Self-adaptive course control method for unmanned surface vessel based on input state quantization and output constraint of disturbance observer

Abstract

The invention provides an input state quantization and output constraint unmanned surface vessel self-adaptive course control method based on a disturbance observer. The method comprises the following steps: modeling a control input quantization process by adopting a linear analysis framework; linear description is carried out on an input quantization process, and a controller does not need priori information of any quantization parameter; aiming at the composite disturbance characteristic of the system, constructing a disturbance observer to ensure the exponential convergence of a disturbance estimation error; a constraint processing mechanism based on a logarithm barrier function is adopted, state variables are strictly kept within a preset safety boundary, consistent final boundaries of all closed-loop signals are proved, and boundaries of internal signals and quantization errors are clarified. According to the method, the state input quantization and the output constraint are combined, the signal communication frequency between equipment on board is reduced, the communication burden is relieved, and the utilization efficiency of communication resources is improved. The effectiveness of the control method is verified through a simulation experiment.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to an adaptive heading control method for an unmanned surface vessel based on input state quantization and output constraints of a disturbance observer. Background Art

[0002] As a fundamental guarantee for unmanned surface vehicles to perform their missions, heading control requires high-precision trajectory tracking capabilities in complex marine environments and under restricted communication conditions. However, the inherent strong nonlinear characteristics of the unmanned surface vehicle dynamic system are coupled with environmental disturbances. At the same time, to cope with the limited communication bandwidth at sea, the control signal needs to be quantized and transmitted. This process may cause quantization errors to accumulate and lead to system instability. In addition, specific mission requirements such as narrow channel navigation impose strict constraints on the output state, exposing the limitations of traditional control methods in ensuring system robustness and safety under strict constraints. Therefore, building an intelligent control framework that integrates anti-interference, communication optimization, and safety constraints has become a key challenge to improving the navigation safety of unmanned surface vehicles.

[0003] In recent years, researchers around the world have proposed various advanced techniques to address the challenges of heading control for unmanned surface vehicles (USVs). These include input quantization, event triggering, disturbance observers, and output constraints. For example, input quantization is introduced via a uniform quantizer to adapt continuous signals to a limited bandwidth. To address communication resource constraints, an event-triggered mechanism (ETM) is proposed to reduce the communication burden by minimizing the transmission frequency of control signals. Regarding interference suppression, a heading control method based on a disturbance observer is developed, which uses the disturbance observer to estimate slowly time-varying disturbances. To address output constraints, a barrier Lyapunov function (BLF) is used to limit the tracking error to a predetermined range, combined with a prescribed performance function (PPF) to ensure transient and steady-state response specifications. It is worth noting that existing research has mainly focused on the application of a single technique to improve the accuracy and stability of heading tracking control.

[0004] Quantization research has attracted increasing attention from scholars, and in recent years, quantitative control theory has made significant progress in fields such as unmanned aerial vehicles (UAVs) and robotics. However, in the field of ship motion control, most existing research focuses solely on state quantization or input quantization, while research that simultaneously involves input and state quantization remains relatively rare. In the practical application of quantization technology, uniform quantizers and hysteresis quantizers are two classic signal discretization tools. Previous studies have applied these quantizers to heading tracking control systems for USVs to address communication bandwidth limitations. However, these methods have theoretical limitations in managing quantization errors—they only impose empirical constraints on the quantization process through predefined error bounds and fail to establish a linear system model for the quantizer. This unstructured error handling approach results in the dynamic characteristics of the quantization error being excluded from the stability analysis framework of the control system. Therefore, introducing a linearized quantization error propagation model is of great theoretical significance for improving the robustness of control algorithms.

[0005] In maritime practice, heading control systems must not only counteract external environmental disturbances such as wind, waves, and currents but also meet output constraints imposed by specific conditions, including navigation regulations, mission requirements, servo saturation, and angular velocity safety thresholds. While the aforementioned research has primarily focused on output constraints, there is still significant potential for further research in integrating output constraints with control systems involving state and input quantization, particularly in practical maritime applications such as USV heading control. This integration requires comprehensive analysis to address the unique challenges posed by the marine environment. Summary of the Invention

[0006] In response to the aforementioned technical problems, a method for adaptive heading control of unmanned surface vessels based on input state quantization and output constraints using a disturbance observer is provided. This method combines state input quantization with output constraints, reducing the frequency of signal communication between onboard devices, alleviating the communication burden and improving the efficiency of communication resource utilization. To enhance robustness against slow-varying disturbances, a nonlinear disturbance observer is integrated into the control framework. Output constraints are systematically incorporated to adapt to the vessel's dynamic characteristics, safety regulations, and mission requirements, thereby better meeting the actual navigation needs of unmanned vessels. The stability of the developed heading control method is rigorously proven based on the Lyapunov stability theorem.

