A Quantization-Tolerant Adaptive Bilateral Tracking Control Method for Unmanned Aerial Vehicles

Abstract

This invention discloses a quantization-tolerant adaptive bilateral tracking control method for unmanned aerial vehicles (UAVs). It utilizes a topology graph to represent the information interaction between UAV swarms in each subsystem. Considering sensor faults and hysteresis nonlinearities during UAV flight, a nonlinear position system model of the UAVs is established based on the Newton-Euler theorem. Adaptive estimation combined with neural networks handles hysteresis nonlinearity and input quantization issues. Simultaneously, an adaptive neural network compensation control method is used to address sensor fault problems. Combined with backstepping control, a distributed adaptive quantization-tolerant controller is designed to ensure that the system maintains its original control performance even when sensor faults and hysteresis nonlinearities occur, while also exhibiting good formation performance. By simultaneously considering the effects of sensor faults and hysteresis nonlinearities when designing the nonlinear controller for the UAVs, distributed adaptive leader-follower bilateral tracking consistency control performance is achieved, improving the system's safety and reliability.

Description

Technical Field

[0001] This invention relates to a quantized fault-tolerant distributed adaptive control method for aircraft, specifically a quantized fault-tolerant adaptive bilateral tracking control method for unmanned aerial vehicles. Background Technology

[0002] Unmanned aerial vehicles (UAVs), also known as drones, are autonomous or remotely controllable aircraft. They are unmanned aircraft controlled primarily by radio remote control equipment and onboard program control devices, or operated fully or intermittently autonomously by an onboard computer. Compared to manned aircraft, UAVs offer advantages such as lower cost, no threat of human injury, and greater flexibility. Furthermore, the rapid development of control technology, communication technology, computer science, and materials technology in recent years has brought UAVs considerable attention, especially in military and civilian applications. In military applications, UAVs are categorized into reconnaissance aircraft and target drones. Civilian applications primarily include aerial photography, agriculture, plant protection, surveying, disaster relief, express delivery, wildlife observation, miniature selfies, disaster relief, infectious disease monitoring, news reporting, power line inspection, film and television production, and creating romantic moments, greatly expanding the uses of UAVs. Developed countries are also actively expanding industry applications and developing UAV technology.

[0003] However, no matter how much the functionality and effectiveness of a single drone improves, its performance is limited. Multi-drone cooperative control can effectively compensate for the limitations of a single drone's performance. For example, if a drone is destroyed by enemy weapons or malfunctions during a mission and cannot continue, other drones in the swarm can continue the mission. Furthermore, drone swarming technology includes the generation, maintenance, and transformation of drone formations. Due to different missions, drone swarms need to use different formations to better cooperate and coordinate, thus compensating for the low survivability, low mission efficiency, and poor safety of a single drone.

[0004] During actual drone flight, issues such as sensor failure and hysteresis nonlinearity are unavoidable. Drone systems contain numerous sensors, such as vertical gyroscopes, angular rate sensors, and accelerometers. The operating environment of sensors on drone platforms is unique, and many factors can induce failure. Sensor failure or instability can, in severe cases, lead to the drone losing control and crashing. Furthermore, the presence of hysteresis nonlinearity can easily limit the accuracy of the controller's positioning, causing static errors, jitter, and other control problems. Moreover, the asymmetry and hysteresis memory inherent in hysteresis systems can lead to system divergence or instability.

[0005] Furthermore, if a follower drone performs periodic sampling and transmits the collected data to the navigator drone or adjacent follower drones in real time, a large amount of redundant data will inevitably be generated if the sample data does not change significantly, causing communication link blockage or even collapse. Summary of the Invention

[0006] Purpose of the invention: To address the above-mentioned shortcomings, this invention provides a quantized fault-tolerant adaptive bilateral tracking control method for unmanned aerial vehicles (UAVs) that takes into account the effects of sensor failure and hysteresis nonlinearity, can maintain stability with less communication resources, and can achieve consistent leader-follower bilateral tracking control performance.

[0007] Technical solution: To solve the above problems, this invention adopts a quantization-tolerant adaptive bilateral tracking control method for unmanned aerial vehicles (UAVs), comprising the following steps:

[0008] (1) Use a topology diagram to represent the information interaction between drone swarms in each subsystem, including the information transmission from the leader drone to the follower drones and the information communication between the follower drones; a subsystem is the drone swarm communication topology corresponding to a task or environment;

[0009] (2) Considering sensor failures and hysteresis nonlinearity during the flight of the UAV, a nonlinear position system model of the UAV is established based on the Newton-Euler theorem;

[0010] (3) Adaptive estimation combined with neural networks to handle hysteresis nonlinearity and input quantization problems reduces their negative impact on the control system. At the same time, adaptive neural network compensation control method is used to solve sensor failure problems.

