Tracking control method for cruise missile system with full state constraints and input saturation under preset performance

Abstract

The present invention discloses a tracking control method for a cruise missile system with full-state constraints and input saturation under preset performance. In order to solve the conflict between the preset performance boundary, input saturation and full-state constraints, a novel adaptive tubular preset performance boundary and a new barrier Lyapunov function are introduced; an adaptive neural network controller is developed by integrating adaptive control and backstepping; the combination of command filtering technology helps to avoid the feasibility assumption of the virtual controller and the computational complexity problem caused by the backstepping method; in addition, two auxiliary systems are introduced to compensate for the filtering error and reduce the error caused by input saturation, aiming to achieve stable control without overshoot and vibration, and contribute new ideas and methods to the field of control system design.

Description

Technical Field

[0001] The present invention belongs to the technical field of cruise missile system tracking control, and in particular relates to a cruise missile system tracking control method with full-state constraints and input saturation under preset performance. Background Art

[0002] In the context of exploring the tracking control of cruise missile systems, robust tracking control technologies for nonlinear uncertain environments are particularly important. These technologies are widely used in aerospace docking, multi-agent collaboration, and UAV navigation. Traditional nonlinear tracking control strategies, such as sliding mode control, adaptive control, and backstepping control, each have their own characteristics. Among them, backstepping control is particularly suitable for high-order systems because it simplifies the design process in combination with adaptive control. In order to cope with system uncertainties and external disturbances, fuzzy logic and neural networks (NNs) are introduced to enhance control performance. At present, an adaptive neural network control scheme based on stochastic gradient descent (SGD) has been proposed, which achieves efficient function approximation and tracking by optimizing NN parameters.

[0003] For uncertain cruise missile systems with complex characteristics, such as input saturation and unmeasured states, researchers used radial basis function neural networks (RBFNNs) for function approximation and designed state observers to handle unmeasured states. Combined with adaptive backstepping technology, an adaptive tracking control method that ensures the boundedness of system signals is proposed. However, the traditional backstepping method faces computational complexity challenges due to the need to derive the virtual controller. Although the introduction of dynamic surface control (DSC) can alleviate this problem, the error problem caused by the filter still needs to be solved. The application of command filters effectively avoids complex derivations, while providing error compensation and maintaining the stability of backstepping control.

[0004] With the advancement of science and technology, the demand for high-performance automatic control systems is growing, especially in the face of uncertainty, friction and hysteresis effects, it is crucial to achieve accurate transient and steady-state behavior. Preset performance control (PPC) addresses the challenge of nonlinear uncertainty by setting the transformation function of tracking error and performance limit. However, PPC has the problem of UUB tracking limitation and PPB parameter adjustment, which can easily lead to overshoot and jitter. Although existing studies have proposed some solutions to the strict safety constraints of actual engineering systems, especially input saturation and full-state constraints, they are mostly limited to specific models and lack a general framework and asymptotic tracking capabilities. Summary of the invention

[0005] The object of the present invention is to provide a tracking control method for a cruise missile system with full state constraints and input saturation under preset performance.

[0006] The technical solution to achieve the purpose of the present invention is: a tracking control method for a cruise missile system with full state constraints and input saturation under preset performance, comprising the following steps:

[0007] Step 1: Construct a cruise missile system with input saturation, unknown nonlinear dynamics and external disturbances, use a smooth function to avoid the impact of the sawtooth of the saturation function on the system, and use RBFNN to fit the unknown nonlinear dynamics and external disturbances to obtain a new controlled system;

[0008] Step 2: Construct an adaptive tubular preset performance boundary by designing a monitoring function;

[0009] Step 3: Design the error conversion function to solve the preset performance and state constraints in the same framework;

[0010] Step 4: construct an error system based on the error transfer function and the adaptive tubular preset performance boundary;

[0011] Step 5: Use the command filtering method combined with the signal compensator to compensate for the filtering error;

[0012] Step 6: Design the virtual controller, actual controller and adaptive rate using backstepping method, adaptive control and signal compensator to achieve asymptotic tracking of the reference signal.

[0013] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, a tracking control method for a cruise missile system with full-state constraints and input saturation under preset performance described in the present invention is implemented.

[0014] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a tracking control method for a cruise missile system with full-state constraints and input saturation under preset performance as described in the present invention.

[0015] A computer program product includes a computer program. When the computer program is executed by a processor, the computer program implements a tracking control method for a cruise missile system with full state constraints and input saturation under preset performance described in the present invention.