[0007] The technical means adopted in the present invention are as follows:

[0008] An adaptive heading control method for an unmanned surface vehicle based on input state quantization and output constraints of a disturbance observer, comprising:

[0009] S1. Model the control input quantization process using a linear analysis framework;

[0010] S2, linearly describe the input quantization process, and the controller does not require any prior information on the quantization parameters;

[0011] S3. According to the complex disturbance characteristics of the system, a disturbance observer is constructed to ensure the exponential convergence of the disturbance estimation error;

[0012] S4. A constraint processing mechanism based on logarithmic barrier functions is adopted to strictly keep the state variables within the preset safety boundaries, prove the consistent ultimate boundedness of all closed-loop signals, and clarify the boundedness of internal signals and quantization errors.

[0013] Furthermore, step S1 specifically includes:

[0014] S11. Establish a mathematical model for USV heading control as follows:

[0015]

[0016] Among them, φ represents the ship's heading angle; r represents the ship's yaw rate; ω represents the disturbance caused by factors such as wind, waves, and currents; τ represents the control input of the system; b represents the control system gain, Where K represents the ship's turning index, T represents the ship's following index; R(r) represents the interference inside the unmanned surface vessel, R(r)=c1r+c2r 3 , where c1 and c2 represent nonlinear coefficients;

[0017] S12. Design a uniform quantizer as follows:

[0018]

[0019] Where l = φ and r; i∈Z + , the quantization step size is expressed as χ>0, L i =χ,L i+1 =L i +χ, the quantization error is lq(l), satisfying

[0020] S13. After quantification, the mathematical model of USV heading control is expressed as:

[0021]

[0022] Where Q(τ) represents the quantized value of the control input τ, represents the internal uncertainty of the model.

[0023] Furthermore, step S2 specifically includes:

[0024] Let Q(τ)=q1(t)τ+q2(t), and:

[0025]

[0026] Among them, q1(t) is unknown and its sign remains unchanged during the quantization process. From the above formula, we can see that q1(t)>0. When |τ(t)|<a, Q(τ(t)) is also bounded. Therefore, it can be deduced that q2(t) is bounded.

[0027] Furthermore, step S3 specifically includes:

[0028] S31. Incorporate the uncertainty term g into the composite perturbation d = g + w, where d represents a bounded derivative. Under these conditions, a disturbance observer is systematically designed to estimate and compensate for the total disturbance effect as follows:

[0029]

[0030] Among them, a1>0 and a2>0 are design parameters, denote the estimated values ​​of d and r respectively;

[0031] S32, due to The observation error is obtained as follows:

[0032]

[0033] Among them, the observation error and They are defined as as well as

[0034] Furthermore, step S4 specifically includes:

[0035] S41. Prove that without considering state quantization, all signals in the closed-loop system are ultimately bounded and the tracking error of the system can converge to a small residual set;

[0036] S42. Prove that the designed heading control system with state quantization and output constraints is stable, all state variables and intermediate signals in the closed-loop system are uniformly bounded, and all tracking errors eventually converge to a residual set near zero.

[0037] Furthermore, step S41 specifically includes:

[0038] S411, assume Z1={z1∈R:-k a <z1<k b}∈R and N=R l ×Z1∈R l+1 For any positive constant All are open sets. Consider the error system as follows:

[0039]

[0040] where ζ = [z1, z2] T ∈N, and R + ×N→R l+1 Piecewise continuous with respect to t and locally Lipschitz continuous with respect to z;

[0041] S412, assuming that there are continuously differentiable and positive definite functions V1 and V2, define the position output x1 and the position error z1 = φ-y d , the following conditions are met:

[0042] When z1→-k a or z1→k b When V1(z1)→∞;

[0043] ι1(||z2||)≤V(z2)≤ι2(||z2||), where ι1 and ι2 are K ∞ Function-like; assume |z1(0)|<K b , V(ζ)=V1(z1)+V2(z2) If the inequality holds, then:

[0044]

[0045] In the collection , and μ, λ are positive constants, then z2 remains bounded, and

[0046] S413. The inequality in step S412 is valid for any positive constant k. b >0 is true, Then we have:

[0047]

[0048] S414, let z1 = φ - y d , and z2=r-α, where α represents a stable function, consider the following barrier Lyapunov function:

[0049]

[0050] Among them, k b =k d -B0, constrain z1 to |z1| < k b , from which we can conclude that z1 is positive definite; and taking the derivative of the barrier Lyapunov function, we get:

[0051]

[0052] S415, design stability function α as Where k1>0 represents a constant. Substituting the stability function into the derived barrier Lyapunov function, we get:

[0053]

