An unmanned system trajectory tracking optimization control method under asymmetric input constraints
Patent Information
- Application Number
- CN202611112165.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-24
- Publication Date
- 2026-10-13
AI Technical Summary
值得注意的是，但就非对称输入约束下的轨迹跟踪优化控制而言，目前尚无相关算法发明
[0076]有益效果：与现有技术相比，本申请实施例提供的一种非对称输入约束下无人系统的轨迹跟踪优化控制方法，包括获取无人系统的位置数据和速度数据;将所述位置数据和所述速度数据输入预制的控制信号模型，获取控制信号；基于所述控制信号对所无人系统进行优化控制；所述控制信号模型包括：自适应神经网络观测器，用于基于所述位置数据和所述速度数据，获取复合不确定项的估计，所述复合不确定项的估计包括环境扰动和动力学不确定项；自适应反步控制器，用于基于所述位置数据和所述速度数据，获取自适应反步控制输入；优化控制器，用于基于所述位置数据、所述速度数据和所述自适应反步控制输入，获取最优控制输入；非对称光滑饱和子模型，用于基于所述自适应反步控制输入、所述复合不确定项的估计和所述最优控制输入，获取所述控制信号。本申请通过自适应神经网络观测器完成对扰动及不确定项的动态估计；然后，基于反步法与自适应控制理论，建立自适应反步控制律，既获得仿射形式的误差动态系统，又有效削弱饱和与估计误差的不利影响。
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Figure CN122902611A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of unmanned system control technology, specifically relating to a trajectory tracking optimization control method for unmanned systems under asymmetric input constraints. Background Technology
[0002] Unmanned systems are a class of comprehensive platforms capable of autonomously completing tasks, typically including driverless vehicles, unmanned ships, underwater vehicles, and drones. Driven by artificial intelligence, information technology, and robotics, these systems have penetrated into many key areas such as intelligent transportation, emergency rescue, environmental monitoring, marine exploration, intelligent manufacturing, and national defense, significantly improving operational efficiency and safety, and demonstrating broad application prospects.
[0003] As a key intelligent equipment with autonomous operation capabilities, unmanned systems rely heavily on high-precision trajectory tracking control for successfully executing various complex tasks. However, in practical engineering applications, the physical size and structural characteristics of actuators inevitably lead to amplitude saturation constraints in their control inputs, and these physical constraints often exhibit significant asymmetry. Simultaneously, unmanned systems operating in complex dynamic environments face not only internal uncertainties such as modeling errors caused by the difficulty in accurately measuring kinematic parameters and unmodeled dynamics, but also the severe impact of long-term external time-varying environmental disturbances. These internal uncertainties, coupled with complex external disturbances, severely weaken the system's trajectory tracking performance and robustness. Furthermore, unmanned systems typically rely on their own limited energy resources (such as high-energy batteries or fuel) for power, and control energy consumption directly determines their endurance for continuous operation. However, neural networks possess universal approximation properties, providing an effective approach to solving the dynamics and disturbance problems of such unmanned systems. Moreover, optimal control theory can effectively optimize the energy consumption of trajectory tracking control in unmanned systems. It is noteworthy that, currently, no relevant algorithms have been invented for trajectory tracking optimization control under asymmetric input constraints. Therefore, the unmanned system trajectory tracking optimization control method of this invention has important application value and practical significance. Summary of the Invention
[0004] Purpose of the invention: This application develops a trajectory tracking optimization control method for unmanned systems under asymmetric input constraints, aiming to solve the technical problems in the prior art.
[0005] Technical Solution: In a first aspect, embodiments of this application provide a trajectory tracking optimization control method for an unmanned system under asymmetric input constraints, comprising:
[0006] Acquire position and velocity data from the unmanned system;
[0007] The position data and velocity data are input into a pre-made control signal model to obtain a control signal.
[0008] The unmanned system is optimized and controlled based on the control signals.
[0009] The control signal model includes:
[0010] An adaptive neural network observer is used to obtain an estimate of a composite uncertainty based on the position data and the velocity data, the estimate of which includes environmental disturbances and dynamic uncertainties.
[0011] An adaptive backstepping controller is used to obtain adaptive backstepping control input based on the position data and the velocity data;
[0012] An optimization controller is configured to obtain optimized control inputs based on the position data, the velocity data, and the adaptive backstepping control input;
[0013] An asymmetric smooth saturated sub-model is used to obtain the control signal based on the adaptive backstepping control input, the estimation of the composite uncertainty term, and the optimized control input.
[0014] In some embodiments, the step of obtaining an estimate of the composite uncertainty term includes:
[0015] The velocity data is estimated by using the known composite uncertainty term and the adaptive neural network observer.
[0016] Based on the velocity data and the estimation of the velocity data, the observer error is obtained;
[0017] Based on the observer error, an estimate of the ideal neural network weight matrix is obtained;
[0018] The estimate of the composite uncertainty term is updated based on the estimate of the neural network weight matrix.
