Non-singular preset performance safety approximate optimal control method

Abstract

The invention discloses a non-singular preset performance safety approximate optimal control method, and belongs to the technical field of aircraft control. The method comprises the following steps: constructing a control-oriented aircraft attitude tracking error model based on an aircraft attitude dynamic model, and giving out task-based performance constraints; based on performance constraint requirements, designing a safety boundary by using a control barrier function, and solving a safety control set meeting constraints; a performance index function containing control precision and control consumption is constructed, a baseline optimal controller is designed through self-adaptive dynamic programming, and an approximate optimal control instruction is solved; and constructing a quadratic programming problem in combination with the safety control set and the approximate optimal control quantity, and solving to obtain an approximate optimal control instruction meeting the safety constraint. The control singularity risk caused by the fact that the control value error approaches the preset performance boundary in a traditional preset performance control method is avoided, the adaptability of the system to deviation and uncertainty is improved, and the adaptability of the system to complex flight environments and diversified tasks is enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to a non-singular preset performance safety approximate optimal control method, belonging to the technical field of aircraft control. BACKGROUND

[0002] In the existing aircraft control system, in order to meet the transient performance and steady-state performance requirements of attitude control, a preset performance control method is usually used. However, in engineering practice, due to the limited control ability of the aircraft itself, the complex and changeable flight environment and other factors, the existing preset performance control method does not consider the optimality in the control process, which leads to the fact that the attitude control value error of the aircraft tends to approach the preset performance boundary, and further causes control singular phenomenon, which seriously threatens flight safety.

[0003] Therefore, it is urgent to develop a non-singular preset performance safety approximate optimal control method to solve the control singularity problem caused by the control value error approaching the preset performance boundary in the prior art, while considering the optimality of the control process, so as to improve the control performance and safety of the aircraft control system. SUMMARY

[0004] In order to solve the problems in the background art, the present application provides a non-singular preset performance safety approximate optimal control method.

[0005] To achieve the above-mentioned purpose, the present application adopts the following technical solution: a non-singular preset performance safety approximate optimal control method, the method comprising the following steps:

[0006] S1: aircraft safety control model construction: based on the aircraft attitude dynamics model, an aircraft attitude tracking error model for control is constructed, and a task-based performance constraint is given;

[0007] The S1 comprises the following steps:

[0008] S101: based on the motion characteristics of the aircraft around the center of mass, an attitude dynamics model is established:

[0009] (1)

[0010] In formula (1):

[0011] is the attitude angle vector, wherein: is the angle of attack, is the sideslip angle, is the roll angle;

[0012] is the first derivative of the attitude angle vector ;

[0013] is the attitude angular velocity matrix;

[0014] is the attitude angular velocity vector, where: are the angular velocities about axis, axis, and axis, respectively;

[0015] is the first derivative of the attitude angular velocity vector ;

[0016] is the inertia matrix;

[0017] is the control input, where: are the control torques about axis, axis, and axis, respectively;

[0018] is the sum of the model internal and external disturbance torques;

[0019] S102: Define the guidance command as , where: are the guidance commands for the angle of attack , the sideslip angle , and the roll angle ; the attitude tracking error is , then the aircraft attitude tracking error model is:

[0020] (2)

[0021] In equation (2):

[0022] is the model uncertainty term;

[0023] is the control matrix;

[0024] is the lumped disturbance;

[0025] S103: Use a pre-defined performance function as the safety boundary for attitude control, set the attitude control error , where: each component of satisfies the following performance constraints:

[0026] (3)

[0027] In equation (3):

[0028] The preset performance function is defined as:

[0029] S104: defining the preset performance function as:

[0030] (4)

[0031] In formula (4):

[0032] is a constant, is an initial performance boundary value, is a steady-state performance boundary value;

[0033] is used to adjust the convergence speed of the preset performance function.

[0034] S2: solving the safety control set: based on the performance constraint requirement, the safety boundary is designed by using the control barrier function, and the safety control set satisfying the constraint is solved;

[0035] The S2 includes the following steps:

[0036] S201: defining two control barrier functions according to formula (3):

[0037] (5)

[0038] S202: assuming that the lumped disturbance is bounded, and the derivative of the control barrier function is constrained:

[0039] (6)

[0040] In formula (6):

[0041] is a constant, which is used to adjust the strength of the derivative constraint of the control barrier function;

[0042] is the upper limit of the lumped disturbance .

[0043] S203: combining the control barrier function and the derivative constraint, the safety control set is obtained as:

[0044] (7)

[0045] In formula (7):

[0046] is a component of the control input .

