Self-adaptive global preset performance formation control design method for unmanned ship cluster

Abstract

The invention discloses a self-adaptive global preset performance formation control design method for an unmanned ship cluster, and relates to the technical field of unmanned ship control, and the method comprises the steps: building an unmanned ship dynamics model with sensor fault and saturation input; constructing a topological communication network of the unmanned ship cluster, and defining a formation adjacent tracking error according to the expected formation offset; constructing a generalized global preset performance function with a saturation tolerance characteristic, and obtaining an equivalent error variable by designing a barrier function; establishing a coordinate conversion equation according to the equivalent error variable, and constructing a self-adaptive predetermined time global preset performance formation controller based on a self-adaptive backstepping control method; and analyzing the stability of the closed-loop system based on the Lyapunov stability theory, and determining a to-be-designed control gain. According to the self-adaptive global preset performance formation control method provided by the invention, the formation tracking performance can be effectively improved, and formation control of an unmanned ship cluster is ensured to be realized under the conditions of sensor faults and limited input.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned boat control, and in particular to a method for designing an adaptive global preset performance formation control of an unmanned boat cluster. Background Art

[0002] Unmanned boats are an important component of marine unmanned systems, with advantages such as small size, high mobility and low cost. With the rapid development of automatic control technology, they have gradually become the main carrier for performing marine operations. The traditional single-boat working mode has problems such as low work efficiency, limited operating range, lack of robustness and adaptability. The formation control technology of multiple unmanned boats working in coordination can effectively make up for the disadvantages of single-boat operation.

[0003] Most of the existing unmanned boat formation control methods focus on ensuring the stability of the closed-loop system, but cannot effectively adjust the transient steady-state performance of the system. The unmanned boat formation control method based on traditional preset performance improves the system dynamic performance by designing a performance constraint function with specified expected performance, but ignores the impact of saturated input on formation performance. When the unmanned boat actuator is saturated, the operating efficiency of the rudder is significantly reduced, causing the formation tracking error to increase beyond the preset performance function boundary and even affect the stability of the closed-loop system. In addition, the problem of sensor failure is difficult to avoid during the long-term navigation of unmanned boats, so that only damaged system signals can be used for the design of formation control strategies. In particular, most formation control methods usually assume that the sensors always work properly, and no fault compensation mechanism is designed to deal with sensor failure problems.

[0004] Therefore, there is an urgent need to invent an adaptive global preset performance formation control method for unmanned boat swarms to solve the formation control problem of unmanned boat swarms in the case of sensor failure and saturated input. Summary of the invention

[0005] In view of the shortcomings of the existing unmanned boat swarm formation control technology, the present invention provides an adaptive global preset performance formation control design method for an unmanned boat swarm. By designing a generalized global preset performance function with saturation tolerance characteristics, formation performance constraints within a specified time are implemented to ensure that the preset performance formation control of the unmanned boat swarm is achieved in the event of sensor failure and saturated input.

[0006] The technical solution adopted by the present invention is as follows:

[0007] An adaptive global preset performance formation control design method for an unmanned boat swarm, comprising:

[0008] Construct a dynamic model of an unmanned vehicle with sensor failure and saturated input;

[0009] Construct a topological communication network of the unmanned boat swarm and define the neighboring formation tracking error according to the expected formation offset;

[0010] Based on the unmanned boat dynamics model, the tracking error of adjacent formations and the saturation compensation function, a generalized global preset performance function with saturation tolerance characteristics is constructed, and the equivalent error variable is obtained by designing the error conversion function.

[0011] According to the equivalent error variable, an auxiliary signal with a predetermined time convergence characteristic and two error surfaces are introduced to establish the coordinate transformation equation, a predetermined time differentiator and a hyperbolic tangent function are introduced, and based on the adaptive backstepping control method, a virtual controller, a parameter update law and an adaptive predetermined time global preset performance formation controller are designed;

[0012] The stability of the closed-loop system is analyzed based on Lyapunov stability theory, and the control gain to be designed is determined.

[0013] As a further description of the above technical solution, the sensor fault model is defined as:

[0014]

[0015] in:

[0016] i=1,2,...,N; N represents the number of followers in the unmanned boat formation system; ω i =[x i ,y i ,ψ i ] T is the output signal of the i-th unmanned boat, including the position coordinates (x i ,y i ) and heading angle ψ i , and is the unknown sensor fault parameter;

[0017] The saturation input constraint is:

[0018]

[0019] Among them, γ iv is the actual control input of the i-th unmanned boat, is the saturation input boundary.

