CN113110430B - Unmanned ship model-free fixed time accurate track tracking control method - Google Patents
Unmanned ship model-free fixed time accurate track tracking control method Download PDFInfo
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Abstract
The invention provides a model-free fixed time accurate track tracking control method for an unmanned ship, which comprises the following steps: constructing a USV model with input saturation and complex disturbance; designing a fixed time lumped observer based on the constructed USV model; designing an adaptive auxiliary system based on the designed fixed time lumped observer; based on the designed self-adaptive auxiliary system, designing a rapid nonsingular terminal sliding mode; and designing a model-free fixed time accurate tracking control strategy based on the designed fixed time lumped observer, the self-adaptive auxiliary system and the rapid nonsingular terminal sliding mode. The technical scheme of the invention can ensure that the unmanned ship which is simultaneously subjected to input saturation, complex environmental disturbance and completely unknown model dynamics accurately tracks the expected track within an expected time, obtains faster convergence speed and tracking precision, and solves the problems of singularity and slow convergence speed in the traditional sliding mode strategy.
Description
Technical Field
The invention relates to the technical field of fast and accurate tracking control of unmanned ships, in particular to a model-free fixed time accurate track tracking control method of unmanned ships.
Background
In recent years, unmanned surface vessels (unmanned surface vehicle, USVs) have been widely used in engineering practices and scientific experiments such as water quality monitoring, ocean exploration, underwater topography measurement, and the like. For the above reasons, more and more scholars are focusing on the tracking of the USV and have achieved some results in this field. In order to ensure that USV can achieve accurate trajectory tracking under complex ocean conditions, many researchers have designed suitable trackers taking into account external disturbances, system uncertainties and actuator dynamics. Because of the good convergence performance and the strong anti-disturbance and anti-uncertainty performance, the sliding mode control (sliding mode control, SMC) method is adopted to solve the problem of accurate track tracking. For example, an adaptive SMC method combining a radiation basis function neural network and a disturbance observer is adopted to process uncertainty and complex disturbance of a USV model, so that quick response, outstanding convergence performance and high-precision tracking are realized.
In consideration of dynamic uncertainty and time-varying disturbance, a rapid non-singular value SMC method is developed for USV to track a reference track, and a convergence speed is faster than that of the existing non-singular value SMC manifold. With event triggered policies for SMC tracking systems, the method has external disturbances, can reduce control updates and ensure asymptotic stability of the system and optimization of resource usage and cost. Furthermore, the SMC method aims to receive limited time convergence. Limited time strategies in combination with command filtering SMC have been used on autonomous airships in pursuit of better tracking performance. However, the above documents ignore the uncertainty of the system, although they do a good job in terms of convergence rate. In consideration of the parameter uncertainty of the USV track tracking system, disturbance and actuator faults, a novel finite time fault-tolerant tracking controller combining self-adaptive control and time-varying SMC is provided. The controller can ensure that the USV tracks the reference trajectory for a limited time and without the need for known inertial parameters. Researchers have developed a finite time SMC method and a finite time control scheme based on negative homogeneous control, respectively, in combination with observation techniques to eliminate the negative effects of uncertainty and time-varying disturbances on trajectories. In addition, the finite time scheme can achieve a good convergence speed, but the convergence time is affected by the initial state. In response to this problem, a fixed time control scheme has been proposed, and many achievements have been made in the control field. A novel fixed-time nonsingular slipform manifold is designed based on the bipolar homogeneous theory, so that the track of the unmanned aerial vehicle is tracked within a set time, but the upper limit of disturbance needs to be known in advance. Considering the state constraints and system uncertainties of unmanned aircraft, the et al developed a new barrier lyapunov function to ensure that the fixed time stability did not violate the state constraints.
To further address the adverse effects of the disturbance, researchers have proposed several methods such as disturbance observers, adaptive fuzzy control, intelligent learning algorithms, and the like. For example, researchers have designed a self-constructing nerve, with online fuzzy approximation lumped unknowns. A disturbance observer was studied by a learner to identify and compensate for the disturbance. In addition, a learner designs a fixed-time disturbance observer, which can accurately identify complex disturbance in a fixed time. In practice, actuator saturation typically occurs in the control system due to physical limitations. If the actuator is in a saturated state for a long time, the actuator is damaged, and the track tracking precision is seriously reduced. Researchers use the barrier Li Yapu nof and nonlinear observers to handle the effects of actuator saturation and interference. In consideration of parameter uncertainty, unknown interference and actuator nonlinearity, researchers solve the input saturation problem by combining an adaptive control method. Furthermore, researchers have designed an auxiliary system to counteract the effects of input saturation, but this approach needs to ensure that the uncertainty is bounded. However, in the field of unmanned ship fixed time trajectory tracking control, the influence of input saturation is not dealt with in the existing literature, which may significantly reduce the control quality and even cause instability of the system.
