An adaptive neural network preset tracking performance control method, system and medium

Abstract

The application claims a kind of adaptive neural network preset tracking performance control method, system and medium, belong to switching system tracking control technical field, in order to reach ideal tracking control performance and eliminate the problem of "calculation explosion" produced in the process of designing controller in backstepping method, by using the method of command filtering, a kind of adaptive neural network preset tracking performance control strategy based on command filtering is designed.The proposed control scheme eliminates the "calculation explosion" problem in the process of controller design, compensates the filtering error, and relaxes the constraint conditions of reference signal.The algorithm proves that the closed-loop system is semi-global ultimate consistent bounded, and ensures that the tracking error is always limited in the specified area defined by the performance function.The application combines actual problems, establishes model and solves model to obtain results, and provides new ideas and solutions for the cross research of mathematics and engineering problems.

Description

Technical Field

[0001] This invention belongs to the field of tracking control technology for switching systems, and particularly relates to an adaptive neural network preset tracking performance control method, system, and medium. Background Technology

[0002] Based on the characteristics of switched systems, uncertain switched nonlinear systems can more accurately model real-world systems under complex environments. Disturbances are an unavoidable and common problem in system uncertainty. Previous research assumed that the system disturbance d(t) satisfies |d(t)| ≤ d*, where d* is an unknown constant. Under this assumption, the disturbance problem is transformed into dealing with the unknown constant parameter d*. It is well known that adaptive methods are one of the effective tools for handling unknown constant parameters. Therefore, when the control system contains unknown constant parameters, adaptive methods can efficiently design a controller that achieves / approaches the optimal system state, saving time and resources and significantly improving work efficiency. However, the above algorithm is proposed under relatively ideal assumptions and also has a significant impact on periodic time-varying disturbances / parameters in practical applications. Compared to time-dependent periodic time-varying parameters, which are more complex than constant parameters, this increases the difficulty of system control design.

[0003] Furthermore, with technological advancements, the demands for tracking performance have become increasingly stringent, such as pre-defined convergence domains for the tracking signal, faster convergence speeds, smaller overshoot, and shorter convergence times. However, most existing research on tracking control in recent years only ensures that the tracking error asymptotically converges to a small but unknown neighborhood of zero. To achieve convergence of the tracking error to this ideal small neighborhood, continuous adjustment of the corresponding control parameters is necessary, which not only consumes significant time and resources but also incurs wear and tear on the machine during the debugging process. To ensure the convergence performance of the tracking signal, some researchers have introduced two special switching functions to address the tracking control problem of preset tracking accuracy in switched nonlinear systems under arbitrary switching signals. This ensures that the tracking error converges to a small neighborhood of a pre-defined zero point, largely avoiding the process of repeatedly adjusting design parameters and achieving steady-state performance of the tracking error. In addition, some researchers have proposed a preset performance control method, ensuring that the tracking error converges to the pre-defined boundaries of the performance function, the convergence speed is greater than or equal to a pre-defined constant, and the allowed maximum value does not exceed a pre-defined constant. However, this only considers nonlinear systems without switching signals and with periodic time-varying disturbances.

[0004] Furthermore, the control strategy considered for switching nonlinear systems is proposed using the adaptive backstepping method. The actual controller designed using this recursive algorithm contains the partial derivatives of the virtual controller at various orders. When the system order is small, the calculation of the virtual controller's partial derivatives is relatively simple, and the controller is easy to implement. However, as the system order increases, the computational complexity of these derivatives increases explosively, leading to greater difficulty in controller design and implementation. To address the "computational explosion" problem, some scholars have designed adaptive neural network controllers based on dynamic surface control algorithms, but they neglect the filtering error generated when the virtual controller passes through the filter, which may prevent obtaining accurate system performance. To optimize the algorithm, other scholars have introduced command filtering methods into the adaptive backstepping method, introducing a compensation mechanism to compensate for the filtering error.

[0005] In summary, the existing technologies suffer from several problems: they consider relatively simple disturbance signal structures, failing to represent disturbance signals under more complex environments. General nonlinear systems cannot model real-world systems in complex environments. Furthermore, with increasing practical demands, simple tracking control strategies require time and effort to adjust parameters, increasing experimental costs. Moreover, control strategies designed for high-order switched nonlinear systems within the backstepping framework inevitably suffer from the "computational explosion" problem.

[0006] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0007] (1) The actual system under complex environment is more complex. The problem of pre-defined performance control of time-varying nonlinear parameterized uncertain switching nonlinear system with unknown period is more difficult to handle. How to design the corresponding control algorithm still needs in-depth research.

[0008] (2) Most existing research on tracking control only ensures that the tracking error asymptotically converges to a small but unknown neighborhood of zero, or only guarantees the steady-state performance of the tracking error signal, while ignoring the transient performance of the tracking error signal. How can we design a preset tracking performance control algorithm for this switching nonlinear system that can simultaneously guarantee both the steady-state and transient performance of the tracking error?

[0009] (3) For high-order uncertain switching nonlinear systems, how to avoid the "computation explosion" problem that makes the design and implementation of the controller very difficult under the backstepping method control framework.

[0010] (4) It is quite difficult to improve the approximation algorithm for uncertain switching nonlinear systems with periodic parameters; it is also quite difficult to deal with the explosive growth of computational problems in high-order switching nonlinear systems under the framework of backstepping controller design; at the same time, it is technically difficult to ensure both transient and steady-state performance of tracking error signals.