[0016] Compared with the prior art, the significant advantages of the present invention are as follows: in order to resolve the conflict between preset performance boundaries, input saturation, and full-state constraints, the present invention introduces a novel preset performance boundary based on an adaptive tube and a new barrier Lyapunov function; an adaptive neural network controller is developed by integrating adaptive control and backstepping; the combination of command filtering technology helps to avoid the "feasibility assumption" of the virtual controller and the "complexity explosion" problem caused by backstepping; in addition, two auxiliary systems are introduced to compensate for filtering errors and reduce errors caused by input saturation; and tracking control of a cruise missile system with full-state constraints and input saturation under preset performance is achieved.

[0017] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The present invention is a flowchart of the preset performance asymptotic tracking control method of the cruise missile system.

[0019] Figure 2 Schematic diagram of the adaptive tubular preset performance boundary designed for the method of the present invention.

[0020] Figure 3 This is a full system control block diagram of the method of the present invention.

[0021] Figure 4 Graph showing the tracking error and system output evolution in an embodiment of the method of the present invention.

[0022] Figure 5 Graph showing the evolution of system status and control input in an embodiment of the method of the present invention. DETAILED DESCRIPTION

[0023] In order to overcome the problems existing in the prior art, this paper focuses on a high-order uncertain cruise missile system with asymmetric time-varying full-state constraints and input saturation, and studies its preset performance asymptotic tracking control. By introducing the barrier Lyapunov function (BLF) to handle the full-state constraints and innovatively combining PPC and DSC technology, it aims to achieve stable control without overshoot and vibration, and contribute new ideas and methods to the field of control system design.

[0024] like Figure 1~Figure 3 As shown, the present invention proposes a tracking control method for a cruise missile system with full state constraints and input saturation under preset performance, comprising the following steps:

[0025] Step 1: Consider a cruise missile system with input saturation, unknown nonlinear dynamics and external disturbances. Use a smooth function to avoid the impact of the sawtooth of the saturation function on the system. Use RBFNN to fit the unknown nonlinear dynamics and external disturbances to obtain a new controlled system.

[0026] Step 2: Considering the tracking time, overshoot, and accuracy requirements of the system, a class of tubular preset performance boundaries without overshoot is designed. To solve the impact of input saturation, a detection function is designed to construct an adaptive tubular preset performance boundary to avoid the conflict between input saturation and PPF.

[0027] Step 3: A new error conversion function is designed to solve the preset performance and state constraints in the same framework;

[0028] Step 4: Convert the new controlled system and construct the error system based on the error transfer function and the adaptive tubular preset performance boundary;

[0029] Step 5: To address the “differential explosion” problem caused by the backstepping method and the “feasibility condition” caused by the error transfer function, a new instruction filtering method is designed and combined with a signal compensator to compensate for the filtering error;

[0030] Step 6: Design the controller and the adaptive rate using backstepping, adaptive control and signal compensator to achieve asymptotic tracking of the reference signal.

[0031] Preferably, in step 1, the model is simplified. First, consider a class Step The dimension-uncertain cruise missile system is as follows:

[0032] (1)

[0033] in , is the system status; is the system output; is an unknown smooth nonlinear function; is an unknown external disturbance, and ,in is an unknown constant. And represents the actual control input with asymmetric saturation nonlinearity, where For the Virtual controller of the system.

[0034] (2)

[0035] in represents the desired control input, and are the upper and lower bounds of the known control constraints. The system state Faced with strict continuity constraints, define To indicate the status The lower bound of Indicates status The upper bound of satisfy ,for ; In order to reduce the adverse effects of actuator saturation on the system, the present invention introduces a method to solve the saturation function by estimating The sharp angle method, i.e. ,in Represents the smoothed The control input of the dimension satisfies the following equation:

[0036] (3)

[0037] and is the approximation error, and is defined ,but:

[0038] ; (4)

[0039] To deal with the unknown nonlinear function in (1) , t is time, and a neural network is introduced to fit. For any unknown continuous nonlinear function ,in Defined on a compact set We can use radial basis function neural network (RBFNN) This is an exact approximation to any given precision:

[0040] (5)

[0041] in is the approximation error, is an unknown constant. is an ideal constant weight vector given by

[0042] (6)

[0043] in is the output layer weight vector, where is the number of NN nodes. is a Gaussian function vector, as shown below:

[0044] (7)

[0045] in and They are basic functions Therefore, the unknown continuous nonlinear function in system (1) is It can be expressed as ,in is the function approximation error. The optimal weight vector can be expressed as:

[0046] ; (8)

[0047] but The cruise missile system (1) is further expressed as:

[0048] (9)

[0049] in , and ,as well as . It can be determined ,in is an unknown constant.

