Static output feedback dynamic decoupling control method for unmanned surface vehicle

Abstract

The invention provides a static output feedback dynamic decoupling control method for an unmanned surface vehicle, and belongs to the technical field of motion control and intelligent decision of the unmanned surface vehicle. Comprising the following steps: modeling a motion control system of the unmanned surface vehicle into a discrete time linear system model; a zero block is added into a matrix related to control input, a real matrix is correspondingly introduced into control gain, and a closed-loop system is augmented, so that an additional degree of freedom is introduced for a proposed comprehensive condition. On the basis of the provided multiple Lyapunov functions, the functions are formed by the sum of the Lyapunov functions depending on the system states at different moments, and sufficient conditions represented by linear matrix inequality are deduced to ensure the stability and expected performance of the closed-loop system. Compared with an existing method, decoupling can be achieved without a specific structure of a correlation matrix, and a better result can be obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of motion control and intelligent decision-making of unmanned surface vessels, and particularly relates to a static output feedback dynamic decoupling control method for unmanned surface vessels. Background Art

[0002] As a key equipment in the fields of ocean exploration, environmental monitoring, maritime rescue, etc., the autonomous navigation and precise control capabilities of unmanned surface vessels are the basis for realizing efficient task execution. With the complexity and diversification of ocean tasks, higher requirements are put forward for the control systems of unmanned surface vessels, especially in terms of stability, robustness, and dynamic performance. Static output feedback control, which only relies on system output information and does not require complete state data, shows stronger engineering practicability and flexibility compared with state feedback control, and has become a research hotspot in the technical field of motion control and intelligent decision-making of unmanned surface vessels. However, existing invention patents on static output feedback control methods still face many challenges in practical applications. For example, the design of static output feedback controllers usually involves non-convex optimization problems, which are caused by the non-linear coupling relationship between the output matrix and the feedback gain matrix. Traditional methods are difficult to directly solve such non-convex optimization problems and often need to introduce additional equality constraints or assumptions, which greatly limit the applicable scope and performance of the controllers. Therefore, it is of great significance to seek an effective and practical static output feedback controller design method and carry out research on the stable control of unmanned surface vessels.

[0003] In addition, the Lyapunov function, as an important tool for analyzing system stability, occupies a core position in control theory. The form of traditional Lyapunov functions is relatively fixed, such as quadratic Lyapunov functions. Although remarkable achievements have been made in practical applications, when dealing with some complex systems or special control problems, they cannot fully reflect the dynamic characteristics of the system, resulting in poor controller design effects. Especially in the field of controlling unmanned surface vessels, due to the complexity and uncertainty of the ocean environment, traditional Lyapunov functions are difficult to provide sufficient stability guarantee and performance optimization space. In recent years, with the continuous development and innovation of control theory, the research on new types of Lyapunov functions has gradually become a hotspot. New types of Lyapunov functions are more flexible and diverse in form, such as fuzzy Lyapunov functions, polynomial Lyapunov functions, and piecewise Lyapunov functions, etc., which can better adapt to the characteristics of different systems and provide new ideas and methods for solving the control problems of complex systems. In the field of static output feedback control of unmanned surface vessels, the design method based on new types of Lyapunov functions has shown great potential. By reasonably designing new types of Lyapunov functions, the non-convex optimization problems in static output feedback control can be more effectively handled, and the performance and stability of the controllers can be improved. Summary of the Invention

[0004] In view of the challenges such as non-convex optimization problems and the coupling of control gains and output matrices existing in the existing static output feedback control methods for unmanned surface vessels, the present invention focuses on the static output feedback control problem of unmanned surface vessels based on a new Lyapunov function, and provides a static output feedback control method for unmanned surface vessels based on multiple Lyapunov functions. By constructing a new Lyapunov function composed of the sum of Lyapunov functions related to the system states at different times, establishing linear matrix inequality conditions, realizing the stability and ideal performance of the closed-loop system, and adopting a new decoupling strategy to break through the dependence on the structure of the associated matrix of the traditional method, the control performance is improved. The purpose of the present invention is to deeply explore how to use the new Lyapunov function to design a static output feedback controller with better performance, and give a new decoupling method to achieve the decoupling between the control gain and the output matrix. This not only helps to improve the autonomous navigation and precise control capabilities of unmanned surface vessels, promotes their application and development in the fields of ocean exploration, environmental monitoring, maritime rescue, etc., but also provides new ideas and methods for the development of control theory.