[0011] The difficulty in solving the above problems and defects lies in the fact that, due to system uncertainties, the existence of periodic time-varying parameters, the explosive growth of computational load under the backstepping method design framework, and the tracking target of ensuring the achievement of the preset tracking error performance, it is technically difficult and challenging to design a new approximation algorithm and an adaptive neural network control strategy based on command filtering.

[0012] CN112947089A discloses an adaptive neural network tracking control method and system with preset tracking accuracy. To approximate unknown nonlinear functions and unknown periodic time-varying parameters, radial basis function neural networks and Fourier series expansions are introduced, and the upper bound of the approximation error is addressed for the first time. Two bilaterally smooth switching functions are introduced to construct a common Lyapunov function satisfying all subsystems. A novel adaptive neural network control scheme is constructed using the backstepping method and the theory of the common Lyapunov function. This invention achieves the convergence of the tracking error to the neighborhood of a preset zero, ensuring the preset performance of the tracking error and the semi-globally consistent eventual boundedness of all signals in the closed-loop system. This invention combines practical problems, establishes a model, and solves the model to obtain results, providing new ideas and solutions for the interdisciplinary research of mathematical and engineering problems.

[0013] The aforementioned patents only consider periodically time-varying linear parameterized switching systems, and the algorithms designed cannot be directly applied to more complex and general periodically time-varying nonlinear parameterized switching systems. Regarding tracking performance, the algorithms proposed in the aforementioned patents can only ensure the steady-state performance of the tracking error signal, without considering the transient performance of the tracking error. This invention combines the Fourier series expansion method and the radial basis function neural network method to design a new approximation algorithm: the Fourier series-radial basis function neural network approximation algorithm. The principle is to first approximate the unknown periodically time-varying parameters using a Fourier series layer, and then use this as the input to the neural network to identify the entire unknown system function. This invention employs a pre-defined performance control method, designing a performance function combined with the error signal for error transformation, and designing a corresponding adaptive controller for the controlled system, so that the tracking error always remains within the pre-defined bounds of the performance function, and stabilizes within a bounded range as the performance function converges. This invention avoids the parameter adjustment process that inevitably wastes a lot of time and resources. It not only ensures that the tracking error converges to a small neighborhood pre-defined by the performance function, but also avoids overshoot of the tracking error signal, while ensuring the steady-state and transient performance of the tracking error. Summary of the Invention

[0014] This invention aims to solve the problems of the prior art. It proposes an adaptive neural network preset tracking performance control method, system, and medium. The technical solution of this invention is as follows:

[0015] An adaptive neural network preset tracking performance control method includes the following steps:

[0016] Step 1: The periodic time-varying nonlinear parameterized switching system output signal, reference signal, and preset performance function are used as inputs for error transformation;

[0017] Step 2: Combine the Fourier series expansion method and the radial basis function neural network method to handle the unknown periodic time-varying nonlinear parameterized function in the system;

[0018] Step 3: Combining backstepping, adaptive control, and command filtering algorithms, handle unknown constant parameters and design compensation signals, and address the "computational explosion" problem that arises during the backstepping controller design process;

[0019] Step 4: Design the appropriate controller and apply it to the controlled system.

[0020] Furthermore, step one, where the system output signal, reference signal, and preset performance function are used as inputs for error transformation, specifically includes:

[0021] 1) Based on the pre-defined performance function ρ(t)=(ρ0-ρ ∞ )e -ct +ρ ∞ , positive constants ρ0, ρ ∞ Let represent the initial value of the performance function and the maximum allowable tracking error e1(t) under steady state, respectively; c represents the decreasing rate of the performance function ρ(t), which also controls the convergence rate and time t of e1(t). Combined with the tracking error signal, an error transformation is performed, and a Lyapunov function V1 is constructed: v1 is the error compensation signal;

[0022] 2) Differentiating the designed Lyapunov function, due to the uncertainty of the periodically time-varying parameterized system, a switching function with unknown periodically time-varying parameters will emerge. This represents the system switching signal. θ1(t) represents the system state vector and an unknown time-varying parameter with a known period, respectively. According to Young's inequality, the unknown function is divided into an unknown periodic time-varying switching function Λ1 and a constant. A new approximation algorithm, FSE-RFBNN, is constructed using Fourier series and neural networks to handle unknown functions of the system.

[0023]

[0024] Wherein, basis functions input vector W1 * W1 represents the weight vector of the approximation algorithm. *T and Both are transposes of the weight vectors; upper bound of the approximation error μ1 It is an unknown constant;

[0025] 3) Based on 2), design the corresponding virtual controller according to the backstepping method;

[0026] 4) Building upon 3), to avoid the computational explosion problem caused by calculating the partial derivatives of the virtual controller, a second-order command filter is used to pass through the virtual controller, and a compensation signal is designed to compensate for the corresponding filtering error. Based on the adaptive backstepping method, the adaptive law of the compensation signal ξ1 is designed as follows: χ1 is a function related to the error signal and the performance function. The derivative of the compensated signal, l1 is a positive constant, x 2,c ξ1 represents the derivative of the output of the command filter with the virtual controller α1 designed for the first subsystem as input, and ξ2 is the compensation signal designed for the second subsystem.

[0027] 5) To handle the unknown weights A1 in the approximation algorithm *T W1 *T Given the approximation error δ1, redesign the Lyapunov function: in Let λ1 be a positive definite diagonal matrix, and let λ1 be a positive constant. Based on the adaptive backstepping method, λ1 is used to estimate the weights and approximation error of the approximation algorithm. and Design the corresponding adaptive control law:

[0028]

[0029] Where c1 and λ1 are positive constants, and Γ1 = Γ1 T and Y1 = Y1 T They are all adaptive gain matrices; The basis function vectors of the approximation algorithm and These are the estimation errors of the approximation algorithm weights and the approximation error, respectively.