Disclosure of Invention
According to the technical problems, the unmanned ship model-free fixed time accurate track tracking control method is provided. The invention mainly considers a USV model with input saturation and complex disturbance, designs a fixed time lumped uncertainty observer, regards external unknown disturbance items and unknown hydrodynamic coefficient items as a set total uncertainty item, and accurately and rapidly observes and compensates the external unknown disturbance items and the unknown hydrodynamic coefficient items in a fixed time; designing a quick nonsingular terminal sliding mode with a fixed time stability characteristic, and integrating a fixed time idea into a sliding mode control technology; an adaptive auxiliary system is designed to eliminate negative influence of input saturation on the system; a model-free fixed time accurate track tracking control strategy is designed, so that an unmanned ship which encounters complex ocean current disturbance, is completely unknown in system dynamics and is saturated in input can track an expected track within a fixed time.
The invention adopts the following technical means:
a unmanned ship model-free fixed time accurate track tracking control method comprises the following steps:
s1, constructing a USV model with input saturation and complex disturbance;
s2, designing a fixed time lumped observer based on the constructed USV model;
s3, designing a self-adaptive auxiliary system based on the designed fixed time lumped observer;
s4, designing a rapid nonsingular terminal sliding mode based on the designed self-adaptive auxiliary system;
s5, designing a model-free fixed time accurate tracking control strategy based on the fixed time lumped observer, the self-adaptive auxiliary system and the rapid nonsingular terminal sliding mode designed in the steps S2-S4.
Further, the step S1 specifically includes:
s11, taking input saturation and complex disturbance into consideration, constructing a USV model, wherein the USV model is as follows:
wherein η= [ x y ψ ]] T Representing the position and heading in the earth coordinate system OXY,v＝[u v r] T representing velocity vectors in an appendage coordinate system, G (η, v) = -C (v) v-D (v) representation systemDynamic of system, C (v) represents diagonal matrix, < ->C(v)＝-C T (v) The method comprises the steps of carrying out a first treatment on the surface of the D (v) represents a damping matrix,d＝MR T delta and delta= [ delta ] 1 ,δ 2 ,δ 3 ] T Representing a complex time-varying disturbance, M representing inertia, < ->M＝M T > 0; τ represents the control input limited by actuator saturation,τ i,max is the maximum torque which can be provided by the actuator, tau c,i Is an ideal control input, i=u, v, r;
s12, based on the constructed USV model, introducing the following matrix:
there is a case that the following equation holds:
s13, an expected track equation is given by the following formula:
wherein Q (eta) d ,v d )＝-C(v d )v d -D(v d )v d ，η d ＝[x d y d ψ d ] T And v d ＝[u d v d r d ] T Representing the desired position and velocity vectors, respectively;
s14, for the above formulaν，ν d The following transformations were introduced:
wherein,representing the auxiliary variable introduced-> Represents an auxiliary variable in the desired state, +.>R represents a variable matrix related to the actual state, r=r (ψ), R d Representing a matrix of variables related to the desired state, R d ＝R(ψ d )；
S15, combining the formulas (1), (3) and (5) to obtain the following formula:
wherein H (eta, v) represents an introduced intermediate variable,
s16, combining the formulas (3), (4) and (5) to obtain the following formula:
wherein Γ (η) d ,ν d ) Representing introduced intermediate variables for simplifying operations
S17, obtaining an unmanned ship track tracking error control system according to the formulas (6) and (7), wherein the control system is as follows:
wherein,Ω＝Ω(η,ν,η d ,ν d δ) represents a lumped unknowns comprising unknown perturbations and unmodeled dynamics, specifically expressed as follows:
Ω(·)＝RM -1 G(η，ν)+d-R d M -1 τ d -R d M -1 Q(η d ，ν d )。
further, the fixed time lumped observer designed in the step S2 is specifically as follows:
wherein the observer coefficient lambda 1 ,λ 2 ,λ 3 Respectively represent constant parameters satisfying certain constraint conditions, lambda 1 ,λ 2 ,λ 3 ＞0，λ 3 ＞d，β 1 ,β 2 Respectively represent observer exponentiation, beta 1 ,β 2 Satisfy beta 1 ＞1,0＜β 2 < 1, observer variable z 1 ,z 2 Respectively representEstimate of Ω (·).