[0005] The technical solution of the present invention:

[0006] A static output feedback dynamic decoupling control method for an unmanned surface vessel, comprising:

[0007] First, the object of the present invention is the motion control system of an unmanned surface vessel, and a linear model of the motion control system of the unmanned surface vessel is constructed;

[0008] Second, for the constructed system model, a static output feedback controller is designed;

[0009] Third, multiple Lyapunov functions are constructed, and the performance analysis conditions of the static output feedback controller are deduced;

[0010] Fourth, the controller design conditions for enabling the unmanned surface vessel system to obtain satisfactory performance are established, and the controller gain is solved;

[0011] Finally, the control signal generated by the controller is transmitted to the actuator of the unmanned surface vessel, so as to achieve the purpose of stable control.

[0012] The beneficial effects of the present invention: The static output feedback control method for unmanned surface vessels based on multiple Lyapunov functions provided by the present invention can achieve system stability and performance optimization. Compared with the existing methods, the present invention expands the closed-loop system by introducing additional zero blocks and real matrices, provides additional design freedoms, can achieve the decoupling of the control gain and the output matrix without a specific structure matrix, significantly reduces the complexity of the non-convex optimization problem, and improves the flexibility of controller design and the actual application effect. Description of the Drawings

[0013] Figure 1It is a block diagram of the control method steps of the present invention.

[0014] Figure 2 It is a schematic diagram of the motion coordinates of the unmanned surface vehicle in the present invention.

[0015] Figure 3 It is a system state diagram of the unmanned surface vehicle in the embodiment of the present invention.

[0016] Figure 4 It is a performance output diagram of the unmanned surface vehicle in the embodiment of the present invention.

[0017] Figure 5 It is a multiple Lyapunov function V diagram in the embodiment of the present invention.

[0018] Figure 6 It is a Lyapunov function V1 diagram in the embodiment of the present invention.

[0019] Figure 7 It is a Lyapunov function V2 diagram in the embodiment of the present invention.

[0020] Figure 8 It is a Lyapunov function V3 diagram in the embodiment of the present invention. Detailed implementation manners

[0021] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0022] In this embodiment, the static output feedback dynamic decoupling control method for an unmanned surface vehicle includes the following steps:

[0023] Step 1: The present invention focuses on the field of the motion control system of an unmanned surface vehicle. The schematic diagram of the setting of the motion coordinates of the unmanned surface vehicle is as Figure 2 shown, and the motion equation of the unmanned surface vehicle is described as follows:

[0024]

[0025] where, υ(t) is the sway rate (affected by the rudder movement), represents the derivative of υ(t), χ(t) is the yaw rate, represents the derivative of χ(t), p(t) is the heading angle, represents the derivative of p(t), φ(t) is the roll rate, represents the derivative of φ(t), ψ(t) is the roll angle, represents the derivative of ψ(t), δ(t) is the rudder deflection angle, is the wave response caused by sway, is the wave response caused in the yaw channel, ζ is the damping coefficient, is the undamped natural frequency; T υand T χ are the time constants of the motion equations respectively; K dυ , K υχ , K dχ , K υp , K dp are the preset gain parameters respectively; F(t) represents the nonlinear term, and are the coefficients of the nonlinear term respectively.