[0020] As a further description of the above technical solution, the tracking error between adjacent formations e i Defined as:

[0021]

[0022] in, is the reference trajectory, is the vertex set of the topological communication network, is the edge set of the topological communication network, a ij is the identifier of whether the i-th unmanned boat and the j-th unmanned boat are communicating, d i is the identifier of whether the i-th unmanned boat can receive the leader's information. and are the expected formation offsets of the i-th unmanned boat and the j-th unmanned boat, respectively. and are the output signals of the i-th unmanned boat and the j-th unmanned boat respectively.

[0023] As a further description of the above technical solution, the generalized global preset performance function is designed as:

[0024]

[0025] in:

[0026] ν=1,2,3;Λ iv and ρ 0,iv is a positive design parameter, ρ iν (t) is the performance constraint function, is the saturation compensation function, 0≤q(t)<ρ 0,iv- ρ iv (t);

[0027] Saturation compensation function Designed for:

[0028]

[0029] in,

[0030] w iv and is a positive design parameter;

[0031] The error conversion function is The equivalent error variable is

[0032] As a further description of the above technical solution, the coordinate transformation equation is:

[0033]

[0034] The first error surface Second error surface

[0035] is a virtual controller;

[0036] Auxiliary signal Designed for:

[0037]

[0038] Where v = 1, 2, 3, χ iv is a positive design parameter,

[0039] As a further description of the above technical solution, the virtual controller Designed for:

[0040]

[0041] Where R(ψ) is the rotation matrix, Θ i =diagθ i1 ,θ i2 ,θ i3 , Λ i =b i +d i , b i is the in-degree of the i-th unmanned boat in the topological network,

[0042]

[0043]

[0044] ι iv and iv is a positive design parameter, and The unknown parameters λ are iv and The estimated value of S iv is the basis function vector.

[0045] As a further description of the above technical solution, the parameter update law and They are:

[0046]

[0047] in,

[0048]

[0049] b iv , ι iv , ε iv , and is the control gain to be designed, ξ iν (t) is a time-varying and bounded design parameter.

[0050] As a further description of the above technical solution, the adaptive scheduled time global preset performance formation controller γ iv for:

[0051]

[0052] in,

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) The formation control method provided by the present invention introduces an auxiliary signal with a predetermined time convergence characteristic into the traditional backpropagation control framework to eliminate the saturation error and construct two compensation signals: and To weaken the adverse effects caused by sensor failure and complex disturbances, the hyperbolic tangent function tanh and the predetermined time differentiator are introduced to solve the control input singularity problem and the computational dimension explosion problem.

[0055] (2) Different from the existing finite-time formation control method and fixed-time formation control method, the adaptive scheduled time global preset performance formation controller designed in the present invention ensures the scheduled time stability of the closed-loop system, provides a system stability time upper limit determination scheme that is independent of the initial position of the controlled unmanned boat, and effectively simplifies the parameter adjustment process in practical engineering.

[0056] (3) The present invention proposes a performance constraint strategy based on a generalized global preset performance function, which not only eliminates the initial boundary constraint imposed on the formation neighbor tracking error by the traditional preset performance control method, but also provides a flexible performance constraint function selection scheme. By introducing a saturation compensation signal, the generalized global preset performance function has a saturation tolerance characteristic, which enables it to flexibly adjust the performance function boundary according to the saturation input error amplitude, prevent the preset performance constraint boundary from being violated, and effectively improve the formation tracking performance of the unmanned boat cluster.

