbance suppression under conditions of unknown crane dynamics, limited communication access, and external disturbances has become a key technological bottleneck driving the development of bridge crane systems towards intelligence and efficiency. Thus, achieving stable, collaborative, and energy-optimized control of bridge crane systems under conditions of unknown models, limited communication resources, and external disturbances is a technical problem that needs to be solved. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology by providing an event-triggered game-theoretic modelless optimal control method for bridge cranes. This method integrates modelless online identification, non-zero-sum game optimization, and event-triggered mechanism to construct a unified adaptive dynamic programming framework. Under the conditions of completely unknown crane dynamics, interference, and limited communication resources, it achieves intelligent collaborative control that ensures closed-loop stability and optimality while significantly reducing computational and communication load.

[0006] The objective of this invention can be achieved through the following technical solutions: According to one aspect of the present invention, a game-theoretic model-free optimal control method for bridge cranes based on event triggering is provided, characterized in that the specific steps include: S1. Real-time acquisition of state vector data of bridge crane to obtain state vectors including trolley displacement, load swing angle, trolley speed and load swing angle angular velocity, establish nonlinear multi-player system model of bridge crane, and define non-zero-sum game performance index function for each player. S2. Input the state vector into the identifier neural network to estimate the unknown dynamic function and input gain matrix in the nonlinear multiplayer system model online; S3. Based on the event triggering mechanism, determine whether to trigger based on the error between the current state vector and the most recently triggered sampled state vector; if triggered, trigger the dynamic update instruction, otherwise retain the instruction from the previous moment. S4. Under the framework of non-zero-sum game, through the adaptive evaluator network, based on the estimation results of S2 and the current state vector sampled by the event triggering mechanism in S3, the gradient of the optimal value function of each player is approximately solved, and the event triggering optimal control law of each player based on the sampled state vector is generated. S5. The event triggers the optimal control law, which is then processed by the zero-order hold and output as a physical drive signal to control the operation of the bridge crane.

[0007] Furthermore, the nonlinear multiplayer system model in S1 is a crane control system model, and the model expression is: , , in, For the state vector data of the crane, For system model functions The derivative with respect to time, For the displacement of the crane, For the load swing angle, For speed, The load angular velocity; Characterizing the unknown drift dynamics of a system, i.e., unknown dynamic functions; The input represents the control strategy required by the motor for the crane. The input matrix maps the driving force of the motor into changes in position and velocity in the state; that is, the input gain matrix. For unknown disturbances, including wind resistance And the influence of track slope ,Right now Furthermore, the perturbation is pre-defined as bounded.

[0008] Furthermore, the non-zero-sum game performance index function for each player... for: , in, For utility function, It is a positive definite matrix. It is a symmetric positive definite matrix. It includes state information such as the crane's displacement, velocity, block swing angle, and angular velocity. Includes coupling information from multiplayer control system inputs. For robust compensation items ; For state vectors, For the first i Individual player control strategies To exclude the first i The set of control inputs for all players other than the player in question; For matrix The largest eigenvalue.

[0009] Furthermore, the online estimation result of the discriminator neural network in S2 is as follows: , in, For the estimated unknown dynamic function, For the estimated input gain matrix, and The fixed weights obtained from training the neural network of the identifier are... and This refers to the neural network reconstruction error generated during the approximation process. and It is an activation function, consisting of a state vector.

[0010] Furthermore, in S3, the error judgment of the event triggering mechanism is based on the norm of the error between the current state vector and the most recently triggered sampled state vector, expressed as: , in, For state error, , , , , For preset positive numbers, and It is a pre-defined positive definite matrix.

[0011] Furthermore, in S4, the adaptive evaluator network approximates the gradient of the optimal value function for player i. for: , in, Let be the transpose of the activation function of the judge neural network with respect to the Jacobian matrix of the state vector. This is the weight vector of the judge neural network.

[0012] Furthermore, in S4, the expression for the event-triggered optimal control law is: , in, For the first j The optimal feedback control law for each player For coupling gain, Let be the optimal control law for the j-th player under ideal conditions. The cost of controlling the j-th player's own energy. This is the transpose of the input gain matrix. The optimal value function is... The most recent event trigger time The sampled state vector.

