An unmanned ship course tracking control method with state / input quantization

Abstract

The application provides an unmanned ship course tracking control method with state / input quantization, which comprises the following steps: a system control law is designed based on a backstepping method, and a dynamic surface technology is combined to reduce the calculation amount expansion problem of a virtual control law; an extended state observer is used to estimate uncertain terms and external disturbances in the control system; a uniform quantizer is used to quantize state variables and control inputs in the control system respectively, and the quantized state feedback information is only used for tracking control; an unmanned ship course controller based on the extended state observer is designed by using the quantized state recursion, and the unmanned ship course with state quantization and input quantization is tracked. The technical scheme of the application solves the problem of the unmanned ship course tracking with state quantization and input quantization by designing the unmanned ship course controller based on the extended state observer in view of the problem that the marine communication of the water surface unmanned ship is limited.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to an unmanned ship heading tracking control method with state / input quantization. Background Art

[0002] With the rapid development of smart navigation technology, unmanned surface vehicles (USVs) have garnered widespread attention. These intelligent, remotely controlled or autonomous unmanned ocean transport platforms are valuable for their ability to balance safety and economic efficiency while operating in complex marine environments.

[0003] As a key technology for unmanned vessels, ship heading control has long been a research focus and hotspot. However, most studies have focused solely on enhancing the accuracy, stability, and robustness of ship heading tracking control. In maritime practice, control signals must be transmitted via communication channels. Given the limited bandwidth of maritime communications, ship heading tracking control with input and state quantization is more practical to ensure system operation within a given bandwidth.

[0004] Quantization is the process of converting a continuous signal into a set of discrete symbols or integer values. In ship heading control systems, subjectively quantizing control inputs can not only reduce the burden of signal transmission and the frequency of steering gear execution, but also reduce the steering amplitude, thus better aligning with the control laws of steering gear servo systems in maritime practice. Quantizing system signals can reduce the burden of signal transmission, but because quantization approximates the data, it inevitably produces quantization errors, which can accumulate over time. When the error is excessive, it can lead to reduced tracking performance and decreased control system stability. Therefore, analyzing quantization errors is particularly important. Research on quantitative feedback control and quantization errors has received widespread attention. However, theoretical research results on quantitative feedback heading tracking control for unmanned ships with state quantization and input quantization are currently lacking. Summary of the Invention

[0005] In response to the aforementioned technical issues surrounding limited communication bandwidth in maritime practice, the present invention addresses the problem of unmanned vessel heading tracking control with state and input quantization. This method reduces the signal transmission burden and actuator execution frequency, further aligning with the control principles of steering servo systems in maritime practice. A quantitative feedback tracking controller based on the extended state observer is designed to ensure that the unmanned vessel tracks the desired heading while also estimating unknown disturbances and system uncertainties.

[0006] The technical means adopted in the present invention are as follows:

[0007] An unmanned ship heading tracking control method with state / input quantization, comprising:

[0008] S1, a system control law is designed based on a backstepping method, and an extended state observer is used to estimate the uncertain terms and external disturbances in the control system;

[0009] S2, a uniform quantizer is used to quantize the state variables and control inputs in the control system respectively, and the quantized state feedback information is only used for tracking control;

[0010] S3, an unmanned ship heading controller based on the extended state observer is designed using the quantized state recursion, and the boundedness of the error between the quantized variables and the non-quantized variables in the closed-loop control system is proved;

[0011] S4, based on Lyapunov stability theory, it is proved that the stability of the designed unmanned ship heading tracking control system with state quantization and input quantization is considered.