[0057] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the embodiments of the present invention are specifically cited below and described in detail with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0059] Figure 1It is a flow chart of an adaptive global preset performance formation control method of an unmanned boat swarm according to the present invention;

[0060] Figure 2 Design a block diagram for the adaptive scheduled time global preset performance formation controller of the unmanned boat swarm;

[0061] Figure 3 This is the topological communication network structure diagram of the unmanned boat cluster;

[0062] Figure 4 It is the formation trajectory diagram of the unmanned boat cluster on the two-dimensional plane;

[0063] Figure 5 Output trajectory and expected trajectory diagram for the unmanned boat;

[0064] Figure 6 It is the state response trajectory diagram of the unmanned boat swarm system;

[0065] Figure 7 This is the trajectory diagram of the tracking error between the unmanned boat formation neighbors;

[0066] Figure 8 Input trajectory map for UAV control. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0068] Please refer to Figure 1 and Figure 2 The present invention provides a method for designing an adaptive global preset performance formation control of an unmanned boat cluster, comprising the following steps:

[0069] Step S1: construct the following dynamic model of the i-th unmanned boat with sensor failure and saturation input:

[0070]

[0071] in:

[0072] i=1,2,...,N; N represents the number of followers in the unmanned boat formation system; is the position coordinate of the i-th unmanned boat (x i ,y i ) and heading angle ψ i ; is the forward speed, sway speed and bow angular velocity of the i-th unmanned boat; is the control input force and torque of the i-th unmanned boat; R(ψi ), M i , and D i (ω i ) represent the inertia matrix, rotation matrix, Coriolis-centripetal force matrix and damping matrix of the i-th unmanned boat respectively; w i (t) is an external unknown disturbance; is the output signal of the sensor failure. i ), M i , and D i (ω i ) is defined as follows:

[0073]

[0074] definition and Where ΔM i , ΔC i and ΔD i The unknown uncertain part is used to approximate the uncertainty of the unmanned boat dynamics model, so the unmanned boat dynamics model can be rewritten as:

[0075]

[0076] in:

[0077]

[0078]

[0079] The sensor failure model suffered by the i-th unmanned boat is defined as:

[0080]

[0081] in, and is an unknown sensor fault parameter and satisfies

[0082] Sensor failure types are divided into the following four categories:

[0083] (1) Energy efficiency loss failure: and

[0084] (2) Loss of accuracy failure: and

[0085] (3) Drift fault: And 0<κ iν <<1;

[0086] (4) Paranoid failure: and

[0087] The saturation input constraint suffered by the i-th unmanned boat is:

[0088]

[0089] Among them, γ iν is the actual control input of the unmanned boat, is the saturation input boundary.

[0090] In order to solve the discontinuity problem caused by saturated input, the following approximate alternative is designed:

[0091]

[0092] Further calculation can be obtained:

[0093]

[0094] in,

[0095] Step S2: construct the topological communication network of the unmanned boat cluster using a directed graph represents the information interaction network between N unmanned boats, is the vertex set, is an edge set. Definition is an adjacency matrix that satisfies The neighbor set of the i-th unmanned boat is defined as The in-degree matrix is ​​defined as The in-degree of node i is Directed Graph The Laplacian matrix of Define the leader as 0, and define the extended directed graph as d i =1 means the i-th unmanned boat can receive the leader's information, otherwise d i =0.

[0096] According to the expected formation offset Neighbor formation tracking error Defined as:

[0097]

[0098] in, is the reference trajectory.

[0099] Step S3: Combine the tracking error e obtained in step S2 with the adjacent formation tracking error e i, construct the following generalized global preset performance function with saturation tolerance characteristics

[0100]

[0101] Among them, Λ iv and ρ 0,iv is a positive design parameter, ρ iv (t) is the performance constraint function, is the saturation compensation signal, 0≤q(t)<ρ 0,iv -ρ iv (t).

[0102] Performance constraint function ρ iv (t) Select as:

[0103]

[0104] in, ρ 0,iv and ρ ∞,iv is a positive design parameter.

[0105] Saturation compensation signal Designed for:

[0106]

[0107] in, w iν and is a positive design parameter.

[0108] By designing the error transfer function Get the equivalent error variable ζ iv (t) is:

[0109]

[0110] Step S4: Based on the equivalent error variable ζ obtained in step S3 iv (t), establish the following coordinate transformation equation:

[0111]

[0112] The first error surface Second error surface

[0113] For virtual controller.

[0114] Auxiliary signal Designed for:

[0115]

[0116] Where v = 1, 2, 3, χ iv is a positive design parameter,

[0117] Step S5: Based on the coordinate transformation equation (13) obtained in step S4, for the first error surface η i Establish the following first Lyapunov function

[0118]

[0119] in, and They are iν and The estimated value of .

[0120] For the first Lyapunov function Find the time derivative and calculate:

[0121]

[0122] Among them, Θ i =diagθ i1 ,θ i2 ,θ i3 ,

[0123] Λ i =b i +d i , is the identity matrix.