[0030] 6) Substitute the virtual controller designed in 3), the adaptive law of the compensation signal in 4), and the adaptive law designed in 5) into the first subsystem of the controlled system, and simplify the derivative of the Lyapunov function.

[0031] Furthermore, step two, which combines the Fourier series expansion method and the radial basis function neural network method to process the unknown periodic time-varying nonlinear parameterized function in the system, specifically includes:

[0032] Design corresponding Lyapunov functions for the first n-1 subsystems of the controlled system. vi Representing the compensation error signal in step i, the design process is repeated to design a virtual controller α for the i-th subsystem. i :

[0033]

[0034] Compensation signal ξ i Adaptive law: And parameter adaptive law: Where k i c i and λ i For positive constants, z i Z is the error signal; i It is the input vector of the approximation algorithm; The virtual controller α is designed for the (i-1)th subsystem. i-1 ξ is the derivative of the output of the input command filter; i It is a compensation signal designed for the i-th subsystem; The basis function vectors of the approximation algorithm and These are the estimates of the approximation algorithm weights and the approximation error, respectively. These represent the estimation errors of the approximation algorithm weights and the approximation error, respectively; Γ i =Γ i T and Y i =Y i T Both are adaptive gain matrices. Then, the designed virtual controller and the designed adaptive law are substituted into the corresponding subsystems of the controlled system, and the derivative of the Lyapunov function is simplified.

[0035] Furthermore, the combination of backstepping, adaptive control, and command filtering algorithms to handle unknown constant parameters and design compensation signals, and to eliminate the "computational explosion" problem generated during the backstepping controller design process, specifically includes:

[0036] Based on the first n-1 steps, design a common Lyapunov function that satisfies all subsystems for the entire n-order system: in This is the estimation error of the upper bound of the Fourier series-radial basis neural network approximation error. Based on the adaptive backstepping method, the design process of the first n-1 steps is repeated to design the actual controller:

[0037]

[0038] Compensation signal adaptive law: And parameter adaptive law:

[0039] Define the state error variable: Command filtering: And define the compensation error variable: Where ζ1 is the transformation error, satisfying e1(t)=ρ(t)R(ζ1), and the error signal e1(t) is defined as e1(t)=y1(t)-y d (t), ξ i A compensation signal is used to compensate for filtering errors caused when the virtual controller passes through the filter. The aforementioned controller u is applied to the controlled system. and Let y be the derivative of the i-th and n-th system states, and y be the system output signal. A Lyapunov function is chosen. By substituting the adaptive law of the design and applying Lyapunov stability theory and related mathematical lemmas, it can be proven that... And satisfy the inequality in g , It is a constant greater than zero.

[0040] Furthermore, the adaptive backstepping method specifically includes:

[0041] The complex nonlinear system is decomposed into many subsystems that do not exceed the system order. Then, according to the Lyapunov stability theorem, intermediate virtual control variables and adaptive laws are designed for each subsystem. This is then "inversely extrapolated" to the entire system to design the overall control law of the system.

[0042] The command filtering algorithm specifically includes:

[0043] The virtual control signal is passed through a second-order filter. A compensation signal is designed based on the filtering error generated when the virtual control passes through the filter to compensate for the generated error, thereby avoiding the need to calculate the repeated derivative of the virtual signal.

[0044] Furthermore, the dynamic equation of the nonlinear parameterized switching system is as follows: The controller is in y is the system state vector; y is the system output signal; This represents the system's switching signal; for any i = 1, 2, ..., n, It is an unknown smooth nonlinear function and satisfies θ i (t) is an unknown time-varying parameter with a known period; It is the output signal of the command filter that takes the virtual controller as input; v n-1 This indicates the error compensation signal; The estimated vector representing the weight vectors from the second to the third layer of the neural network; These are the neural network basis function vectors, where It is the estimated vector of the weight vector from the first layer to the second layer of the neural network and Z. n The input vector representing the neural network; This represents the estimated value of the upper bound of the approximation error.

[0045] A preset tracking performance control system based on an adaptive neural network, comprising:

[0046] The signal input module is used to implement the system output signal, reference signal, and preset performance function as inputs to the error transformation function of preset tracking performance control;

[0047] The function processing module is used to design new approximation algorithms by combining Fourier series expansion methods and radial basis neural networks to process unknown periodic time-varying nonlinear parameterized functions in the system.

[0048] The unknown constant parameter processing module is used to process unknown constant parameters by combining the backstepping method and the adaptive control algorithm.

[0049] The command filtering module is used to combine backstepping, command filtering and adaptive algorithms to eliminate the explosive growth of computational load when calculating the partial derivatives of the virtual controller under the framework of backstepping controller design.

[0050] The controller design module is used to design the corresponding controller and apply it to the controlled system.

[0051] A computer device comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform an adaptive neural network preset tracking performance control method as described in any one of the claims.

[0052] A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform an adaptive neural network preset tracking performance control method as described in any one of the claims.

[0053] A data processing terminal for a van der Bohr oscillator, wherein the data processing terminal for the van der Bohr oscillator is used to implement a preset tracking performance control system as described above using an adaptive neural network.