[0019] In some embodiments, the step of obtaining the adaptive neural network observer includes:
[0020] Based on the estimation of the velocity data and the position data, an estimate of the composite uncertainty term is obtained by combining a radial basis function neural network;
[0021] Based on the estimation of the composite uncertainty, the estimation of the velocity data, and the position data, the adaptive neural network observer is obtained, and its characterization formula includes:
[0022] ;
[0023] ;
[0024] ;
[0025]
[0026] ;
[0027] in, For speed data The estimate; for The derivative with respect to time; Location data; It is a nonlinear function composed of known dynamic model parameters; It is the inverse of the inertia matrix; It is a saturated nonlinear function; For unconstrained control inputs; This is the gain matrix; For observer error; For composite uncertainty terms The estimate; Estimation of weight matrix for neural networks The renewal law, for The estimate, The weight matrix is the ideal weight matrix for the neural network; T is the transpose. The activation function vector; These are design parameters.
[0028] In some embodiments, the characterization formula of the asymmetric smooth saturated sub-model includes:
[0029] ;
[0030] ;
[0031] , ;
[0032] ;
[0033] ;
[0034] in, The control signal; For control input; For adaptive backstepping control input; This is the optimal control input; This is an estimate of the composite uncertainty term; This represents the output of an asymmetric smooth saturated model; n is the dimension controlling the input. , To control the maximum value of the input, To control the minimum input value, It is a symbolic function; The Gaussian error function; For time.
[0035] In some embodiments, the step of obtaining the adaptive backstepping control input includes:
[0036] Obtain the position error corresponding to the position data, and the velocity error corresponding to the velocity data;
[0037] Obtain the backstepping virtual control law, and combine it with the position error to obtain the backstepping virtual control input;
[0038] Obtain the adaptive law, and combine it with the backstepping virtual control input and the speed error to obtain the adaptive input;
[0039] Obtain the adaptive backstepping control law, and combine the adaptive input and the speed error to obtain the adaptive backstepping control input.
[0040] In some embodiments, the characterization formula of the backstepping virtual control law includes:
[0041] ;
[0042] ;
[0043] in, This is the backstepping virtual control input; The design matrix is positive definite. This refers to the positional error; Location data; Let be the derivative of the desired trajectory with respect to time; For the desired trajectory;
[0044] The formula for representing the adaptive law includes:
[0045] ;
[0046] ;
[0047] ;
[0048] in, For the updated , For adaptive parameter vectors, For ideal adaptive parameter vectors; For design parameters; It is a diagonal matrix composed of tangent functions; For speed error; For speed; For virtual control input; For backstepping virtual control input; This is the optimal virtual control input;
[0049] The characterization formula of the adaptive backstepping control law includes:
[0050] ;
[0051] ;
[0052] in, For adaptive backstepping control input; The design matrix is positive definite. For speed error; For speed; These are the parameters of the nominal dynamic model; The derivative of the virtual control input with respect to time; It is a diagonal matrix composed of tangent functions; For adaptive parameter vectors, An adaptive parameter vector with ideal parameters; , Given the known dynamic error, , To control the dimensions of the input, For location data, Given a known dynamic model, For virtual control input.
[0053] In some embodiments, the step of obtaining the optimal control input includes:
[0054] Based on the known optimal control input and optimal virtual control input, obtain the approximate Hamiltonian function;
[0055] Obtain the position error corresponding to the position data, and the velocity error corresponding to the velocity data;
[0056] The evaluation network weights are obtained based on the position error and the velocity error, combined with the weight update law and the approximate Hamiltonian function.
[0057] Based on the position error and the velocity error, and combined with the evaluation network weights and the activation function of the evaluation network, the optimal cost function is obtained;
[0058] The optimal control input is updated based on the optimal cost function and the evaluation network weights.
[0059] In some embodiments, the representation formula of the weight update law includes:
[0060] ;
[0061] in, for The renewal law, for The estimate, The ideal weight matrix for a neural network; For design parameters; To Find the remainder after partial derivative. , for Compared to gradient, Let be a vector composed of neural network activation functions. Let it be a vector consisting of position and velocity errors. The matrix is obtained by multiplying the activation function vector, the inverse of the inertia matrix, and the transpose of the activation function vector. Discount factor; This is a transpose operation; For Hamiltonian function error, , For approximate Hamiltonian function, It is a vector composed of position and velocity error vectors. It is an ideal Hamiltonian function.
[0062] In some embodiments, the step of obtaining the optimization control input includes:
[0063] Obtain an approximate optimal control law, and obtain the optimal control input through the approximate optimal control law. The characterization formula of the approximate optimal control law includes:
[0064] ;
[0065] ;
[0066] in, for The estimate; This is the optimal virtual control input; This is the optimal control input; It is a positive definite matrix; It is the inverse of the inertia matrix; This is a transpose operation; , for Compared to gradient, Let be a vector consisting of activation functions. , For positional error, For speed error; for The estimate, This is the ideal weight matrix for a neural network.
[0067] Secondly, embodiments of this application also provide a trajectory tracking optimization control system for an unmanned system under asymmetric input constraints, comprising:
[0068] The data acquisition module is used to acquire the position and velocity data of the unmanned system.