[0011] (4) Combine the backstepping control method and use steps (1)-(3) and adaptive control theory to design a distributed adaptive quantization fault-tolerant controller to ensure that the system can maintain its original control performance when sensor failure and hysteresis nonlinearity occur, and has a good formation effect.

[0012] Beneficial effects: Compared with the prior art, the significant advantage of this invention is that when designing a nonlinear controller for a UAV, the effects of sensor failure and hysteresis nonlinearity are considered simultaneously, thereby achieving distributed adaptive leader-follower bilateral tracking consistency control performance and improving the safety and reliability of the system. Attached Figure Description

[0013] Figure 1 The diagram shown is a system control flowchart of this invention;

[0014] Figure 2 The diagram shown is a communication topology diagram of the UAV swarm in this invention. Detailed Implementation

[0015] like Figure 1 As shown in this embodiment, a quantization-tolerant adaptive bilateral tracking control method for UAVs enables the UAV to maintain stability with minimal communication resources while considering the effects of sensor failures and hysteresis nonlinearity, and simultaneously achieves leader-follower bilateral tracking consistency control performance. First, graph theory is introduced to represent the information interaction between UAV swarms in each subsystem using a topological graph. Then, a nonlinear position dynamic model of the UAVs is established. Next, adaptive estimation techniques are combined with neural network methods to handle the difficulties caused by hysteresis nonlinearity and input quantization, reducing their negative impact on the system. Simultaneously, an adaptive neural network compensation control method is used to address the problems caused by sensor failures. Finally, a distributed adaptive control scheme designed using the backstepping method can solve the quantization-tolerant bilateral tracking control problem of UAVs that simultaneously considers sensor failures and hysteresis nonlinearity.

[0016] like Figure 2 As shown, graph theory is introduced to represent the information interaction between drone swarms in each subsystem using a topological graph. The drone swarm consists of N drones, one of which is the drone leader and the remaining N-1 are drone followers. A leader-follower bilateral tracking consistency directed graph is introduced to represent the information exchange between drones. A graph is defined. in Represents a non-empty set of nodes. For edge set, This is the relevant adjacency matrix. This represents an edge from node i to node j, and the adjacency matrix... This represents the interaction between nodes. Indicates a cooperative relationship. They are competitors; otherwise Let be the absolute in-degree matrix, where The Laplace matrix is The neighbor set of an agent is represented as

[0017] It is an augmented graph, in which 0 is called the leader node; let θ i,0 Let θ be the weight of the edge from the leader node to the follower node. i,0 >0 indicates a cooperative relationship, θ i,0 <0 indicates a competing relationship. Then define...

[0018] Augmented graph It contains a spanning tree, where node 0 is the root node if there is at least one directed path from the root node to all other nodes.

[0019] For the following UAV position dynamic model:

[0020]

[0021] In the formula, Θ3 = [0,0,1] T ,Δ=[ρ,θ,ξ] T and Φ=[υ ρ ,υ θ ,υ ξ ] T Here, M is the drone's position vector, G is the gravitational acceleration, T is the net external force, Γ = diag{r1, r2, r3} represents the unknown diagonal aerodynamic matrix, and T1 is the transformation matrix between the body coordinate system and the ground coordinate system, expressed as follows:

[0022]

[0023] Where χ, φ, and ψ represent Euler angles.

[0024] Under the quantitative control system, considering the sensor failures and hysteresis nonlinearities that the UAV may experience during flight, and combining equations (1)-(2), the nonlinear equation of the UAV position can be rewritten as:

[0025]

[0026] in x i,11 =ρ i x i,21 =θ i x i,31 =ξ i x i,12 =υ ρi x i,22 =υ θi x i,32 =υ ξi , and This indicates the parts of the system that are not modeled or ignored. It is an external disturbance, y i,m Is and u i,m These represent the drone's output and input, respectively. This indicates a sensor malfunction. and ∈ i,m (t) is the fault parameter, and Q(u) i,m ) indicates quantized input.