[0054] After substituting into the control law, the coupling term Will be decomposed, assuming z2=0, and get V1≤0;

[0055] S416. Since the ship's yaw rate r does not need to be limited, a Lyapunov function is defined as follows:

[0056]

[0057] The time derivative of the above equation is as follows:

[0058]

[0059] make From this we get:

[0060]

[0061] S417. Set the remarks: Since the lower limit of q1(t) is uncertain and changes with time, it is estimated using adaptive estimation. To avoid singular difficulties caused by estimating zero values, the lower limit of q1(t) is u=1 / q1(t). min Expressed as, and define the time-varying gain u=1 / q1(t) min ;

[0062] S418. Calculate the control rate using the following formula:

[0063]

[0064] S419: Calculate the adaptive rate. The calculation formula is as follows:

[0065]

[0066] Where k2 is a constant, k2>0, γ1, P and σ are all positive constants, represents the estimated value of u, and

[0067] S4110. Use a uniform quantizer to quantize the state variables and intermediate signals in the system as follows:

[0068]

[0069] in, They are z1, z2, φ, r, a, u, The quantitative value of

[0070] S4111. Calculate the quantized control law. The calculation formula is as follows:

[0071]

[0072] S4112. Prove the stability of the observer. Considering the observer estimation error, the Lyapunov function is designed as follows:

[0073]

[0074] And taking the time derivative of the above formula, we get:

[0075]

[0076] According to the designed disturbance observer and the quantized heading model, we can obtain:

[0077]

[0078] Among them, the interference d is a slowly time-varying signal, approaching a very small value; when a1 takes a larger value, assuming when hour, According to LaSalle's invariance principle, when t→∞, By adopting this observer, the d term is effectively observed, thereby achieving compensation control;

[0079] S4113. When state quantization is not considered, the stability of the closed-loop system is analyzed. The analysis process is as follows:

[0080] If the initial error satisfies |z e |<k b , given the control law and adaptation rate, all signals in the entire closed-loop system are ultimately bounded, and the error in the entire signal process will not exceed the specified limit;

[0081] S4114. Design the Lyapunov function as follows:

[0082]

[0083] And taking the time derivative of the above formula, we get:

[0084]

[0085] Substituting the control law, we get:

[0086]

[0087] S4115. Substituting the adaptation rate into the above formula, we get:

[0088]

[0089] because So make From this we get:

[0090]

[0091] From the notes set in step S417, it can be seen that considering Then we have:

[0092]

[0093] Substitute the above formula into the inequality in step S4115 get:

[0094]

[0095] S4116, set the equation as follows:

[0096]

[0097] From the above equations, we can get:

[0098]

[0099] S4117. According to the formula in step S413, we obtain:

[0100]

[0101] in,

[0102] S4118. According to step S4113, since V is bounded, z1, z2 and Bounded, and Satisfy |z1|<k b , for all When t approaches ∞, V(t) approaches The convergence accuracy depends on ε. Therefore, according to Lyapunov stability theory, when state quantization is not considered, all signals in the closed-loop system are ultimately bounded, and the tracking error of the system can converge to a smaller residual set.

[0103] Furthermore, step S42 specifically includes:

[0104] S421, define the quantization error of state variables, intermediate signals and control inputs as

[0105] In a constant Make the conditions Established;

[0106] S422, according to the uniform quantizer, we get φ,r is quantized as From this we get:

[0107]

[0108] From the above formula and step S4110, we get:

[0109]

[0110] Combining the above formula, we get:

[0111]

[0112] As determined in step S4118, without quantization, the control system is stable and the system error is bounded, so it is concluded that It is bounded.

[0113] S423, the control rate τ and the quantized control law is expressed as:

[0114]

[0115] According to step S411 and step S422, z1 and is bounded, then we have:

[0116]

[0117] in, and is a positive constant;

[0118] S424. In maritime practice, there is an upper limit to the yaw angular velocity of an unmanned surface vehicle (USV), so there are constants A and B that satisfy the following equation:

[0119]

[0120] Then we have: Among them, γ is a positive constant;

[0121] S425, from step S422 and the comprehensive formula get:

[0122]

[0123] S426. From step S423, we obtain:

[0124]

[0125] S427. Based on step S422 and step S426, obtain:

[0126]

[0127] S428. For the estimation error of the disturbance observer with quantized state, the observation error is uniformly bounded. Considering the state quantization in the disturbance observer design, the Lyapunov function is constructed as follows:

[0128]

[0129] in accordance with get:

[0130]

[0131] Combined with the stability proof of disturbance observer, we get:

[0132]

[0133] According to the LaSalle invariance principle, the observation error of the disturbance observer with quantized state will eventually converge and remain in a small residual set;

[0134] S429: When considering state quantization, the closed-loop system is internally stable. When state quantization, input quantization, and output constraints are considered simultaneously in the heading tracking control system, the following is obtained from step S4114:

[0135]

[0136] As determined in step S4118, the quantization errors of the state variables and the intermediate signals in the control system are bounded, and there is a constant Make the inequality Therefore, based on the derivation process of step S4115, it is concluded that:

[0137]

[0138] in, Based on the Lyapunov stability theorem, it is proved that the designed heading control system with state quantization and output constraints is stable, all state variables and intermediate signals in the closed-loop system are uniformly bounded, and all tracking errors eventually converge to a residual set near zero.