[0124] For any positive constant Interval Type-2 Fuzzy Logic System Approximate unknown function Satisfy Δ iv (z iv ) to satisfy The approximate error of .

[0125] Designing a virtual controller for:

[0126]

[0127] in,

[0128]

[0129] ι iv and iv is a positive design parameter.

[0130] Parameter update law and parameter update law Designed for:

[0131]

[0132] in, b iv , iv , ε iv and is the control gain to be designed,

[0133] The designed virtual controller Parameter update law And parameter update law Substituting into formula (16), we can get:

[0134]

[0135] in,

[0136] Furthermore, for the second error surface Construct the following second Lyapunov function

[0137]

[0138] in, and They are and κ iv The estimated value of .

[0139] For the second Lyapunov function Find the time derivative and calculate:

[0140]

[0141] For any given positive constant Interval Type-2 Fuzzy Logic System Approximate unknown functions online Satisfy To satisfy The approximate error of .

[0142] In order to solve the problem of computational complexity explosion caused by repeated differentiation of the virtual controller, the following predetermined time differentiator is introduced:

[0143]

[0144] in, l iv is a positive design parameter and satisfies T′ r is the upper bound of the convergence time.

[0145] Actual adaptive scheduled time global preset performance formation controller γ iv Designed for:

[0146]

[0147] in,

[0148] Parameter update law and parameter update law Designed for:

[0149]

[0150] in, and is the control gain to be designed, ξ iν (t) is a time-varying and bounded design parameter.

[0151] The designed adaptive scheduled time global preset performance formation controller γ iv , parameter update law And parameter update law Substituting into formula (22), we can obtain by simplifying:

[0152]

[0153] in,

[0154] Step S5: Analyze the stability of the closed-loop system based on the Lyapunov stability theory and determine the control gain to be designed. Design the overall Lyapunov function for:

[0155]

[0156] According to steps S3 and S4, the overall Lyapunov function time derivative is calculated:

[0157]

[0158] in,

[0159] Based on the Lyapunov stability theory of predetermined time, the adaptive global preset performance formation control method of the unmanned boat cluster described in the present invention includes a virtual controller Parameter update law Parameter update law Parameter update law And parameter update law Adaptive scheduled time global preset performance formation controller γ iv , so that the actual scheduled time of the unmanned boat cluster system is stable, and all signals of the closed-loop system will be The inner convergence is to the following interval:

[0160]

[0161] According to the convergence characteristics of the designed generalized global preset performance function, it can be concluded that the tracking error between neighbors of the formation will be iν Converge to the expected performance range Right now:

[0162]

[0163] in,

[0164] The following simulation experiments are carried out in the simulation software MATLAB R2020a / SIMULINK to illustrate in detail the effectiveness and feasibility of the fault-tolerant controller design method designed in the present invention.

[0165] The reference trajectory and the desired formation offset are set as: x d ,y d ,ψ d =0.1t,sin(0.2t),0.02t,

[0166] The external unknown disturbance setting is: D iu ,D iv ,D ir =0.5sint,0.5sint,0.5sint.

[0167] The initial conditions of the unmanned boat and the parameter update law are selected as:

[0168] [u i (0),v i (0),r i (0)] = [0,0,0],

[0169] The uncertainty of the existence of the unmanned boat is set to: ΔM i =0.1M i ,

[0170] The controller parameters are chosen as: 0，iv =1.5,ρ ∞，iv =0.1, T r =T iv =3,∈=2 / 99,ξ iv (t) = e -10t , o iν =0.02, w iν =20, χ iν =3.

[0171] The upper and lower bounds of the saturated input are set as:

[0172] The sensor fault parameters are selected as:

[0173]

[0174] Fault time: t≥20s.

