A robust dynamic output feedback predictive control method for unmanned surface vessels

Abstract

This invention relates to a robust dynamic output feedback predictive control method for unmanned surface vessels (USVs), comprising: establishing an interval type-two fuzzy model of the USV; establishing an optimization problem for online state feedback robust predictive control; obtaining an online state feedback predictive control algorithm by solving the optimization problem; establishing an interval type-two observer for the USV based on the interval type-two fuzzy model; and performing dynamic robust model prediction on the USV using the online state feedback predictive control algorithm and the dynamic output feedback predictive control algorithm to achieve stable control of the USV. This invention can improve the accuracy of disturbance rejection and stabilization control of USVs, efficiently and robustly stabilize the system, and ensure the safety of USVs in complex environments.

Description

Technical Field

[0001] This invention relates to the field of unmanned surface vessel (USV) control technology, and in particular to a robust dynamic output feedback predictive control method for USVs. Background Technology

[0002] Unmanned surface vessels (USVs) are small, intelligent marine transport platforms with remote or autonomous navigation capabilities. Integrating multiple advanced technologies, they possess all-weather mission capabilities, particularly in performing dangerous, arduous, and time-consuming tasks in harsh marine environments, thus having broad applications across various fields and promising future prospects. With the rapid development of unmanned driving technology, USVs have attracted increasing attention due to their autonomy, flexibility, small size, and low cost, especially demonstrating significant potential in reducing human casualties and performing high-risk missions. Therefore, designing feedback control strategies for USVs is of significant practical importance.

[0003] However, current feedback control strategies neglect the restoring force matrix, and the stabilization control of unmanned surface vessels does not incorporate membership function information. This leads to poor performance of the control strategies in practical applications, making it difficult to effectively cope with environmental changes and maintain system stability, thus affecting the stabilization performance of the system. Summary of the Invention

[0004] This invention provides a robust dynamic output feedback predictive control method for unmanned surface vessels to overcome the shortcomings of existing technologies.

[0005] This invention provides a robust dynamic output feedback predictive control method for unmanned surface vessels, comprising:

[0006] S1: Establish an interval type II fuzzy model of the unmanned surface vessel;

[0007] S2: Establish the optimization problem of online state feedback robust predictive control, and obtain the online state feedback predictive control algorithm by solving the optimization problem;

[0008] S3: Based on the aforementioned interval type II fuzzy model, establish an interval type II observer for the unmanned surface vessel;

[0009] S4: The unmanned surface vessel is dynamically robustly predicted using the online state feedback predictive control algorithm and the dynamic output feedback predictive control algorithm to achieve stable control of the unmanned surface vessel.

[0010] According to the robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention, step S1 further includes:

[0011] S11: Based on the surface motion characteristics of unmanned surface vessels, establish a state-space model of the unmanned surface vessel;

[0012] S12: Based on the state-space model, establish a basic type II fuzzy model;

[0013] S13: By discretizing the basic type-II fuzzy model, an interval type-II fuzzy model is obtained.

[0014] According to the robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention, step S11 further includes:

[0015] S111: Select a three-degree-of-freedom unmanned surface vessel dynamics model as the basic model;

[0016] S112: Based on the stabilization and control problem of unmanned surface vessels, a simplified model is obtained by ignoring the centripetal force and Coriolis force matrices of the basic model;

[0017] S113: Based on the correspondence between the state and position of the unmanned surface vessel and the correspondence between the state and the speed of travel, the simplified model is converted into a state-space model in the form of state equations.

[0018] According to the robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention, step S12 further includes:

[0019] S121: Based on the range of bow angle variation of unmanned surface vessels (USVs), define type II fuzzy rules for USVs;

[0020] S122: Define the upper and lower bound membership weight functions to obtain the type II membership weight functions;

[0021] S123: Based on the type-II fuzzy rules and the type-II membership weight function, obtain the basic type-II fuzzy model.

[0022] According to the robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention, step S2 further includes:

[0023] S21: Establishing an optimization problem for robust predictive control with online state feedback;

[0024] S22: Introduce the robust positive invariant set into the optimization problem to obtain the updated problem;

[0025] S23: A method for solving the update problem based on robust positive invariant sets and membership function information, thereby obtaining an online state feedback predictive control algorithm.

[0026] According to the robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention, step S21 further includes:

[0027] S211: Characterize the input control torque and state constraints of the unmanned surface vessel (USV) to obtain the input control torque and state constraints;

[0028] S212: Based on the non-parallel allocation compensation method, establish an interval type II observer for unmanned surface vessels;

[0029] S213: Based on the input control torque, the state constraints, and the interval type II observer, establish an infinite time-domain unmanned surface vessel stabilization control optimization problem and obtain the optimization problem.