[0054] The advantages and beneficial effects of this invention are as follows:

[0055] First, based on the universal approximation characteristic of radial basis function (RBF) neural networks, this invention considers using RBF neural network algorithms to process unknown system functions. Since the system function contains periodic time-varying parameters, considering the ability of Fourier series expansion methods to identify periodic time parameters, this invention combines Fourier series expansion methods and RBF neural network methods to design a new approximation algorithm: the Fourier series-RBF neural network approximation algorithm. The principle is to first approximate the unknown periodic time-varying parameters using Fourier series layers, and then use this as the input to the neural network to identify the entire unknown system function. Simultaneously, this invention designs a corresponding adaptive law for the approximation error of the approximation algorithm to more intuitively demonstrate the approximation effect. Compared to directly using the RBF neural network algorithm to approximate the unknown system function, the approximation algorithm designed in this invention yields more accurate results. The adaptive law designed for the approximation weights can be corrected / adjusted online according to changes in parameters or operating indicators during system operation. This online automatic adjustment method not only saves time and resources but also greatly improves work efficiency. The designed new approximation algorithm identifies unknown nonlinear functions containing periodic time-varying nonlinear parameterized functions and switching signals, expanding the application scope of the adaptive backstepping method.

[0056] Based on a pre-defined performance control algorithm, an error transformation is performed by combining a performance function with the error signal. A corresponding adaptive controller is designed for the controlled system, ensuring that the tracking error remains within the pre-defined boundaries of the performance function and stabilizes within a bounded range as the performance function converges. Compared to determining the tracking error convergence region by continuously adjusting control parameters, this invention avoids the time-consuming and resource-intensive parameter adjustment process. It not only guarantees that the tracking error converges to a small neighborhood pre-defined by the performance function but also avoids overshooting of the tracking error signal, while simultaneously ensuring both steady-state and transient performance of the tracking error.

[0057] Within the framework of the backstepping algorithm, a recursive algorithm, the "computational explosion" problem inevitably arises when designing practical controllers for high-order switched nonlinear systems. To address this challenge, a command filtering method is introduced into the backstepping algorithm, which not only solves the "computational explosion" problem and reduces the computational burden but also relaxes the constraints on the reference signal. Compared to the complex calculation process of solving the partial derivatives of the virtual controller, this invention improves the efficiency of controller design and reduces the design difficulty.

[0058] The technical advantage of the controller designed in this invention lies in its ability to simultaneously guarantee both transient and steady-state performance of tracking error when applying the controller u to a switching nonlinear system. This avoids the machine damage and resource waste caused by repeatedly adjusting control parameters to achieve a pre-set tracking performance, thus greatly improving work efficiency. Furthermore, the use of a controller based on command filtering reduces the difficulty of controller design and implementation, and simplifies proving the boundedness of all signals in the closed-loop system.

[0059] Second, considering the technical solution as a whole or from a product perspective, the technical effects and advantages of the technical solution to be protected by this invention are specifically described as follows:

[0060] 1) Handling Nonlinear and Complex Systems: Adaptive Neural Networks (NNs) can model and approximate nonlinear systems, exhibiting strong adaptability and generalization capabilities. This gives the algorithm an advantage in handling nonlinear and complex systems, enabling more accurate modeling and control system construction, and improving control performance. 2) Anti-interference and Robustness: The adaptive NN preset tracking performance control algorithm possesses adaptive learning capabilities, automatically adjusting network parameters to adapt to system changes and disturbances. It maintains good control performance under uncertain and noisy environments, improving system robustness. 3) Fast Response and Tracking Accuracy: The algorithm achieves fast response and tracking of a given reference signal. Through adaptive learning and parameter adjustment, it can quickly adapt to changes in the reference signal and provide accurate tracking performance, meeting the system's requirements for real-time performance and accuracy. 4) System Optimization and Efficiency Improvement: The adaptive NN preset tracking performance control algorithm can continuously optimize the system's control strategy through online learning and parameter adjustment. It can adapt to dynamic changes in the system and optimize control performance, improving system efficiency and energy utilization. 5) Wide Application: The adaptive NN preset tracking performance control algorithm can be applied to multiple fields, including industrial automation, robot control, aerospace, traffic control, and power systems. It can adapt to different system characteristics and needs, and has broad application potential.

[0061] Third, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0062] The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0063] The pre-set tracking performance control algorithm proposed in this project is highly intelligent and adaptable, capable of adaptively adjusting various uncertain parameters, and can be widely applied in various fields such as industry, aviation, and transportation. Therefore, the main forms of technology transfer will be through technology-for-equity investment or technology transfer. Potential partners are primarily companies or research institutions in the military, transportation, and mechanical control sectors.

[0064] The technical solution of this invention fills a technological gap in the industry both domestically and internationally:

[0065] This invention fills the gap in preset tracking performance control for nonlinear systems with periodic time-varying parameters and switching signals. The controlled system is more practically significant than systems with unknown constant parameter functions. Compared to the tracking error converging to a small but unknown residual set, the obtained tracking control performance ensures that the tracking error is always confined within the predetermined boundaries of the performance function and remains stable within a defined bounded domain. The proposed preset tracking control algorithm avoids the process of continuously adjusting parameters to converge the tracking error and is applied for the first time to a switching nonlinear system. This effectively fills the technical gap in preset tracking control for periodic time-varying nonlinear parameterized switching nonlinear systems. By introducing the command filtering method into the backstepping method, a corresponding preset tracking performance control algorithm is designed for the controlled system, optimizing the control algorithm based on the backstepping method and overcoming the problems of designing and implementing high-order system controllers.