[0012] Further, the step S1 specifically comprises:

[0013] S11, a mathematical model of unmanned ship heading control is constructed, as shown below:

[0014]

[0015] Wherein, ψ is the ship heading angle, r is the ship yaw angle velocity; δ is the ship rudder angle, ω is the unknown disturbance of the system, a1=-1 / T, a2=-a / T, a is the nonlinear coefficient of Norrbin motion model, b=K / Τ is the gain of the control system, K is the turning index of the ship, T1, T2, T3 are the following indexes of the ship, T=T1+T2+T3; τ is the system control input;

[0016] S12, (ψ, r) is selected as the state variable, and x1=ψ is defined, f(x,t)=a1r+a2r 3 +ω, τ=δ is selected, τ represents the system control input, Q(τ) represents the quantized control input of the system; Quantization will convert continuous signals into piecewise constant signals, so the mathematical model of unmanned ship heading control after input quantization is introduced, as shown below:

[0017]

[0018] S13, define the error surface as follows:

[0019] η1=x1-x 1d

[0020] Wherein, x 1dis the expected heading signal;

[0021] S14. Define the error surface as follows:

[0022] η2=x2-α

[0023] Among them, α is a virtual signal The filtered signal;

[0024] S15. Select a first-order low-pass filter as shown below:

[0025]

[0026] in, is the filtering parameter of the first-order low-pass filter, which is a positive constant;

[0027] S16, error surface η1 = x1-x 1d Taking the derivative, we get:

[0028]

[0029] Select virtual signal As shown below:

[0030]

[0031] Where c1 is a positive constant;

[0032] In the inverse design, if Will lead to Time differential explosion, based on dynamic surface technology, will Input a first-order low-pass filter to get the low-pass filter α, and we get:

[0033]

[0034] S17. Derivative the error surface η2 = x2 - α to obtain:

[0035]

[0036] S18. Design the extended state observer as follows:

[0037]

[0038] The designed extended state observer can realize that when t→∞, Where ε>0, is the observer state, Then ο1 is the observation error, and the polynomial Satisfy Hurwitz conditions;

[0039] S19. Design a non-quantized auxiliary control input signal as follows:

[0040]

[0041] Where c2 is a positive constant.

[0042] Furthermore, the step S2 specifically includes:

[0043] S21, using a uniform quantizer, quantize the state variables x1, x2 and the control input τ as follows:

[0044]

[0045] Among them, s = x1, x2, τ, χ>0 represents the quantization step size, L1 = χ, L i+1 =L i +χ; After quantization, the state variable and input variable s become Q(s). This process will produce a quantization error, and the quantization error sQ(s) satisfies |sQ(s)|≤χ;

[0046] S22. Assume that the quantized state variables Q(x1) and Q(x2) are used to design the control input of the system, that is, only the quantized heading angle and yaw angular velocity are used to design the controller.

[0047] Furthermore, the step S3 specifically includes:

[0048] S31. Design of an unmanned ship heading controller based on an extended state observer using quantized state recursion.

[0049] S32, considering the closed-loop system consisting of the controlled object of step S12, the low-pass filter of step S15 and the control law of step S19, the filtering error is bounded;

[0050] S33. Prove the boundedness of the observation error of the designed extended state observer;

[0051] S34. Prove the boundedness of the error surface, virtual signal, filtering error and quantization error of control input.

[0052] Furthermore, the step S31 specifically includes:

[0053] S311. The error surface and virtual signal based on the quantized state are:

[0054]

[0055]

[0056]

[0057] In the formula, the virtual signal Input the first-order low-pass filter to get the filtered signal

[0058] S312. Define the first-order low-pass filter as:

[0059]

[0060] in, is the filtering parameter of the first-order low-pass filter, which is a positive constant;

[0061] S313. Design the extended state observer as follows:

[0062]

[0063] When t→∞, Among them, ε>0, is the observer state, Then o2 is the observation error, and the polynomial Satisfy Hurwitz conditions;

[0064] S314, the quantitative feedback control input τ can be obtained:

[0065]

[0066] Furthermore, the step S32 specifically includes:

[0067] S321. Define the filtering error generated during the filtering process as:

[0068]