[0030] According to the robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention, step S23 further includes:

[0031] S231: Transform the Lyapunov decay and robust performance constraints into the first matrix inequality and the second matrix inequality, respectively;

[0032] S232: Based on the second matrix inequality combining the robust positive invariant set, the control input constraints and state constraints are transformed into the third matrix inequality and the fourth matrix inequality respectively according to the input control torque and state constraints;

[0033] S233: Based on the membership function vertex envelope method, membership function information is introduced into the first matrix inequality, the third matrix inequality, and the fourth matrix inequality to obtain the membership matrix inequality;

[0034] S234: Solve the update problem based on the membership matrix inequality to obtain the online state feedback predictive control algorithm.

[0035] According to the robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention, the online state feedback predictive control algorithm in step S234 specifically includes:

[0036] S2341: Initialize system state;

[0037] S2342: Solve the update problem to obtain the state feedback sub-gain;

[0038] S2343: Combine the state feedback sub-gain with the membership function to obtain the local control law;

[0039] S2344: Input the control signal corresponding to the local control law into the control system, and update the control according to the time step.

[0040] According to the robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention, step S3 further includes:

[0041] S31: Establish an interval-type type II Luneburger observer based on the system output when the state of the unmanned surface vessel system is unmeasurable;

[0042] S32: Construct an error system based on the interval type II fuzzy model and the interval type II Romberg observer;

[0043] S33: Based on the error evolution trajectory corresponding to the error system, expand the system state to obtain an interval type II observer based on the type II augmented system of observation error.

[0044] According to the robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention, step S4 further includes:

[0045] S41: Based on the system estimated state, establish a type II feedback control law, and substitute the type II feedback control law into the interval type II observer to obtain the basic dynamic output feedback system;

[0046] S42: Introduce robust positive invariant set and membership function information into the basic dynamic output feedback system to obtain an updated dynamic output feedback system;

[0047] S43: Solve the updated dynamic output feedback system using the online state feedback predictive control algorithm and the corresponding dynamic output feedback predictive control algorithm to perform robust dynamic output feedback predictive control on the unmanned surface vessel.

[0048] This invention provides a robust dynamic output feedback predictive control method for unmanned surface vessels (USVs). When establishing the interval type-II fuzzy model of the USV, it fully considers the surface motion characteristics of the USV. By incorporating the restoring force matrix, the model of this invention is more accurate and can better reflect the actual motion characteristics of the USV, thereby improving the effectiveness and stability of the control strategy. This invention introduces membership function information into the optimization problem and control algorithm. By introducing membership function information, this invention can more accurately describe the state and control input uncertainty of the USV system, thereby improving the performance of stabilization control. Furthermore, this invention also ensures that the control algorithm can achieve high performance through efficient algorithm design. Adjustments are made within a specified time, avoiding problems such as response lag or system loss of control. This invention fully considers various constraints of the unmanned surface vessel system in its control strategy, including physical constraints such as linear velocity, angular velocity, thrust, and rudder deflection. By considering these constraints, this invention can design control algorithms that are more in line with practical applications, avoiding safety problems caused by ignoring constraints. This invention adopts an online state feedback robust predictive control algorithm, which can dynamically adjust according to the real-time state of the unmanned surface vessel, thereby improving the robustness and adaptability of the system. In addition, by introducing robust positive invariant sets and membership function information, this invention further enhances the stability and performance of the system.

[0049] This invention provides new ideas and methods for the development of unmanned surface vessel (USV) control technology. By combining technologies such as fuzzy control and predictive control, it provides strong support for the realization of autonomous navigation, intelligent obstacle avoidance, and collaborative operation of USVs. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0051] Figure 1 A schematic diagram of a robust dynamic output feedback predictive control method for unmanned surface vessels provided by the present invention;

[0052] Figure 2 A flowchart illustrating the method for obtaining a type II fuzzy model of an interval provided by the present invention;

[0053] Figure 3 A flowchart illustrating the online state feedback predictive control algorithm acquisition method provided by the present invention;

[0054] Figure 4 A flowchart illustrating the method for obtaining a type II observer in an interval provided by the present invention;

[0055] Figure 5 This is a flowchart illustrating the method for dynamic output feedback robust model prediction of unmanned surface vessels provided by the present invention.

[0056] Figure 6 A schematic diagram of the actual state of an unmanned surface vessel under state feedback predictive control provided by the present invention;

[0057] Figure 7 A schematic diagram of the actual state of an unmanned surface vessel under output feedback predictive control provided by the present invention;

[0058] Figure 8 This is a schematic diagram of the observation state of an unmanned surface vessel under output feedback predictive control provided by the present invention.

[0059] Figure 9 This is a schematic diagram of the control input for the output feedback predictive control unmanned surface vessel provided by the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, embodiments of this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. In the description of this invention, it should be understood that the terminology used is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0061] To better understand the embodiments of the present invention, the research background of the present invention will be explained in detail below.