[0027] Define leader dynamics as:

[0028]

[0029] Where Θ 0,mIt is the state of the leader, y d,m It is the leader's output, f m (Θ 0,m (,t) represents a bounded differentiable function. Furthermore, the asymmetric hysteresis quantization input Q(u) i,m The description format is as follows:

[0030]

[0031] Where Q(u) i,m (t - )) represents Q(u i,m The state before (t)). Quantized value and It can be obtained through the following formula:

[0032]

[0033] Where c = 1, 2, ... and The parameter representing the dead zone, and It is a constant used to determine the roughness of the quantizer.

[0034] Based on the above analysis, asymmetric hysteresis quantization can be decomposed into the following form:

[0035] Q(u i,m )=D(u i,m )u i,m +O(u i,m (5)

[0036] Where D(u) i,m ) is satisfied with the condition Control coefficient, O(u) i,m ) is satisfied by the condition |O(u) i,m )|≤ν m The type of interference items, and

[0037] Furthermore, hysteresis nonlinearity may occur in the actuator. The hysteresis model considered in this embodiment is the Prandtl-Ishlinskii hysteresis model:

[0038]

[0039] in This indicates a hysteretic nonlinear input. Represents an unknown positive integer. It is caused by hysteresis nonlinear input A fixed set of line segments determined by some extreme values, and for λi,m (c)≥0 is the density function that disappears at the horizon R.

[0040] After analysis, the Prandtl-Ishlinskii hysteresis model can be decomposed into the following form:

[0041]

[0042] in

[0043] Based on the above analysis, it is possible to have

[0044]

[0045] Where b 0,m >0 is a known prior parameter, μ i,m It is a formula The upper bound of μ, and μ i,m It is an unknown constant.

[0046] For sensor failures, the parameters of the failure must meet the following conditions: in This represents the minimum sensor efficiency. ∈ m and They are respectively ∈ i,m The upper and lower bounds of (t).

[0047] In addition, this embodiment considers four types of faults, as follows:

[0048] ① Sensor fixed deviation fault: And ∈ i,m (t) is a constant.

[0049] ② Sensor drift deviation fault: And |∈ i,m (t)|=π1t, where 0<π1<<1.

[0050] ③ Sensor accuracy decreases: and Where ∈ i,m (t)→0.

[0051] ④ Sensor completely failed: And ∈ i,m (t) = 0.

[0052] Based on the analysis of sensor malfunctions, the following formula can be derived:

[0053] y i,m =x i,m1 +h i,mh (8)

[0054] in It is an unknown function.

[0055] Then, to handle the uncertainties in the system, a radial basis function neural network is introduced. For any precision ε > 0, the approximation property of the radial basis function neural network can be used to approximate the compact set Ω ∈ R. q The unknown nonlinear function f(U) on the given surface is shown below:

[0056]

[0057] Where ∈(U) represents the approximation error and satisfies |∈(U)|≤ε, Φ(U)=[Φ1(U),Φ2(U),...,Φ κ (U)] T Let Φ represent the basis function vector and κ > 1 be the number of nodes in the neural network. i (U) is generally expressed in Gaussian function form, ξ * =[ξ1,ξ2,...,ξ κ ] T ∈R κ It is an ideal weight vector. Based on the above analysis, the following equation holds.

[0058]

[0059] Where ξ is the weight vector. Furthermore, Φ i (U) can be represented as

[0060]

[0061] Where w i =[w i1 ,w i2 ,...,w iq ] T As the center of the receiving domain, is the width of the Gaussian function.

[0062] For unmanned aerial vehicle (UAV) systems, the reference signal y d and its derivative It is bounded. At the same time, all states are measurable and usable. During the flight of the UAV, its attitude angles constantly change between (-90°, 90°). External disturbances are bounded.

[0063] Is not singular, let ζ .m1 =(ζ 1,m1 ,ζ 2,m1 ,...,ζ N,m1 ) T y .m=(y 1,m ,y 2,m ,...,y N,m ) T , y .d =(y d,m ,y d,m ,…,y d,m ) T , The following relationship holds true

[0064]

[0065] in, yes The smallest eigenvalue, ζ i,m1 It will be defined later.

[0066] Represents the state vector. Let m represent the basis function vector. Then, for any positive integer m ≥ n, the following relation holds.

[0067]

[0068] Considering the UAV system model with sensor failure and hysteresis nonlinearity (3), a distributed leader-follower bilateral tracking consistent control strategy is designed to suppress the impact of failure and hysteresis on the system.

