CN113848887A - Under-actuated unmanned ship trajectory tracking control method based on MLP method - Google Patents

Abstract

The invention discloses an under-actuated unmanned ship trajectory tracking control method based on an MLP (maximum likelihood prediction) method. Modeling the under-actuated surface unmanned ship to obtain a USV kinematic model; approximating an unmodeled kinetic function by adopting a radial basis function neural network, and performing model kinetic conversion; model conversion of under-actuated dynamics is carried out, and a USV tracking error system is expanded into three orders so as to realize the relativity of cross tracking dynamics; converting the USV integrated robust finite time controller to perform finite time USV trajectory tracking; stability analysis was performed. The numerical simulation result shows that the controller not only has good tracking precision, but also has good anti-interference capability.

Description

Under-actuated unmanned ship trajectory tracking control method based on MLP method

Technical Field

The invention relates to the technical field of unmanned ship control, in particular to an under-actuated unmanned ship trajectory tracking control method based on an MLP (maximum likelihood prediction) method.

Background

Unmanned boats have great potential in a variety of marine tasks, including coastal and water area monitoring, marine observation, and military tasks. Trajectory tracking control plays an important role in accomplishing these tasks, among other automation techniques. In particular, the main core of the tracking technology is to drive the unmanned boat to cruise on a desired trajectory without the need for human intervention. However, many challenges remain for the controller designer to achieve ideal tracking performance, such as unmodeled dynamics, ocean disturbances, and existing computational resource constraints. Despite these challenges, researchers have made extensive efforts at this problem and have achieved fruitful results such as robust control, neural network control, fuzzy control, regulatory performance control, and adaptive back-stepping control.

In the ship trajectory tracking problem, the tracking performance is reduced due to external interference such as complex model dynamics and unpredictable sea disturbance and changes of internal parameters. In order to improve the control performance in an uncertain dynamic environment, the neural network is widely applied to processing the unknown dynamic environment based on the general approximate characteristics of the neural network. To this end, two conventional neural approximators are constructed using Radial Basis Function Neural Networks (RBFNNs) to compensate for the unknown dynamics. However, although these methods can effectively alleviate the adverse effects caused by unknown dynamics, the node weight identification requires a large amount of computing resources, which not only increases the computing complexity of the system, but also reduces the running speed of the algorithm. Fortunately, the Minimum Learning Parameter (MLP) technique is an effective approach to solve this problem. Thus, MLP-based algorithms have successfully implemented unknown dynamic estimates in surface vessel path tracking control, trajectory tracking control, and formation control problems. The present invention will employ an MLP-based approximation technique for uncertainty estimation.

The above method, while effective, is only achieved with asymptotic stabilization. For vessels performing tracking tasks in harsh environments, limited time stability is always essential due to their performance. Compared with the asymptotic control method, the finite time controller not only can provide faster convergence speed and higher tracking precision, but also can stabilize the whole tracking system at an early stage to resist external interference. By reverting to the back-stepping design approach, trace tracking for a limited time can be accomplished with the desired accuracy. However, although these methods have better performance than asymptotically stable systems, the control system introduces the complexity explosion problem of complex structures. Due to the inherent problem of backstepping, the terminal SMC-based method is more suitable for tracking tasks in engineering implementation.

It is noted that most of the above results are for fully driven boats, not for unmanned boats with insufficient drive. Therefore, these algorithms will no longer be valid for USVs. Integration of USV controllers is more challenging and complex than the full-drive type due to the problem of model underdrive in lateral dynamics. In existing studies, models need to be transformed to achieve a relative degree of model dynamics in order to accomplish the USV tracking task. For example, a yaw guidance method, a diagonal transformation method, and a lateral function method are designed for this purpose. As a result of the model transformation, the synthesis of the controller is inevitably split into two independent channels (surge and yaw). Under the premise, not only the design complexity is increased, but also the use of backstepping design cannot be avoided, so that the methods are not suitable for engineering realization facing simplicity. In practical applications, it is important to design the tracking controller without separating the initial system into two subsystems, position tracking and height tracking. To date, it remains a challenge how to design a tracking controller in a comprehensive manner, taking into account limited time stability. At present, no relevant control scheme is reported in the existing literature.