[0062] The motion characteristics of unmanned surface vessels (USVs) present significant challenges. First, the mathematical model of USV motion is crucial for controller design and analysis; due to its nonlinear nature, the modeling process is complex and costly. Furthermore, USV motion models contain numerous uncertainties, including uncertainties in model parameters, unmodeled dynamics, and disturbances from wind, waves, and currents in the marine environment. USV control systems are typically underactuated, with the propulsion system's control inputs fewer than its degrees of freedom, making them typical underactuated systems. This renders traditional feedback linearization methods ineffective in solving their motion models, and Brockett's theorem indicates that fixed-point regulation cannot be achieved through time-invariant, smooth state feedback controllers. Due to limitations in actuator capabilities, USV motion models must consider physical constraints such as velocity, angular velocity, thrust, and rudder deflection; neglecting these constraints can lead to degraded control performance or even system instability. Moreover, in practical applications, while USV position information can be obtained through positioning systems like GPS, velocity information cannot be directly measured. Although accelerometers can provide acceleration information, they cannot directly acquire velocity. While Doppler logs can measure velocity, their high cost makes them unsuitable for large-scale applications, especially for low-cost, small USVs. Therefore, designing effective velocity observers and feedback control strategies is of significant practical importance, as it can significantly reduce the implementation cost of control algorithms. Designing a control algorithm that comprehensively considers the characteristics of unmanned surface vessels is particularly crucial.

[0063] For current unmanned surface vessel (USV) control methods, existing USV interval type II modeling techniques ignore the restoring force matrix. However, omitting the restoring force will lead to poor performance of the control strategy in practical applications, making it unable to effectively cope with environmental changes and maintain system stability.

[0064] Secondly, existing unmanned surface vessel (USV) stabilization control systems do not incorporate membership function information, which contains crucial information about the USV. Ignoring this will affect the system's stabilization performance. Introducing membership functions while ensuring algorithm efficiency is also crucial; otherwise, if the control algorithm fails to adjust within the specified time, it may lead to response lag or system malfunction.

[0065] Furthermore, current technology does not take system constraints into account. The mathematical model of unmanned surface vessel (USV) motion contains physical constraints such as linear velocity, angular velocity, thrust, and rudder deflection. These constraints are related to the USV's propulsion capabilities and system state limitations. Therefore, ignoring these constraints will lead to a failure to ensure the safety of the USV, rendering the control algorithm ineffective in practical applications.

[0066] Finally, most existing unmanned surface vessel (USV) control systems are based on state feedback, but since some states of USVs cannot be directly measured in a low-cost manner, this poses a challenge to the design and application of the control system.

[0067] The embodiments of the present invention are described below with reference to the figures.

[0068] like Figure 1 As shown, this invention provides a robust dynamic output feedback predictive control method for unmanned surface vessels, comprising:

[0069] S1: Establish an interval type II fuzzy model of the unmanned surface vessel.

[0070] The purpose of step S1 of this invention is to establish a mathematical model for the dynamic behavior of unmanned surface vessels that can handle uncertainty and fuzziness. Compared with traditional fuzzy models, the interval type II fuzzy model established in step S1 can better handle the uncertainty in input and output, thereby improving the robustness of the control system.

[0071] like Figure 2 As shown, step S1 further includes:

[0072] S11: Based on the surface motion characteristics of unmanned surface vessels, establish a state-space model of the unmanned surface vessel.

[0073] Step S11 further includes:

[0074] S111: Select a three-degree-of-freedom unmanned surface vessel dynamics model as the basic model.

[0075] Furthermore, this invention considers a dynamic model of a three-degree-of-freedom USV, specifically expressed as follows:

[0076]

[0077] η=[η x ,η t ,η ψ ]∈R 3 Let η be the position vector of USV. x ,η y ) represents the position in the geodetic coordinate system, η ψ It is the heading angle in the geodetic coordinate system, v = [v x ,v y ,v ψ ]∈R 3 It is the USV's speed vector, where v x The oscillation velocity, v y The sway velocity, v ψ The y-axis refers to the bow speed, τ refers to the desired control input, and S∈R 3×3 It is a positive definite symmetric inertial matrix, C(v)∈R3×3 Represents the centripetal and Coriolis force matrices, D(v)∈R 3×3 Let G represent the damping matrix, G be the restoring force caused by gravity, buoyancy and ocean currents, ω be the unknown disturbance and model uncertainty, and γ(η) be the non-singular transformation matrix from the ship coordinate system to the geodetic coordinate system.

[0078] S112: Based on the stabilization and control problem of unmanned surface vessels, a simplified model is obtained by ignoring the centripetal force and Coriolis force matrices of the basic model.