[0069] A control signal acquisition module is used to input the position data and the velocity data into a pre-made control signal model to acquire control signals.
[0070] An optimized control module is used to optimize the control of the unmanned system based on the control signal;
[0071] The control signal model includes:
[0072] An adaptive neural network observer is used to obtain an estimate of a composite uncertainty based on the position data and the velocity data, the estimate of which includes environmental disturbances and dynamic uncertainties.
[0073] An adaptive backstepping controller is used to obtain adaptive backstepping control input based on the position data and the velocity data;
[0074] An optimization controller is used to obtain the optimal control input based on the position data, the velocity data, and the adaptive backstepping control input;
[0075] An asymmetric smooth saturated sub-model is used to obtain the control signal based on the adaptive backstepping control input, the estimation of the composite uncertainty term, and the optimal control input.
[0076] Beneficial Effects: Compared with the prior art, the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application includes acquiring position data and velocity data of the unmanned system; inputting the position data and velocity data into a pre-built control signal model to acquire a control signal; and performing optimization control on the unmanned system based on the control signal. The control signal model includes: an adaptive neural network observer for acquiring an estimate of a composite uncertainty term based on the position data and velocity data, the estimate of the composite uncertainty term including environmental disturbances and dynamic uncertainties; an adaptive backstepping controller for acquiring an adaptive backstepping control input based on the position data and velocity data; an optimization controller for acquiring an optimal control input based on the position data, velocity data, and the adaptive backstepping control input; and an asymmetric smooth saturated sub-model for acquiring the control signal based on the adaptive backstepping control input, the estimate of the composite uncertainty term, and the optimal control input. This application uses an adaptive neural network observer to dynamically estimate disturbances and uncertainties; then, based on the backstepping method and adaptive control theory, an adaptive backstepping control law is established, which not only obtains an affine error dynamic system, but also effectively reduces the adverse effects of saturation and estimation errors. Attached Figure Description
[0077] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0078] Figure 1 A flowchart illustrating the steps of the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application embodiment;
[0079] Figure 2 A flowchart illustrating the steps for obtaining an estimate of composite uncertainty terms in the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application embodiment;
[0080] Figure 3 A flowchart illustrating the steps for obtaining adaptive backstepping control input in the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application embodiment;
[0081] Figure 4 A flowchart illustrating the steps for obtaining the optimal control input in the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application embodiment;
[0082] Figure 5A module connection diagram of the trajectory tracking optimization control system for an unmanned system under asymmetric input constraints provided in this application embodiment;
[0083] Figure 6 A control system block diagram of the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in an embodiment of this application;
[0084] Figure 7 A flowchart of the control algorithm for the trajectory tracking optimization control method of an unmanned system under asymmetric input constraints provided in an embodiment of this application;
[0085] Figure reference numerals: 10, data acquisition module; 20, control signal acquisition module; 30, optimization control module. Detailed Implementation
[0086] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.
[0087] Unmanned systems are a class of comprehensive platforms capable of autonomously completing tasks, typically including driverless vehicles, unmanned ships, underwater vehicles, and drones. Driven by artificial intelligence, information technology, and robotics, these systems have penetrated into many key areas such as intelligent transportation, emergency rescue, environmental monitoring, marine exploration, intelligent manufacturing, and national defense, significantly improving operational efficiency and safety, and demonstrating broad application prospects.
[0088] As a key intelligent equipment with autonomous operation capabilities, unmanned systems rely heavily on high-precision trajectory tracking control for successfully executing various complex tasks. However, in practical engineering applications, the physical size and structural characteristics of actuators inevitably lead to amplitude saturation constraints in their control inputs, and these physical constraints often exhibit significant asymmetry. Simultaneously, unmanned systems operating in complex dynamic environments face not only internal uncertainties such as modeling errors caused by the difficulty in accurately measuring kinematic parameters and unmodeled dynamics, but also the severe impact of long-term external time-varying environmental disturbances. These internal uncertainties, coupled with complex external disturbances, severely weaken the system's trajectory tracking performance and robustness. Furthermore, unmanned systems typically rely on their own limited energy resources (such as high-energy batteries or fuel) for power, and control energy consumption directly determines their endurance for continuous operation. However, neural networks possess universal approximation properties, providing an effective approach to solving the dynamics and disturbance problems of such unmanned systems. Moreover, optimal control theory can effectively optimize the energy consumption of trajectory tracking control in unmanned systems. It is noteworthy that, currently, no relevant algorithms have been invented for trajectory tracking optimization control under asymmetric input constraints. Therefore, the unmanned system trajectory tracking optimization control method of this invention has important application value and practical significance.