[0139] Compared with the prior art, the present invention has the following advantages:

[0140] 1. The present invention provides an adaptive heading control method for unmanned surface vehicles based on input state quantization and output constraints of a disturbance observer. This method combines state input quantization with output constraints, reduces the signal communication frequency between onboard equipment, alleviates the communication burden, and improves the efficiency of communication resource utilization, while complying with ship safety regulations and mission requirements.

[0141] 2. Compared with current quantization control technologies, most quantization methods either require prior knowledge of quantization parameters or treat quantized variables as disturbances of unquantized variables. The present invention overcomes these shortcomings by using a uniform quantizer to linearly describe the quantization process.

[0142] Based on the above reasons, the present invention can be widely promoted in fields such as artificial intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0143] 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.

[0144] Figure 1 Flow chart of the method of the present invention.

[0145] Figure 2 This is a diagram of the unmanned ship heading tracking results provided by an embodiment of the present invention.

[0146] Figure 3 This is an unmanned heading tracking error diagram provided by an embodiment of the present invention.

[0147] Figure 4 This is an interference estimation diagram provided by an embodiment of the present invention.

[0148] Figure 5 A comparison diagram of the control input curves provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0149] In order to enable those skilled in the art to better understand the solutions of the present invention, 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 embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0150] It should be noted that the terms "including" and "having" and any variations thereof in the specification and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units that are not explicitly listed or are inherent to these processes, methods, products or apparatuses.

[0151] like Figure 1 The present invention provides an input state quantization and output constraint unmanned surface vehicle adaptive heading control method based on a disturbance observer, comprising:

[0152] S1. A linear analysis framework is used to model the control input quantization process. Its advantage is that the proposed quantitative feedback controller does not require the prediction of quantization parameters during operation;

[0153] S2, linearly describe the input quantization process, and the controller does not require any prior information on the quantization parameters;

[0154] S3. According to the complex disturbance characteristics of the system, a disturbance observer is constructed to ensure the exponential convergence of the disturbance estimation error;

[0155] S4. A constraint processing mechanism based on a logarithmic barrier function is used to strictly keep state variables within a preset safety margin, prove the consistent ultimate boundedness of all closed-loop signals, and illustrate the boundedness of internal signals and quantization errors. This invention introduces a logarithmic barrier Lyapunov function to ensure that the system state remains within a reasonable range;

[0156] In specific implementation, as a preferred embodiment of the present invention, step S1 specifically includes:

[0157] S11. Establish a mathematical model for USV heading control as follows:

[0158]

[0159] Among them, φ represents the ship's heading angle; r represents the ship's yaw rate; ω represents the disturbance caused by factors such as wind, waves, and currents; τ represents the control input of the system; b represents the control system gain, Where K represents the ship's turning index, T represents the ship's following index; R(r) represents the interference inside the unmanned surface vessel, R(r)=c1r+c2r 3 , where c1 and c2 represent nonlinear coefficients;

[0160] S12. Design a uniform quantizer as follows:

[0161]

[0162] Where l = φ and r; i∈Z + , the quantization step size is expressed as χ>0, L i =χ,L i+1 =L i +χ, the quantization error is lq(l), satisfying Due to the limited capacity of the maritime network communication channel, quantitative control is adopted when considering the heading tracking problem. Input quantization and state quantization are introduced, and a uniform quantizer is used for quantization. All state variables φ and r and control input τ are quantized by the uniform quantizer.

[0163] S13. After quantification, the mathematical model of USV heading control is expressed as:

[0164]

[0165] Where Q(τ) represents the quantized value of the control input τ, represents the internal uncertainty of the model.

[0166] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0167] Let Q(τ)=q1(t)τ+q2(t), and:

[0168]

[0169] Among them, q1(t) is unknown and its sign remains unchanged during the quantization process. From the above formula, we can see that q1(t)>0. When |τ(t)|<a, Q(τ(t)) is also bounded. Therefore, it can be deduced that q2(t) is bounded.