[0069] First, define the distributed synchronization error as:

[0070]

[0071] Then, define a constant:

[0072]

[0073] in It is a weight vector, γ i,mq It is a normal number. It is γ i,mq The estimate, and the estimation error is... Based on dynamic surface control technology, the error surface can be designed as follows:

[0074]

[0075] Where c i,m2 It is determined by the virtual control function χ i,m1 The state vector obtained from the first-order filter, and z i,m2 This refers to boundary layer error.

[0076] Step 1: Based on system (3) and formula (11), the synchronization error ζ is calculated.i,m1 Differentiation yields

[0077]

[0078] Where y j,m This represents information about the neighbor j of the i-th drone.

[0079] Define Lyapunov function V i,m1 as follows

[0080]

[0081] Where ρ i,m1 This indicates the positive design parameters.

[0082] Then V i,m1 The derivative is

[0083]

[0084] According to Young's inequality, the following formula holds:

[0085]

[0086] Define the unknown auxiliary nonlinear function as:

[0087]

[0088] Because of the function Includes unknown functions so It cannot be directly used in virtual controller design. Therefore, radial basis function neural networks... Introduced, among which for have

[0089]

[0090] in It is the estimation error.

[0091] Then, based on the properties of radial basis function neural networks and Young's inequality, we have

[0092]

[0093] in

[0094] because Including the state in the second step, existing methods for handling strictly feedback systems cannot solve the algebraic ring problem in purely feedback nonlinear systems. Based on the characteristics of radial basis function neural networks, namely Lemma 3, the above problem can be effectively solved, which makes the adaptive neural backpropagation method more adaptive.

[0095] The virtual control law and parameter adaptive law are designed as follows:

[0096]

[0097]

[0098] Where β i,m1 τ i,m1 and These are the positive parameters to be designed.

[0099] Based on the above analysis, we can conclude that:

[0100]

[0101] The second step involves obtaining the filtered virtual control signal c through the following first-order filtering. i,m2

[0102]

[0103] Among them ι i,m2 >0 is a constant.

[0104] Considering system (3), equation (7), error surface (11), and formula (20), the following formula can be obtained.

[0105]

[0106] in

[0107]

[0108] Then select the Lyapunov function V. i,m2 as follows

[0109]

[0110] Where ρ i,m2 and ξ i,m These are the positive parameters to be designed. It is the estimation error, and It is μ i,m The estimate.

[0111] For V i,m2 Differentiation yields

[0112]

[0113] By using Young's inequality, we have

[0114]

[0115]

[0116] Among them o i,m2 >0 is a design constant. yes The upper boundary, W i,m2 ≤C i,m2 And C i,m2 It is the maximum value on the compact set.

[0117] Define an unknown auxiliary function H i,m2 for

[0118]

[0119] By using Young's inequality, we can obtain

[0120]

[0121] Where τ i,m2 These are positive design parameters. The definition is the same as in the first step.

[0122] The virtual control law and parameter adaptive law are designed as follows:

[0123]

[0124]

[0125]

[0126] Where β i,m1 , r and r are positive parameters to be designed.

[0127] Then, substituting equations (24) to (29) into equation (23), we can obtain the following inequalities:

[0128]

[0129] By using the above formula, we can obtain

[0130]

[0131] in

[0132] Based on equation (31), we can obtain the following:

[0133]

[0134] in

[0135] Based on the above analysis and discussion, a UAV position dynamic system (3) considering sensor faults and hysteresis nonlinearity is obtained. The parameter adaptive laws are selected as (18), (28) and (29). The designed distributed quantization fault-tolerant bilateral controllers (17) and (27) can ensure that the signal of the entire closed-loop system is eventually bounded, and at the same time can realize the distributed adaptive leader-follower bilateral tracking consistency control performance.

[0136] Consider all Lyapunov functions:

[0137]

[0138] Based on equation (32), we can obtain

[0139]

[0140] in, and

[0141] According to equation (34), the final conclusion is proved.