[0069] The error surfaces in steps S13 and S14 are derived separately to obtain:

[0070]

[0071]

[0072] Where,

[0073] S322. Define the Lyapunov function of the filtering error as:

[0074] V γ =γγ / 2

[0075]

[0076] S323. Derivative the filtering error, and we get:

[0077]

[0078] S324, there exists an upper bound function B,

[0079]

[0080] Make The maximum value of B is denoted as M, then B 2 / M 2 -1≤0, then:

[0081]

[0082] Where, when Take enough hours to ensure

[0083] Furthermore, the step S33 specifically includes:

[0084] S331: For the extended state observer in step S18, define θ = [θ1 θ2 θ3] T ,in:

[0085]

[0086]

[0087]

[0088] S332, due to Then the error state equation of the observer is:

[0089]

[0090] Where,

[0091] S333. Assume that the unknown term f(x,t) satisfies Among them, f * is a positive constant; in navigation practice, the speed and acceleration of unmanned ships have upper bounds, so the assumption is reasonable;

[0092] S334. Define the Lyapunov function of the observer as:

[0093] V O =εθ T Pθ

[0094] Where P is a symmetric positive definite matrix that satisfies the following Lyapunov equation:

[0095]

[0096] Where Q is any given symmetric positive definite matrix, then:

[0097]

[0098] Where λ min (Q) is the minimum eigenvalue of Q;

[0099] S335, by The convergence condition of the observer is:

[0100]

[0101] Among them, the smaller ε is, the faster θ converges, ||θ|| is O(ε), and as ε decreases, the observation errors o1 and o2 gradually converge.

[0102] Furthermore, the step S34 specifically includes:

[0103] S341. Define the error surface, virtual signal, filtering error, and quantization error of the control input as follows:

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111] S342, Existence Constant make Available Bounded;

[0112]

[0113] S343, Existence Constant make Available Bounded;

[0114]

[0115]

[0116] S344, from step S32, it can be seen that the filtering error is bounded, and there is a constant make

[0117] S345, Existence Constant make We can get β a Bounded;

[0118]

[0119] S346, Existence Constant make Available Bounded;

[0120]

[0121] S347, Existence Constant make Available Bounded;

[0122]

[0123] S348, Existence Constant make We can get β τ Bounded;

[0124]

[0125] Furthermore, the step S4 specifically includes:

[0126] S41. Considering heading tracking, virtual control and filtering errors, the Lyapunov function is defined as:

[0127] V S =η1 2 / 2+η2 2 / 2+γ 2 / 2

[0128] S42, when V S =p, then B is bounded, denoted as M, then B 2 / M 2 -1≤0;

[0129] S43, V S Derivative:

[0130]

[0131] Where, c1≥1+Ω2, c2≥2+Ω2, Ω2>0, Δ=(b 2 χ 2 +b 2 β τ 2+Λ) / 2, o1<Λ;

[0132]

[0133] S44, Comprehensive Consideration System

[0134]

[0135] When Ω2 is large enough and ε is small enough, it can be guaranteed that Therefore, considering the quantized closed-loop system, take V S (0)≤p,p>0, the closed-loop system error signal is uniformly bounded, and the convergence rate depends on Ω2 and the observer parameter ε.

[0136] Compared with the prior art, the present invention has the following advantages:

[0137] 1. The unmanned ship heading tracking control method with state / input quantization provided by the present invention takes into account the problem of limited communication bandwidth in navigation practice, and simultaneously considers the problems of state quantization and input quantization, thereby reducing the signal transmission burden and the execution frequency of the actuator, and is more in line with the control law of the steering gear servo system in navigation practice.

[0138] 2. In response to existing research that only considers the system input quantization or state quantization problem, the present invention proposes a quantization error consideration and closed-loop system stability determination method that is both systematic and universal, and strictly proves the boundedness of the quantization error and the closed-loop stability of the control system.