[0089] In view of this, embodiments of this application provide a trajectory tracking optimization control method for unmanned systems under asymmetric input constraints, including acquiring position and velocity data of the unmanned system; inputting the position and velocity data into a pre-designed control signal model to acquire a control signal; and performing optimization control on the unmanned system based on the control signal. The control signal model includes: an adaptive neural network observer for acquiring an estimate of a composite uncertainty term based on the position and velocity data, the estimate of which includes environmental disturbances and dynamic uncertainties; an adaptive backstepping controller for acquiring an adaptive backstepping control input based on the position and velocity data; an optimization controller for acquiring an optimal control input based on the position, velocity, and adaptive backstepping control input; and an asymmetric smooth saturation sub-model for acquiring the control signal based on the adaptive backstepping control input, the estimate of the composite uncertainty term, and the optimal control input. This application designs a neural network trajectory tracking control method that can achieve energy consumption optimization for unmanned systems with asymmetric input saturation, uncertain dynamics, and environmental disturbances. This method first constructs an asymmetric smooth saturation model using a Gaussian error function to constrain the amplitude of the control input. Second, it uses an adaptive neural network observer to dynamically estimate the disturbance and uncertainty terms. Then, based on the backstepping method and adaptive control theory, it establishes an adaptive backstepping control law, which not only obtains the affine error dynamic system but also effectively reduces the adverse effects of saturation and estimation errors. Finally, it uses an adaptive dynamic programming method to design an approximate optimal control law.
[0090] In some embodiments, please refer to Figure 6 and Figure 7 , Figure 6 This is a control system block diagram of the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in an embodiment of this application. Figure 7 The flowchart of the control algorithm for the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application embodiment illustrates that, before performing optimization control, a mathematical model of the unmanned system is established to reflect the system's operational data and assist in optimization control. Specifically, an unmanned system with asymmetric input constraints can be described using the following Eulerian-Lagrange system:
[0091] (1)
[0092] in, , and Let these represent the inertial matrix, Coriolis force-centrifugal force matrix, and gravity vector of the unmanned system, respectively. , as well as ,and , and For the nominal dynamic model parameters, and , , and For uncertain dynamic model parameters, , and These represent the position, velocity, and acceleration vectors of the unmanned system, respectively. Indicates environmental disturbance. For control inputs with asymmetric input constraints, i.e.:
[0093] (2)
[0094] in, , To control the input, To control the dimensions of the input, and These represent the maximum and minimum values of the control input, respectively.
[0095] To facilitate design control, , as well as Simultaneously, environmental disturbances and dynamic uncertainties are lumped together into a composite uncertainty. Therefore, equation (1) is reformulated as
[0096] (3)
[0097] (4)
[0098] in, , , .
[0099] In some embodiments, since equation (2) is a non-smooth saturation function, this application designs a smooth saturation function to replace it. The characterization formula of the asymmetric smooth saturation sub-model includes:
[0100] ;
[0101] ;
[0102] , (5)
[0103] (6)
[0104] ;
[0105] in, For control signals; For control input; For adaptive backstepping control input; This is the optimal control input; This is an estimate of the composite uncertainty term; This represents the output of an asymmetric smooth saturated model; n is the control input dimension. , To control the maximum value of the input, To control the minimum input value, For symbolic functions, This is the function for toggling the maximum value. The Gaussian error function; For time.
[0106] In some embodiments, please refer to Figure 1 , Figure 1 This is a flowchart illustrating the steps of the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application embodiment. The trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application embodiment is specifically implemented through steps 100 to 300:
[0107] Step 100: Obtain the position and velocity data of the unmanned system.
[0108] Step 200: Input the position data and velocity data into the pre-made control signal model to obtain the control signal.
[0109] In some embodiments, the control signal model includes an adaptive neural network observer, an adaptive backstepping controller, an optimal controller, and an asymmetric smooth saturated sub-model. The adaptive neural network observer is used to obtain an estimate of the composite uncertainty based on position data and velocity data, the estimate of the composite uncertainty including environmental disturbances and dynamic uncertainties. The adaptive backstepping controller is used to obtain the adaptive backstepping control input based on position data and velocity data. The optimal controller is used to obtain the optimal control input based on position data, velocity data, and the adaptive backstepping control input. The asymmetric smooth saturated sub-model is used to obtain the control signal based on the adaptive backstepping control input, the estimate of the composite uncertainty, and the optimal control input.
[0110] In some embodiments, please refer to Figure 6 and Figure 7 , Figure 6 This is a control system block diagram of the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in an embodiment of this application. Figure 7 The flowchart of the control algorithm for the trajectory tracking optimization control method of an unmanned system under asymmetric input constraints provided in this application embodiment describes how, based on velocity data estimation and position data, a radial basis function neural network is used to obtain an estimate of the composite uncertainty term; based on the estimate of the composite uncertainty term, the velocity data estimation, and the position data, an adaptive neural network observer is obtained, whose characterization formula includes:
[0111] (7)
[0112] ;
[0113] (9)
[0114]
[0115] (10)
[0116] in, For speed data The estimate, For speed data; for The derivative with respect to time; Location data; for The estimate, , for The time derivative; It is a nonlinear function composed of known dynamic model parameters; It is the inverse of the inertia matrix; It is a saturated nonlinear function; For unconstrained control inputs; This is the gain matrix; For observer error; For composite uncertainty terms The estimate; For neural network weight estimation The renewal law, for The estimate, For an ideal neural network weight matrix, , It represents the number of neurons; T is the transpose. It is a vector of activation functions composed of Gaussian functions; For design parameters, .