Disclosure of Invention

In order to ensure that the unmanned ship has good tracking performance when unmodeled dynamics and interference occur, the controller design of surge motion and yaw motion is integrated by constructing a model transformation method. By adopting a sliding mode control method, the limited time stability of the system is ensured under the condition of not carrying out any backstepping design.

The invention provides an under-actuated unmanned ship trajectory tracking control method based on an MLP (maximum likelihood prediction) method, which provides the following technical scheme:

an under-actuated unmanned ship trajectory tracking control method based on an MLP method comprises the following steps:

step 1: modeling the under-actuated surface unmanned ship to obtain a USV kinematic model;

step 2: approximating an unmodeled kinetic function by adopting a radial basis function neural network, and performing model kinetic conversion;

and step 3: model conversion of under-actuated dynamics is carried out, and a USV tracking error system is expanded into three orders so as to realize the relativity of cross tracking dynamics;

and 4, step 4: converting the USV integrated robust finite time controller to perform finite time USV trajectory tracking;

and 5: stability analysis was performed.

Preferably, the step 1 specifically comprises:

defining the expected trajectory of the USV on a horizontal plane according to the fixed earth coordinate O_EX_EY_EAnd fixed object coordinate O_BX_BY_BDescribing the motion of the USV, the kinematic model of the USV at these two coordinates is:

wherein x, y represent the position of the USV,

representing a yaw angle; u, v and r are each independently of O_BX_BY_BThe relevant longitudinal speed, roll speed and yaw speed;

the dynamic model of the USV is described as follows:

in the formula, m_iiWhere i is 1,2,3 is the normal number of the inertia mass of the ship, and τ_uAnd τ_rFor control input, τ_ud,τ_vdAnd τ_rdRespectively representing unknown time-varying external disturbance caused by ocean current, wind and wave, and nonlinear hydrodynamic damping h_iI ═ u, v, r, represented by the following formula:

wherein, X_(·),Y_(·)And N_(·)Linear and secondary hydrokinetic coefficients representing surge, yaw and yaw motions, respectively.

Preferably, the step 2 specifically comprises:

radial basis function neural networks are used to approximate unmodeled kinetic functions, unknown smooth functions

The approximation is:

wherein W ═ W₁,w₂，…,w_m]^TIs a weight vector, m is the number of ganglion points, vector X_n＝[x₁,x₂,...,x_n]^TRepresenting the network input, and recording the approximate error as o;

gaussian function xi (X)_n)＝[ξ₁(X_n),ξ₂(X_n),...,ξ_n(X_n)]^TRepresented by the formula:

wherein, c_i,i＝1,.., m is a column vector representing X_nCentral distribution of (b) < beta >_iIs representative of xi_i(X_n) Is measured.

Preferably, the step 3 specifically comprises:

for a given smooth reference trajectory η_d＝(x_d,y_d) The tracking error is defined as:

the derivation can be:

calculating to obtain a derivative:

wherein the coupling term f_uIs defined as f_u＝(m₂₂vr-h_u)/m₁₁

To obtain a second order system, two auxiliary variables are constructed as follows:

to obtain e₂(x) Derivative of (a):

according to

The above equation is rewritten as:

g and F are redefined as G ═ G₂,F＝F₂(ii) a The expressions for d and Q are:

a second-order system is obtained, and through the application of the system, xi is converted_uWith an initial value xi_u(0) Integrating at 0 to obtain the actual propulsion τ of the USV_u。

Preferably, the step 4 specifically includes:

in order to facilitate the integration of the integrated controller, the following sliding mode manifold is constructed:

S＝e₂+k₁e₁+k₂H(e₁)

wherein k1, k2 are positive tuning gains k1>0, k2> 0;

vector H (e)₁) Represents the switching function, the expression is as follows

Wherein eta is_iI is 1,2 is a design control parameter, 0 < eta_i＜1，δ_iIs defined as

By the above formula, the controller of the USV is integrated into one channel, introducing a non-linear function H (e)₁) To avoid singularities when the system approaches the equilibrium point, the following results are obtained:

wherein,

as follows:

the hydrodynamic term F and the synthetic external disturbance d are assumed to be unknown a priori, and the unmodeled dynamics F can be approximated by the following neural network:

wherein,

for the weight matrix of the network, n >0 is the number of the designed ganglion points, xi_n×1(X_n)＝[ξ₁(X_n),ξ₂(X_n),...,ξ_n(X_n)]^TIs a vector of Gaussian function, X_n＝[u,v,r]^TIs an approximate error vector.