Further, the adaptive assistance system designed in the step S3 is specifically as follows:
wherein χ is 1 ＝[χ 1,u χ 1,v χ 1,r ] T ,χ 2 ＝[χ 2,u χ 2,v χ 2,r ] T Representing auxiliary variables, c 1 ,c 2 Represents a suitable parameter matrix, Δτ=τ c -τ，τ c And τ represents control input after not considering actuator constraints and actuator constraints, respectively.
Further, the step S4 specifically includes:
s41, designing a fixed-time rapid nonsingular terminal sliding mode, wherein the fixed-time rapid nonsingular terminal sliding mode comprises the following steps:
wherein σ= [ σ ] u σ v σ r ] T ,e 1 ＝η e -χ 1 ＝[e 1,u e 1,v e 1,r ] T ，γ 1 ,γ 2 ＞0,n 1 ＞1，f(e 1 ) The expression is as follows:
wherein ε is a very small positive constant, 0 < n 2 ＜1,1＜n 3 ＜n 4 ，n 1 ,n 2 ,n 3 ,n 4 ,γ 1 ,γ 2 There is a relationship between:
s42, deriving the designed fixed-time rapid nonsingular terminal sliding mode to obtain:
wherein,can be described as:
wherein:
further, the model-free fixed time precise tracking control strategy designed in the step S5 is specifically as follows:
wherein alpha is j Represents a constant parameter, alpha, satisfying a certain condition j ＞0(j＝1,2,3)，m 1 ,m 2 Is positive odd and satisfies m 1 ＞m 2 。
Further, the step S5 further includes introducing an auxiliary variable g sat To eliminate potential jitter caused by symbol discontinuities, in particular:
wherein g sat The auxiliary variables φ, χ, and σ are constant coefficients satisfying a certain condition.
Compared with the prior art, the invention has the following advantages:
1. the unmanned ship model-free fixed time accurate track tracking control method provided by the invention can ensure that the unmanned ship which is simultaneously subjected to input saturation, complex environment disturbance and model dynamic complete unknown accurately tracks an expected track in an expected time, and can obtain faster convergence speed, tracking precision and stronger robustness.
2. The unmanned ship model-free fixed time accurate track tracking control method provided by the invention overcomes the problems of singularity and slow convergence speed in the traditional sliding mode strategy. And meanwhile, the external disturbance and unmodeled dynamic items in the unmanned ship track tracking control system are regarded as lumped uncertain items, and the unmanned ship track tracking control system is rapidly identified and compensated within a preset time by designing a fixed time lumped observer. Thereby realizing the precise track tracking control independent of the unmanned ship model. The validity and superiority of the designed trajectory tracking control strategy are verified by strict mathematical proof and simulation test.
Based on the reasons, the invention can be widely popularized in the fields of unmanned ships, such as fast and accurate tracking control, and the like.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort to a person skilled in the art.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a three-degree-of-freedom mathematical model of the unmanned ship provided by the embodiment of the invention.
Fig. 3 is a control policy framework diagram provided in an embodiment of the present invention.
Fig. 4 is a trace tracking graph provided in an embodiment of the present invention.
Fig. 5 is a graph of position tracking provided in an embodiment of the present invention.
Fig. 6 is a graph of a position tracking error according to an embodiment of the present invention.
Fig. 7 is a velocity tracking graph provided by an embodiment of the present invention.
Fig. 8 is a graph of a velocity tracking error provided by an embodiment of the present invention.
Fig. 9 is a graph of lumped unknown observations provided by an embodiment of the present invention.
Fig. 10 is a graph of a velocity tracking error provided by an embodiment of the present invention.
Fig. 11 is a graph of saturation control input provided in an embodiment of the present invention.
Fig. 12 is a graph of trace tracking at different initial states according to an embodiment of the present invention.
Fig. 13 is a graph of position tracking in different initial states according to an embodiment of the present invention.