[0013] Furthermore, in S5, during non-triggering moments, the zero-order hold maintains the control law generated in S4 at the most recent triggering moment unchanged and continuously outputs the corresponding driving force signal.

[0014] According to a second aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement the method described thereon.

[0015] According to a third aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described thereon.

[0016] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention combines the identifier neural network with the adaptive evaluator network and introduces a dynamic event triggering mechanism based on state error, which effectively reduces the update frequency of the control signal and the communication and computation burden of the system. The identifier neural network estimates the unknown dynamics of the system online, providing a model basis for subsequent optimal control. Under the event triggering mechanism, the evaluator network updates the optimal control law based on the latest sampled state only when the system state error exceeds the preset threshold. At non-triggering times, the zero-order hold maintains the instruction of the previous time, avoiding continuous calculation and transmission, reducing the amount of real-time data interaction between the controller and the actuator. Thus, while ensuring control performance, it significantly alleviates the communication bandwidth pressure and high energy consumption problem caused by traditional continuous or timed control, and improves the applicability of the system in resource-constrained environments.

[0017] (3) This invention adopts an adaptive dynamic programming method based on a non-zero-sum game framework. Without the need for an accurate system model, it realizes the automatic trade-off and collaborative optimization of multiple conflict control objectives of bridge cranes, such as accurate positioning and load anti-sway. It designs a performance index function for each "player" (i.e. a control sub-objective) and approximates the gradient of its optimal value function online through an adaptive evaluator network. Then, it solves the joint control strategy that makes all players reach Nash equilibrium. It does not rely on the difficult-to-obtain accurate crane dynamic model. At the same time, the game framework inherently handles the target conflict between positioning efficiency and operation safety, enabling the system to autonomously learn the optimal control command that resists external disturbances, such as wind resistance and uneven track, while taking into account operation efficiency and hoisting stability, thus improving the intelligence and overall performance of the control.

[0018] (3) This invention, by constructing a composite Lyapunov functional and conducting rigorous stability analysis, theoretically guarantees the robust stability of the closed-loop control system and the consistent eventual boundedness of all signals. It also derives the dynamic event triggering condition related to the system state, which is a sufficient condition derived from the Lyapunov stability analysis. As long as the control update complies with this triggering condition, it can be ensured that all closed-loop signals, such as the state of the crane system, the weight estimation error of the identifier and evaluator network, are stable and bounded even in the presence of model estimation errors, neural network approximation errors, and external bounded disturbances. This provides a solid theoretical guarantee for the reliability and safety of the proposed model-free, event-triggered control scheme in practical applications, and reduces the risk of system runaway due to model mismatch or communication delay. Attached Figure Description

[0019] Figure 1 The flowchart shows a game-theoretic model-free optimal control method for bridge cranes based on event triggering. Figure 2 This is a schematic diagram of crane control. Figure 3This is a system state component diagram of the crane. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0021] like Figure 1 As shown in this embodiment, a model-free optimal control method for bridge cranes based on event triggering is provided. The specific steps include: S1. Real-time acquisition of state vector data of bridge crane to obtain state vectors including trolley displacement, load swing angle, trolley speed and load swing angle angular velocity, establish nonlinear multi-player system model of bridge crane, and define non-zero-sum game performance index function for each player. S2. Input the state vector into the identifier neural network to estimate the unknown dynamic function and input gain matrix in the nonlinear multiplayer system model online; S3. Based on the event triggering mechanism, determine whether to trigger based on the error between the current state vector and the most recently triggered sampled state vector; if triggered, trigger the dynamic update instruction, otherwise retain the instruction from the previous moment. S4. Under the framework of non-zero-sum game, through the adaptive evaluator network, based on the estimation results of S2 and the current state vector sampled by the event triggering mechanism in S3, the gradient of the optimal value function of each player is approximately solved, and the event triggering optimal control law of each player based on the sampled state vector is generated. S5. The event triggers the optimal control law, which is then processed by the zero-order hold and output as a physical drive signal to control the operation of the bridge crane.