[0175] The system parameters of the unmanned boat are selected as follows:

[0176]

[0177] Table 1

[0178]

[0179] The simulation results are plotted on Figures 3 to 8 . Figure 3 The topological communication network structure diagram of the unmanned boat cluster is depicted. Figure 4 The formation navigation trajectory diagram of the unmanned boat cluster on the two-dimensional plane is drawn. It can be found from the figure that the follower realizes formation tracking control with the desired formation offset. Figure 5 The response curves of the damaged signal and the reference trajectory are shown. Based on the simulation results, it can be concluded that even if the unmanned sensor fails, the system output trajectory can still accurately track the reference trajectory. Figure 6 Plot the system state u i 、v i and r i Response trajectory. Figure 7 In the figure, sub-figures (a) to (e) respectively show the formation neighbor tracking errors e of followers 1 to 5. ivThe response curve of the proposed generalized global preset performance function can be found in the figure. It has the ability to flexibly adjust the performance function boundary, adaptively expand the performance function envelope during the actuator saturation period to prevent the preset constraint boundary from failing, and effectively suppress the formation neighbor tracking error e when the sensor fails. iv Momentary fluctuations. Figure 8 In the figure, sub-figures (a) to (e) respectively plot the control input trajectory diagrams of followers 1 to 5. Combined with the simulation experimental results, it can be concluded that the adaptive global preset performance formation control method disclosed in the present invention achieves a trade-off between performance constraints and saturation input constraints, so that the tracking error between neighbors of the formation is within the preset time T iν Converge to the desired performance range and ensure that the globally preset performance formation control is achieved under sensor failure and saturated input conditions.

[0180] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An adaptive global preset performance formation control design method for unmanned boat swarms, characterized in that: include: Construct a dynamic model of an unmanned vehicle with sensor failure and saturated input; Construct a topological communication network of the unmanned boat swarm and define the neighboring formation tracking error according to the expected formation offset; Based on the unmanned boat dynamics model, the tracking error of adjacent formations and the saturation compensation function, a generalized global preset performance function with saturation tolerance characteristics is constructed, and the equivalent error variable is obtained by designing the error conversion function. According to the equivalent error variable, an auxiliary signal with a predetermined time convergence characteristic and two error surfaces are introduced to establish the coordinate transformation equation, a predetermined time differentiator and a hyperbolic tangent function are introduced, and based on the adaptive backstepping control method, a virtual controller, a parameter update law and an adaptive predetermined time global preset performance formation controller are designed; The stability of the closed-loop system is analyzed based on Lyapunov stability theory, and the control gain to be designed is determined.

2. The method according to claim 1, characterized in that The sensor fault model is defined as: in: i=1,2,…,N; N represents the number of followers in the unmanned boat formation system; is the output signal of the i-th unmanned boat, including the position coordinates (x i ,y i ) and heading angle ψ i , and is the unknown sensor fault parameter; The saturation input constraint is: Among them, γ iν is the actual control input of the i-th unmanned boat, is the saturation input boundary.

3. The method according to claim 2, characterized in that Neighbor formation tracking error e i Defined as: in, is the reference trajectory, is the vertex set of the topological communication network, is the edge set of the topological communication network, a ij is the identifier of whether the i-th unmanned boat and the j-th unmanned boat are communicating, d i is the identifier of whether the i-th unmanned boat can receive the leader's information; and are the expected formation offsets of the i-th unmanned boat and the j-th unmanned boat, respectively. and are the output signals of the i-th unmanned boat and the j-th unmanned boat respectively.

4. The method according to claim 3, characterized in that The generalized global preset performance function is designed as: in: v=1,2,3;Λ iv and ρ 0,i is a positive design parameter, ρ iv (t) is the performance constraint function, is the saturation compensation function, 0≤q(t)<ρ 0,iv -ρ iv (t); Saturation compensation function Designed for: in, w iv and is a positive design parameter; The error conversion function is The equivalent error variable is 5. The method according to claim 4, characterized in that The coordinate transformation equation is: The first error surface Second error surface is a virtual controller; Auxiliary signal Designed for: Where v = 1, 2, 3, is a positive design parameter, 6. The method according to claim 5, characterized in that Virtual Controller Designed for: Where R(ψ) is the rotation matrix, Θ i =diagθ i1 ,θ i2 ,θ i3 , Λ i =b i +d i , b i is the in-degree of the i-th unmanned boat in the topological network, ι iv and iv is a positive design parameter, and The unknown parameters λ are iv and θ iv The estimated value of S iν is the basis function vector.

7. The method according to claim 6, characterized in that Parameter update law and They are: in, b iν , ι iν , ε iν , and is the control gain to be designed, ξ iν (t) is a time-varying and bounded design parameter.

8. The method according to claim 7, characterized in that Adaptive scheduled time global preset performance formation controller γ iv for: in,

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