[0066] The significance of addressing the above problems and shortcomings is as follows: Achieving the target tracking performance with preset tracking capabilities is of great importance and plays a significant role in technological development. Practical problems such as drone rescue, missile tracking, and robotic arm handling place increasingly higher demands on tracking performance. Most existing research on tracking control in recent years only ensures that the tracking error asymptotically converges to a small but unknown neighborhood of zero. To achieve convergence of the tracking error to an ideal small neighborhood, continuous adjustment of the corresponding control parameters is required, which not only consumes a significant amount of time and resources but also incurs wear and tear on the machine during the debugging process. Therefore, how to achieve or ensure preset performance control of the tracking error (pre-set convergence region, small overshoot, short convergence time, and fast convergence speed) is a very meaningful research area. Furthermore, considering the complexity of the environment, in practical applications, these controlled systems are frequently subjected to disturbances. Considering general disturbances and periodic perturbations, the designed controller may fail, and the system's stability may deteriorate. Furthermore, based on the characteristics of the adaptive backstepping method, as the order of the controlled system increases, the controller design requires continuously calculating the partial derivatives of the virtual control at various orders. This leads to an explosive increase in the computational load of the controller design, rapidly increasing the difficulty of its design and implementation. Therefore, under existing conditions, it is crucial to quickly handle periodic time-varying disturbances, eliminate the "computational explosion" problem, and achieve the preset tracking performance target. This avoids the process of constantly adjusting parameters, eliminates the "computational explosion" problem, optimizes the algorithm, ensures the transient and steady-state performance of the tracking error, and satisfies the system's robustness. This is also the focus of this invention, addressing real-world problems, possessing strong applicability, and providing support for research in multiple practical application fields. Attached Figure Description

[0067] Figure 1 This is a flowchart of the adaptive neural network preset tracking performance control method according to a preferred embodiment of the present invention;

[0068] Figure 2 This is a schematic diagram of the structure of the adaptive neural network preset tracking performance control system provided in an embodiment of the present invention;

[0069] Figure 3 This is a flowchart illustrating the implementation of the adaptive neural network preset tracking performance control method provided in this embodiment of the invention.

[0070] Figure 4 This is a state diagram of the output signal and reference signal provided in an embodiment of the present invention;

[0071] Figure 5 This is a trajectory diagram of tracking error and performance function provided in an embodiment of the present invention;

[0072] Figure 6 This is a compensation signal diagram provided in an embodiment of the present invention;

[0073] Figure 7 This is a control input trajectory diagram provided in an embodiment of the present invention;

[0074] Figure 8 This is a switching signal diagram provided in an embodiment of the present invention;

[0075] Figure 9 This is a 2-norm trajectory diagram of the approximation algorithm weight estimation provided in this embodiment of the invention;

[0076] Figure 10 This is the F-norm trajectory diagram of the approximation algorithm weight estimation provided in the embodiments of the present invention;

[0077] Figure 11 This is a trajectory diagram of the upper bound estimation of the approximation error of the Fourier series-radial basis neural network provided in the embodiment of the present invention;

[0078] Figure 12 This is a state diagram of the van der Bohr oscillator provided in an embodiment of the present invention;

[0079] Figure 13 This is a state diagram of the output signal and reference signal provided in an embodiment of the present invention;

[0080] Figure 14 This is a trajectory diagram of tracking error and performance function provided in an embodiment of the present invention;

[0081] Figure 15 This is a compensation signal diagram provided in an embodiment of the present invention;

[0082] Figure 16 This is a switching signal diagram provided in an embodiment of the present invention;

[0083] Figure 17 This is a 2-norm trajectory diagram of the approximation algorithm weight estimation provided in this embodiment of the invention;

[0084] Figure 18 This is the F-norm trajectory diagram of the weight estimation of the approximation algorithm provided in the embodiments of the present invention;

[0085] Figure 19 This is a trajectory diagram of the estimated value of the upper bound of the approximation error provided in the embodiment of the present invention.

[0086] In the diagram: 1. Signal input module; 2. Function processing module; 3. Unknown constant parameter processing module; 4. Command filtering module; 5. Controller design module. Detailed Implementation

[0087] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0088] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0089] This invention constructs a novel approximator by combining Fourier series expansion with radial basis function neural networks to identify unknown periodic time-varying parameterized functions. Utilizing a preset performance control method, command filtering, and adaptive backstepping, a new adaptive neural network preset tracking performance control scheme based on command filtering is proposed. A new compensation signal is constructed to eliminate filtering errors, thereby ensuring the performance of the preset tracking error.

[0090] This invention is an adaptive neural network-based preset tracking performance control method. It employs a nonlinear parameterized switching system model to accurately describe the dynamic characteristics of complex nonlinear systems. It proposes the concept of a preset performance function, which allows for pre-defining the expected performance indicators of the control system, providing performance constraints for the design of the control strategy. Using an error transformation method and a novel approximation algorithm, complex nonlinear systems can be equivalently transformed into linear time-invariant systems, simplifying the design of the control strategy while ensuring control effectiveness. Applying Lyapunov stability theory, it analyzes the stability of the control system, ensuring that the control strategy will not lead to system instability. The use of an adaptive neural network enables online adjustment of the control strategy parameters, allowing the control system to adapt to changes in system parameters and the influence of the external environment.

[0091] like Figure 1 As shown, the adaptive neural network preset tracking performance control method provided by the present invention includes the following steps:

[0092] S101: The system output signal, reference signal, and preset performance function serve as the inputs to the error transformation function of the preset tracking performance control;

[0093] S102: A new approximation algorithm for handling time-varying parameterized functions with unknown periods in systems;

[0094] S103: Combining adaptive backstepping, preset performance control, and command filtering algorithms, it handles unknown periodic time-varying functions and the "computational explosion" problem, while also considering the filtering error generated by the filter.

[0095] S104: Design the corresponding controller and apply it to the controlled system.