[0026] In the above system description, there are multiple key variables involved: the swaying rate υ(t) (affected by the rudder motion), the yaw rate χ(t), the heading angle p(t), the roll rate φ(t), the roll angle ψ(t), and the rudder deflection angle δ(t). In addition, the wave responses and induced by external disturbances in the swaying and yaw channels are also taken into consideration. The system model contains a nonlinear term caused by complex hydrodynamic effects, whose functional form is represented by F(t), and the corresponding coefficients are To optimize the system performance, the preset gain parameters K dυ , K υχ , K dχ , K υp , K dp are introduced. In terms of dynamic characteristics, T υ , T χ , ζ and together constitute the basis of the system dynamics.

[0027] The above motion control equation of the unmanned surface vehicle is a continuous-time linear model. After sampling at 0.01 seconds, a discrete-time system model is constructed as follows:

[0028] x(k + 1) = Ax(k) + Bu(k) + Dw(k)

[0029] y(k) = Cx(k)

[0030] z(k) = Ex(k)

[0031] Among them, x(k) represents the system state, y(k) represents the measurement output, u(k) represents the control input, z(k) represents the performance output, x(k + 1) represents the next state of the system state x(k), and w(k) is an external disturbance and is energy-bounded. A, B, D, C, and E are system matrices.

[0032] A multiple Lyapunov function will be constructed to derive the performance analysis conditions of the static output feedback controller, where each Lyapunov function in the multiple Lyapunov function depends separately on the system states at different times. Based on this idea, the discrete-time system model is reconstructed according to different times as follows:

[0033] x(k + t) = Ax(k + t - 1) + Bu(k + t - 1) + Dw(k + t - 1)

[0034] y(k + t - 1) = Cx(k + t - 1)

[0035] z(k + t - 1) = Ex(k + t - 1), t = 1, …, N

[0036] where N is a positive integer representing the total number of operating steps, t is independent of k and can take any integer between 1 and N.

[0037] Step 2: Design a static output feedback controller and construct a closed-loop system;

[0038] (1) Design a static output feedback controller for the discrete-time system model at different times as follows:

[0039] u(k + t - 1) = Ly(k + t - 1), t = 1, …, N

[0040] where L is the controller gain matrix to be designed.

[0041] Substitute the static output feedback controller into the system models at different times to obtain the closed-loop system as follows:

[0042] x(k + t) = (A + BLC)x(k + t - 1) + Dw(k + t - 1)

[0043] z(k + t - 1) = Ex(k + t - 1), t = 1, …, N

[0044] To avoid the choice of slack variables being too restricted due to convex problems, the above closed-loop system can be rewritten as a closed-loop augmented system as follows:

[0045]

[0046] z(k + t - 1) = Ex(k + t - 1), t = 1, …, N

[0047] where new matrices are defined and Γ is an arbitrary real matrix.

[0048] (2) Establish a multiple Lyapunov function V k(x(k)), where the sum of Lyapunov functions that depend on the system states at different times constitutes the object to be designed V k (x(k)), which is given as follows:

[0049]

[0050] where,

[0051]

[0052] P q represents the Lyapunov function matrix, q represents an arbitrary integer from t to N, and ∑ is the summation symbol.

[0053] (3) Static output feedback controller performance analysis conditions.

[0054] In the embodiments of the present invention, for the system models at different times, a static output feedback controller is designed, and a closed-loop system and a closed-loop augmented system are constructed. If there exist a Lyapunov matrix P t > 0, a positive definite matrix Q t-1 > 0, t = 1, 2,..., N, and a scalar β > 0 such that the following inequality holds:

[0055]

[0056]

[0057] where, * represents the symmetric terms in the symmetric matrix, and I is the identity matrix with appropriate dimensions.

[0058] Then the system can achieve ideal performance.

[0059] (4) Static output feedback controller design conditions.