[0079] In stabilization control problems, in order to simplify the model and reduce the complexity of control design, this invention chooses to ignore the centripetal force and Coriolis force matrices. These forces may be more significant during high-speed motion or large-scale turning, but in stabilization control problems, in order to grasp the main contradictions, they can be ignored to appropriately simplify the model.

[0080] Specifically, this invention considers the stabilization control problem of unmanned surface vessels. The control objective is to stabilize the vessel to a set equilibrium point and maintain the desired orientation. In practice, this manifests as positioning control, automatic berthing, etc. For underactuated vessels, since the system is subject to a second-order nonholonomic constraint of non-integrable acceleration, there is no smooth time-invariant feedback control law to make the system asymptotically stable.

[0081] Regarding the centripetal force and Coriolis force matrices, on the one hand, when the unmanned surface vessel (USV) is traveling at low speed on the water surface, the drag it experiences can usually be approximated as linear with its speed. In this case, the hydrodynamic drag term in the dynamic model can be constructed in a linear form. On the other hand, when modeling, considering that the USV mainly moves in the horizontal plane, we ignore the vertical, roll, and pitch motions of the USV, thus simplifying the six-degree-of-freedom hydrodynamic equations into three-degree-of-freedom hydrodynamic equations in the horizontal plane. In this case, the influence of centripetal force and Coriolis force is relatively small, and we can consider simplifying or ignoring the influence of these forces. Therefore, omitting the centripetal force and Coriolis force matrices, the USV's motion model on the water surface becomes:

[0082]

[0083] S113: Based on the correspondence between the state and position of the unmanned surface vessel and the correspondence between the state and the speed of travel, the simplified model is converted into a state-space model in the form of state equations.

[0084] Specifically, in step S113 of this invention, the correspondence between the state and the position and speed of the unmanned surface vessel is defined, that is, let x1 = η, x2 = v, u = τ, then the general USV dynamic system is expressed as:

[0085]

[0086] Expressed in the form of state equations:

[0087]

[0088] In the formula,

[0089] In step S113 of this invention, the simplified dynamic model of the unmanned surface vessel is converted into a state-space model in the form of state equations. A state-space model is a mathematical tool for describing the dynamic behavior of a system. It uses state variables to describe the internal state of the system and uses state equations to describe how these state variables change over time. Step S113 is to enable the design of a controller using modern control theory and methods.

[0090] S12: Based on the state space model, establish a basic type II fuzzy model.

[0091] Step S12 further includes:

[0092] S121: Based on the range of bow angle variation of the unmanned surface vessel (USV), define the type II fuzzy rules for USV.

[0093] This invention considers the heading angle at... Internal changes, thus from Define the interval type II fuzzy rule for unmanned surface vessels as follows:

[0094] Rule i: If sin(η) ψ ) is M i1 And cos(η) ψ ) is M i1 ,So:

[0095]

[0096]

[0097] In step S121, the present invention defines a type II fuzzy rule based on the bow angle variation range of the unmanned surface vessel. Compared with the traditional type I fuzzy rule, the type II fuzzy rule can better handle fuzziness and uncertainty, and the provided rule describes the possible behavior and response of the unmanned surface vessel under different bow angle states.

[0098] S122: Define the upper and lower bound membership weight functions to obtain the type II membership weight functions.

[0099] In step S122, firstly, the upper and lower bound membership weight functions are defined, and then the average centroid method is used for defuzzification, resulting in:

[0100] The activation strength of the i-th fuzzy rule can be expressed as:

[0101]

[0102] The membership function of the i-th fuzzy rule is:

[0103]

[0104] in, The predefined nonlinear weighting function satisfies

[0105] In step S122, the present invention defines upper and lower bound membership weight functions to describe the uncertainty of membership in type II fuzzy sets. Through these weight functions, the present invention can more accurately describe the uncertainty of the unmanned surface vessel's state.

[0106] S123: Based on the type-II fuzzy rules and the type-II membership weight function, obtain the basic type-II fuzzy model.

[0107] Furthermore, combining the results of steps S121 and S122 above, the type-II fuzzy system can be obtained, and its specific expression is as follows:

[0108]

[0109] The obtained model can describe the fuzzy behavior and uncertainties of unmanned surface vessels under different states.

[0110] S13: By discretizing the basic type-II fuzzy model, an interval type-II fuzzy model is obtained.

[0111] Furthermore, the application of discrete control in modern control systems is inevitable. It provides an effective way to achieve efficient, reliable, and flexible control strategies. The zero-order hold is superior to the Euler method in terms of accuracy and stability. If the sampling time is T, then according to the parameter matrix of the type II model system, considering that the restoring force matrix G is often a singular matrix, resulting in A not being of full rank, we resort to the Euler method. The specific expression is:

[0112] In practical control systems, due to limitations in computer processing power and real-time requirements, continuous-time models often need to be discretized. Therefore, in step S13, the researchers discretized the basic type II fuzzy model to obtain an interval type II fuzzy model. The interval type II fuzzy model allows the membership function to vary within a certain interval, thus having a stronger ability to handle uncertainty and fuzziness.