[0022] like Figure 2 As shown, in this embodiment, the bridge crane consists of a trolley on a track and a load block below the trolley. For a mass of... The small car only travels along the horizontal track ( When in motion (direction), it possesses kinetic energy, while its potential energy remains constant. for: , in, It is the displacement of the car. For speed. Due to the tension of the suspension cable and gravity, the trolley can... direction and Directional movement. The position of the payload is: , in, The length of the suspension cable. This indicates the angle at which the suspension cable swings.

[0023] Therefore, the velocity component of the effective load is , If the mass of the suspended load block is Its kinetic and potential energy loads (with the trolley's trajectory as the zero potential energy reference) change with displacement and time, and their values ​​are: , in, and These are increasing rope elongation and angular velocity, respectively. This is the acceleration due to gravity.

[0024] Therefore, the total kinetic energy of the crane control system Total potential energy It can be described as: , Lagrange function The expression is as follows: The Euler-Lagrange equations are given as follows: , in, , Suffered by the car The driving force of direction, The tension force required to pull a load onto a rope.

[0025] By using the Lagrange function mentioned above Solving the above standard Euler-Lagrange equations, we obtain the equations of motion for the bridge crane lifting system: , The Euler-Lagrange equations can be simplified as follows: , in, , , .

[0026] Furthermore, the deformation of the steel cable can be ignored, denoted as . Therefore, we obtain , Solving for: , Therefore, the nonlinear multiplayer system model in S1 is the control system model of the crane, and the model expression is: , , in, For the state vector data of the crane, For system model functions The derivative with respect to time, For the displacement of the crane, For the load swing angle, For speed, The load angular velocity; Characterizing the unknown drift dynamics of a system, i.e., unknown dynamic functions; The input represents the control strategy required by the motor for the crane. The input matrix maps the driving force of the motor into changes in position and velocity in the state; that is, the input gain matrix. For unknown disturbances, including wind resistance And the influence of track slope ,Right now And the perturbation is presupposed to be bounded. ,remember Let the set of all players be... Furthermore, the definition .

[0027] Specifically, the unknown dynamic function and the input gain matrix are expressed as: , , , in, Furthermore, the swing angle is usually kept to a minimum, especially near the steady point, which is approximately equal to... , Therefore, we get: , Solving for: , Therefore, the unknown dynamic function and the input gain matrix are obtained: , , Non-zero-sum game performance index function for each player for: , in, For utility function, It is a positive definite matrix. It is a symmetric positive definite matrix. It includes state information such as the crane's displacement, velocity, block swing angle, and angular velocity. Includes coupling information from multiplayer control system inputs. For robust compensation items ; For state vectors, For the first i Individual player control strategies To exclude the first i The set of control inputs for all players other than the player in question; For matrix The largest eigenvalue. Among them, Its function is to map the effects of the disturbance to the first... The performance metrics of each player are considered, thus automatically taking disturbance suppression into account when designing the optimal controller.

[0028] For nonlinear multiplayer system models, it is necessary to find an optimal controller for the sequence. To ensure the system is protected from disturbances The stability of the crane is achieved by minimizing the cost function, thus enabling the crane to perform its work under optimal control. For this purpose, an appropriate value function is introduced: , The local Hamiltonian function is defined as follows: in, .set up The optimal control input is then obtained as: , The online estimation results of the discriminator neural network in S2 are as follows: , in, For the estimated unknown dynamic function, For the estimated input gain matrix, and The fixed weights obtained from training the neural network of the identifier. and This refers to the neural network reconstruction error generated during the approximation process. and The activation function is composed of a state vector. This varies with the number of neurons. and The estimation error tends towards infinity. and It tends towards 0.

[0029] The nonlinear multiplayer system model is defined as: , in, , .