Claims

1. A quantization-tolerant adaptive bilateral tracking control method for unmanned aerial vehicles (UAVs), characterized in that, Includes the following steps: (1) Use a topology diagram to represent the information interaction between drone swarms in each subsystem, including information transmission from the leader drone to the follower drones and information communication between the follower drones; A subsystem is a communication topology for a drone swarm corresponding to a specific task or environment; (2) Considering sensor failures and hysteresis nonlinearity during the flight of the UAV, a nonlinear position system model of the UAV is established based on the Newton-Euler theorem; The nonlinear position system model of the UAV is as follows: in x i,11 =ρ i x i,21 =θ i x i,31 =ξ i x i,12 =υ ρi x i,22 =υ θi x i,32 =υ ξi , and This indicates the parts of the system that are not modeled or ignored. It is an external disturbance, y i,m and u i,m These represent the drone's output and input, respectively. This indicates a sensor malfunction. and ∈ i,m (t) is the fault parameter, and Q(u) i,m ) represents the asymmetric hysteresis quantization input; ρ, θ, ξ and υ ρ ,υ θ ,υ ξ These represent the position and velocity variables along the x, y, and z axes, respectively. (3) Adaptive estimation is combined with neural networks to handle hysteresis nonlinearity and input quantization problems. At the same time, adaptive neural network compensation control method is used to solve sensor failure problems. (4) Combine the backstepping control method and use steps (1)-(3) and adaptive control theory to design a distributed adaptive quantization fault-tolerant controller to ensure that the system can maintain its original control performance when sensor failure and hysteresis nonlinearity occur.

2. The UAV quantization fault-tolerant adaptive bilateral tracking control method according to claim 1, characterized in that, In step (1), the drone swarm consists of N drones, of which 1 is the drone leader and the remaining N-1 are drone followers; a leader-follower bilateral tracking consistency directed graph is introduced to represent the information exchange between the drones; a graph is defined. in Represents a non-empty set of nodes. For edge set, The relevant adjacency matrix; This represents an edge from node i to node j, and the adjacency matrix... Represents the interactions between nodes. Indicates a cooperative relationship. They are competitors; otherwise Let be the absolute in-degree matrix, where The Laplace matrix is The neighbor set of drones is represented as It is an augmented graph, in which 0 is called the leader node; let θ i,0 The weight of the edge from the leader node to the follower node; θ i,0 >0 indicates a cooperative relationship, θ i,0 <0 indicates a competing relationship; then define 3. The UAV quantization fault-tolerant adaptive bilateral tracking control method according to claim 2, characterized in that, The dynamic model of the drone's position is as follows: Where, Θ3 = [0,0,1] T Δ=[ρ,θ,ξ] T and Φ=[υ ρ ,υ θ ,υ ξ ] T These are the position and velocity vectors of the UAV, respectively. Additionally, ρ, θ, ξ, and υ... ρ ,υ θ ,υ ξ Let x, y, and z represent the position and velocity variables along the x, y, and z axes, respectively. M is the mass of the UAV, G is the gravitational acceleration, T is the net external force, Γ represents the unknown diagonal aerodynamic matrix, and T1 is the transformation matrix between the body coordinate system and the ground coordinate system, expressed as follows: Where χ, φ, and ψ represent Euler angles; Combining equations (1) and (2), we obtain the nonlinear position system model of the UAV. Define leader dynamics as Where, Θ 0,m It is the state of the leader, y d,m It is the leader's output, f m (Θ 0,m (t) denotes a bounded differentiable function Furthermore, the asymmetric hysteresis quantization input Q(u) i,m The description format is as follows: Where Q(u) i,m (t - )) represents Q(u i,m The state before (t)); and Indicates the quantized value; and These are constants used to determine the roughness of the quantizer; c = 1, 2, ... and Parameters representing the dead zone; Quantized value and The following formula is used to obtain: Based on the above analysis, the asymmetric hysteresis quantization input Q(u) i,m It can be decomposed into the following forms: Q(u i,m )=D(u i,m )u i,m +O(u i,m ) (5) Wherein, D(u) i,m ) is satisfied with the condition Control coefficient, O(u) i,m ) is satisfied by the condition |O(u) i,m )|≤ν m The type of interference items, and drone input u i,m Hysteresis model: in, This indicates a hysteretic nonlinear input. Represents an unknown positive integer. It is caused by hysteresis nonlinear input A fixed set of line segments determined by some extreme values, and for λ i,m (c)≥0 is the density function that vanishes at the horizon R; The hysteresis model can be decomposed into the following form: in, 4. The UAV quantization fault-tolerant adaptive bilateral tracking control method according to claim 3, characterized in that, In step (3), the state variables and control input signals are first defined. Everything is bounded; obtaining... Among them, b 0,m >0 is a known prior parameter, μ i,m It is a formula The upper bound of μ, and μ i,m It is an unknown constant; For sensor failures, the parameters of the failure must meet the following conditions: in This represents the minimum sensor efficiency. ∈ m and They are respectively ∈ i,m The upper and lower bounds of (t); Four fault types are defined as follows: ① Sensor fixed deviation fault: And ∈ i,m (t) is a constant; ② Sensor drift deviation fault: And |∈ i,m (t)|=π1t, where 0<π1<<1; ③ Sensor accuracy decreases: and Where ∈ i,m (t)→0; ④ Sensor completely failed: And ∈ i,m (t) = 0; Secondly, based on the analysis of sensor faults, the following formula is obtained: y i,m =x i,m1 +h i,mh (8) in, It is an unknown function; Then, to handle uncertainties in the control system, a radial basis function neural network is introduced. For any precision ε > 0, the approximation property of the radial basis function neural network is used to approximate the compact set Ω ∈ R. q The unknown nonlinear function f(U) on the given surface is shown below: Where ∈(U) represents the approximation error and satisfies |∈(U)|≤ε, Φ(U)=[Φ1(U),Φ2(U),...,Φ κ (U)] T Let Φ represent the basis function vector and κ > 1 be the number of nodes in the neural network. i (U) can be expressed in Gaussian function form, ξ * =[ξ1,ξ2,…,ξ κ ] T ∈R κ It is an ideal weight vector; Based on the above analysis, the following equation holds true. Where ξ is the weight vector; Φ i (U) is represented as Among them, w i =[w i1 ,w i2 ,…,w iq ] T ζ is the center of the receiving field. i is the width of the Gaussian function.