[0047] S3: Baseline approximate optimal controller design: Based on the aircraft attitude tracking error model of S1, construct a performance index function containing control accuracy and control consumption, design a baseline optimal controller using adaptive dynamic programming, and obtain the approximate optimal control command;

[0048] The S3 includes the following steps:

[0049] S301: Let Then according to formula (2), we have:

[0050] (8)

[0051] S302: Ignore the lumped disturbance Then the nominal form of formula (8) is:

[0052] (9)

[0053] S303: For formula (9), construct a performance index function containing control accuracy and control consumption :

[0054] (10)

[0055] In formula (10):

[0056] is a symmetric positive definite matrix of control accuracy;

[0057] is a normal number, indicating the weight coefficient of control consumption;

[0058] is an integral variable;

[0059] is a gradient operator;

[0060] S304: Define the HJB function through formula (9) and formula (10):

[0061] (11)

[0062] The partial derivative of the control input is , and the optimal control amount is:

[0063] (12)

[0064] In formula (12):

[0065] is the optimal performance function;

[0066] S305: Design a single Critic neural network to approximate the optimal performance function:

[0067] (13)

[0068] In formula (13):

[0069] is the ideal weight;

[0070] is the neural network activation function;

[0071] is the number of neurons;

[0072] is the approximation error;

[0073] S306: Let the estimated value of the ideal weight be , and the estimated value of the optimal performance function be ; the corresponding approximate optimal control amount :

[0074] (14)

[0075] S307: Use the gradient descent method of parallel learning of current data and historical data to design the Critic neural network update law:

[0076] (15)

[0077] (16)

[0078] In formula (15):

[0079] is the learning rate;

[0080] is the HJB equation estimation error calculated when , and ;

[0081] is the number of historical states.

[0082] S4: Safety approximate optimal control instruction solving: combine the safety control set of S2 and the approximate optimal control amount of S3 to construct a quadratic programming problem to obtain the approximate optimal control instruction that satisfies the safety constraint.

[0083] The S4 includes the following steps:

[0084] S401: security control set combined with S2 Approximately optimal control amount with S3 The optimal security control law is:

[0085] (17)

[0086] S402: solve equation (17), and the explicit expression of the optimal security control law is:

[0087] (18)

[0088] In equation (18):

[0089] (19)

[0090] S403: the actual control amount of the aircraft can be obtained by converting the control matrix .

[0091] Compared with the prior art, the beneficial effects of the present application are:

[0092] The present application combines the preset performance function with the control barrier function to construct the security control set, effectively avoiding the control singular risk caused by the control value error approaching the preset performance boundary in the traditional preset performance control method; by designing a performance function containing control accuracy and control consumption index, and realizing optimal performance function approximation based on adaptive dynamic programming and Critic neural network, an approximately optimal control law with weak model dependence is formed, which improves the adaptability of the system to deviations and uncertainties; finally, by combining the security control set and the approximately optimal control instruction through quadratic programming, the final control instruction satisfying the safety constraint is obtained, which realizes high-precision attitude tracking while ensuring the safety of the control process, thereby improving the control performance and safety of the aircraft control system and enhancing the adaptability of the system to complex flight environments and diversified tasks. BRIEF DESCRIPTION OF DRAWINGS

[0093] Figure 1 is a flowchart of the present application. DETAILED DESCRIPTION

[0094] The technical solutions in the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0095] A non-singular preset performance security approximate optimal control method, the method comprising the following steps:

[0096] S1: Aircraft safety control model construction: based on the aircraft attitude dynamics model, the aircraft attitude tracking error model is constructed for control, and the performance constraints based on the task are given;

[0097] The S1 includes the following steps:

[0098] S101: Based on the aircraft (for example, a glider) around the mass motion characteristics, the attitude dynamics model is established:

[0099] (1)

[0100] In formula (1):

[0101] is the attitude angle vector, wherein: is the attack angle, is the sideslip angle, is the roll angle;

[0102] is the first derivative of the attitude angle vector ;

[0103] is the attitude angle velocity conversion matrix;

[0104] is the attitude angle velocity vector, wherein: are the angular velocities around axis, axis and axis, respectively;

[0105] is the first derivative of the attitude angle velocity vector ;

[0106] is the moment of inertia matrix;

[0107] is the control input, wherein: are the control moments around axis, axis and axis, respectively;

[0108] is the sum of the internal and external disturbance moments of the model;

[0109] S102: Define the guidance command as , wherein: are the guidance commands of the attack angle , the sideslip angle and the roll angle , respectively; the attitude tracking error is Then the aircraft attitude tracking error model is:

[0110] (2)

[0111] In formula (2), the following applies:

[0112] is a model uncertainty term;

[0113] is a control matrix;

[0114] is a lumped disturbance;

[0115] S103: According to the mission requirements of the aircraft, a preset performance function is used as a safety boundary for attitude control, to accurately constrain the convergence dynamic process and the steady-state process of the attitude control error , and set each component of the attitude control error to correspond to the angle of attack , the sideslip angle , and the roll angle error, respectively, to satisfy the following performance constraints (safety boundary):

[0116] (3)

[0117] In formula (3), the following applies:

[0118] is a preset performance function, corresponding to the error lower boundary and upper boundary function, respectively;

[0119] S104: The preset performance function is defined as:

[0120] (4)

[0121] In formula (4), the following applies:

[0122] is a normal number, is an initial time performance boundary value, is a steady-state performance boundary value;

[0123] is used to adjust the convergence speed of the preset performance function.