[0170] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0171] S31. Incorporate the uncertainty term g into the composite perturbation d = g + w, where d represents a bounded derivative. Under these conditions, a disturbance observer is systematically designed to estimate and compensate for the total disturbance effect as follows:

[0172]

[0173] Among them, a1>0 and a2>0 are design parameters, denote the estimated values ​​of d and r respectively;

[0174] S32, due to The observation error is obtained as follows:

[0175]

[0176] Among them, the observation error and They are defined as as well as

[0177] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0178] S41. Prove that without considering state quantization, all signals in the closed-loop system are ultimately bounded and the tracking error of the system can converge to a small residual set;

[0179] S42. Prove that the designed heading control system with state quantization and output constraints is stable, all state variables and intermediate signals in the closed-loop system are uniformly bounded, and all tracking errors eventually converge to a residual set near zero.

[0180] In specific implementation, as a preferred embodiment of the present invention, step S41 specifically includes:

[0181] S411, assume Z1={z1∈R:-k a <z1<k b}∈R and N=R l ×Z1∈R l+1 For any positive constant All are open sets. Consider the error system as follows:

[0182]

[0183] where ζ = [z1, z2] T ∈N, and R + ×N→R l+1 Piecewise continuous with respect to t and locally Lipschitz continuous with respect to z;

[0184] S412, assuming that there are continuously differentiable and positive definite functions V1 and V2, define the position output x1 and the position error z1 = φ-y d , the following conditions are met:

[0185] When z1→-k a or z1→k b When V1(z1)→∞;

[0186] ι1(||z2||)≤V(z2)≤ι2(||z2||), where ι1 and ι2 are K ∞ Function-like; assume |z1(0)|<K b , V(ζ)=V1(z1)+V2(z2) If the inequality holds, then:

[0187]

[0188] In the collection , and μ, λ are positive constants, then z2 remains bounded, and

[0189] S413. The inequality in step S412 is valid for any positive constant k. b >0 is true, Then we have:

[0190]

[0191] S414, let z1 = φ - y d , and z2=r-α, where α represents a stable function, consider the following barrier Lyapunov function:

[0192]

[0193] Among them, k b =k d -B0, constrain z1 to |z1| < k b , from which we can conclude that z1 is positive definite; and taking the derivative of the barrier Lyapunov function, we get:

[0194]

[0195] S415, design stability function α as Where k1>0 represents a constant. Substituting the stability function into the derived barrier Lyapunov function, we get:

[0196]

[0197] After substituting into the control law, the coupling term Will be decomposed, assuming z2=0, to get

[0198] S416. Since the ship's yaw rate r does not need to be limited, a Lyapunov function is defined as follows:

[0199]

[0200] The time derivative of the above equation is as follows:

[0201]

[0202] make From this we get:

[0203]

[0204] S417. Set the remarks: Since the lower limit of q1(t) is uncertain and changes with time, it is estimated using adaptive estimation. To avoid singular difficulties caused by estimating zero values, the lower limit of q1(t) is u=1 / q1(t). min Expressed as, and define the time-varying gain u=1 / q1(t) min ;

[0205] S418. Calculate the control rate using the following formula:

[0206]

[0207] S419: Calculate the adaptive rate. The calculation formula is as follows:

[0208]

[0209] Where k2 is a constant, k2>0, γ1, P and σ are all positive constants, represents the estimated value of u, and

[0210] S4110. Use a uniform quantizer to quantize the state variables and intermediate signals in the system as follows:

[0211]

[0212] in, They are z1, z2, φ, r, a, u, The quantitative value of

[0213] S4111. Calculate the quantized control law. The calculation formula is as follows:

[0214]

[0215] S4112. Prove the stability of the observer. Considering the observer estimation error, the Lyapunov function is designed as follows:

[0216]

[0217] And taking the time derivative of the above formula, we get:

[0218]

[0219] According to the designed disturbance observer and the quantized heading model, we can obtain:

[0220]

[0221] Among them, the interference d is a slowly time-varying signal, approaching a very small value; when a1 takes a larger value, assuming when hour, According to LaSalle's invariance principle, when t→∞, By adopting this observer, the d term is effectively observed, thereby achieving compensation control;

[0222] S4113. When state quantization is not considered, the stability of the closed-loop system is analyzed. The analysis process is as follows:

[0223] If the initial error satisfies |z e |<k b , given the control law and adaptation rate, all signals in the entire closed-loop system are ultimately bounded, and the error in the entire signal process will not exceed the specified limit;

[0224] S4114. Design the Lyapunov function as follows:

[0225]

[0226] And taking the time derivative of the above formula, we get:

[0227] Substituting the control law, we get:

[0228]

[0229] S4115. Substituting the adaptation rate into the above formula, we get:

[0230]

[0231] because So make From this we get:

[0232]

[0233] From the notes set in step S417, it can be seen that considering Then we have:

[0234]

[0235] Substitute the above formula into the inequality in step S4115 get:

[0236]

[0237] S4116, set the equation as follows:

[0238]

[0239] From the above equations, we can get:

[0240]

[0241] S4117. According to the formula in step S413, we obtain:

[0242]

[0243] in,

[0244] S4118. According to step S4113, since V is bounded, z1, z2 and Bounded, and Satisfy |z1|<k b , for all When t approaches ∞, V(t) approaches The convergence accuracy depends on ε. Therefore, according to Lyapunov stability theory, when state quantization is not considered, all signals in the closed-loop system are ultimately bounded, and the tracking error of the system can converge to a smaller residual set.