[0139] 3. This paper proposes a systematic and universal method for considering quantization errors and determining the stability of closed-loop systems. This method rigorously demonstrates the stability of the designed unmanned vessel heading tracking control system with state and input quantization. Simulation experiments validate the effectiveness of the control strategy.

[0140] Based on the above reasons, the present invention can be widely promoted in fields such as artificial intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0141] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0142] Figure 1 Flow chart of the method of the present invention.

[0143] Figure 2A simplified block diagram of the proposed quantized feedback tracking control system based on the extended state observer.

[0144] Figure 3 This is a diagram showing the tracking results of the ship's heading angle and yaw angular velocity provided by an embodiment of the present invention.

[0145] Figure 4 This is a diagram of the ship's heading angle error and yaw angular velocity error provided by an embodiment of the present invention.

[0146] Figure 5 This is a diagram of the observation results of the extended state observer provided by an embodiment of the invention.

[0147] Figure 6 A comparison diagram of control input before and after quantization provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0148] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0149] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0150] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0151] Unless otherwise specifically stated, the relative arrangement of the parts and steps, numerical expressions and numerical values ​​described in these embodiments do not limit the scope of the present invention. At the same time, it should be clear that, for ease of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship. The techniques, methods and equipment known to ordinary technicians in the relevant fields may not be discussed in detail, but where appropriate, the techniques, methods and equipment should be considered as part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that similar numbers and letters represent similar items in the following figures, so once an item is defined in one figure, it does not need to be further discussed in subsequent figures.

[0152] In the description of the present invention, it should be understood that the directions or positional relationships indicated by directional words such as "front, back, up, down, left, right", "horizontal, vertical, vertical, horizontal" and "top, bottom" are usually based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description. Unless otherwise specified, these directional words do not indicate or imply that the device or element referred to must have a specific direction or be constructed and operated in a specific direction. Therefore, they cannot be understood as limiting the scope of protection of the present invention: the directional words "inside and outside" refer to the inside and outside relative to the outline of each component itself.

[0153] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used herein to describe the spatial positional relationship of a device or feature to other devices or features as shown in the figures. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figures. For example, if the device in the drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below their position devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0154] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

[0155] like Figure 1As shown, the present invention provides an unmanned ship heading tracking control method with state / input quantization, comprising:

[0156] S1. Design the system control law based on the backstepping method and use the extended state observer to estimate the uncertainties and external disturbances in the control system;

[0157] S2, using a uniform quantizer to quantize the state variables and control inputs in the control system, and the quantized state feedback information is only used for tracking control;

[0158] S3. Design an unmanned ship heading controller based on an extended state observer using quantized state recursion, and prove the boundedness of the error between quantized and non-quantized variables in the closed-loop control system.

[0159] S4. Based on Lyapunov stability theory, the stability of the designed unmanned ship heading tracking control system with state quantization and input quantization is proved when state quantization and input quantization are considered simultaneously.

[0160] In specific implementation, as a preferred embodiment of the present invention, step S1 specifically includes:

[0161] S11. Construct a mathematical model for the heading control of an unmanned ship, as shown below:

[0162]

[0163] Where ψ is the ship's heading angle, r is the ship's yaw angular velocity, d is the ship's rudder angle, ω is the unknown system disturbance, a1 = -1 / T, a2 = -a / T, a is the nonlinear coefficient of the Norrbin motion model, b = K / Τ is the control system gain, K is the ship's turning index, T1, T2, and T3 are the ship's followability indices, T = T1 + T2 + T3; τ is the system control input. In this embodiment, the following parameters are selected: ship length of 349.8 m, ship width of 45.6 m, ship's fully loaded draft of 14.5 m, block coefficient of 0.67, and ship's initial speed of 12.86 m / s. The ship model parameters are calculated as follows: K = 0.08, T = 51.5. The nonlinear coefficient a of the Norrbin motion model is selected as 20.