[0050] Preferably, in step 2, a reasonable preset performance boundary (PPB) is designed. In order to ensure the continuity and differentiability of the PPB, commonly used performance functions are usually constructed as piecewise functions. These preset performance functions (PPFs) are designed as smooth, monotonically decreasing curves to ensure a predetermined convergence time. The present invention uses the following PPF:

[0051] (10)

[0052] in represents the expected convergence speed, represents the expected convergence time, and represent the initial value and steady-state value respectively. The derivation of formula (10) yields:

[0053] ; (11)

[0054] Obviously, when hour, Continuous strictly decreasing, Therefore, in order to ensure the differentiability of the split point, the PPF considered in the present invention exhibits the following characteristics: 1) , 2) and For any , 3) and , for any . Many existing studies directly adopt the above performance function as PPB. However, in the case of asymmetric input saturation, insufficient initial conditions or suboptimal external disturbances may make PPB infeasible. This paper proposes an adaptive tubular preset performance bound (ATPPB) that can dynamically adjust constraints to adapt to system state constraints and input saturation. Such an ATPPB can provide a stricter allowed set, thereby achieving better transient performance. This method is applicable to each component of the tracking error vector , where the output constraints are described as:

[0055] (12)

[0056] for ,in and The tracking performance can be flexibly reduced and restored as specified by the user:

[0057] (13)

[0058] in , is the symbolic function, Tracking error The initial value of represents the PPF consistent with equation (10), The corresponding preset steady state. is an auxiliary state, which aims to alleviate the conflict between PPB and the system full state constraints and input saturation. In order to ensure the tracking error Keep at the set In this paper, a monitoring function is designed; when the tracking error is close to PPB, the function generates an incentive, thereby sacrificing certain performance constraints to give priority to satisfying the full-state constraints and input saturation of the system; this priority is reasonable because the full-state constraints and input saturation are non-negotiable hard constraints for constrained systems. Therefore, the design of the monitoring function takes into account the constraints that the system must comply with, making it extremely important in practice. The monitoring function is as follows:

[0059] (14)

[0060] in is used as a scaling parameter. Obviously, Based on this monitoring function, the auxiliary system The definition is as follows:

[0061] (15)

[0062] in , is the coefficient of the auxiliary system, is a design constant.

[0063] Preferably, in step 3, an error conversion function is constructed. The traditional PPC technology uses a logarithmic mapping function Convert the constrained state to the unconstrained state. However, this method cannot distinguish the corresponding states and cannot be directly applied to the transformation function of the full state constraint, thus avoiding the feasibility condition. Therefore, the present invention proposes a novel error conversion function, which effectively combines the preset performance control with the full state constraint by virtue of its characteristics of always being greater than 0 and monotonically increasing. The tracking error of the system The transformation is as follows:

[0064] ; (16)

[0065] Taking the derivative of (16) we get:

[0066] ; (17)

[0067] To facilitate the subsequent discussion, we define and in , Therefore, formula (17) can be simplified to ,in , For the constrained independent variable , the present invention uses a novel error conversion function:

[0068] (18)

[0069] in is the scale constant parameter, and Respectively represent independent variables lower and upper limits.

[0070] Preferably, in step 4, a tracking error equation is constructed. The following coordinate transformation is defined as:

[0071] (19)

[0072] in is the output of the first order filter, which will be designed in step 5 below. Elements within By the following function and , The instruction filtering technique is used to eliminate the "feasibility conditions" related to the state constraints while avoiding the complexity explosion problem. According to the definition of partial derivatives, we have:

[0073] (20)

[0074] in and For the convenience of subsequent expressions, define , , , Then, (20) is simplified to:

[0075] ;(twenty one)

[0076] Preferably, in step 5, a filter is designed. In order to avoid "complexity explosion", the commonly used DSC technology adopts a first-order filter. In the present invention, in order to dynamically solve the asymmetric state constraint and eliminate the "feasibility condition" of BLF, a first-order filter design based on the above method is proposed:

[0077] (twenty two)

[0078] in is a normal number, As a virtual controller to be designed. In order to compensate for the filtering error , compensation signal , is designed to:

[0079] (twenty three)

[0080] in , , , is the identity matrix, and , , To satisfy Any function of is any positive constant. In addition, and is the design parameter. Then, the compensation error for:

[0081] ;(twenty four)

[0082] Preferably, in step 6, a controller is designed. First, the following equation can be derived:

[0083] ; (25)

[0084] According to (23), (24) and (25) respectively , and The definition of can be obtained:

[0085] (26)

[0086] Design the following Lyapunov equation:

[0087] (27)

[0088] in and is a design constant. is the estimation error, where for The estimated value of . Represents the estimation error .right The derivative is:

[0089] ; (28)

[0090] Define a matrix as follows:

[0091] ; (29)

[0092] To satisfy Any function of is any positive constant. Then we get the following inequality:

[0093] (30)

[0094] in is a normal number, because The virtual controller and adaptive law are designed as:

[0095] (31)

[0096] in Substituting (31) into (28) yields:

[0097] ; (32)

[0098] Second, consider Situation:

[0099] ; (33)

[0100] Similarly, the Lyapunov function is defined as follows:

[0101] (34)

[0102] in and is a design constant. is the estimation error, where for The estimated value of , represents the estimation error, .right The derivative is:

[0103] ; (35)

[0104] Define a matrix as follows:

[0105] ; (36)

[0106] Then we get the following inequality:

[0107] (37)

[0108] in is a normal number, ,because . Designing a virtual controller and Adaptive Law , for:

[0109] (38)

[0110] in and for If it holds, then (35) can be rewritten as:

[0111] ; (39)

[0112] Finally, consider introducing an auxiliary system to compensate for the impact of input saturation on the system as follows:

[0113] (40)

[0114] The variables represents the output of the auxiliary system (40), which is used to offset the adverse effects of input saturation on the system. Definition of compensation error for:

[0115] ; (41)

[0116] but:

[0117] ; (42)

[0118] definition in and is the design constant. is the estimation error, where for The estimated value of . Represents the estimation error .right The derivative is:

[0119] ; (43)

[0120] Define the matrix as follows:

[0121] ; (44)

[0122] but:

[0123] (45)

[0124] in is a normal number, ,because . Designing a virtual controller , Adaptive Law , and the actual controller is :

[0125] (46)

[0126] in Then, based on controllers (31), (38) and (46), the entire system can achieve global asymptotic stability.

[0127] The present invention will be further described below in conjunction with the embodiments.

[0128] Example

[0129] Consider the following loitering munitions systems:

[0130]

[0131] in , , as well as The system is subject to full state constraints and input saturation In this simulation example, the preset performance constraint PPF parameters are set to and . ATPPB parameter settings are as follows: and . Select the reference signal 100 nodes are used to approximate the unknown nonlinearity and the RBFNN is selected The controller parameters are selected as follows: , as well as .

[0132] The simulation results are as follows Figure 4-5 As shown, the initial conditions of the system are set to .from Figure 4 It can be seen that under the virtual control law and adaptive neural network controller, the output of the system can gradually track the reference signal , without violating the predetermined performance function. In addition, Figure 4 It can be clearly seen from the left sub-figure of that when the tracking error violates the monitoring function constraint, the ATPPB designed by the present invention can be adjusted spontaneously to relax the predetermined performance boundary. Once the tracking error returns to the monitoring function range, the performance function will quickly return to the preset state to handle external interference, state constraints and input saturation. Figure 5 The changes in the system state and system input shown show that even with time-varying state constraints and asymmetric input saturation, the cruise munition system can still meet the asymptotic tracking of the reference signal.

[0133] The specific embodiments described in the present invention are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the attached claims.