Fig. 14 is a graph of position tracking error at different initial states according to an embodiment of the present invention.
Fig. 15 is a graph of velocity tracking at different initial conditions provided by an embodiment of the present invention.
Fig. 16 is a graph showing a velocity tracking error at different initial states according to an embodiment of the present invention.
Detailed Description
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present invention and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in FIG. 1, the invention provides a model-free fixed time accurate track tracking control method for an unmanned ship, which comprises the following steps:
s1, constructing a USV model with input saturation and complex disturbance; fig. 2 is a schematic diagram of a three-degree-of-freedom mathematical model of an unmanned ship according to an embodiment of the present invention.
In specific implementation, as a preferred embodiment of the present invention, the step S1 specifically includes:
s11, taking input saturation and complex disturbance into consideration, constructing a USV model, wherein the USV model is as follows:
wherein η= [ x y ψ ]] T Representing the position and heading in the earth coordinate system OXY,v＝[u v r] T represents the velocity vector in the appendage coordinate system, G (η, v) = -C (v) v-D (v) represents the system dynamics, C (v) represents the diagonal matrix,/->C(v)＝-C T (v) The method comprises the steps of carrying out a first treatment on the surface of the D (v) represents a damping matrix,d＝MR T delta and delta= [ delta ] 1 ,δ 2 ,δ 3 ] T Representing a complex time-varying disturbance, M representing inertia, < ->M＝M T > 0; τ represents the control input limited by actuator saturation,τ i,max is the maximum torque which can be provided by the actuator, tau c,i Is ideal controlA system input, i=u, v, r;
s12, based on the constructed USV model, introducing the following matrix:
there is a case that the following equation holds:
s13, an expected track equation is given by the following formula:
wherein Q (eta) d ,v d )＝-C(v d )v d -D(v d )v d ，η d ＝[x d y d ψ d ] T And v d ＝[u d v d r d ] T Representing the desired position and velocity vectors, respectively;
s14, for v, v in the formula d The following transformations were introduced:
wherein,representing the auxiliary variable introduced-> Represents an auxiliary variable in the desired state, +.>R represents a variable matrix related to the actual state, r=r (ψ), R d Representing a matrix of variables related to the desired state, R d ＝R(ψ d )；
S15, combining the formulas (1), (3) and (5) to obtain the following formula:
wherein H (eta, v) represents an introduced intermediate variable,
s16, combining the formulas (3), (4) and (5) to obtain the following formula:
wherein Γ (η) d ,ν d ) Representing introduced intermediate variables for simplifying operations
S17, obtaining an unmanned ship track tracking error control system according to the formulas (6) and (7), wherein the control system is as follows:
wherein,Ω＝Ω(η,ν,η d ,ν d δ) represents a lumped unknowns comprising unknown perturbations and unmodeled dynamics, specifically expressed as follows:
Ω(·)＝RM -1 G(η，ν)+d-R d M -1 τ d -R d M -1 Q(η d ，ν d )。
suppose 1: assuming that the lumped unknowns in (15) are microscopic and bounded, and satisfy:
||Ω(·)||≤d
where the constant d < ++β, |x| represents the euclidean norm of the standard.
In this embodiment, the system dynamic matrix C (v), D (v) and vector D are all unknown, and the matrix C (v), D (v) is subject to variations in ocean wave currents. The invention aims to design a model-free fixed time track tracking control scheme for an unmanned ship encountering complex unknown and input saturation influences. The scheme can ensure tracking error eta e ,ν e The closed loop system converges to a small range centered at the origin within a set time and the closed loop system is stable in time.
S2, designing a fixed time lumped observer based on the constructed USV model;
in practice, as a preferred embodiment of the present invention, in order to obtain high-precision tracking performance, it is necessary to accurately identify and compensate the lumped unknown items in the track tracking error control system, so the fixed time lumped observer designed in step S2 is specifically as follows:
wherein the observer coefficient lambda 1 ,λ 2 ,λ 3 Respectively represent constant parameters satisfying a certain constraint, lambda 1 ,λ 2 ,λ 3 ＞0，λ 3 ＞d，β 1 ,β 2 Represents a constant exponent power satisfying a constraint, and beta 1 ＞1,0＜β 2 < 1, observed variable z 1 ,z 2 Representing intermediate variables, respectivelyThe estimates of the disturbance Ω (·) are lumped.