[0117] Specifically, this application uses a radial basis function neural network to approximate the composite uncertainty. , The characterization formulas include:
[0118] (8)
[0119] in, , It is a vector of activation functions composed of Gaussian functions; , This is the approximate error vector.
[0120] because It is unknown, therefore this application order for The estimated value, then
[0121] (9)
[0122] The weight update law is designed as follows:
[0123] (10)
[0124] In some embodiments, please refer to Figure 6 and Figure 7 , Figure 6 This is a control system block diagram of the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in an embodiment of this application. Figure 7The flowchart of the control algorithm for the trajectory tracking optimization control method of an unmanned system under asymmetric input constraints provided in this application embodiment is shown. To transform equations (3) and (4) into an affine error dynamic system and reduce the influence of input saturation and observer estimation errors, this application designs a backstepping controller using backstepping and adaptive control techniques. The position error vector and velocity error vector are defined as follows:
[0125] (11)
[0126] (12)
[0127] in, For the backstepping virtual control input vector and optimal virtual control input vector The constructed virtual control input vector, i.e. ; This represents the desired trajectory.
[0128] Step 1: Substituting equations (3) and (12) into the time derivative of equation (11), we get:
[0129] (13)
[0130] Choose the following Lyapunov functions:
[0131] (14)
[0132] Substituting equation (13) into The time derivative is obtained.
[0133] (15)
[0134] The backstepping virtual control law is designed as follows:
[0135] (16)
[0136] in, This represents a positive definite design matrix.
[0137] Then, substituting equation (16) into equation (15), we can obtain
[0138] (17)
[0139] Step 2: According to equation (4), the time derivative of equation (12) is as follows:
[0140] (18)
[0141] in, , This indicates that the input vector is controlled by adaptive backstepping. Optimal control input vector and the estimated value of the composite uncertainty term The constructed control input vector, i.e. .
[0142] Introduce an adaptive robustness term in the following design. Let... It is by The vector formed by the upper bounds of each component, i.e. ,and It is by The vector formed by the upper bounds of each component, i.e. .make , for The estimated vector, To estimate the error vector.
[0143] Choose the Lyapunov function for:
[0144] (19)
[0145] in, It is a positive definite design matrix.
[0146] Substituting equations (17) and (18) into the time derivative of equation (19), we can obtain...
[0147] (20)
[0148] The adaptive backstepping control law is designed as follows:
[0149] ;(twenty one)
[0150] in, , for The components in For adjustable design parameters, , It is a positive definite design matrix.
[0151] Substituting equation (21) into equation (20), according to the Cauchy-Schwarz and Young's inequality, It can be deduced as follows:
[0152] (twenty two)
[0153] in, .
[0154] Based on equation (22), the following adaptive law is designed:
[0155] ;(twenty three)
[0156] in, These are design parameters.
[0157] Substitute equation (23) into equation (22) and consider the inequality. We can obtain:
[0158] ;(twenty four)
[0159] in, It is a vector composed of position error and velocity error. It is a vector consisting of the virtual optimal control input and the optimal control input.
[0160] Step 3: The following will use single-network adaptive dynamic programming and online adaptive techniques to design and optimize the controller. According to equation (24), the following affine error dynamic system can be obtained:
[0161] (25)
[0162] in, , .
[0163] For equation (25), the infinite time-domain cost function is designed as follows:
[0164] (26)
[0165] in, Indicates the discount factor. and and It is a positive definite matrix.
[0166] definition for The set of permissible controls on, i.e. ,in It is a compact set. To solve for optimal control, the Hamiltonian function is defined as:
[0167] (27)
[0168] in, express Compared to The gradient.
[0169] By solving The optimal control law is obtained as follows:
[0170] (28)
[0171] in, For the optimal cost function Compared to The gradient.
[0172] Based on equations (27) and (28), the following Hamilton-Jacobi-Bellman equations can be obtained:
[0173] (29)
[0174] in, .
[0175] Design an evaluation network to approximate the optimal cost function. Its expression is as follows:
[0176] (30)
[0177] in, To evaluate the ideal weight vector of the network and This represents the number of neurons in the hidden layer. To evaluate the activation function vector of the network, To evaluate the approximation error of the network.
[0178] and then, The gradient can be expressed as follows:
[0179] (31)
[0180] in, and They represent and Compared to The gradient.
[0181] Substituting equation (31) into equation (29), the optimal control law can be rewritten as follows:
[0182] (32)
[0183] Substituting equations (30), (31), and (32) into equation (29), we can obtain
[0184] (33)
[0185] in, It is the residual of the approximate Hamiltonian function. It is the ideal error equation under optimal control. .
[0186] definition for The estimation of the optimal cost function and its gradient is expressed as follows:
[0187] (34)
[0188] (35)
[0189] According to equations (32) and (35), the approximate optimal control law can be expressed as follows:
[0190] (36)
[0191] Substituting equations (34) and (35) into equation (29), we can obtain the approximate Hamiltonian function as:
[0192] (37)
[0193] To obtain the evaluation network weights The update law is used, and the objective function is selected as follows:
[0194] (38)
[0195] in, .