[0245] In specific implementation, as a preferred embodiment of the present invention, step S42 specifically includes:

[0246] S421, define the quantization error of state variables, intermediate signals and control inputs as

[0247] In a constant Make the conditions Established;

[0248] S422, according to the uniform quantizer, we get φ,r is quantized as From this we get:

[0249]

[0250] From the above formula and step S4110, we get:

[0251]

[0252] Combining the above formula, we get:

[0253]

[0254] As determined in step S4118, without quantization, the control system is stable and the system error is bounded, so it is concluded that It is bounded.

[0255] S423, the control rate τ and the quantized control law is expressed as:

[0256]

[0257] According to step S411 and step S422, z1 and is bounded, then we have:

[0258]

[0259] in, and is a positive constant;

[0260] S424. In maritime practice, there is an upper limit to the yaw angular velocity of an unmanned surface vehicle (USV), so there are constants A and B that satisfy the following equation:

[0261]

[0262] Then we have: Among them, γ is a positive constant;

[0263] S425, from step S422 and the comprehensive formula get:

[0264]

[0265] S426. From step S423, we obtain:

[0266]

[0267] S427. Based on step S422 and step S426, obtain:

[0268]

[0269] S428. For the estimation error of the disturbance observer with quantized state, the observation error is uniformly bounded. Considering the state quantization in the disturbance observer design, the Lyapunov function is constructed as follows:

[0270]

[0271] in accordance with get:

[0272]

[0273] Combined with the stability proof of disturbance observer, we get:

[0274]

[0275] According to the LaSalle invariance principle, the observation error of the disturbance observer with quantized state will eventually converge and remain in a small residual set;

[0276] S429: When considering state quantization, the closed-loop system is internally stable. When state quantization, input quantization, and output constraints are considered simultaneously in the heading tracking control system, the following is obtained from step S4114:

[0277]

[0278] As determined in step S4118, the quantization errors of the state variables and the intermediate signals in the control system are bounded, and there is a constant Make the inequality Therefore, based on the derivation process of step S4115, it is concluded that:

[0279]

[0280] in, Based on the Lyapunov stability theorem, it is proved that the designed heading control system with state quantization and output constraints is stable, all state variables and intermediate signals in the closed-loop system are uniformly bounded, and all tracking errors eventually converge to a residual set near zero.

[0281] Example

[0282] In order to verify the effectiveness of the solution of the present invention, this embodiment uses MATLAB to conduct computer simulation research. The simulation object is the "Lanxin" unmanned ship of Dalian Maritime University. The parameters are set as follows:

[0283] The initial state of the actual controlled object is [0,1], and the controller designed in step S3 is used to control the unmanned ship; the ideal heading of the unmanned ship is set to φ d =0.2sin(2t). The initial state of the actual controlled object is [0,1]. The controller designed in this invention is used to control the unmanned ship. The parameter configuration of the proposed controller is k1=300, k2=300, a1=230, a2=85, P=0.02, χ=0.1, σ=0.2, γ1=0.1, γ2=1.

[0284] A uniform quantizer is used to process the state variables φ and r, as well as the control input τ. A control algorithm is developed in MATLAB to simulate a closed-loop system with quantized communication. A desired heading and yaw rate are designed for simulation experiments to verify that the actual heading and yaw rate can successfully track the desired heading and yaw rate. The control algorithm developed in MATLAB then calculates the desired heading and yaw rate. Figure 2-5 The simulation results of USV heading control are shown.

[0285] Figure 2 The tracking response of the USV's heading angle and yaw rate is illustrated. The results show that when the proposed adaptive control law and parameter update law are used, the system converges quickly from the initial state to the desired heading within a short transient time, thus confirming the transient performance and convergence of the control algorithm. Figure 3 The dynamic characteristics of the heading angle and yaw rate tracking errors are quantitatively analyzed. Despite the combined effects of quantization error, model uncertainty, and external disturbances, the controller maintains bounded error stability, verifying its strong robustness. Figure 4 As shown, a disturbance observer is incorporated into the control framework to achieve real-time estimation of slowly time-varying disturbances. The estimated disturbance quickly converges to the ideal disturbance profile, fully verifying the dynamic tracking performance and effectiveness of the observer. Figure 5 A comparative study of quantization mechanisms for control efficiency was conducted. Although quantization introduces slight high-frequency oscillations, it significantly reduces communication bandwidth usage, making it more suitable for low-bandwidth, high-reliability transmission requirements in marine engineering applications.