Preferably, the step 5 specifically comprises:

setting a Lyapunov function:

wherein,

and

calculate V₁The time derivative of (a) is:

substituting to obtain:

for any initial value

Calculate out

Also, in

On the premise of (A) under the condition of (B),

using, the following inequality is obtained:

-g(·)S^T tanh(g(·)S)≤-g(·)||S||+2ε

wherein ε. 0.2785 and g (. cndot.) represent a set

Combining the above formula:

wherein, K₁＝min{2,γ₁γ₂,γ₃γ₄}，

S and estimation error

Are consistent and ultimately bounded;

presence of unknown constants

Satisfy the requirement of

And

on this basis, the following Lyapunov function was constructed to verify the finite time convergence rate of S:

can be calculated as:

the upper bound of μ and R is

And

with an unknown variable epsilon_μ≥0,ε_RNot less than 0

Combining these properties, one can obtain:

to give out

Due to the fact that

Coupling term

And

the development was as follows:

finally, combining the above equation yields:

wherein:

the invention has the following beneficial effects:

the invention ensures that the unmanned ship has good tracking performance when unmodeled dynamics and interference occur. In the current literature, a backstepping design is indispensable for the development of controllers. Unlike this design, the integration is done in an integrated manner, rather than splitting it into two subsystems, thus avoiding the use of a back-stepping design. Therefore, the result structure of the user can be more concise and is more suitable for practice.

Compared with an asymptotic method, the finite time stability of the tracking system can be ensured, and the method has higher robustness to unknown dynamics. Furthermore, only one MLP approximator is needed to identify unmodeled dynamics, which is completely different from the two existing MLP approximators. Aiming at the problem of design of an unmanned submarine limited time trajectory tracking controller with inaccessible system dynamics and interference, a comprehensive solution is provided. By constructing a model transformation method, the controller designs of the surge motion and the yaw motion are integrated. By adopting a sliding mode control method, the limited time stability of the system is ensured under the condition of not carrying out any backstepping design. The numerical simulation result shows that the controller not only has good tracking precision, but also has good anti-interference capability.

Drawings

FIG. 1 is a coordinate definition of the USV's motion in the horizontal plane;

FIG. 2 is a conversion process;

FIG. 3 is a control structure of the sliding mode controller;

FIG. 4 is a time response of location trajectories under scenario I and scenario II;

FIG. 5 shows tracking errors x for scenario one and scenario two_e(a) And y_e(b)；

FIG. 6 shows that in scenario one and scenario two, the time response of the controller is ξ_u(a)，τ_u(b)，τ_r(c) And the velocity of the USV u (d), v (e), r (f);

FIG. 7 time response delay acquisition

And estimation under a scene

I and II;

FIG. 8 is a time response of a position trajectory under different control schemes;

FIG. 9 is a plan view ofUnder the same control scheme, the tracking error x_e(a) And y_e(b) Time response of (d);

FIG. 10 shows the controller output τ under different control schemes_u(a)，τ_r(b) And time responses of USV velocities u (c), v (d), r (e).

Detailed Description

The present invention will be described in detail with reference to specific examples.

The first embodiment is as follows:

as shown in fig. 1 to 10, the present invention provides an under-actuated unmanned ship trajectory tracking control method based on an MLP method, including the following steps:

step 1: modeling the under-actuated surface unmanned ship to obtain a USV kinematic model;

the step 1 specifically comprises the following steps:

defining the desired trajectory of the USV on a horizontal plane, FIG. 1 defines two coordinates to describe the motion of the USV, according to the fixed earth coordinate O_EX_EY_EAnd fixed object coordinate O_BX_BY_BDescribing the motion of the USV, the kinematic model of the USV at these two coordinates is:

wherein x, y represent the position of the USV,

representing a yaw angle; u, v and r are each independently of O_BX_BY_BThe relevant longitudinal speed, roll speed and yaw speed;

the dynamic model of the USV is described as follows:

in the formula, m_iiWhere i is 1,2,3 is the normal number of the inertia mass of the ship, and τ_uAnd τ_rFor control input, τ_ud,τ_vdAnd τ_rdRespectively representing unknown time-varying external disturbance caused by ocean current, wind and wave, and nonlinear hydrodynamic damping h_iI ═ u, v, r, represented by the following formula:

wherein, X_(·),Y_(·)And N_(·)Linear and secondary hydrokinetic coefficients representing surge, yaw and yaw motions, respectively.