S3, designing a self-adaptive auxiliary system based on the designed fixed time lumped observer;
in fact, due to the limitation of the saturation of the actuator, the actuator often cannot provide enough control torque, and in practice, as a preferred embodiment of the present invention, in order to handle the input saturation, the adaptive auxiliary system designed in step S3 is specifically as follows:
wherein χ is 1 ＝[χ 1,u χ 1,v χ 1,r ] T ,χ 2 ＝[χ 2,u χ 2,v χ 2,r ] T Representing auxiliary variables, c 1 ,c 2 Represents a suitable parameter matrix, Δτ=τ c -τ，τ c And τ represents control input after not considering actuator constraints and actuator constraints, respectively.
S4, designing a rapid nonsingular terminal sliding mode based on the designed self-adaptive auxiliary system;
in specific implementation, as a preferred embodiment of the present invention, the step S4 specifically includes:
s41, designing a fixed-time rapid nonsingular terminal sliding mode, wherein the fixed-time rapid nonsingular terminal sliding mode comprises the following steps:
wherein σ= [ σ ] u σ v σ r ] T ,e 1 ＝η e -χ 1 ＝[e 1,u e 1,v e 1,r ] T ，γ 1 ,γ 2 ＞0,n 1 ＞1，f(e 1 ) The expression is as follows:
wherein ε is a very small positive constant, 0 < n 2 ＜1,1＜n 3 ＜n 4 ，n 1 ,n 2 ,n 3 ,n 4 ,γ 1 ,γ 2 Is stored betweenIn the following relation:
s42, deriving the designed fixed-time rapid nonsingular terminal sliding mode to obtain:
wherein,can be described as:
wherein:
s5, designing a model-free fixed time accurate tracking control strategy based on the fixed time lumped observer, the self-adaptive auxiliary system and the rapid nonsingular terminal sliding mode designed in the steps S2-S4.
In specific implementation, as a preferred embodiment of the present invention, the model-free fixed time precise tracking control strategy designed in step S5 is specifically as follows:
wherein alpha is j Represents a constant parameter, alpha, satisfying a certain condition j ＞0(j＝1,2,3)，m 1 ,m 2 Is positive odd and satisfies m 1 ＞m 2 。
In particular, as a preferred embodiment of the present invention, the step S5 further includes introducing g sat To eliminate potential jitter caused by symbol discontinuities, in particular:
wherein g sat Representing the auxiliary variables, phi, chi and sigma represent constant parameters meeting certain conditions.
In summary, the fixed time lumped observer designed in the invention can realize accurate observation of lumped unknown items including environmental disturbance and unmodeled dynamics in a fixed time. The model-free fixed time track tracking control scheme can enable the unmanned ship which is simultaneously subjected to input saturation, complex environment disturbance and model dynamic complete unknown to accurately track the expected track within an expected time, and the convergence time is irrelevant to the initial state of the unmanned ship and is only related to the designed parameters.
In order to verify the effectiveness and superiority of the method, simulation tests are carried out, and as shown in fig. 4-16, the method can ensure that an unmanned ship which is simultaneously subjected to input saturation, complex environment disturbance and model dynamic complete unknown accurately tracks an upper expected track in an expected time, and achieves higher convergence speed, tracking precision and stronger robustness.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (4)
1. The unmanned ship model-free fixed time accurate track tracking control method is characterized by comprising the following steps of:
s1, constructing a USV model with input saturation and complex disturbance; the step S1 specifically includes:
s11, taking input saturation and complex disturbance into consideration, constructing a USV model, wherein the USV model is as follows:
wherein η= [ x y ψ ]] T Representing the position and heading in the earth coordinate system OXY,v＝[u v r] T represents the velocity vector in the appendage coordinate system, G (η, v) = -C (v) v-D (v) represents the system dynamics, C (v) represents the diagonal matrix,/->C(v)＝-C T (v) The method comprises the steps of carrying out a first treatment on the surface of the D (v) represents a damping matrix,d＝MR T delta and delta= [ delta ] 1 ,δ 2 ,δ 3 ] T Representing a complex time-varying disturbance, M representing an inertial matrix, < ->M＝M T > 0; τ represents the control input limited by actuator saturation,τ i,max is the maximum torque which can be provided by the actuator, tau c,i Is an ideal control input, i=u, v, r;