[0124] S2: Safety control set solving: based on the performance constraint requirements, a safety boundary is designed using a control barrier function, and a safety control set that satisfies the constraint is solved;

[0125] The S2 includes the following steps:

[0126] S201: Two control barrier functions are defined according to formula (3):

[0127] (5)

[0128] Only if both control barrier functions are greater than 0, equation (3) can be satisfied to guarantee the attitude error within the safe range.

[0129] S202: Assume lumped disturbance The derivative of the control barrier function is bounded, and a constraint is proposed:

[0130] (6)

[0131] In equation (6):

[0132] is a positive constant, used to adjust the strength of the derivative constraint of the control barrier function;

[0133] is the upper bound of the lumped disturbance ;

[0134] Then any Lipschitz continuous controller belonging to the safe control set will make equation (3) be satisfied.

[0135] S203: Combining the control barrier function and the derivative constraint, the safe control set can be obtained is:

[0136] (7)

[0137] In equation (7):

[0138] is the component of the control input , corresponding to one of the control moments around the axis, axis and axis.

[0139] S3: Baseline approximate optimal controller design: based on the aircraft attitude tracking error model in S1, a performance index function containing control accuracy and control consumption is constructed, and a baseline optimal controller is designed using adaptive dynamic programming to obtain the approximate optimal control command;

[0140] The S3 includes the following steps:

[0141] S301: For convenience of design, let Then according to equation (2), we have:

[0142] (8)

[0143] S302: Ignore lumped disturbances Then the nominal form of equation (8) is:

[0144] (9)

[0145] S303: For equation (9), construct a performance index function that includes control accuracy and control consumption. :

[0146] (10)

[0147] In formula (10):

[0148] A symmetric positive definite matrix for controlling accuracy;

[0149] A positive number indicates a weighting coefficient for controlling consumption;

[0150] For integration variables;

[0151] For gradient operators;

[0152] S304: Define the HJB function using equations (9) and (10):

[0153] (11)

[0154] Another control input partial derivatives The optimal control quantity is obtained by solving for:

[0155] (12)

[0156] In equation (12):

[0157] This is the optimal performance function;

[0158] S305: Designing a single Critic neural network to approximate the optimal performance function:

[0159] (13)

[0160] In equation (13):

[0161] Ideal weights;

[0162] For neural network activation functions;

[0163] The number of neurons;

[0164] for approximation error;

[0165] S306: Let the estimation value of ideal weight be , then the estimation value of optimal performance function is ; the corresponding approximate optimal control amount :

[0166] (14)

[0167] S307: In order to relax the constraint of persistent incentive condition, the gradient descent method of parallel learning of current data and historical data is used to design the update law of Critic neural network:

[0168] (15)

[0169] (16)

[0170] In formula (15):

[0171] is the learning rate;

[0172] is the HJB equation estimation error calculated when , and ;

[0173] is the number of historical states.

[0174] S4: Safety approximate optimal control instruction solving: combine the safety control set of S2 with the approximate optimal control amount of S3 to construct a quadratic programming problem and solve to obtain the approximate optimal control instruction that satisfies the safety constraint.

[0175] The S4 includes the following steps:

[0176] S401: Combine the safety control set of S2 with the approximate optimal control amount of S3, and the optimal safety control law is:

[0177] (17)

[0178] S402: Solve formula (17), and the explicit expression of the optimal safety control law is:

[0179] (18)

[0180] In formula (18):

[0181] (19)

[0182] S403: due to the gliding segment aircraft side slip angle , control matrix is reversible, then the actual control amount of the aircraft can be obtained through the transformation of the control matrix .

[0183] It is apparent for a person skilled in the art that the present application is not limited to the details of the above-described exemplary embodiments, but can be implemented in other forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be considered in all respects as illustrative and not restrictive, the scope of the present application being defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and range of equivalency of the claims are embraced therein. Any reference signs in the claims should not be construed as limiting the claims to the figures in which the reference signs are used.