It should be noted that in model dynamics, there are only two control inputs τ_uAnd τ_rAnd the control force in terms of sway is not provided. Thus, the USV described herein is under-driven. In the problem of track tracking control of the unmanned submarine, the difficulty is how to eliminate the cross tracking error with uncontrollable swing dynamics. The control problem of under-actuated USVs is more challenging than that of fully-actuated USVs.

In engineering applications, unmanned boats are often designed to be under-actuated due to the high cost of installing the thrust cross-over, and the impact on the hydrodynamic performance of the hull at high speeds. In practice, marine missions generally require only propulsion and yaw moments. This means that the contribution of this work will be a meaningful practice.

Hydrodynamic coefficient d of unmanned ship_iiAnd i is 1,2 and 3 composed of several hydrodynamic terms such as potential energy damping, wave-floating damping and surface friction. Therefore, it is a great challenge to accurately acquire such information in practice. In this context, d_iiI 1,2,3 is unknown to the controller designer.

Step 2: approximating an unmodeled kinetic function by adopting a radial basis function neural network, and performing model kinetic conversion;

the step 2 specifically comprises the following steps:

radial basis function neural networks are used to approximate unmodeled kinetic functions, unknown smooth functions

The approximation is:

wherein W ═ W₁,w₂，…,w_m]^TIs a weight vector, m is the number of ganglion points, vector X_n＝[x₁,x₂,...,x_n]^TRepresenting the network input, and recording the approximate error as o;

gaussian function xi (X)_n)＝[ξ₁(X_n),ξ₂(X_n),...,ξ_n(X_n)]^TRepresented by the formula:

wherein, c_iI 1.. m is a column vector representing X_nCentral distribution of (b) < beta >_iIs representative of xi_i(X_n) Is measured.

For scalar b, sign (b) represents the sign function, | b | represents its absolute value, sig^η(·)＝|·|^ηsign (·). For vector v ═ v₁,v₂,...,v_n]^T,

Represents the Euclidean norm sig of the same^η(v)＝[sig^η(v₁),sig^η(v₂),...,sig^η(v_n)]. For matrix a, det (a) represents its determinant.

Assumption 1. for inertial mass in the above equation, assume m₁₁≠m₂₂This is always true.

Assume 2. for the USV, the surge velocity u is a non-zero velocity, and u, v, r are all defined in a tight set with known boundaries.

Hypothesis 3. external disturbance τ_ud，τ_rdIs time-varying continuously differentiable. The external disturbance and its time derivative,

bounded sum | τ_ud·≤D_u,|τ_rd|≤D_r,

D_u,D_r,D_uu,D_rrIs an unknown positive constant.

Note 4. for a vessel, the inertial mass is determined by the platform displacement m and the additional mass Δ m_iiI is 1,2,3, i.e. m_ii＝m+Δm_ii. The additional mass is the inherent hydrodynamic properties of the object in a fluid environment, determined primarily by the hull shape and direction of motion. Therefore, we can always obtain Δ m₁₁≠Δm₂₂The unmanned surface vehicle. Thus, assume 1 holds.

Theory 1 in arbitrary x_iE R, i ═ 1,2]The following attributes hold:

lemma 2 considers the system

If a Lyapunov function V (x) exists, the scalar α e (0,1), ρ >0, Δ e (0, + ∞) satisfies V (x ≦ - ρ V^α(x) + Δ, the system is actually stabilized by a finite time (PFTS) and state x can converge to zero in a small neighborhood within a finite time.

Lem 3 for any μ >0, the following inequality holds:

lemma 4 RBFNNs defined in (4), there are always satisfied

Such that:

in order to overcome the obstacle caused by model underactuation in the transverse dynamics, the USV tracking error system is firstly expanded to three orders so as to realize the relativity of cross tracking dynamics. Two auxiliary variables are then defined to determine the feasibility of the sliding mode control method. Fig. 2 summarizes the architecture of the conversion process.