[0286] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for adaptive heading control of an unmanned surface vehicle based on input state quantization and output constraint of a disturbance observer, characterized in that: include: S1. Model the control input quantization process using a linear analysis framework; S2, linearly describe the input quantization process, and the controller does not require any prior information on the quantization parameters; S3. According to the complex disturbance characteristics of the system, a disturbance observer is constructed to ensure the exponential convergence of the disturbance estimation error; S4. A constraint processing mechanism based on logarithmic barrier functions is adopted to strictly keep the state variables within the preset safety boundaries, prove the consistent ultimate boundedness of all closed-loop signals, and clarify the boundedness of internal signals and quantization errors.

2. The method for adaptive heading control of an unmanned surface vehicle based on input state quantization and output constraint of a disturbance observer according to claim 1 is characterized in that: Step S1 specifically includes: S11. Establish a mathematical model for USV heading control as follows: Among them, φ represents the ship's heading angle; r represents the ship's yaw rate; ω represents the disturbance caused by factors such as wind, waves, and currents; τ represents the control input of the system; b represents the control system gain, Where K represents the ship's turning index, T represents the ship's following index; R(r) represents the interference inside the unmanned surface vessel, R(r)=c1r+c2r 3 , where c1 and c2 represent nonlinear coefficients; S12. Design a uniform quantizer as follows: Where l = φ and r; i∈Z + , the quantization step size is expressed as χ>0, L i =χ,L i+1 =L i +χ, the quantization error is lq(l), satisfying S13. After quantification, the mathematical model of USV heading control is expressed as: Where Q(τ) represents the quantized value of the control input τ, represents the internal uncertainty of the model.

3. The method for adaptive heading control of an unmanned surface vehicle based on input state quantization and output constraint of a disturbance observer according to claim 1 is characterized in that: Step S2 specifically includes: Let Q(τ)=q1(t)τ+q2(t), and: Among them, q1(t) is unknown and its sign remains unchanged during the quantization process. From the above formula, we can see that q1(t)>0. When |τ(t)|<a, Q(τ(t)) is also bounded. Therefore, it can be deduced that q2(t) is bounded.

4. The method for adaptive heading control of an unmanned surface vehicle based on input state quantization and output constraint of a disturbance observer according to claim 1 is characterized in that: Step S3 specifically includes: S31. Incorporate the uncertainty term g into the composite perturbation d = g + w, where d represents a bounded derivative. Under these conditions, a disturbance observer is systematically designed to estimate and compensate for the total disturbance effect as follows: Among them, a1>0 and a2>0 are design parameters, denote the estimated values ​​of d and r respectively; S32, due to The observation error is obtained as follows: Among them, the observation error and They are defined as as well as 5. The method for adaptive heading control of an unmanned surface vehicle based on input state quantization and output constraint of a disturbance observer according to claim 1 is characterized in that: Step S4 specifically includes: S41. Prove that without considering state quantization, all signals in the closed-loop system are ultimately bounded and the tracking error of the system can converge to a small residual set; S42. Prove that the designed heading control system with state quantization and output constraints is stable, all state variables and intermediate signals in the closed-loop system are uniformly bounded, and all tracking errors eventually converge to a residual set near zero.