Claims

1. A tracking control method for a cruise missile system with full state constraints and input saturation under preset performance, characterized in that: The following steps are involved: Step 1: Construct a cruise missile system with input saturation, unknown nonlinear dynamics and external disturbances, use a smooth function to avoid the impact of the sawtooth of the saturation function on the system, and use RBFNN to fit the unknown nonlinear dynamics and external disturbances to obtain a new controlled system; the specific method is as follows: Build a Step The dimension-uncertain cruise missile system is as follows: (1) in , is the system status; is the system output; is an unknown smooth nonlinear function; is an unknown external disturbance, and ,in is an unknown constant; and represents the actual control input with asymmetric saturation nonlinearity, where For the Virtual controller of the hierarchical system; (2) in represents the desired control input, and are the upper and lower bounds of the known control constraints; the system state Faced with strict continuity constraints, define To indicate the status The lower bound of Indicates status The upper bound of satisfy ,for ; Introduce a method to solve the saturation function by using estimation The sharp angle method, i.e. ,in Represents the smoothed The control input of the dimension satisfies the following equation: (3) and is the approximation error, and is defined ,but: ；(4) To deal with the unknown nonlinear function in (1) , t is time, neural network is introduced to fit; for any unknown continuous nonlinear function ,in Defined on a compact set On the radial basis function neural network This is an exact approximation to any given precision: (5) in is the approximation error, is an unknown constant; and is an ideal constant weight vector given by (6) in is the output layer weight vector, where is the number of NN nodes; is a Gaussian function vector, as shown below: (7) in and They are basic functions The center and width of ; therefore, the unknown continuous nonlinear function in system (1) It can be expressed as ,in is the function approximation error; the optimal weight vector can be expressed as: (8) but The cruise missile system is represented as: (9) in , , ,as well as ;Sure ,in is an unknown constant; Step 2: Construct an adaptive tubular preset performance boundary by designing a monitoring function; the specific method is as follows: The following preset performance functions are used: (10) in represents the expected convergence speed, represents the expected convergence time, and represent the initial value and steady-state value respectively; the derivation of formula (10) yields: (11) when hour, Continuous strictly decreasing, Continuous and strictly increasing; the preset performance function exhibits the following characteristics: 1) , 2) , 3) ;when When , the preset performance function exhibits the following characteristics: 1) , 2) ; An adaptive tubular preset performance bound is proposed, which dynamically adjusts the constraints to adapt to system state constraints and input saturation. This method is applicable to each component of the tracking error vector , where the output constraints are described as: (12) for ,in and Ability to reduce and restore user-specified tracing performance: (13) in , is the symbolic function, Tracking error The initial value of represents the preset performance function consistent with equation (10), is the corresponding preset steady state, It is an auxiliary state; design a monitoring function: (14) in is used as a scaling parameter; obviously, Always true; based on this monitoring function, the auxiliary system The definition is as follows: (15) in , is the coefficient of the auxiliary system, is the design constant; Step 3: Design an error conversion function to solve the preset performance and state constraints in the same framework; the specific method is as follows: Tracking error of the system The transformation is as follows: ；(16) Taking the derivative of (16) we get: ；(17) definition and in , Therefore, formula (17) can be simplified to ,in , ; For constrained independent variables , the error conversion function is: (18) in is the scale constant parameter, and Respectively represent independent variables The lower and upper limits of Step 4: Construct an error system based on the error transfer function and the adaptive tubular preset performance boundary; the specific method is as follows: Define the following coordinate transformation as: (19) in is the output of the first-order filter, The elements within and Elements within The following functions are respectively and composition, , ; According to the definition of partial derivative, we have: (20) in and ;definition , , , ; Then, (20) is simplified to: (21)； Step 5: Use the command filtering method and the signal compensator to compensate for the filtering error; the specific method is as follows: Design a first-order filter: (22) in is a normal number, As a virtual controller to be designed; in order to compensate for the filtering error , compensation signal , is designed to: (23) in , , , is the identity matrix, and , , To satisfy Any function of is any positive constant; and is a design parameter; then, the compensation error for: (24)； Step 6: Use backstepping, adaptive control and signal compensator to design virtual controller, actual controller and adaptive law to achieve asymptotic tracking of reference signal; the specific method is as follows: First derive the following equation: ；(25) in is the derivative of the desired output signal, according to (23), (24) and (25) respectively , and The definition of , we get: (26) Design the following Lyapunov equation: (27) in and is the design constant; is the estimation error, where for The estimated value of ; Represents the estimation error ;right The derivative is: (28) Define a matrix as follows: (29) To satisfy Any function of is any positive constant; then we get the following inequality: (30) in is a normal number, ,because ; Design the virtual controller and adaptive law as: (31) in ; Substituting (31) into (28) we obtain: ； (32) consider Situation: (33) The Lyapunov function is defined as follows: (34) in and is the design constant; is the estimation error, where for The estimated value of , represents the estimation error, ;right The derivative is: ；(35) Define a matrix as follows: ；(36) Then we get the following inequality: (37) in is a normal number, ,because ;Design virtual controller and Adaptive Law , for: (38) in and for If it holds, then (35) can be rewritten as: (39) Finally, consider introducing an auxiliary system to compensate for the impact of input saturation on the system as follows: (40) The variables represents the output of the auxiliary system (40), which is used to offset the adverse effect of input saturation on the system; defines the compensation error for: ；(41) but: ；(42) definition in and is the design constant; is the estimation error, where for The estimated value of ; Represents the estimation error ;right The derivative is: (43) Define the matrix as follows: (44) but: (45) in is a normal number, ,because ;Design virtual controller , Adaptive Law , and the actual controller is : (46) in ; Based on controllers (31), (38) and (46), the entire system achieves global asymptotic stability.

2. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method according to claim 1 are implemented.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to claim 1 are implemented.

4. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to claim 1 are implemented.

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