[0060] In the embodiments of the present invention, for the system models at different times, a static output feedback controller is designed, and a closed-loop system and a closed-loop augmented system are constructed. If there exist a Lyapunov matrix P t > 0, a positive definite matrix Q t-1 > 0, t = 1, 2,..., N, a scalar β > 0, a positive definite matrix Y > 0, a positive definite matrix X1 > 0, matrices X2, X3, X4, and a new matrix K = YL such that the following inequality holds:

[0061]

[0062] where, the matrix X is defined as the matrix U is defined as Other matrices are as follows:

[0063]

[0064]

[0065] Then the augmented closed-loop system will achieve ideal performance.

[0066] (5) Determine the static output feedback controller gain.

[0067] By solving the linear matrix inequality in (4) of Step 2, matrices K and Y can be obtained, and then the gain of the static output feedback controller can be calculated as L = (Y -1 K) T , where Y -1 represents the inverse matrix of Y, and T represents the transpose symbol.

[0068] Step 3: Transmit the control signal u(k + t - 1) generated by the static output feedback controller to the actuator of the unmanned surface vehicle, so as to achieve the purpose of stable control.

[0069] The purpose of this embodiment is to ensure that the designed static output feedback controller can effectively stabilize the control system of the unmanned surface vehicle. Compared with the existing invention patents, the present invention can achieve decoupling without the need for the relevant matrix to have a specific structure, and can obtain better control results.

[0070] In addition, it should be noted that the multiple Lyapunov function V k (x(k)) proposed in the present invention can be degraded to the existing one-dimensional Lyapunov function.

[0071] Next, the method in the present invention is applied to the motion control scenario of the unmanned surface vehicle to test its actual effectiveness. The corresponding parameter matrices are described as follows:

[0072]

[0073] E = [1.0000 0.0200 0.0200 1.0000 1.0000], C = [1.0000 0.8000 1.0000 -1.0000 1.0000].

[0074] The purpose of the present invention is to design a control scheme for the motion control system of the unmanned surface vehicle to achieve the stability of the system and ideal performance. In the design of the specific scheme, to avoid high computational complexity, a triple Lyapunov function is constructed to analyze the performance of the closed-loop system. By solving the linear matrix inequality in (4) of Step 2 and the gain matrix solution formula in (5), the gain of the static output feedback controller can be obtained as follows:

[0075] L = -0.1331

[0076] To prove the effectiveness of the technical solution proposed in the present invention, the following discussion is carried out:

[0077] Suppose the disturbance enters the system at the initial moment. Subsequently, based on the controller gains obtained as described above, the main simulation results can be obtained, as Figures 3 - 8 shown. Among them, the system state is as Figure 3 shown, from which it can be observed that as the disturbance approaches zero, the system state finally converges to zero. Figure 4 shows the performance output z(k), from which it can be clearly seen that the performance output can effectively suppress external disturbances. This further verifies the effectiveness of the technical method proposed in the present invention.

[0078] In addition, Figures 5 - 8 respectively show the constructed triple Lyapunov function and each of the Lyapunov functions therein. From Figures 5 - 8 it can be seen that the Lyapunov functions V1 and V2 are negative definite, while V3 is positive definite. Similarly, the Lyapunov function V is also positive definite. This verifies the correctness of the multiple Lyapunov functions designed in the present invention. Specifically, the multiple Lyapunov functions are composed of multiple Lyapunov functions, and each individual Lyapunov function is not required to be positive definite. Instead, the entire Lyapunov function is positive definite and its derivative is negative definite.