[0164] S12. Select (ψ, r) as the state variable and define x1 = ψ, f(x,t)=a1r+a2r 3 +ω, select τ=δ, τ represents the system control input, Q(τ) represents the quantized control input of the system; quantization converts the continuous signal into a piecewise constant signal, so the mathematical model of the unmanned ship heading control after input quantization is introduced as follows:

[0165]

[0166] S13. Define the error surface as follows:

[0167] η1=x1-x 1d

[0168] Among them, x 1d is the expected heading signal;

[0169] S14. Define the error surface as follows:

[0170] η2=x2-α

[0171] Among them, α is a virtual signal The filtered signal;

[0172] S15. Select a first-order low-pass filter as shown below:

[0173]

[0174] in, is the filtering parameter of the first-order low-pass filter, which is a positive constant;

[0175] S16, error surface η1 = x1-x 1d Taking the derivative, we get:

[0176]

[0177] Select virtual signal As shown below:

[0178]

[0179] Where c1 is a positive constant;

[0180] In the inverse design, if Will lead to Time differential explosion, based on dynamic surface technology, will Input a first-order low-pass filter to get the low-pass filter α, and we get:

[0181]

[0182] S17. Derivative the error surface η2 = x2 - α to obtain:

[0183]

[0184] S18. Assume that the uncertain term f(x, t) is an unknown continuous function, and its time derivative exists and is bounded. Using the extended state observer to observe the unknown term can overcome the uncertainty of the model. The extended state observer is designed as follows:

[0185]

[0186] The designed extended state observer can realize that when t→∞, Where ε>0, is the observer state, Then ο1 is the observation error, and the polynomial Satisfy Hurwitz conditions;

[0187] S19. Design a non-quantized auxiliary control input signal as follows:

[0188]

[0189] Wherein, c2 is a positive constant, and the parameter c2=2 is selected.

[0190] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0191] S21, using a uniform quantizer, quantize the state variables x1, x2 and the control input τ as follows:

[0192]

[0193] Among them, s = x1, x2, τ, χ>0 represents the quantization step size, L1 = χ, L i+1 =L i +χ; After quantization, the state variable and input variable s become Q(s). This process will produce a quantization error, and the quantization error sQ(s) satisfies |sQ(s)|≤χ;

[0194] S22. Assume that the quantized state variables Q(x1) and Q(x2) are used to design the control input of the system, that is, only the quantized heading angle and yaw angular velocity are used to design the controller.

[0195] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0196] S31. Design of an unmanned ship heading controller based on an extended state observer using quantized state recursion.

[0197] S32, considering the closed-loop system consisting of the controlled object of step S12, the low-pass filter of step S15 and the control law of step S19, the filtering error is bounded;

[0198] S33. Prove the boundedness of the observation error of the designed extended state observer;

[0199] S34. Prove the boundedness of the error surface, virtual signal, filtering error and quantization error of control input.

[0200] In specific implementation, as a preferred embodiment of the present invention, step S31 specifically includes:

[0201] S311. The error surface and virtual signal based on the quantized state are:

[0202]

[0203]

[0204]

[0205] In the formula, the virtual signal Input the first-order low-pass filter to get the filtered signal

[0206] S312. Define the first-order low-pass filter as:

[0207]

[0208] in, is the filtering parameter of the first-order low-pass filter, which is a positive constant;

[0209] S313. Design the extended state observer as follows:

[0210]

[0211] When t→∞, Among them, ε>0, is the observer state, Then o2 is the observation error, and the polynomial Satisfy Hurwitz conditions;

[0212] S314, the quantitative feedback control input τ can be obtained:

[0213]

[0214] In specific implementation, as a preferred embodiment of the present invention, step S32 specifically includes:

[0215] S321. Define the filtering error generated during the filtering process as:

[0216]

[0217] The error surfaces in steps S13 and S14 are derived separately to obtain:

[0218]

[0219]