[0030] To suppress disturbances Construct the following filter variables: , in These are constant filter coefficients, which leads to: , in, Through a low-pass filter The result is obtained by multiplying both sides of the above equation by... get: , In order to estimate We need to obtain the filtered result. and Therefore, construct the regression matrix. and Filtering forms: , in, It is a constant. Its solution is expressed as: , Furthermore, we obtain: in, It is the residual error, which indicates that when hour, It will disappear.

[0031] Furthermore, let and They represent and The estimated values, they can constitute The estimated value Then an auxiliary matrix is ​​introduced. And define the estimation error as .therefore, It can be represented as The key point is that... Includes estimation error This information makes it suitable for the adaptive update law driving the weights of the discriminator network. : , in, This is a constant representing the update step size. Auxiliary matrix. and The introduction of this is for extracting matrices. This ensures that the above adaptive update law can make the estimated weights converge.

[0032] Based on the above identifier network estimation, we obtain: , in, It is an approximation error.

[0033] To address the limitations of computational and communication bandwidth, an event-triggered mechanism was introduced. Therefore, continuous sampling is necessary. At the triggering time The sampling state jumps to Its value remains unchanged until the next trigger occurs, as expressed below: During non-triggered periods, a zero-order hold is used to retain the last updated data, which reduces signal transmission between the controller and actuator. To distinguish this method from time-triggered schemes, the control input form, which depends on the sampled state, can be expressed as: .

[0034] Due to the effect of the zero-order hold, the state is maintained. An error function will be generated between the sampled state and the continuous state, as shown below: , The local Hamiltonian function is restated as follows: The optimal control input at different times can be expressed as follows: In S3, the error judgment of the event triggering mechanism is based on the norm of the error between the current state vector and the most recently triggered sampled state vector, expressed as: , in, For state error, , , , , For preset positive numbers, and It is a pre-defined positive definite matrix.

[0035] In S4, in order to obtain the solution that is difficult to solve... , No. The value function for each player is: , in, It is the ideal weight vector; It is an activation function; It is the approximation error. The gradient of the optimal function for player i in the adaptive evaluator network is defined as: , in, and yes and Partial derivatives.

[0036] Therefore, the adaptive evaluator network approximates the gradient of the optimal value function for player i. for: , in, Let be the transpose of the activation function of the judge neural network with respect to the Jacobian matrix of the state vector. This is the weight vector of the judge neural network.

[0037] In S4, the expression for the event-triggered optimal control law is: , in, For the first j The optimal feedback control law for each player For coupling gain, Let be the optimal control law for the j-th player under ideal conditions. The cost of controlling the j-th player's own energy. This is the transpose of the input gain matrix. The optimal value function is... The most recent event trigger time The sampled state vector.

[0038] In order to estimate The approximate Hamiltonian for each player can be described as: , in, .

[0039] Definition Item : When the control input is the optimal value hour, Therefore, multiply both sides by the term. ,get: , Auxiliary filter regression matrix and for: , in, It is a constant. The solution is: , get: in, Time residual error. Then, an auxiliary matrix is ​​introduced. And define the estimation error as .therefore, It can be further expressed as . Includes estimation error This information makes it suitable for the adaptive update law driving the weights of the discriminator network. : in, It is a constant.

[0040] When there is a set of feedback gain parameters (for all) Furthermore, when the triggering conditions are met, the designed controller and adaptive law can ensure the stability of the system state, the neural network estimation error, and the weights. and All are consistent and eventually bounded.

[0041] In S5, at non-triggering times, the zero-order hold maintains the control law generated by S4 at the most recent triggering time unchanged and continues to output the corresponding driving force signal.

[0042] To theoretically verify and guarantee the stable closed-loop performance of the event-triggered control system constructed using the above method, a rigorous stability analysis of the system is required. This embodiment demonstrates the uniform eventual boundedness of all signals in the system by constructing a composite Lyapunov functional and analyzing its evolution behavior under an event-triggered mechanism. Specifically, the construction and analysis process of the Lyapunov functional L is as follows: , in:

[0043] Case 1: Not triggered : in, Furthermore, Furthermore, Case 1: Triggered , Through Lyapunov stability analysis, it is proved that all signals, including system state and neural network weight estimation error, are uniformly eventually bounded (UUB), and a practical Nash equilibrium for non-zero-sum games is achieved.