5. The UAV quantization fault-tolerant adaptive bilateral tracking control method according to claim 4, characterized in that, In step (4), considering the nonlinear position system model of the UAV, a distributed leader-follower bilateral tracking consistent control strategy is designed to suppress the impact of faults and hysteresis on the system; First, define the distributed synchronization error as: Where y j,m This represents the output of neighbor j of the i-th drone; Then, define a constant: in, It is a weight vector, γ i,mq It is a positive number; It is γ i,mq The estimate, and the estimation error is... Based on dynamic surface control technology, the error surface is designed as follows: Among them, c i,m2 It is determined by the virtual control function χ i,m1 The state vector obtained from the first-order filter, and z i,m2 This refers to boundary layer error; Based on the nonlinear position system model of the UAV (3) and formulas (9) and (11), the synchronization error ζ is analyzed. i,m1 Taking the derivative, we get Define Lyapunov function V i,m1 as follows: Where, ρ i,m1 Indicates positive design parameters; Then V i,m1 The derivative is According to Young's inequality, the following formula holds: Define the unknown auxiliary nonlinear function as: Radial basis function neural networks Introduced, among which for have in, It is an estimation error; Then, based on the properties of radial basis function neural networks and Young's inequality, we have in, The virtual control law and parameter adaptive law are designed as follows: Where, β i,m1 τ i,m1 and These are the positive parameters to be designed; have to: The following first-order filter is used to obtain the filtered virtual control signal c. i,m2 Among them, ι i,m2 >0 is a constant; Considering the nonlinear position system model of the UAV (3), formula (7), error surface (11), and formula (20), the following formula is obtained. in, Then select the Lyapunov function V. i,m2 as follows Where ρ i,m2 and ξ i,m These are the positive parameters to be designed. It is the estimation error, and It is μ i,m The estimate; For V i,m2 Differentiating gives By using Young's inequality, we have Among them, o i,m2 >0 is a design constant. yes The upper boundary, W i,m2 ≤C i,m2 And C i,m2 It is the maximum value on the compact set; Define an unknown auxiliary function H i,m2 for By using Young's inequality, we obtain Where, τ i,m2 These are positive design parameters. The virtual control law and parameter adaptive law are designed as follows: Where, β i,m1 , and r are positive parameters to be designed; Then, substituting equations (24) to (29) into equation (23), we obtain the following inequalities: By using the above formula, we obtain in, Based on equation (31), we can obtain the following: in, Considering the nonlinear position system model of the UAV (3), the parameter adaptive law is selected as Equation (18), Equation (28) and Equation (29). The designed distributed quantization fault-tolerant bilateral controller Equation (17) and Equation (27) make the signal of the entire closed-loop system ultimately bounded.

Images