[0220] Where,

[0221] S322. Define the Lyapunov function of the filtering error as:

[0222] V γ =γγ / 2

[0223]

[0224] S323. Derivative the filtering error, and we get:

[0225]

[0226] S324, there exists an upper bound function B,

[0227]

[0228] Make The maximum value of B is denoted as M, then B 2 / M 2 -1≤0, then:

[0229]

[0230] Where, when Take enough hours to ensure

[0231] In specific implementation, as a preferred embodiment of the present invention, step S33 specifically includes:

[0232] S331: For the extended state observer in step S18, define θ = [θ1 θ2 θ3] T ,in:

[0233]

[0234]

[0235]

[0236] S332, due to Then the error state equation of the observer is:

[0237]

[0238] Where,

[0239] S333. Assume that the unknown term f(x,t) satisfies Among them, f * is a positive constant; in navigation practice, the speed and acceleration of unmanned ships have upper bounds, so the assumption is reasonable;

[0240] S334. Define the Lyapunov function of the observer as:

[0241] V O =εθ T Pθ

[0242] Where P is a symmetric positive definite matrix that satisfies the following Lyapunov equation:

[0243]

[0244] Where Q is any given symmetric positive definite matrix, then:

[0245]

[0246] Where λ min (Q) is the minimum eigenvalue of Q;

[0247] S335, by The convergence condition of the observer is:

[0248]

[0249] Among them, the smaller ε is, the faster θ converges, ||θ|| is O(ε), and as ε decreases, the observation errors o1 and o2 gradually converge.

[0250] In specific implementation, as a preferred embodiment of the present invention, step S34 specifically includes:

[0251] S341. Define the error surface, virtual signal, filtering error, and quantization error of the control input as follows:

[0252]

[0253]

[0254]

[0255]

[0256]

[0257]

[0258]

[0259] S342, Existence Constant make Available Bounded;

[0260]

[0261] S343, Existence Constant make Available Bounded;

[0262]

[0263]

[0264] S344, from step S32, it can be seen that the filtering error is bounded, and there is a constant make

[0265] S345, Existence Constant make We can get β α Bounded;

[0266]

[0267] S346, Existence Constant make Available Bounded;

[0268]

[0269] S347, Existence Constant make Available Bounded;

[0270]

[0271] S348, Existence Constant make We can get β τ Bounded;

[0272]

[0273]

[0274] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0275] S41. Considering heading tracking, virtual control and filtering errors, the Lyapunov function is defined as:

[0276] V S =η12 / 2+η2 2 / 2+γ 2 / 2

[0277] S42, when V S =p, then B is bounded, denoted as M, then B 2 / M 2 -1≤0;

[0278] S43, V S Derivative:

[0279]

[0280] Where, c1≥1+Ω2, c2≥2+Ω2, Ω2>0, Δ=(b 2 χ 2 +b 2 β τ 2 +Λ) / 2, o1<Λ;

[0281]

[0282] S44, Comprehensive Consideration System

[0283]

[0284] When Ω2 is large enough and ε is small enough, it can be guaranteed that Therefore, considering the quantized closed-loop system, take V S (0)≤p,p>0, the closed-loop system error signal is uniformly bounded, and the convergence rate depends on Ω2 and the observer parameter ε.

[0285] Example

[0286] In order to verify the effectiveness of the solution of the present invention, this embodiment uses MATLAB to perform heading tracking control simulation, and the parameter settings refer to steps S1 and S2. Figure 3-6 The expected heading instructions are x 1d = the heading tracking results, tracking error, observation results of the extended state observer, and control inputs before and after quantization in sint. Figure 3 The tracking results of the ship's heading angle and bow angular velocity are given. Figure 4 The ship heading angle error Q(x1)-x is given 1d and the ship's bow angular velocity error Q(x2)-x 2d ,According to the simulation results, the designed controller has a good ,effect on ship control, can achieve heading tracking well, and the error ,can quickly converge to a smaller residual set. Figure 5The observation result of the extended state observer is given, the function estimation curve of the extended state observer can quickly coincide with the original function curve, and the observation effect is ideal. Figure 6 The control input τ and Q(τ) before and after quantization are given, according to the simulation result, the quantization process reduces the execution frequency of the controller, reduces the rudder amplitude, and can effectively reduce the signal transmission burden in the network; the simulation result verifies that considering the state quantization and input quantization in the control system does not significantly sacrifice the control quality of the heading tracking.