[0113] S2: Establish the optimization problem of online state feedback robust predictive control, and obtain the online state feedback predictive control algorithm by solving the optimization problem.

[0114] like Figure 3As shown, step S2 further includes:

[0115] S21: Establish an optimization problem for robust predictive control with online state feedback.

[0116] Step S21 further includes:

[0117] S211: Characterize the input control torque and state constraints of the unmanned surface vessel (USV) to obtain the input control torque and state constraints.

[0118] In step S211 of this invention, the control input torque of the unmanned surface vessel and its state constraints are first formally characterized, assuming that the control input torque and state of the unmanned surface vessel are subject to the following constraints:

[0119]

[0120] Among them, u max It is the upper bound of the control input, [*] α It is the α-th element in *, M∈R 1×n ξ represents the number of constraints on the system state.

[0121] S212: Based on the non-parallel allocation compensation method, establish an interval type II observer for unmanned surface vessels.

[0122] Secondly, in step S212, the present invention designs a type II fuzzy controller for unmanned surface vessels with a non-parallel allocation compensation method for the design interval. The type II fuzzy controller for unmanned surface vessels with a non-parallel allocation compensation method for the design interval is as follows:

[0123] u=K n x;

[0124]

[0125] in, It is a predefined nonlinear weighting function, and satisfies Compared to Take it as a constant value. Being a nonlinear function can reduce the conservatism in controller design.

[0126] S213: Based on the input control torque, the state constraints, and the interval type II observer, establish an infinite time-domain unmanned surface vessel stabilization control optimization problem and obtain the optimization problem.

[0127] In step S213, combining the results obtained in steps S211 and S212, an infinite-time-domain unmanned surface vessel stabilization control optimization problem is established, the specific expression of which is:

[0128]

[0129] in, The objective function is Q>0 and R>0 is a known weight matrix. *(k+c|k) represents the value of k+c predicted for the future time using the current information.

[0130] S22: Introduce a robust positive invariant set into the optimization problem to obtain the update problem.

[0131] In step S22, a robust positive invariant set is introduced to transform the infinite time domain robust predictive control optimization min / max problem in step S213 into a min problem that minimizes the upper bound of the performance exponent. The specific process is as follows.

[0132] First, define the quadratic Lyapunov function as follows:

[0133] V(k)=x T (k|k)P x x(k|k);

[0134] Where P x >0, assuming the difference between the predicted Lyapunov function at k+c and k+c+1 satisfies:

[0135] V(k+c+1|k)-V(k+c|k)+x(k+c|k) T Qx(k+c|k)+u(k+c|k) T Ru(k+c|k)≤0;

[0136] Adding the above expression from c = 0 to c = ∞, lim c→∞ x(k+c|k=0, when lim c→∞ When V(x(k+c|k))=0, we can obtain Considering V(k|k)≤γ, introduce H ∞ Performance index: ∥y(k)∥2≤γ c The optimization issue can be updated as follows: ∥ω∥2

[0137]

[0138] This refers to the min problem mentioned above, which involves minimizing the upper bound of the performance exponent.

[0139] S23: A method for solving the update problem based on robust positive invariant sets and membership function information, thereby obtaining an online state feedback predictive control algorithm.

[0140] Step S23 further includes:

[0141] S231: Transform the Lyapunov decay and robust performance constraints into the first matrix inequality and the second matrix inequality, respectively.

[0142] In step S231, the Lyapunov decay and robustness constraints are first transformed into matrix inequalities. The Lyapunov decay under robust constraints can be guaranteed by the following equation:

[0143]

[0144] In the formula matrix front and back multiplication diag{N x γ, I}, define Y n =K n N x , And by using Schur's complement, we get:

[0145]

[0146] S232: Based on the second matrix inequality combining the robust positive invariant set, the control input constraints and state constraints are transformed into the third matrix inequality and the fourth matrix inequality, respectively, according to the input control torque and state constraints.

[0147] Furthermore, in step S232, it is necessary to combine the robust positive invariant set to transform the control input constraints and state constraints into matrix inequalities. The specific steps are as follows.

[0148] Regarding terminal constraints, if at the current time x(k|k) T P x If x(k|k)≤γ, then the terminal time must satisfy V(k+N|k)≤γ, which can be transformed into a linear expression using Schur's complement.