[0096] The adaptive neural network preset tracking performance control method provided by this invention can also be implemented by those skilled in the art using other steps. Figure 1 The adaptive neural network preset tracking performance control method provided by this invention is merely a specific embodiment.

[0097] like Figure 2 As shown, the adaptive neural network preset tracking performance control system provided by the present invention includes:

[0098] Signal input module 1 is used to implement the system output signal, reference signal and preset performance function as input to the error transformation function of preset tracking performance control;

[0099] Function processing module 2 uses two approximation algorithms to design a new approximation algorithm to process unknown periodic time-varying nonlinear parameterized functions in the system;

[0100] The unknown constant parameter processing module 3 is used to process unknown constant parameters by combining the backstepping method and the adaptive control algorithm.

[0101] Command filtering module 4 is used to combine backstepping, command filtering and adaptive control algorithms to eliminate the explosive growth of computational load when calculating the partial derivatives of the virtual controller under the framework of backstepping controller design, which is caused by high-order switching nonlinearity.

[0102] Controller design module 5 is used to design the corresponding controller and apply it to the controlled system.

[0103] The adaptive neural network tracking control scheme proposed in this invention is implemented in n steps:

[0104] Step 1:

[0105] 1) Based on the pre-defined performance function ρ(t)=(ρ0-ρ ∞ )e -ct +ρ ∞ By combining the tracking error signal, an error transformation is performed, and a Lyapunov function is constructed:

[0106] 2) Differentiating the designed Lyapunov function will result in a switching function with time-varying parameters of unknown period due to system uncertainty. According to Young's inequality, the unknown function is divided into two parts: the unknown periodic time-varying function, the switching function Λ1, and a constant. New approximation algorithms for handling unknown functions of a system are constructed using Fourier series and neural networks:

[0107]

[0108] Wherein, basis functions input vector Approximation error upper bound It is an unknown constant;

[0109] 3) Based on 2), design the corresponding virtual controller according to the backstepping method;

[0110] 4) Building upon 3), to avoid calculating the partial derivatives of the virtual controller, a second-order command filter is used to pass the virtual controller, and a new compensation signal is designed to compensate for the corresponding filtering errors. Based on the adaptive backstepping method, the adaptive law of the compensation signal is designed as follows:

[0111] 5) To handle the unknown weights A in the approximation algorithm *T W *T Redesign the Lyapunov function: in Given a positive definite diagonal matrix; based on the adaptive backstepping method, a corresponding adaptive control law is designed for estimating the weights of the approximation algorithm:

[0112]

[0113] 6) Substitute the virtual controller designed in 3), the compensation signal in 4), and the adaptive law designed in 5) into the first subsystem of the controlled system, and simplify the derivative of the Lyapunov function.

[0114] Step n-1:

[0115] For the first n-1 subsystems of the controlled system, design the corresponding Lyapunov functions: And repeat the design process to design virtual controllers for each of the n-1 subsystems:

[0116]

[0117] Compensation signal adaptive law And parameter adaptive law: Then, the designed virtual controller and the designed adaptive law are substituted into the corresponding subsystem of the controlled system, and the derivative of the Lyapunov function is simplified.

[0118] Step n: Based on the previous n-1 steps, for the entire nth-order system, design a common Lyapunov function that satisfies all subsystems and, for the first time, incorporate the estimation error of the upper bound of the approximation error: in This is the estimation error of the upper bound of the Fourier series-radial basis neural network approximation error. Based on the adaptive backstepping method, the design process of the first n-1 steps is repeated to design the actual controller: Compensation signal adaptive law And parameter adaptive law:

[0119] Define the state error variable: Command filtering: Define the compensation error variable: Where ζ1 is the transformation error, satisfying e1(t)=ρ(t)R( ζ 1) Error signal e1(t)=y1(t)-y d (t), ξ i This is a compensation signal to compensate for the filtering error generated when the virtual controller passes through the filter. The aforementioned controller u is applied to the controlled system. Choosing Lyapunov functions Substituting the adaptive law of the above design into the equation, and using Lyapunov stability theory and related mathematical lemmas, it can be proven that... And satisfy the inequality

[0120] The above theory can explain that by constructing a common Lyapunov function that satisfies all subsystems, the designed controller and adaptive law avoid the "computation explosion" problem and eliminate the impact of filtering error on system performance. It also avoids the process of constantly adjusting parameters to achieve ideal tracking performance, and realizes the goal of the tracking error converging to a pre-given small neighborhood.

[0121] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0122] III. Evidence of the Relevant Effects of the Embodiments. The embodiments of the present invention have achieved some positive effects during research and development or use, and indeed possess significant advantages compared to existing technologies. The following description, in conjunction with data, charts, and other materials from the experimental process, illustrates these advantages.

[0123] The technical effects of the present invention will be described in detail below with reference to simulation.

[0124] Table 1 Simulation Implementation Conditions and Parameter Values

[0125]

[0126]

[0127] Among them 0 [5] It is a 5-dimensional column vector ([0, 0, 0, 0, 0]). T ) and diag{10} are identity matrices whose diagonal elements are all 10.

[0128] 2) Simulation results: The simulation results are as follows Figure 4-11 As shown.

[0129] Simulation 2 applies the algorithm proposed in this invention to a van der Bohr oscillator with a real physical context. For example, its internal principles are shown in Figure 12 1) Simulation conditions: Parameters satisfy a = 0.7, b = 0.8, p = 0, q = 0.74, ω = 1, and the reference trajectory is y. d = sin(3t) + cos(t), the time-varying periodic parameter is set as F(t) = qcos(ωt), and the system function is and f 2,1 =f2,2 =0.1(x1+0.7+0.8x2). The initial conditions and parameter values ​​in the simulation are shown in Table 2.