s12, based on the constructed USV model, introducing the following matrix:
there is a case that the following equation holds:
s13, an expected track equation is given by the following formula:
wherein Q (eta) d ,v d )＝-C(v d )v d -D(v d )v d ，η d ＝[x d y d ψ d ] T And v d ＝[u d v d r d ] T Representing the desired position and velocity vectors, respectively;
s14, for v, v in the formula d The following transformations were introduced:
wherein,representing the auxiliary variable introduced-> Representing the auxiliary variable in the desired state,r represents a variable matrix related to the actual state, r=r (ψ), R d Representing a matrix of variables related to the desired state, R d ＝R(ψ d )；
S15, combining the formulas (1), (3) and (5) to obtain the following formula:
wherein H (eta, v) represents an introduced intermediate variable,
s16, combining the formulas (3), (4) and (5) to obtain the following formula:
wherein Γ (η) d ,ν d ) Representing introduced intermediate variables for simplifying operations
S17, obtaining an unmanned ship track tracking error control system according to the formulas (6) and (7), wherein the control system is as follows:
wherein,Ω＝Ω(η,v,η d ,ν d δ) represents a lumped unknowns comprising unknown perturbations and unmodeled dynamics, specifically expressed as follows:
Ω(g)＝RM -1 G(η，ν)+d-R d M -1 τ d -R d M -1 Q(η d ，v d )；
s2, designing a fixed time lumped observer based on the constructed USV model; the fixed time lumped observer designed in the step S2 is specifically as follows:
wherein the observer coefficient lambda 1 ,λ 2 ,λ 3 Respectively represent constant parameters satisfying a certain constraint, lambda 1 ,λ 2 ,λ 3 ＞0，λ 3 ＞d，β 1 ,β 2 Represents a constant exponent power satisfying a constraint, and beta 1 ＞1,0＜β 2 < 1, observed variable z 1 ,z 2 Representing intermediate variables, respectivelyLumped disturbance omega (·) estimation;
s3, designing a self-adaptive auxiliary system based on the designed fixed time lumped observer; the self-adaptive auxiliary system designed in the step S3 is specifically as follows:
wherein χ is 1 ＝[χ 1,u χ 1,v χ 1,r ] T ,χ 2 ＝[χ 2,u χ 2,v χ 2,r ] T Representing auxiliary variables, c 1 ,c 2 Represents a suitable parameter matrix, Δτ=τ c -τ，τ c And τ represents control input irrespective of actuator constraints and actuator constraints, respectively;
s4, designing a rapid nonsingular terminal sliding mode based on the designed self-adaptive auxiliary system;
s5, designing a model-free fixed time accurate tracking control strategy based on the fixed time lumped observer, the self-adaptive auxiliary system and the rapid nonsingular terminal sliding mode designed in the steps S2-S4.
2. The unmanned ship model-free fixed time precise track tracking control method according to claim 1, wherein the step S4 specifically comprises:
s41, designing a fixed-time rapid nonsingular terminal sliding mode, wherein the fixed-time rapid nonsingular terminal sliding mode comprises the following steps:
wherein σ= [ σ ] u σ v σ r ] T ,e 1 ＝η e -χ 1 ＝[e 1,u e 1,v e 1,r ] T ，γ 1 ,γ 2 ＞0,n 1 ＞1，f(e 1 ) The expression is as follows:
wherein ε is a very small positive constant, 0 < n 2 ＜1,1＜n 3 ＜n 4 ，n 1 ,n 2 ,n 3 ,n 4 ,γ 1 ,γ 2 There is a relationship between:
s42, deriving the designed fixed-time rapid nonsingular terminal sliding mode to obtain:
wherein, can be described as:
wherein:
3. the unmanned ship model-free fixed time precise track tracking control method according to claim 2, wherein the model-free fixed time precise track tracking control strategy designed in the step S5 is specifically as follows:
wherein,α j represents a constant parameter, alpha, satisfying a certain condition j ＞0，j＝1,2,3，m 1 ,m 2 Is positive odd and satisfies m 1 ＞m 2 。
4. The unmanned ship model-free fixed time precise track tracking control method according to claim 3, wherein the step S5 further comprises introducing a variable g sat To eliminate potential jitter caused by symbol discontinuities, in particular:
wherein g sat Representing the auxiliary variables, phi, chi and sigma represent constant parameters meeting certain conditions.
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