And step 3: model conversion of under-actuated dynamics is carried out, and a USV tracking error system is expanded into three orders so as to realize the relativity of cross tracking dynamics;

the step 3 specifically comprises the following steps:

for a given smooth reference trajectory η_d＝(x_d,y_d) The tracking error is defined as:

the derivation can be:

calculating to obtain a derivative:

wherein the coupling term f_uIs defined as f_u＝(m₂₂vr-h_u)/m₁₁

Due to G₁Is singular and it is not possible for the designer to synthesize the controller directly. In prior approaches, this obstacle was typically addressed by splitting the controller design into two channels through appropriate model transformations. Furthermore, these methods require a back-stepping design to achieve the virtual speed. Therefore, these methods are complex for engineering applications. Completely different from the existing USV model conversion method, a new integration method is deduced in the subsequent design.

Under hypothesis 1 and hypothesis 2, we have m₁₁≠m₂₂And u ≠ 0. Thus, G₂Is reversible, enabling the design of integrated controllers. However, the transformed system is a three-order system, and sliding mode control cannot be directly performed. Therefore, an additional conversion is required to reduce the order of the resulting system.

To obtain a second order system, two auxiliary variables are constructed as follows:

to obtain e₂(x) Derivative of (a):

according to

The above equation is rewritten as:

g and F are redefined as G ═ G₂,F＝F₂(ii) a The expressions for d and Q are:

a second-order system is obtained, and through the application of the system, xi is converted_uWith an initial value xi_u(0) Integrating at 0 to obtain the actual propulsion τ of the USV_u。

A second order system is obtained. Through the application of the system, xi is_uWith an initial value xi_u(0) The actual propulsion force τ of the USV can be obtained by integrating 0_u. In this way, the SMC-based integrated design method can be applied to USVs without any back-stepping design.

The converted dynamics are used here to develop the controller. On the basis of this equation, e is given₁And e₂Has the property of limited time convergence. The method adopts an integrated design method, integrates the controllers of surge motion and yaw motion in a single-channel design, does not carry out backstepping design, and designs a finite-time USV trajectory tracking controller based on a neural network. And the MLP technology is adopted to approximate unmodeled dynamics, so that the calculation complexity is low. The overall control strategy is shown in fig. 3.

And 4, step 4: converting the USV integrated robust finite time controller to perform finite time USV trajectory tracking;

the step 4 specifically comprises the following steps:

in order to facilitate the integration of the integrated controller, the following sliding mode manifold is constructed:

S＝e₂+k₁e₁+k₂H(e₁)

wherein k1, k2 are positive tuning gains k1>0, k2> 0;

vector H (e)₁) Represents the switching function, the expression is as follows

Wherein eta is_iI is 1,2 is a design control parameter, 0 < eta_i＜1，δ_iIs defined as

By the above equation, the controller design of the USV of the present invention is integrated into only one channel, rather than integrating it into two separate channels. Compared with the existing SMC method for USV, the SMC method disclosed herein can guarantee tracking error vector e₁And the method converges to a small set close to zero in a limited time, and a backstepping design is not needed. In addition, a non-linear function H (e) is introduced in the design₁) To avoid the singular problem when the system approaches the equilibrium point.

Further, the following results were obtained:

wherein

As follows.

To make our results more practical to implement, both the hydrodynamic term F and the integrated external disturbance d are assumed to be unknown a priori. From the above, the unmodeled dynamic F can be approximated with the following neural network:

wherein,

for the weight matrix of the network, n >0 is the number of the designed ganglion points, xi_n×1(X_n)＝[ξ₁(X_n),ξ₂(X_n),...,ξ_n(X_n)]^TIs a vector of Gaussian function, X_n＝[u,v,r]^TIs an approximate error vector.

From the engineering perspective, the model fluid dynamics of the USV has strong correlation with the state thereof, and the external disturbance has the characteristics of randomness and high nonlinearity. In other words, if we use a neural network to identify external disturbances, it may lead to a worse approximation result. Thus, only the model fluid dynamics are identified by the neural network, and external disturbances will be compensated by the robust design in the subsequent environment.

For neural network based approximators, there are:

wherein psi (X)_n) And μ and o denote the gaussian function vector ξ (X)_n) The weight matrix and the euclidean norm of the approximate error vector o. To guarantee the limited time stability of S, the following control inputs are proposed:

wherein R ═ o + d represents a combination of unknowns.

And

the estimates for R and μ, respectively, are as follows:

and 5: stability analysis was performed.