[0130] Table 2 Simulation Implementation Conditions and Parameter Values

[0131]

[0132]

[0133] 2) Simulation results are as follows Figure 13 As shown in –19. From Figure 13 As can be seen, the output signal can quickly track the reference signal. For example... Figure 14 The tracking error trajectory shown is always confined within the limits predetermined by the performance function and converges as the performance function converges. The trajectories of the compensation signal and the arbitrarily selected switching signal are shown below. Figure 15 -16. Weight Estimation The trajectory estimated by the norm and the upper bounds of the approximation errors δ1 and δ2, such as Figure 17 As shown in –19, these signals are clearly bounded.

[0134] In summary, the algorithm proposed in this invention is effective. It not only optimizes the adaptive backstepping method but also avoids the process of constantly adjusting parameters to achieve ideal tracking performance. It realizes that the tracking error converges to the target within a bounded range given by the performance function in advance, and that all signals in the entire closed-loop system are bounded.

[0135] Here are two specific examples:

[0136] Example 1: Robot Arm Control

[0137] Suppose we need to control a robotic arm with multiple joints, making it move along a predetermined trajectory in an unknown, time-varying environment. The unknown time-varying parameters might be caused by factors such as changes in external load or friction. To achieve effective control of this robotic arm, we can employ the aforementioned adaptive neural network preset tracking performance control method.

[0138] 1. First, according to the method described above, the dynamic model of the robot arm is represented as a nonlinear parameterized switching system.

[0139] 2. Design preset performance functions, such as tracking error and upper limit of control input, to quantify the desired control performance.

[0140] 3. Using the error transformation method and the new approximation algorithm to process the unknown periodic time-varying nonlinear parameterized function, the nonlinear dynamic model of the robot arm is converted into a linear time-invariant system.

[0141] 5. Combining backstepping, adaptive control, and command filtering algorithms, we can handle unknown constant parameters and design compensation signals.

[0142] 6. Design a corresponding controller and apply it to the robot arm so that it can move along a predetermined trajectory in an unknown, periodically changing environment.

[0143] Example 2: Aircraft Attitude Control

[0144] Suppose we need to control an aircraft (such as a drone or airplane) to maintain a stable attitude in an unknown, periodically varying wind field. To achieve effective control of this aircraft, we can employ the aforementioned adaptive neural network preset tracking performance control method.

[0145] 1. First, according to the method described above, the dynamic model of the aircraft is represented as a nonlinear parameterized switching system.

[0146] 2. Design preset performance functions, such as attitude angle error and upper limit of control input, to quantify the desired control performance.

[0147] 3. Using the error transformation method and the new approximation algorithm to process the unknown periodic time-varying nonlinear parameterized function, the nonlinear dynamic model of the aircraft is converted into a linear time-invariant system.

[0148] 5. Combining backstepping, adaptive control, and command filtering algorithms, we can handle unknown constant parameters and design compensation signals.

[0149] 6. Design a corresponding controller and apply it to the aircraft so that it can maintain a stable attitude in an unknown periodic time-varying wind field.

[0150] Through these two examples, we can see the advantages of the adaptive neural network preset tracking performance control method in handling unknown periodic time-varying parameterized functions and ensuring system performance. This method can be widely applied to the control of various complex nonlinear systems, such as autonomous vehicles and industrial automation equipment.

[0151] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, a computer can be, for example, a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email device, game console, tablet computer, wearable device, or any combination of these devices.

[0152] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0153] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0154] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. An adaptive neural network preset tracking performance control method, characterized in that, Includes the following steps: Step 1: The periodic time-varying nonlinear parameterized switching system output signal, reference signal, and preset performance function are used as inputs for error transformation; Step 2: Combine the Fourier series expansion method and the radial basis function neural network method to handle the unknown periodic time-varying nonlinear parameterized function in the system; Step 3: Combining backstepping, adaptive control, and command filtering algorithms, handle unknown constant parameters and design compensation signals, and address the "computational explosion" problem that arises during the backstepping controller design process; Step 4: Design the appropriate controller and apply it to the controlled system; Step one: The system output signal, reference signal, and preset performance function are used as inputs for error transformation, specifically including: 1) Based on the pre-defined performance function of the design normal numbers These represent the initial value of the performance function and the tracking error in steady state, respectively. Maximum allowable quantity; Represents performance function The rate of decrease is also a control. Convergence speed and time By combining the tracking error signal, an error transformation is performed, and a Lyapunov function is constructed. : ; It is a compensation error signal; 2) Differentiating the designed Lyapunov function, due to the uncertainty of the periodically time-varying parameterized system, a switching function with unknown periodically time-varying parameters will emerge. , This represents the system switching signal. Let represent the system state vector and an unknown time-varying parameter with a known period, respectively. According to Young's inequality, the unknown function is divided into a time-varying switching function with an unknown period. and constant A new approximation algorithm is constructed using Fourier series and neural networks: the Fourier series-neural network approximation algorithm. Handling unknown functions of the system: Wherein, basis functions input vector , Represents the weight vector of the approximation algorithm; Indicates the approximation error. and Both are transposes of the weight vectors; approximation error Upper Realm It is an unknown constant; 3) Based on 2), design the corresponding virtual controller according to the backstepping method; 4) Building upon 3), to avoid the computational explosion problem caused by calculating the partial derivatives of the virtual controller, a second-order command filter is used to pass the virtual controller, and a compensation signal is designed to compensate for the corresponding filtering error; based on the adaptive backstepping method, the compensation signal... The adaptive law design is as follows: ; Functions related to error signals and performance functions, The derivative of the compensated signal, It is a positive number. Indicated to the first Virtual controller for subsystem design The derivative of the output of the input command filter. It is aimed at the first Compensation signals for each subsystem design; 5) To handle unknown weights in the approximation algorithm and approximation error Redesign the Lyapunov function: in It is a positive definite diagonal matrix. These are positive constants; based on the adaptive backstepping method, they are used to estimate the weights and approximation error of the approximation algorithm. , and Design the corresponding adaptive control law: in, and For positive numbers, and They are all adaptive gain matrices; The basis function vectors of the approximation algorithm and ; These are the estimation errors of the approximation algorithm weights and the approximation error, respectively. 6) Substitute the virtual controller designed in 3), the adaptive law of the compensation signal in 4), and the adaptive law designed in 5) into the first subsystem of the controlled system, and simplify the derivative of the Lyapunov function; Step two: Combining the Fourier series expansion method and the radial basis function neural network method to process the unknown periodic time-varying nonlinear parameterized function in the system, specifically including: For the front of the controlled system For each subsystem, design the corresponding Lyapunov function. : , Representing the The error signal in the step is compensated, and the design process is repeated, respectively for the first step. Design a virtual controller for each subsystem : Compensation signal Adaptive law: And parameter adaptive law: ,in , and For positive constants This is an error signal; It is the input vector of the approximation algorithm; Therefore, it is aimed at the first Virtual controller for subsystem design The derivative of the output of the input command filter; It is aimed at the first Compensation signals for each subsystem design; The basis function vectors of the approximation algorithm and ; These are the estimates of the approximation algorithm weights and the approximation error, respectively. These are the estimation errors of the approximation algorithm weights and the approximation error, respectively. and Both are adaptive gain matrices. Then, the designed virtual controller and the designed adaptive law are substituted into the corresponding subsystems of the controlled system, and the derivative of the Lyapunov function is simplified.