[0079] 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 preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A static output feedback dynamic decoupling control method for unmanned surface vessels, characterized in that, It includes the following steps: Step 1: The motion equation of the unmanned surface vehicle is described as follows: Among them, υ(t) is the swaying rate, represents the derivative of υ(t), χ(t) is the yaw rate, represents the derivative of χ(t), p(t) is the course angle, represents the derivative of p(t), φ(t) is the roll rate, represents the derivative of φ(t), ψ(t) is the roll angle, represents the derivative of ψ(t), δ(t) is the rudder deflection angle, is the wave response caused by swaying, is the wave response caused in the yaw channel, ζ is the damping coefficient, is the undamped natural frequency; T υ and T χ are the time constants of the motion equation respectively; K dυ 、K υχ 、K dχ 、K υp 、K dp are the preset gain parameters respectively; F(t) represents the non - linear term, and are the coefficients of the non - linear term respectively; The above-mentioned motion control equation of the unmanned surface vehicle is a continuous-time linear model. After sampling, it is constructed into a discrete-time system model, specifically as follows: x(k + 1) = Ax(k) + Bu(k) + Dw(k) y(k) = Cx(k) z(k) = Ex(k) where x(k) represents the system state, y(k) represents the measured output, u(k) represents the control input, z(k) represents the performance output, x(k + 1) represents the next state of the system state x(k), and w(k) is an external disturbance and is energy-bounded; A, B, D, C, and E are system matrices; The discrete-time system model is reconstructed according to different moments, as shown below: x(k + t) = Ax(k + t - 1) + Bu(k + t - 1) + Dw(k + t - 1) y(k + t - 1) = Cx(k + t - 1) z(k + t - 1) = Ex(k + t - 1), t = 1, …, N where N is a positive integer representing the total number of running steps, t is independent of k, and takes any integer between 1 and N; Step 2: Design a static output feedback controller to construct a closed-loop system; (1) Design a static output feedback controller for the discrete-time system model at different moments, as shown below: u(k + t - 1) = Ly(k + t - 1), t = 1, …, N where L is the controller gain matrix to be designed; Substitute the static output feedback controller into the system model at different moments, and the closed-loop system can be obtained, as shown below: x(k + t) = (A + BLC)x(k + t - 1) + Dw(k + t - 1) z(k + t - 1) = Ex(k + t - 1), t = 1, …, N To avoid the selection of slack variables being too restricted due to convex problems, the above closed-loop system can be rewritten as a closed-loop augmented system, as shown below: z(k + t - 1) = Ex(k + t - 1), t = 1, …, N Among them, a new matrix is defined and Γ is an arbitrary real matrix; (2) Establish a multiple Lyapunov function \(V\) k (x(k)), where the sum of Lyapunov functions that depend on the system states at different times constitutes the designed object \(V\) k (x(k)), which is given as follows: where P q represents the Lyapunov function matrix, q represents any integer between t and N, and ∑ is the summation symbol; (3) Conditions for performance analysis of the static output feedback controller; Design a static output feedback controller for the system model at different times, and construct a closed-loop system and a closed-loop augmented system. If there exists a Lyapunov matrix P t > 0, a positive definite matrix Q t-1 > 0, t = 1, 2, …, N, a scalar β > 0, such that the following inequality holds: where * represents the symmetric terms in the symmetric matrix, and I is the identity matrix with appropriate dimensions; Then the system can achieve ideal performance; (4) Design conditions for the static output feedback controller; Design a static output feedback controller for the system model at different times, and construct a closed-loop system and a closed-loop augmented system. If there exist Lyapunov matrix P t > 0, positive definite matrix Q t-1 > 0, t = 1, 2, …, N, scalar β > 0, positive definite matrix Y > 0, positive definite matrix X1 > 0, matrix X2, matrix X3, matrix X4, new matrix K = YL, such that the following inequalities hold: Among them, matrix X is defined as Matrix U is defined as Other matrices are as follows: Then the augmented closed-loop system will achieve ideal performance; (5) Determine the gain of the static output feedback controller; The matrices K and Y can be obtained by solving the linear matrix inequality in (4) of step 2, and then the gain of the static output feedback controller can be calculated as L = (Y -1 K) T , where Y -1 represents the inverse matrix of Y, and T represents the transpose symbol; Step 3: Transmit the control signal u(k + t - 1) generated by the static output feedback controller to the actuator of the unmanned surface vehicle, so as to achieve the purpose of stable control.

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