[0196] The normalized gradient descent method is used to derive the following... The update law is as follows:
[0197] (39)
[0198] in, For design parameters, and .
[0199] In some embodiments, please refer to Figure 2 , Figure 2 The flowchart illustrates the steps for obtaining an estimate of the composite uncertainty term in the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application embodiment. The method for obtaining an estimate of the composite uncertainty term in this application embodiment is implemented through steps 210 to 240:
[0200] Step 210: Estimate the velocity data by estimating the known composite uncertainty and the adaptive neural network observer.
[0201] Step 220: Obtain the observer error based on the velocity data and the velocity data estimation.
[0202] Step 230: Obtain an estimate of the ideal neural network weight matrix based on the observer error.
[0203] Step 240: Update the estimate of the composite uncertainty term based on the estimation of the neural network weight matrix.
[0204] In some embodiments, please refer to Figure 3 , Figure 3 This is a flowchart illustrating the steps for obtaining adaptive backstepping control input in the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application embodiment. The method for obtaining adaptive backstepping control input in this application is specifically implemented through steps 250 to 280:
[0205] Step 250: Obtain the position error corresponding to the position data and the velocity error corresponding to the velocity data.
[0206] Step 260: Obtain the backstepping virtual control law and combine it with the position error to obtain the backstepping virtual control input.
[0207] In some embodiments, the representation formula of the backstepping virtual control law includes:
[0208] ;
[0209] ;
[0210] in, For backstepping virtual control input; The design matrix is positive definite. This refers to the positional error; Location data; Let be the derivative of the desired trajectory with respect to time; For the desired trajectory;
[0211] Step 270: Obtain the adaptive law, and combine it with the backstepping virtual control input and speed error to obtain the adaptive input.
[0212] In some embodiments, the formula for representing the adaptive law includes:
[0213] ;
[0214] ;
[0215] ;
[0216] in, For the updated , For adaptive parameter vectors, For ideal adaptive parameter vectors; For design parameters; It is a diagonal matrix composed of tangent functions; For speed error; For speed; For virtual control input; For backstepping virtual control input; This is the optimal virtual control input;
[0217] Step 280: Obtain the adaptive backstepping control law, and combine it with the adaptive input and speed error to obtain the adaptive backstepping control input.
[0218] In some embodiments, the characterization formula of the adaptive backstepping control law includes:
[0219] ;
[0220] ;
[0221] in, For adaptive backstepping control input; The design matrix is positive definite. For speed error; For speed; These are the parameters of the nominal dynamic model; The derivative of the virtual control input vector with respect to time; It is a diagonal matrix composed of tangent functions; For adaptive parameter vectors, For ideal adaptive parameter vectors; , Given the known dynamic error, , To control the dimensions of the input, For location data, Given a known dynamic model, For virtual control input.
[0222] In some embodiments, please refer to Figure 4 , Figure 4 This is a flowchart illustrating the steps for obtaining the optimal control input in the trajectory tracking optimization control method for an unmanned system under asymmetric input constraints provided in this application. The method for obtaining the optimal control input in this application is specifically implemented through steps 290 to 21040:
[0223] Step 290: Based on the known optimal control input and optimal virtual control input, obtain the approximate Hamiltonian function.
[0224] In some embodiments, an optimal control law is obtained, and an optimal control input is obtained through the optimal control law. The formula representing the optimal control law includes:
[0225] ;
[0226] ;
[0227] in, for The estimate; This is the optimal virtual control input; This is the optimal control input; It is a positive definite matrix; It is the inverse of the inertia matrix; This is a transpose operation; , for Compared to gradient, Let be a vector consisting of activation functions. , For positional error, For speed error; for The estimate, This is the ideal weight matrix for a neural network.
[0228] Step 21010: Obtain the position error corresponding to the position data and the velocity error corresponding to the velocity data.
[0229] Step 21020: Based on the position error and velocity error, and combined with the weight update law and the approximate Hamiltonian function, obtain the evaluation network weights.
[0230] In some embodiments, the representation formula of the weight update law includes:
[0231] ;
[0232] in, for The renewal law, for The estimate, The ideal weight matrix for a neural network; For design parameters; To Find the remainder after partial derivative. , for Compared to gradient, Let be a vector composed of neural network activation functions. Let it be a vector consisting of position and velocity errors. The moment is obtained by multiplying the activation function vector, the inverse of the inertia matrix, and the transpose of the activation function vector. Discount factor; This is a transpose operation; For Hamiltonian function error, , For approximate Hamiltonian function, It is a vector composed of position and velocity error vectors. It is an ideal Hamiltonian function.
[0233] Step 21030: Based on the position error and velocity error, and combined with the evaluation network weights and the activation function of the evaluation network, obtain the optimal cost function.
[0234] Step 21040: Update the optimal control input based on the optimal cost function and the evaluation network weights.
[0235] Step 300: Optimize the control of the unmanned system based on the control signals.