2. The adaptive neural network preset tracking performance control method according to claim 1, characterized in that, The method combines backstepping, adaptive control, and command filtering algorithms to handle unknown constant parameters and design compensation signals, and eliminates the "computational explosion" problem generated during the backstepping controller design process. Specifically, it includes: in front Based on the previous steps, targeting the entire For a system of order, design a common Lyapunov function that satisfies all subsystems: in It is the estimation error of the upper bound of the approximation error of the Fourier series-radial basis neural network, based on the adaptive backstepping method, repeating the previous... Step-by-step design process, designing the actual controller: Compensation signal adaptive law: And parameter adaptive law: ; Define the state error variable: Command filtering: And define the compensation error variable: in For the transformation error, satisfying Error signal Defined as , The compensation signal is used to compensate for the filtering error generated when the virtual controller passes through the filter, and the above controller... Apply to the controlled system , and For the first The and the first The derivative of each system state, For the system output signal, a Lyapunov function is selected. : By substituting the adaptive law of the design and applying Lyapunov stability theory and related mathematical lemmas, it can be proven that... And satisfy the inequality ,in , It is a constant greater than zero.

3. The adaptive neural network preset tracking performance control method according to claim 2, characterized in that, The adaptive backstepping method specifically includes: The complex nonlinear system is decomposed into many subsystems that do not exceed the system order. Then, according to the Lyapunov stability theorem, intermediate virtual control variables and adaptive laws are designed for each subsystem. This process is then "inversely extrapolated" to the entire system to design the overall control law of the system. The command filtering algorithm specifically includes: The virtual control signal is passed through a second-order filter. A compensation signal is designed based on the filtering error generated when the virtual control passes through the filter to compensate for the generated error, thereby avoiding the need to calculate the repeated derivative of the virtual signal.

4. The adaptive neural network preset tracking performance control method according to any one of claims 1-3, characterized in that, The dynamic equation of the nonlinear parameterized switching system is: The controller is ,in It is the system state vector; For system output signals; This represents the system's switching signal; for any... , It is an unknown smooth nonlinear function and satisfies ; It is an unknown time-varying parameter with a known period; It is the derivative of the output signal of the command filter with the virtual controller as input; This indicates the error compensation signal; The estimated vector representing the weight vectors from the second to the third layer of the neural network; These are the neural network basis function vectors, where It is the estimated vector sum of the weight vectors from the first layer to the second layer of the neural network. The input vector representing the neural network; This represents the estimated value of the upper bound of the approximation error.

5. An adaptive neural network preset tracking performance control system employing the method of claim 1, characterized in that, include: The signal input module is used to implement the system output signal, reference signal, and preset performance function as inputs to the error transformation function of preset tracking performance control; The function processing module is used to design new approximation algorithms by combining Fourier series expansion methods and radial basis neural networks to process unknown periodic time-varying nonlinear parameterized functions in the system. The unknown constant parameter processing module is used to process unknown constant parameters by combining the backstepping method and the adaptive control algorithm. The command filtering module is used to combine backstepping, command filtering and adaptive algorithms to eliminate the explosive growth of computational load when calculating the partial derivatives of the virtual controller under the framework of backstepping controller design. The controller design module is used to design the corresponding controller and apply it to the controlled system.

6. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, causes the processor to perform the adaptive neural network preset tracking performance control method as described in any one of claims 1-4.

7. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the adaptive neural network preset tracking performance control method as described in any one of claims 1-4.

8. A data processing terminal for a van der Bohr oscillator, characterized in that, The data processing terminal of the van der Bohr oscillator is used to implement the adaptive neural network preset tracking performance control system as described in claim 5.

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