[0149] Regarding control input restrictions, we have:

[0150]

[0151] If the above formula holds true, then:

[0152]

[0153] Furthermore, multiplying by N before and after... x We can obtain:

[0154]

[0155] Regarding state constraints, we have:

[0156] max{[Mx(k+c|k)] β |x(k+c|k)∈Ω x}≤1;

[0157] Using the method of Lagrange multipliers, we can ensure this by the following formula:

[0158]

[0159] Use Schur complement and multiply by N before and after. x Therefore, Ω≤0.

[0160] S233: Based on the membership function vertex envelope method, membership function information is introduced into the first, third, and fourth matrix inequalities to obtain the membership matrix inequalities.

[0161] In the unified space of membership functions, the envelope method is adopted. The following algorithm can be used to calculate the envelope vertex of the product of type II membership functions in the membership function space. Thus, the information of type II membership functions is introduced into the Lyapunov function decreasing inequality, state constraints, and sufficient guarantee inequality of input constraints, thereby reducing the conservatism of the solution.

[0162] The specific algorithm for the vertex envelope of the interval type II membership function space is as follows: Let Calculate f i The maximum and minimum values ​​of (x), f imin =min{f i (z)},f imax =max{f i (z)};Calculate the maximum and minimum values ​​of the new membership degree defined as follows: Create variable β svj :β sv0 =α s0 , Finally, Subsequently, through processes such as basis coordinate transformation and modulo operation, the coordinates of the convex envelope vertices are obtained, and the envelope points are used to solve the above matrix inequalities.

[0163] S234: Solve the update problem based on the membership matrix inequality to obtain the online state feedback predictive control algorithm.

[0164] Based on the results of steps S21 to S22, the present invention obtains the following online state feedback predictive control algorithm for unmanned surface vessels.

[0165] Specifically, the online state feedback predictive control algorithm in step S234 includes:

[0166] S2341: Initialize system state.

[0167] S2342: Solve the update problem to obtain the state feedback sub-gain.

[0168] S2343: Combine the state feedback sub-gain with the membership function to obtain the local control law.

[0169] S2344: Input the control signal corresponding to the local control law into the control system, and update the control according to the time step.

[0170] The specific online state feedback predictive control algorithm is as follows: Initialize the system state online, solve the optimization problem in step S21 (the update problem in step S22), and obtain the state feedback sub-gain K. i =Y i (N x ) -1 Then, these sub-gains are combined with membership functions (MFs) to obtain the local control law u(k). If it is not satisfied, then u(k) = 0, and the control signal u(k) is input into the system. Then, k is updated to k+1 and the control signal u(k+1) is input into the system again, and the process is continuously updated.

[0171] The optimization problem established in step S2 assumes that the state of the unmanned surface vessel (USV) system is measurable. However, in practical applications, while the position information of USVs can be obtained through inexpensive global navigation and positioning systems such as GPS and BeiDou, their velocity information cannot be directly measured by these systems. Accelerometers can only measure acceleration, not velocity. Although Doppler logs can directly measure the velocity of USVs, they are expensive and unsuitable for large-scale USV swarm applications, especially for small, low-cost USVs. Therefore, researching velocity observers and their output feedback control is of practical significance and can significantly reduce the implementation cost of control algorithms.

[0172] S3: Based on the aforementioned interval type II fuzzy model, establish an interval type II observer for the unmanned surface vessel.

[0173] like Figure 4 As shown, step S3 further includes:

[0174] S31: Establish an interval type II Luneburger observer based on the system output when the state of the unmanned surface vessel system is unmeasurable.

[0175] S32: Construct an error system based on the interval type II fuzzy model and the interval type II Luneburger observer.

[0176] S33: Based on the error evolution trajectory corresponding to the error system, expand the system state to obtain an interval type II observer based on the type II augmented system of observation error.

[0177] In steps S31 to S33, firstly, when the unmanned surface vessel system state is unmeasurable, based on the system output, this invention designs an interval-type type II Luneburger observer:

[0178]

[0179] Where L is the observer gain, and the estimation error is defined. The observer gain needs to be designed offline. Secondly, a specific error system can be constructed, expressed as:

[0180]

[0181] Based on the constructed error evolution trajectory and the original system state, the system state is expanded.

[0182] S4: The unmanned surface vessel is dynamically robustly predicted using the online state feedback predictive control algorithm and the dynamic output feedback predictive control algorithm to achieve stable control of the unmanned surface vessel.

[0183] In step S4, the theorem is first given: given a scalar β>0, the augmented interval type II fuzzy system converges under the action of the dynamic output feedback control law, and satisfies the control input constraints, state constraints, and H. ∞ Performance Index The premise is that there exists an observation matrix L and a positive definite matrix N. x N c Make the following optimization problems solvable:

[0184]

[0185] At this time, control gain

[0186] like Figure 5 As shown, step S4 further includes:

[0187] S41: Based on the estimated state of the system, establish a type II feedback control law, and substitute the type II feedback control law into the type II observer of the interval to obtain the basic dynamic output feedback system.