In order to prove the boundedness of the sliding mode manifold signal and the estimation signal, the step 5 is specifically as follows:

setting a Lyapunov function:

wherein,

and

calculate V₁The time derivative of (a) is:

substituting to obtain:

for any initial value

Calculate out

Also, in

On the premise of (A) under the condition of (B),

using, the following inequality is obtained:

-g(·)S^T tanh(g(·)S)≤-g(·)||S||+2ε

wherein ε. 0.2785 and g (. cndot.) represent a set

Combining the above formula:

wherein, K₁＝min{2,γ₁γ₂,γ₃γ₄}，

S and estimation error

Are consistent and ultimately bounded;

presence of unknown constants

Satisfy the requirement of

And

on this basis, the following Lyapunov function was constructed to verify the finite time convergence rate of S:

can be calculated as:

the upper bound of μ and R is

And

with an unknown variable epsilon_μ≥0,ε_RNot less than 0

Combining these properties, one can obtain:

to give out

Due to the fact that

Coupling term

And

the development was as follows:

finally, combining the above equation yields:

wherein:

according to lemma 2, we verified that S is PFTS, and

is formed where_iIs a very small normal number.

Thus, the certification of item 1 has been completed.

From the above expression, we can assume that the condition S always exists_1i＝Θ_i＜Δ_iAnd Θ_iIs more than or equal to 0. Thus, for the converted error signal e_1iThe method comprises the following steps:

Θ_i＝e_2i+k₁e_1i+k₂H(e_1i)

it is noted that

Then there are:

the following Lyapunov function is then defined:

reviewing the previous definition, V can be derived_3iFirst time derivative of (d):

based on the above formula, we divide the discussion into the following two cases:

1. when | e_1i|≥δ_iWhen it is established, obtain

Due to k₁＞1，0＜η_i＜1，e₁₁,e₁₂Is the PFTS of lemma 3. Then, if e_1iConverge to (-delta i, delta)_i) Which will lead to the following discussion.

2. When | e_1i|＜δ_iWhen true, the above equation can be written as:

wherein,

over-solved differential inequality

Comprises the following steps:

this means that when the time goes to infinity, V_3iWill converge to

This means that e₁Will converge on

At this time, the proof of point (2) is completed.

Then, to prove (3) of theorem 1, the following Lyapunov function is constructed:

considering the definition in the above formula, there are

V₃The time derivative of (d) can be derived as:

since e is proved₁Is consistent and finally bounded, there is one satisfy | | | e₁||²A small normal number Λ less than or equal to Λ. The combination of the above formula can result in:

thus, V can be obtained by the above formula₄≤(V₄(0)-4Λ)e^-Λt+4 Λ. Demonstrating a tracking error state x_eAnd y_eIs consistent and ultimately bounded. This completes the proof of theorem 1.

Simulation result

The effectiveness and performance of the proposed algorithm is verified here by some numerical simulation experiments. First, the feasibility and robustness of the proposed control strategy was verified in two different perturbation situations. Then, the superiority of the method is demonstrated by comparative experiments with the application of the algorithm. The detailed results of the above experiments will be described later. The control parameter of the developed algorithm is chosen as k₁＝12,k₂＝3,η₁＝η₂0.8. Adaptive parameter selection as gamma₁＝γ₃＝0.01,γ₄＝γ₅0.5. The neural network is composed of 30 nodes, and the centers ci are uniformly distributed in [ -1,3.5 ]]×[-1,3.5]×[-3,3]Upper, width beta_i＝0.6. The initial value of the estimator is set to

The simulated vessel model parameters are shown in table 1.

TABLE 1 USV model parameters

Comparison results under different external disturbances

And simulation results under different disturbances are given. The simulation scenario is as follows:

scheme I tau_ud＝0.05sin(0.1t)-0.05,τ_vd＝0.05cos(0.1t)-0.05,τ_rd＝0.05sin(0.1t)-0.05

Scheme II τ_ud＝0.5sin(0.1t)-0.5,τ_vd＝0.5cos(0.1t)-0.5,τ_rd＝0.5sin(0.1t)-0.5

TABLE 2 definition of reference trajectories

For better illustration, the desired trajectory is shown in table 2, where ω ═ 0.04 denotes the custom determined angular velocity of the circular trajectory, T₁1.5 pi/omega and T ₂2/ω is the auxiliary movement moment. The initial condition of the USV state is as