[0184] Furthermore, it should be understood that although the present specification is described in terms of embodiments, not every embodiment exhibits every characteristic or option described in the specification. In addition, it should be understood that although the specification has been described in terms of embodiments, not every embodiment only contains one independent technical solution, and the specification is described in this way only for the sake of clarity, and a person skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by a person skilled in the art.

Claims

1. A non-singular pre-specified performance safe approximate optimal control method, characterized by: The method comprises the following steps: S1: aircraft safety control model construction: based on the aircraft attitude dynamics model, the aircraft attitude tracking error model is constructed for control, and the performance constraints based on the task are given; S2: safe control set solving: based on the performance constraint requirements, the safety boundary is designed by using the control barrier function, and the safe control set satisfying the constraint is solved; S3: baseline approximate optimal controller design: based on the aircraft attitude tracking error model of S1, the performance index function containing control accuracy and control consumption is constructed, the baseline optimal controller is designed by using adaptive dynamic programming, and the approximate optimal control instruction is solved; S4: Safe approximate optimal control command solving: combine the safe control set of S2 Approximate optimal control amount with S3 Construct a quadratic programming problem to obtain an approximate optimal control command that satisfies safety constraints.

2. The non-singular pre-specified performance safe approximate optimal control method according to claim 1, characterized in that: The S1 comprises the following steps: S101: based on the motion characteristics of the aircraft around the center of mass, the attitude dynamics model is established: (1) In formula (1): is the vector of attitude angles, where: is the angle of attack, is the sideslip angle, is the angle of bank; a first derivative of the attitude angle vector a first derivative of the attitude angle vector is the attitude angular velocity conversion matrix; is the attitude angular velocity vector, where: are the angular velocities about the axis, axis, and axis, respectively. is the first derivative of the attitude angular velocity vector . I is the moment of inertia matrix; for controlling the input, wherein: are control torques about the axis, the axis and the axis, respectively. is the sum of the model internal and external disturbance moments; S102: define the guidance command as where: are the guidance commands for the angle of attack , the sideslip angle , and the roll angle ; and the attitude tracking error is The aircraft attitude tracking error model is: (2) In formula (2): is the model uncertainty term; Control matrix; a lumped perturbation; S103: Adopting the preset performance function as a safety boundary of the attitude control, setting an attitude control error of each component satisfies the following performance constraints: (3) In formula (3): The preset performance function respectively corresponds to the error lower boundary function and the error upper boundary function. S104: define the preset performance function as: (4) In formula (4): is a normal number, is an initial time performance boundary value, is a steady state performance boundary value; for adjusting the convergence speed of the preset performance function.

3. The non-singular pre-specified performance safe approximate optimal control method according to claim 2, characterized in that: The S2 comprises the following steps: S201: two control barrier functions are defined according to formula (3): (5) S202: Assume lumped disturbance Bounded, impose constraints on the derivative of the control barrier function: (6) In formula (6): is a positive constant used to adjust the strength of the control barrier function derivative constraint; an upper bound for the lumped perturbation ; S203: Combining the control barrier function with the derivative constraint, the safe control set can be obtained is: (7) In formula (7): to control the input of the component.

4. The non-singular pre-specified performance safe approximate optimal control method according to claim 3, characterized in that: The S3 comprises the following steps: S301: Let Then, according to equation (2), we have: (8) S302: Ignore lumped perturbations The nominal form of equation (8) is then: (9) S303: For formula (9), a performance index function containing control precision and control consumption is constructed : (10) In formula (10): symmetric positive definite matrix for control accuracy; is a normal number, indicating the weight coefficient of controlling consumption; is the integration variable; is the gradient operator; S304: the HJB function is defined by formula (9) and formula (10): (11) The partial derivative of the control input with respect to the control variable is solved to obtain the optimal control variable: (12) In formula (12): is the optimal performance function; S305: the single Critic neural network is designed to approximate the optimal performance function: (13) In formula (13): is the ideal weight; is a neural network activation function; the number of neurons; is the approximation error; S306: Let the estimate of the ideal weight be ; then the estimate of the optimal performance function is ; and the corresponding approximate optimal control : (14) S307: the gradient descent method of parallel learning of current data and historical data is used to design the Critic neural network update law: (15) (16) In formula (15): learning rate; For The HJB equation estimation error is calculated at the time, and ; Number of historical states.

5. A non-singular pre-specified performance safe approximate optimal control method according to claim 4, characterized in that: The S4 comprises the following steps: S401: Security control set in combination with S2 Approximately optimal control amount with S3 The optimal security control law is obtained as (17) S402: solve formula (17), then the optimal safety control law is expressed as: (18) In formula (18): (19) S403: The actual control amount of the aircraft is obtained by controlling the conversion of the matrix .

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