[0287] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A heading tracking control method for an unmanned ship with state / input quantization, characterized in that: include: S1. Design the system control law based on the backstepping method and use the extended state observer to estimate the uncertainties and external disturbances in the control system. Specifically, S11. Construct a mathematical model for the heading control of an unmanned ship, as shown below: Where, ψ is the ship's heading angle, r is the ship's yaw angular velocity; δ is the ship's rudder angle, ω is the unknown disturbance of the system, a1 = -1 / T, a2 = -a / T, a is the nonlinear coefficient of the Norrbin motion model, b = K / Τ is the control system gain, K is the ship's turning index, T1, T2, T3 are the ship's following index, T = T1 + T2 + T3; τ is the system control input; S12. Select (ψ, r) as the state variable and define x1 = ψ, f(x, t)=a1r+a2r 3 +ω, select τ=δ, τ represents the system control input, Q(τ) represents the quantized control input of the system; quantization converts the continuous signal into a piecewise constant signal, so the mathematical model of the unmanned ship heading control after input quantization is introduced as follows: S13. Define the error surface as follows: η1=x1-x 1d Among them, x 1d is the expected heading signal; S14. Define the error surface as follows: η2=x2-α Among them, α is a virtual signal The filtered signal; S15. Select a first-order low-pass filter as shown below: in, is the filtering parameter of the first-order low-pass filter, which is a positive constant; S16, error surface η1 = x1-x 1d Taking the derivative, we get: Select virtual signal As shown below: Where c1 is a positive constant; In the inverse design, if Will lead to Time differential explosion, based on dynamic surface technology, will Input a first-order low-pass filter to get the low-pass filter α, and we get: S17. Derivative the error surface η2 = x2 - α to obtain: S18. Design the extended state observer as follows: The designed extended state observer can realize that when t→∞, Where ε>0, is the observer state, Then ο1 is the observation error, and the polynomial Satisfy Hurwitz conditions; S19. Design a non-quantized auxiliary control input signal as follows: Where c2 is a positive constant; S2, using a uniform quantizer to quantize the state variables and control inputs in the control system, and the quantized state feedback information is only used for tracking control; S3. Design an unmanned ship heading controller based on an extended state observer using quantized state recursion, and prove the boundedness of the error between quantized and non-quantized variables in the closed-loop control system. S4. Based on Lyapunov stability theory, the stability of the designed unmanned ship heading tracking control system with state quantization and input quantization is proved when state quantization and input quantization are considered simultaneously.

2. The unmanned vessel heading tracking control method with state / input quantization according to claim 1, characterized in that: The step S2 specifically includes: S21, using a uniform quantizer, quantize the state variables x1, x2 and the system control input τ as follows: Among them, s = x1, s = x2, s = τ, χ>0 represents the quantization step size, L1 = χ, L i+1 =L i +χ; After quantization, the state variable and input variable s become Q(s). This process will produce a quantization error, and the quantization error sQ(s) satisfies |sQ(s)|≤χ; S22. Assume that the quantized state variables Q(x1) and Q(x2) are used to design the control input of the system, that is, only the quantized heading angle and yaw angular velocity are used to design the controller.