[0188] In steps S41 to S43, firstly, based on the estimated system state, a type II feedback control law is designed:

[0189]

[0190] Substituting the type-II feedback control law into the observation-error augmentation system, a unified dynamic output feedback dynamic system is formed:

[0191]

[0192] S42: Introduce robust positive invariant set and membership function information into the basic dynamic output feedback system to obtain an updated dynamic output feedback system.

[0193] In step S42, similar to steps S231 to S233, a robust positive invariant set is first introduced to transform the robust predictive control optimization min max problem of dynamic output feedback in infinite time domain into a min problem of minimizing the upper bound of the performance exponent. The Lyapunov decay and robust performance constraints of the observation-error augmented system are transformed into matrix inequalities. Finally, the membership function vertex envelope method is used to introduce membership function information into the augmented system inequalities.

[0194] S43: Solve the updated dynamic output feedback system using the online state feedback predictive control algorithm and the corresponding dynamic output feedback predictive control algorithm to perform robust dynamic output feedback predictive control on the unmanned surface vessel.

[0195] Finally, in step S43, the optimization problem given in step S4 is solved, i.e., there exists an observation matrix L and a positive definite matrix N. x N c The problem that makes the optimization problem solvable can be solved by combining the unmanned surface vessel dynamic output feedback robust model predictive control algorithm obtained in step S2 above, and unmanned surface vessel control can be performed.

[0196] Specifically, the system's observation state and error state are initialized online, and then an optimization problem is solved to obtain the state feedback sub-gain K. i =Y i (N x ) -1 And the observation matrix L, and then combine these sub-gains with membership functions (MFs) to obtain the local control law u(k). If it is not satisfied, then u(k) = 0, the control signal u(k) is input into the system, then k is updated to k+1 and the control signal u(k+1) is input into the system, and the process is continuously updated.

[0197] like Figures 6 to 9 The diagram shown is a schematic representation of the state of an unmanned surface vessel in a specific application example of the present invention. Figure 6 For state feedback predictive control of the unmanned surface vessel's actual state, multiple curves x mn (m = 1, 2; n = 1, 2, ..., 6) represent the actual state of the system under different control laws. Figure 7 To output the actual state of the feedback predictive control unmanned surface vessel and demonstrate the system's robustness when the state is unpredictable, multiple curves x... n (n = 1, 2, ..., 6) represents the actual state of the system under different control laws; Figure 8 To output the feedback predictive control of the unmanned surface vessel's (USV) observation state, this paper demonstrates that, under the presence of disturbances, the USV observation system state convergently approximates the original system state. Multiple curves represent each... The estimated state; Figure 9To demonstrate the convergence of the control input for dynamic output feedback predictive control of the unmanned surface vessel, multiple curves represent the control input convergence for each u. n (n=1,2,3) control inputs.

[0198] Figures 6 to 9 As can be seen, both the system state and the control input converge quickly. Although the disturbance input is relatively large compared to the system state, both the state feedback robust control method algorithm corresponding to step S2 and the output feedback robust control method algorithm corresponding to step S4 can effectively stabilize the system. Moreover, due to its dynamic characteristics, the output feedback can stabilize the unmanned surface vessel even faster.

[0199] This invention comprehensively considers external disturbances, constraints, and the unpredictability of system state, proposing an optimization algorithm based on robust predictive control with online dynamic output feedback, enabling unmanned surface vessels (USVs) to achieve stable control in complex sea conditions. Compared to traditional state-based control methods that do not consider constraints, this invention has the following advantages: Robust adaptation to complex environments: The designed online predictive control algorithm considers external disturbances such as ocean currents and waves, as well as control input and state constraints. Even with disturbances, the USV can still safely achieve stable control; Low conservatism: In the optimization problem, the membership function is used to unify the metric space, and information from the interval type II membership function is introduced through the vertex envelope. This information reflects the nonlinear dynamic behavior of the system to a certain extent, not only expanding the range of stable states of the USV but also improving the dynamic performance of the system; Real-time computation: The original interval cumulative infinite time-domain optimization problem is transformed into a convex optimization problem with linear matrix inequality constraints, which can be solved in real time; Economic efficiency: The designed dynamic output feedback online predictive control algorithm does not require velocity and position sensors to obtain system state, resulting in high economic benefits.