6. The method for adaptive heading control of an unmanned surface vehicle based on input state quantization and output constraint of a disturbance observer according to claim 1, characterized in that: Step S41 specifically includes: S411, assume Z1={z1∈R:-k a <z1<k b }∈R and N=R l ×Z1∈R l+1 For any positive constant All are open sets. Consider the error system as follows: where ζ = [z1, z2] T ∈N, and R + ×N→R l+1 Piecewise continuous with respect to t and locally Lipschitz continuous with respect to z; S412, assuming that there are continuously differentiable and positive definite functions V1 and V2, define the position output x1 and the position error z1 = φ-y d , the following conditions are met: When z1→-k a or z1→k b When V1(z1)→∞; ι1(||z2||)≤V(z2)≤ι2(||z2||), where ι1 and ι2 are K ∞ Function-like; assume |z1(0)|<K b , V(ζ)=V1(z1)+V2(z2) If the inequality holds, then: In the collection , and μ, λ are positive constants, then z2 remains bounded, and S413. The inequality in step S412 is valid for any positive constant k. b >0 is true, Then we have: S414, let z1 = φ - y d , and z2=r-α, where α represents a stable function, consider the following barrier Lyapunov function: Among them, k b =k d -B0, constrain z1 to |z1| < k b , from which we can conclude that z1 is positive definite; and taking the derivative of the barrier Lyapunov function, we get: S415, design stability function α as Where k1>0 represents a constant. Substituting the stability function into the derived barrier Lyapunov function, we get: After substituting into the control law, the coupling term Will be decomposed, assuming z2=0, to get S416. Since the ship's yaw rate r does not need to be limited, a Lyapunov function is defined as follows: The time derivative of the above equation is as follows: make From this we get: S417. Set the remarks: Since the lower limit of q1(t) is uncertain and changes with time, it is estimated using adaptive estimation. To avoid singular difficulties caused by estimating zero values, the lower limit of q1(t) is u=1 / q1(t). min Expressed as, and define the time-varying gain u=1 / q1(t) min ; S418. Calculate the control rate using the following formula: S419: Calculate the adaptive rate. The calculation formula is as follows: Where k2 is a constant, k2>0, γ1, P and σ are all positive constants, represents the estimated value of u, and S4110. Use a uniform quantizer to quantize the state variables and intermediate signals in the system as follows: in, They are z1, z2, φ, r, a, u, The quantitative value of S4111. Calculate the quantized control law. The calculation formula is as follows: S4112. Prove the stability of the observer. Considering the observer estimation error, the Lyapunov function is designed as follows: And taking the time derivative of the above formula, we get: According to the designed disturbance observer and the quantized heading model, we can obtain: Among them, the interference d is a slowly time-varying signal, approaching a very small value; when a1 takes a larger value, assuming when hour, According to LaSalle's invariance principle, when t→∞, By adopting this observer, the d term is effectively observed, thereby achieving compensation control; S4113. When state quantization is not considered, the stability of the closed-loop system is analyzed. The analysis process is as follows: If the initial error satisfies |z e |<k b , given the control law and adaptation rate, all signals in the entire closed-loop system are ultimately bounded, and the error in the entire signal process will not exceed the specified limit; S4114. Design the Lyapunov function as follows: And taking the time derivative of the above formula, we get: Substituting the control law, we get: S4115. Substituting the adaptation rate into the above formula, we get: because So make From this we get: From the notes set in step S417, it can be seen that considering Then we have: Substitute the above formula into the inequality in step S4115 get: S4116, set the equation as follows: From the above equations, we can get: S4117. According to the formula in step S413, we obtain: in, S4118. According to step S4113, since V is bounded, z1, z2 and Bounded, and Satisfy |z1|<k b , for all When t approaches ∞, V(t) approaches The convergence accuracy depends on ε. Therefore, according to Lyapunov stability theory, when state quantization is not considered, all signals in the closed-loop system are ultimately bounded, and the tracking error of the system can converge to a smaller residual set.

7. The method for adaptive heading control of an unmanned surface vehicle based on input state quantization and output constraint of a disturbance observer according to claim 1 is characterized in that: Step S42 specifically includes: S421, define the quantization error of state variables, intermediate signals and control inputs as In a constant Make the conditions Established; S422, according to the uniform quantizer, we get φ,r is quantized as From this we get: From the above formula and step S4110, we get: Combining the above formula, we get: As determined in step S4118, without quantization, the control system is stable and the system error is bounded, so it is concluded that It is bounded. S423, the control rate τ and the quantized control law is expressed as: According to step S411 and step S422, z1 and is bounded, then we have: in, and is a positive constant; S424. In maritime practice, there is an upper limit to the yaw angular velocity of an unmanned surface vehicle (USV), so there are constants A and B that satisfy the following equation: Then we have: Among them, γ is a positive constant; S425, from step S422 and the comprehensive formula get: S426. From step S423, we obtain: S427. Based on step S422 and step S426, obtain: S428. For the estimation error of the disturbance observer with quantized state, the observation error is uniformly bounded. Considering the state quantization in the disturbance observer design, the Lyapunov function is constructed as follows: in accordance with get: Combined with the stability proof of disturbance observer, we get: According to the LaSalle invariance principle, the observation error of the disturbance observer with quantized state will eventually converge and remain in a small residual set; S429: When considering state quantization, the closed-loop system is internally stable. When state quantization, input quantization, and output constraints are considered simultaneously in the heading tracking control system, the following is obtained from step S4114: As determined in step S4118, the quantization errors of the state variables and the intermediate signals in the control system are bounded, and there is a constant Make the inequality Therefore, based on the derivation process of step S4115, it is concluded that: in, Based on the Lyapunov stability theorem, it is proved that the designed heading control system with state quantization and output constraints is stable, all state variables and intermediate signals in the closed-loop system are uniformly bounded, and all tracking errors eventually converge to a residual set near zero.

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