And [ u (0), v (0), r (0)]^T＝[0.01,0.01,0.01]^T。

Fig. 4 and 5 depict the temporal response and tracking error of the trajectories under scene one and scene two, respectively. From an observation of these two figures, we can see that the solution herein enables even in the presence of large perturbationsProviding excellent tracking task performance. In addition, the limited time stability of the tracking system is shown in fig. 5, and all tracking errors are stable within t 15 s. For better performance of steady state performance, the so-called Root Mean Square (RMS) indicator and position error

As shown in table 5. It is clear that the RMS index decreases with time. From the results in both cases, it can be seen that the whole system maintains high robustness against external interference. The controller outputs and USV states are shown in fig. 6. From these pictures we can see that the actuator is buffeting free throughout the tracking task. In addition, when the desired trajectory changes from a straight line to a curved line, the control output may be adaptively changed to ensure control performance. Fig. 7 gives an estimate of the unknown parameters, which remains bounded at all times. The simulation result verifies the validity of theorem 1.

TABLE 3 position error time series under disturbance ρ_eAnd root mean square index thereof

To eliminate the effect of large initial tracking errors, the RMS indices in table 3 are accumulated after the tracking error has stabilized. The following simulation case employed the same RMS index calculation strategy.

Comparing results between different controllers

Comparison results and comparison between different controllers in experiments medium and long term planning proposed to establish a tracking controller (DE-MRC) and a transverse function based adaptive neural network controller (TF-ANNC). For the DE-MRC method, the controller parameters are kept consistent with the previous section. For the sake of brevity, reference will be made to trajectories

The simplification is as follows:

wherein

The reference yaw angle required for the TF-ANNC.

TABLE 4 position error time series ρ under different algorithms_eAnd root mean square index thereof

TABLE 5 calculation loads of DE-MRC and TF-ANNC methods

In the comparative simulation, the external disturbances and initial states of the USV are the same as for scenario i, and it is noted that only the necessary data are given below. The time response and tracking error of the position trajectory are shown in fig. 8 and 9, respectively. It can be seen that DE-MRC has better control performance in both transient response and steady state maintenance. Table 4 lists some more specific performance indicators, including RMS indicator and position error ρ_e. To show the reduction of computational complexity by the MLP algorithm, the computational load of the DE-MRC and TF-ANNC methods is listed in Table 5. Thus, it can be seen that the computational load is greatly reduced. The controller output and USV speed are plotted in fig. 10. The result shows that the DE-MRC method has better control precision and lower energy consumption.

The above description is only a preferred embodiment of the under-actuated unmanned ship trajectory tracking control method based on the MLP method, and the protection range of the under-actuated unmanned ship trajectory tracking control method based on the MLP method is not limited to the above embodiments, and all technical solutions belonging to the idea belong to the protection range of the present invention. It should be noted that modifications and variations which do not depart from the gist of the invention will be those skilled in the art to which the invention pertains and which are intended to be within the scope of the invention.

Claims (6)

1. An under-actuated unmanned ship trajectory tracking control method based on an MLP method is characterized by comprising the following steps: the method comprises the following steps:

step 1: modeling the under-actuated surface unmanned ship to obtain a USV kinematic model;

step 2: approximating an unmodeled kinetic function by adopting a radial basis function neural network, and performing model kinetic conversion;

and step 3: model conversion of under-actuated dynamics is carried out, and a USV tracking error system is expanded into three orders so as to realize the relativity of cross tracking dynamics;

and 4, step 4: converting the USV integrated robust finite time controller to perform finite time USV trajectory tracking;

and 5: stability analysis was performed.

2. The MLP method-based under-actuated unmanned ship trajectory tracking control method as claimed in claim 1, wherein: the step 1 specifically comprises the following steps:

defining the expected trajectory of the USV on a horizontal plane according to the fixed earth coordinate O_EX_EY_EAnd fixed object coordinate O_BX_BY_BDescribing the motion of the USV, the kinematic model of the USV at these two coordinates is:

wherein x, y represent the position of the USV,

representing a yaw angle; u, v and r are each independently of O_BX_BY_BTo aLongitudinal speed, yaw rate and yaw rate;

the dynamic model of the USV is described as follows:

in the formula, m_iiWhere i is 1,2,3 is the normal number of the inertia mass of the ship, and τ_uAnd τ_rFor control input, τ_ud,τ_vdAnd τ_rdRespectively representing unknown time-varying external disturbance caused by ocean current, wind and wave, and nonlinear hydrodynamic damping h_iI ═ u, v, r, represented by the following formula:

wherein, X_(·),Y_(·)And N_(·)Linear and secondary hydrokinetic coefficients representing surge, yaw and yaw motions, respectively.