[0236] Understandably, the trajectory tracking optimization control method for unmanned systems under asymmetric input constraints provided in the embodiments of this application includes acquiring position and velocity data of the unmanned system; inputting the position and velocity data into a pre-designed control signal model to acquire a control signal; and performing optimization control on the unmanned system based on the control signal. The control signal model includes: an adaptive neural network observer for acquiring an estimate of a composite uncertainty term based on the position and velocity data, the estimate of which includes environmental disturbances and dynamic uncertainties; an adaptive backstepping controller for acquiring an adaptive backstepping control input based on the position and velocity data; an optimization controller for acquiring an optimal control input based on the position, velocity, and adaptive backstepping control input; and an asymmetric smooth saturation sub-model for acquiring the control signal based on the adaptive backstepping control input, the estimate of the composite uncertainty term, and the optimal control input. This application designs a neural network trajectory tracking control method capable of energy consumption optimization for unmanned systems with asymmetric input saturation, uncertain dynamics, and environmental disturbances. First, an asymmetric smooth saturation model is constructed using a Gaussian error function to constrain the amplitude of the control input. Second, an adaptive neural network observer is used to dynamically estimate the disturbance and uncertainty terms. Then, based on the backstepping method and adaptive control theory, an adaptive backstepping control law is established, which not only obtains the affine error dynamic system but also effectively reduces the adverse effects of saturation and estimation errors. Finally, an adaptive dynamic programming method is used to design an approximate optimal control law.
[0237] Accordingly, embodiments of this application also provide a trajectory tracking optimization control system for an unmanned system under asymmetric input constraints. Please refer to [link to relevant documentation]. Figure 5 , Figure 5 This is a module connection diagram of the trajectory tracking optimization control system for an unmanned system under asymmetric input constraints provided in this application embodiment. The trajectory tracking optimization control system for an unmanned system under asymmetric input constraints provided in this application embodiment includes:
[0238] Data acquisition module 10 is used to acquire position and velocity data of the unmanned system;
[0239] The control signal acquisition module 20 is used to input position data and velocity data into a pre-made control signal model to acquire control signals.
[0240] The optimization control module 30 is used to optimize the control of the unmanned system based on control signals;
[0241] The control signal model includes:
[0242] An adaptive neural network observer is used to obtain estimates of composite uncertainties based on position and velocity data, including environmental disturbances and dynamic uncertainties.
[0243] An adaptive backstepping controller is used to obtain adaptive backstepping control input based on position and velocity data;
[0244] An optimized controller is used to obtain the optimal control input based on position data, velocity data, and adaptive backstepping control input;
[0245] An asymmetric smooth saturated sub-model is used to obtain control signals based on adaptive backstepping control input, estimation of composite uncertainties, and optimal control input.
[0246] This application has provided a detailed description of a trajectory tracking optimization control method and system for an unmanned system under asymmetric input constraints, as provided in the embodiments of this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A trajectory tracking optimization control method for an unmanned system under asymmetric input constraints, characterized in that, include: Acquire position and velocity data from the unmanned system; The position data and velocity data are input into a pre-made control signal model to obtain a control signal. The unmanned system is optimized and controlled based on the control signals. The control signal model includes: An adaptive neural network observer is used to obtain an estimate of a composite uncertainty based on the position data and the velocity data, the estimate of which includes environmental disturbances and dynamic uncertainties. An adaptive backstepping controller is used to obtain adaptive backstepping control input based on the position data and the velocity data; An optimization controller is configured to obtain optimized control inputs based on the position data, the velocity data, and the adaptive backstepping control input; An asymmetric smooth saturated sub-model is used to obtain the control signal based on the adaptive backstepping control input, the estimation of the composite uncertainty term, and the optimized control input.
2. The trajectory tracking optimization control method for an unmanned system under asymmetric input constraints according to claim 1, characterized in that, The steps for obtaining an estimate of the composite uncertainty term include: The velocity data is estimated by using the known composite uncertainty term and the adaptive neural network observer. Based on the velocity data and the estimation of the velocity data, the observer error is obtained; Based on the observer error, an estimate of the ideal neural network weight matrix is obtained; The estimate of the composite uncertainty term is updated based on the estimate of the neural network weight matrix.
3. The trajectory tracking optimization control method for an unmanned system under asymmetric input constraints according to claim 2, characterized in that, The steps for obtaining the adaptive neural network observer include: Based on the estimation of the velocity data and the position data, an estimate of the composite uncertainty term is obtained by combining a radial basis function neural network; Based on the estimation of the composite uncertainty, the estimation of the velocity data, and the position data, the adaptive neural network observer is obtained, and its characterization formula includes: ； ； ； ； ； in, For speed data The estimate; for The derivative with respect to time; Location data; It is a nonlinear function composed of known dynamic model parameters; It is the inverse of the inertia matrix; It is a saturated nonlinear function; For unconstrained control inputs; This is the gain matrix; For observer error; For composite uncertainty terms The estimate; Estimation of weight matrix for neural networks The renewal law, for The estimate, The weight matrix is the ideal weight matrix for the neural network; T is the transpose. The activation function vector; These are design parameters.