[0044] As shown in Table 1, this embodiment calculates some relevant parameters of the optimal control system for a bridge crane. Figure 3This diagram shows the dynamic response curves of the key state components of a bridge crane system after applying the control method proposed in this invention. It illustrates the dynamic response process of the crane's key state variables—including trolley displacement, load swing angle, and their respective speeds—over time within a complete lifting operation cycle. The curves show that in the initial stage, the system responds rapidly without overshoot, and the trolley can quickly and smoothly approach the target position. Simultaneously, the load swing angle is rapidly suppressed and stabilized within a very small range, with its swing amplitude rapidly decaying to approximately zero. Throughout the process, the state curves converge smoothly without significant oscillations or continuous fluctuations. This intuitively demonstrates that the designed event-triggered optimal controller can effectively achieve the coordinated control objectives of precise positioning and active anti-sway in the presence of unknown models and disturbances, while ensuring that the closed-loop system has excellent transient performance and steady-state accuracy.

[0045] Table 1. Relevant parameters of the optimal control system for bridge cranes This embodiment primarily addresses the challenges of achieving precise synchronization and energy consumption optimization in bridge crane lifting systems under conditions of model uncertainty, external disturbances, and limited communication bandwidth. It proposes a model-free optimal control method based on event-triggered adaptive dynamic programming. By constructing a learning architecture integrating a neural network identifier and evaluator, the unknown dynamics of the crane are estimated online, and the coupled HJB equations in the non-zero-sum game are approximately solved. The core of this method lies in designing an event-triggered mechanism suitable for bridge crane operations. Combining state-dependent triggering conditions and performance thresholds, while ensuring that the crane state and network weight estimation errors are consistent and eventually bounded, and achieving a practical Nash equilibrium, the update frequency of control signals and the system communication burden are significantly reduced.

[0046] Therefore, the integrated identifier-judge architecture in this embodiment improves learning efficiency. The neural network-based identifier employs an advanced filtering technique to accurately estimate the dynamics of the unknown system online. Simultaneously, the event-triggered judge network uses a novel activation function, enhancing its ability to approximate the value function for all players. Furthermore, this embodiment derives an event-triggered mechanism for the crane game structure, which includes both state-dependent and performance-based triggering conditions. Through rigorous Lyapunov-based stability analysis, a formal guarantee is provided for the uniform eventual boundedness of all closed-loop signals (including system states, identifier weights, and judge network weights), while establishing the explicit boundary of its convergence region. Furthermore, this embodiment demonstrates that the developed control strategy can drive the system to a practical Nash equilibrium in a non-zero-sum game. The combined effects of model uncertainty, perturbations, and event-triggered execution are explicitly considered, and a boundary deviating from the ideal Nash equilibrium is established.

[0047] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the described module can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0048] The electronic device of this invention includes a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM may also store various programs and data required for device operation. The CPU, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0049] Multiple components in the device are connected to an I / O interface, including: input units such as a keyboard, mouse, etc.; output units such as various types of displays, speakers, etc.; storage units such as disks, optical disks, etc.; and communication units such as network interface cards, modems, wireless transceivers, etc. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks. The processing unit performs the various methods and processes described above, such as the method of the present invention. For example, in some embodiments, the method of the present invention may be implemented as a computer software program tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and / or installed on the device via ROM and / or the communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more steps of the method of the present invention described above may be performed. Alternatively, in other embodiments, the CPU may be configured to execute the method of the present invention by any other suitable means (e.g., by means of firmware).

[0050] The functions described above in this document can be performed, at least in part, by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: Field Programmable Gate Arrays (FPGAs), Application-Specific Integrated Circuits (ASICs), Application Standard Products (ASSPs), System-on-Chip (SoCs), Complex Programmable Logic Devices (CPLDs), and so on.