3. The MLP method-based under-actuated unmanned ship trajectory tracking control method as claimed in claim 2, wherein: the step 2 specifically comprises the following steps:

radial basis function neural networks are used to approximate unmodeled kinetic functions, unknown smooth functions

The approximation is:

wherein W ═ W₁,w₂，…,w_m]^TIs a weight vector, m is the number of ganglion points, vector X_n＝[x₁,x₂,...,x_n]^TRepresenting the network input, and recording the approximate error as o;

gaussian function xi (X)_n)＝[ξ₁(X_n),ξ₂(X_n),...,ξ_n(X_n)]^TRepresented by the formula:

wherein, c_iI 1.. m is a column vector representing X_nCentral distribution of (b) < beta >_iIs representative of xi_i(X_n) Is measured.

4. The MLP method-based under-actuated unmanned ship trajectory tracking control method as claimed in claim 3, wherein: the step 3 specifically comprises the following steps:

for a given smooth reference trajectory η_d＝(x_d,y_d) The tracking error is defined as:

the derivation can be:

calculating to obtain a derivative:

wherein the coupling term f_uIs defined as f_u＝(m₂₂vr-h_u)/m₁₁

To obtain a second order system, two auxiliary variables are constructed as follows:

to obtain e₂(x) Derivative of (a):

according to

The above equation is rewritten as:

g and F are redefined as G ═ G₂,F＝F₂(ii) a The expressions for d and Q are:

a second-order system is obtained, and through the application of the system, xi is converted_uWith an initial value xi_u(0) Integrating at 0 to obtain the actual propulsion τ of the USV_u。

5. The MLP method-based under-actuated unmanned ship trajectory tracking control method as claimed in claim 4, wherein: the step 4 specifically comprises the following steps:

in order to facilitate the integration of the integrated controller, the following sliding mode manifold is constructed:

S＝e₂+k₁e₁+k₂H(e₁)

wherein k1, k2 are positive tuning gains k1>0, k2> 0;

vector H (e)₁) Represents the switching function, the expression is as follows

Wherein eta is_iI is 1,2 is a design control parameter, 0 < eta_i＜1，δ_iIs defined as

By the above formula, the controller of the USV is integrated into one channel, introducing a non-linear function H (e)₁) To avoid singularities when the system approaches the equilibrium point, the following results are obtained:

wherein,

as follows:

the hydrodynamic term F and the synthetic external disturbance d are assumed to be unknown a priori, and the unmodeled dynamics F can be approximated by the following neural network:

wherein,

for the weight matrix of the network, n >0 is the number of the designed ganglion points, xi_n×1(X_n)＝[ξ₁(X_n),ξ₂(X_n),...,ξ_n(X_n)]^TIs a vector of Gaussian function, X_n＝[u,v,r]^TIs an approximate error vector.

6. The MLP method-based under-actuated unmanned ship trajectory tracking control method as claimed in claim 5, wherein: the step 5 specifically comprises the following steps:

setting a Lyapunov function:

wherein,

and

calculate V₁The time derivative of (a) is:

substituting to obtain:

for any initial value

Calculate out

Also, in

On the premise of (A) under the condition of (B),

using, the following inequality is obtained:

-g(·)S^Ttanh(g(·)S)≤-g(·)||S||+2ε

wherein ε. 0.2785 and g (. cndot.) represent a set

Combining the above formula:

wherein, K₁＝min{2,γ₁γ₂,γ₃γ₄}，

，

S and estimation error

Are consistent and ultimately bounded;

presence of unknown constants

Satisfy the requirement of

And

on this basis, the following Lyapunov function was constructed to verify the finite time convergence rate of S:

can be calculated as:

the upper bound of μ and R is

And

with an unknown variable epsilon_μ≥0,ε_RNot less than 0

Combining these properties, one can obtain:

to give out

Due to the fact that

Coupling term

And

the development was as follows:

finally, combining the above equation yields:

wherein:

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