3. The unmanned vessel heading tracking control method with state / input quantization according to claim 2, characterized in that: The step S3 specifically includes: S31. Design of an unmanned ship heading controller based on an extended state observer using quantized state recursion. S32, considering the closed-loop system consisting of the controlled object of step S12, the low-pass filter of step S15 and the control law of step S19, the filtering error is bounded; S33. Prove the boundedness of the observation error of the designed extended state observer; S34. Prove the boundedness of the error surface, virtual signal, filtering error and quantization error of control input.

4. The unmanned vessel heading tracking control method with state / input quantization according to claim 3, characterized in that: The step S31 specifically includes: S311. The error surface and virtual signal based on the quantized state are: In the formula, the virtual signal Input the first-order low-pass filter to get the filtered signal S312. Define the first-order low-pass filter as: in, is the filtering parameter of the first-order low-pass filter, which is a positive constant; S313. Design the extended state observer as follows: When t, it satisfies Among them, ε>0, is the observer state, Then o2 is the observation error, and the polynomial Satisfy Hurwitz conditions; S314, the quantitative feedback control input τ can be obtained:

5. The unmanned vessel heading tracking control method with state / input quantization according to claim 4, characterized in that: The step S32 specifically includes: S321. Define the filtering error generated during the filtering process as: The error surfaces in steps S13 and S14 are derived separately to obtain: Where, S322. Define the Lyapunov function of the filtering error as: V γ =γγ / 2 S323. Derivative the filtering error, and we get: S324, there exists an upper bound function B, Make The maximum value of B is denoted as M, then B 2 / M 2 -1≤0, then: Where, when Take enough hours to ensure 6. The unmanned vessel heading tracking control method with state / input quantization according to claim 5, characterized in that: The step S33 specifically includes: S331: For the extended state observer in step S18, define θ = [θ1 θ2 θ3] T ,in: S332, due to Then the error state equation of the observer is: Where, S333. Assume that the unknown term f(x,t) satisfies Among them, f * is a positive constant; in navigation practice, the speed and acceleration of unmanned ships have upper bounds, so the assumption is reasonable; S334. Define the Lyapunov function of the observer as: V O =θ T Pth Where P is a symmetric positive definite matrix that satisfies the following Lyapunov equation: Where Q is any given symmetric positive definite matrix, then: Where λ min (Q) is the minimum eigenvalue of Q; S335, by The convergence condition of the observer is: Among them, the smaller ε is, the faster θ converges. ||θ|| is a decreasing function of ε. As ε decreases, the observation errors o1 and o2 gradually converge.

7. The unmanned vessel heading tracking control method with state / input quantization according to claim 6, characterized in that: The step S34 specifically includes: S341. Define the error surface, virtual signal, filtering error, and quantization error of the control input as follows: S342, Existence Constant make Available Bounded; S343, Existence Constant make Available Bounded; S344, from step S32, it can be seen that the filtering error is bounded, and there is a constant make S345, Existence Constant make We can get β α Bounded; S346, Existence Constant make Available Bounded; S347, Existence Constant make Available Bounded; S348, Existence Constant make We can get β τ Bounded; 8. The unmanned vessel heading tracking control method with state / input quantization according to claim 7, characterized in that: The step S4 specifically includes: S41. Considering heading tracking, virtual control and filtering errors, the Lyapunov function is defined as: V S =η1 2 / 2+η2 2 2+c 2 / 2 S42, when V S =p, then B is bounded, denoted as M, then B 2 / M 2 -1≤0; S43, V S Derivative: where \(c1\geq12\), \(c2\geq22\), \(\Omega20\), =(b 2 \(\chi\) 2 +b 2 \(\beta\) τ 2 +\(\Lambda\)) / 2, \(o1\lt\Lambda\); S44, Comprehensive Consideration System When Ω2 is large enough and ε is small enough, V≤0 can be guaranteed. Therefore, considering the quantized closed-loop system, V S (0)≤p, p>0, the closed-loop system error signal is uniformly bounded, and the convergence rate depends on Ω2 and the observer parameter ε.

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