[0051] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0052] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0053] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A model-free optimal control method for bridge cranes based on event-triggered game theory, characterized in that, The specific steps include: S1. Real-time acquisition of state vector data of bridge crane to obtain state vectors including trolley displacement, load swing angle, trolley speed and load swing angle angular velocity, establish nonlinear multi-player system model of bridge crane, and define non-zero-sum game performance index function for each player. S2. Input the state vector into the identifier neural network to estimate the unknown dynamic function and input gain matrix in the nonlinear multiplayer system model online; S3. Based on the event triggering mechanism, determine whether to trigger based on the error between the current state vector and the most recently triggered sampled state vector; if triggered, trigger the dynamic update instruction, otherwise retain the instruction from the previous moment. S4. Under the framework of non-zero-sum game, through the adaptive evaluator network, based on the estimation results of S2 and the current state vector sampled by the event triggering mechanism in S3, the gradient of the optimal value function of each player is approximately solved, and the event triggering optimal control law of each player based on the sampled state vector is generated. S5. The event triggers the optimal control law, which is then processed by the zero-order hold and output as a physical drive signal to control the operation of the bridge crane.

2. The event-triggered game-theoretic model-free optimal control method for bridge cranes according to claim 1, characterized in that, The nonlinear multiplayer system model in S1 is a control system model of a crane, and the model expression is: ， ， in, For the state vector data of the crane, For system model functions The derivative with respect to time, For the displacement of the crane, For the load swing angle, For speed, The load angular velocity; Characterizing the unknown drift dynamics of a system, i.e., unknown dynamic functions; The input represents the control strategy required by the motor for the crane. The input matrix maps the driving force of the motor into changes in position and velocity in the state; that is, the input gain matrix. For unknown disturbances, including wind resistance And the influence of track slope ,Right now Furthermore, the perturbation is presupposed to be bounded.

3. The event-triggered game-theoretic model-free optimal control method for bridge cranes according to claim 1, characterized in that, The non-zero-sum game performance index function for each player for: ， in, For utility function, It is a positive definite matrix. It is a symmetric positive definite matrix. It includes state information such as the crane's displacement, velocity, block swing angle, and angular velocity. Includes coupling information from multiplayer control system inputs. For robustness compensation items ; For state vectors, For the first i Individual player control strategies To exclude the first i The set of control inputs for all players other than the player in question; For matrix The largest eigenvalue.

4. The event-triggered game-theoretic model-free optimal control method for bridge cranes according to claim 1, characterized in that, The online estimation result of the discriminator neural network in S2 is as follows: ， in, For the estimated unknown dynamic function, For the estimated input gain matrix, and The fixed weights obtained from training the neural network of the identifier are... and This refers to the neural network reconstruction error generated during the approximation process. and It is an activation function, consisting of a state vector.

5. The event-triggered game-theoretic model-free optimal control method for bridge cranes according to claim 1, characterized in that, In step S3, the error judgment of the event triggering mechanism is based on the norm of the error between the current state vector and the most recently triggered sampled state vector, expressed as: ， in, For state error, , , , , For preset positive numbers, and It is a pre-defined positive definite matrix.

6. The event-triggered game-theoretic model-free optimal control method for bridge cranes according to claim 1, characterized in that, In step S4, the adaptive evaluator network approximates the gradient of the optimal value function for player i. for: ， in, Let be the transpose of the activation function of the judge neural network with respect to the Jacobian matrix of the state vector. This is the weight vector of the judge neural network.

7. The event-triggered game-theoretic model-free optimal control method for bridge cranes according to claim 6, characterized in that, In S4, the expression for the event-triggered optimal control law is: ， in, For the first j The optimal feedback control law for each player For coupling gain, Let be the optimal control law for the j-th player under ideal conditions. The cost of controlling the j-th player's own energy. This is the transpose of the input gain matrix. The optimal value function is... The most recent event trigger time The sampled state vector.

8. The event-triggered game-theoretic model-free optimal control method for bridge cranes according to claim 1, characterized in that, In S5, at non-triggering times, the zero-order hold maintains the control law generated in S4 at the most recent triggering time unchanged and continuously outputs the corresponding driving force signal.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 8.

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