[0200] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A robust dynamic output feedback predictive control method for unmanned surface vehicle, characterized in that, The method comprises the following steps: S1: establishing an interval type-2 fuzzy model of the unmanned surface vehicle; S2: establishing an optimization problem of online state feedback robust predictive control, and obtaining an online state feedback predictive control algorithm by solving the optimization problem; S3: establishing an interval type-2 observer of the unmanned surface vehicle based on the interval type-2 fuzzy model; wherein, step S3 further comprises: S31: establishing an interval type-2 Luenberger observer based on the system output when the system state of the unmanned surface vehicle is unmeasurable; S32: constructing an error system based on the interval type-2 fuzzy model and the interval type-2 Luenberger observer; S33: expanding the system state according to the error evolution trajectory corresponding to the error system, and obtaining an interval type-2 observer based on a type-2 augmented system of the observation error; S4: performing dynamic robust model prediction on the unmanned surface vehicle by the online state feedback predictive control algorithm and a dynamic output feedback predictive control algorithm based on the interval type-2 observer, so as to realize the stabilization control of the unmanned surface vehicle.

2. The robust dynamic output feedback predictive control method for an unmanned surface vehicle according to claim 1, wherein, Step S1 further comprises: S11: establishing a state space model of the unmanned surface vehicle based on the water surface movement characteristics of the unmanned surface vehicle; S12: establishing a basic type-2 fuzzy model based on the state space model; S13: obtaining an interval type-2 fuzzy model by discretizing the basic type-2 fuzzy model.

3. The robust dynamic output feedback predictive control method for an unmanned surface vehicle according to claim 2, wherein, Step S11 further comprises: S111: selecting a three-degree-of-freedom unmanned surface vehicle dynamics model as a basic model; S112: obtaining a simplified model by ignoring the centripetal force and Coriolis torque matrix of the basic model based on the stabilization control problem of the unmanned surface vehicle; S113: converting the simplified model into a state space model in the form of a state equation based on the correspondence between the state and the position of the unmanned surface vehicle and the correspondence between the state and the sailing speed.

4. The robust dynamic output feedback predictive control method for an unmanned surface vehicle according to claim 2, wherein, Step S12 further comprises: S121: defining a type-2 fuzzy rule of the unmanned surface vehicle based on the variation range of the heading angle of the unmanned surface vehicle; S122: defining an upper and lower bound membership weight function to obtain a type-2 membership weight function; S123: obtaining a basic type-2 fuzzy model based on the type-2 fuzzy rule and the type-2 membership weight function.

5. The robust dynamic output feedback predictive control method for an unmanned surface vehicle according to claim 1, wherein, Step S2 further comprises: S21: establishing an optimization problem of online state feedback robust predictive control; S22: introducing a robust positive invariant set into the optimization problem to obtain an update problem; S23: obtaining an online state feedback predictive control algorithm based on the solving method of the update problem and the information of the robust positive invariant set and the membership function.

6. The robust dynamic output feedback predictive control method for an unmanned surface vehicle according to claim 5, wherein, Step S21 further comprises: S211: characterizing the input control torque of the unmanned surface vehicle and the state constraint of the unmanned surface vehicle to obtain the input control torque and the state constraint; S212: establishing an interval type-2 observer of the unmanned surface vehicle based on a non-parallel assignment compensation method; S213: establishing an unmanned surface vehicle stabilization control optimization problem in an infinite time domain based on the input control torque, the state constraint and the interval type-2 observer to obtain an optimization problem.

7. The robust dynamic output feedback predictive control method for an unmanned surface vehicle according to claim 5, wherein, Step S23 further comprises: S231: converting Lyapunov attenuation and robust performance constraint conditions into a first matrix inequality and a second matrix inequality, respectively; S232: based on the second matrix inequality of the robust positive invariance set, the control input constraint and the state constraint are converted into a third matrix inequality and a fourth matrix inequality respectively according to the input control torque and the state constraint; S233: based on the vertex envelope method of the membership function, the membership function information is introduced into the first matrix inequality, the third matrix inequality and the fourth matrix inequality to obtain a membership matrix inequality; S234: the update problem is solved based on the membership matrix inequality to obtain an online state feedback predictive control algorithm.

8. The robust dynamic output feedback predictive control method for an unmanned surface vehicle according to claim 7, wherein, The online state feedback predictive control algorithm in step S234 specifically includes: S2341: initializing the system state; S2342: solving the update problem to obtain a state feedback sub-gain; S2343: combining the state feedback sub-gain with the membership function to obtain a local control law; S2344: inputting the control signal corresponding to the local control law into the control system and updating the control according to the time step.

9. The robust dynamic output feedback predictive control method of an unmanned surface vehicle according to claim 1, wherein, Step S4 further includes: S41: establishing a two-type feedback control rate according to the estimated state of the system, substituting the two-type feedback control rate into the interval two-type observer to obtain a basic dynamic output feedback system; S42: introducing the robust positive invariance set and the membership function information into the basic dynamic output feedback system to obtain an updated dynamic output feedback system; S43: solving the updated dynamic output feedback system through the online state feedback predictive control algorithm and the corresponding dynamic output feedback predictive control algorithm to perform robust dynamic output feedback predictive control on the unmanned ship.

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