4. The trajectory tracking optimization control method for an unmanned system under asymmetric input constraints according to claim 1, characterized in that, The characterization formula for the asymmetric smooth saturated sub-model includes: ； ； ， ； ； ； in, The control signal; For control input; For adaptive backstepping control input; This is the optimal control input; This is an estimate of the composite uncertainty term; This represents the output of an asymmetric smooth saturated model; n is the dimension controlling the input. , To control the maximum value of the input, To control the minimum input value, It is a symbolic function; The Gaussian error function; For time.
5. The trajectory tracking optimization control method for an unmanned system under asymmetric input constraints according to claim 1, characterized in that, The steps for obtaining the adaptive backstepping control input include: Obtain the position error corresponding to the position data, and the velocity error corresponding to the velocity data; Obtain the backstepping virtual control law, and combine it with the position error to obtain the backstepping virtual control input; Obtain the adaptive law, and combine it with the backstepping virtual control input and the speed error to obtain the adaptive input; Obtain the adaptive backstepping control law, and combine the adaptive input and the speed error to obtain the adaptive backstepping control input.
6. The trajectory tracking optimization control method for an unmanned system under asymmetric input constraints according to claim 5, characterized in that, The characterization formula of the backstepping virtual control law includes: ； ； in, This is the backstepping virtual control input; The design matrix is positive definite. This refers to the positional error; Location data; Let be the derivative of the desired trajectory with respect to time; For the desired trajectory; The formula for representing the adaptive law includes: ； ； ； in, For the updated , For adaptive parameter vectors, For ideal adaptive parameter vectors; For design parameters; It is a diagonal matrix composed of tangent functions; For speed error; For speed; For virtual control input; For backstepping virtual control input; This is the optimal virtual control input; The characterization formula of the adaptive backstepping control law includes: ； ； in, For adaptive backstepping control input; The design matrix is positive definite. For speed error; For speed; These are the parameters of the nominal dynamic model; The derivative of the virtual control input with respect to time; It is a diagonal matrix composed of tangent functions; For adaptive parameter vectors, An adaptive parameter vector with ideal parameters; , Given the known dynamic error, , To control the dimensions of the input, For location data, Given a known dynamic model, For virtual control input.
7. The trajectory tracking optimization control method for an unmanned system under asymmetric input constraints according to claim 4, characterized in that, The steps for obtaining the optimal control input include: Based on the known optimal control input and optimal virtual control input, obtain the approximate Hamiltonian function; Obtain the position error corresponding to the position data, and the velocity error corresponding to the velocity data; The evaluation network weights are obtained based on the position error and the velocity error, combined with the weight update law and the approximate Hamiltonian function. Based on the position error and the velocity error, and combined with the evaluation network weights and the activation function of the evaluation network, the optimal cost function is obtained; The optimal control input is updated based on the optimal cost function and the evaluation network weights.
8. The trajectory tracking optimization control method for an unmanned system under asymmetric input constraints according to claim 7, characterized in that, The characterization formula of the weight update law includes: ； in, for The renewal law, for The estimate, The ideal weight matrix for a neural network; For design parameters; To Find the remainder after partial derivative. , for Compared to gradient, Let be a vector composed of neural network activation functions. Let it be a vector consisting of position and velocity errors. The matrix is obtained by multiplying the activation function vector, the inverse of the inertia matrix, and the transpose of the activation function vector. Discount factor; This is a transpose operation; For Hamiltonian function error, , For approximate Hamiltonian function, It is a vector composed of position and velocity error vectors. It is an ideal Hamiltonian function.
9. The trajectory tracking optimization control method for an unmanned system under asymmetric input constraints according to claim 1, characterized in that, The steps for obtaining the optimized control input include: Obtain an approximate optimal control law, and obtain the optimal control input through the approximate optimal control law. The characterization formula of the approximate optimal control law includes: ； ； in, for The estimate; This is the optimal virtual control input; This is the optimal control input; It is a positive definite matrix; It is the inverse of the inertia matrix; This is a transpose operation; , for Compared to gradient, Let be a vector consisting of activation functions. , For positional error, For speed error; for The estimate, This is the ideal weight matrix for a neural network.
10. A trajectory tracking optimization control system for an unmanned system under asymmetric input constraints, characterized in that, include: The data acquisition module (10) is used to acquire the position and velocity data of the unmanned system; The control signal acquisition module (20) is used to input the position data and the velocity data into a pre-made control signal model to acquire the control signal; An optimization control module (30) is used to optimize the control of the unmanned system based on the control signal; The control signal model includes: An adaptive neural network observer is used to obtain an estimate of a composite uncertainty based on the position data and the velocity data, the estimate of which includes environmental disturbances and dynamic uncertainties. An adaptive backstepping controller is used to obtain adaptive backstepping control input based on the position data and the velocity data; An optimization controller is used to obtain the optimal control input based on the position data, the velocity data, and the adaptive backstepping control input; An asymmetric smooth saturated sub-model is used to obtain the control signal based on the adaptive backstepping control input, the estimation of the composite uncertainty term, and the optimal control input.