Wheeled robot system fault-tolerant control method based on high-precision indirect signal reconstruction

Abstract

The invention discloses a wheeled robot system fault-tolerant control method based on high-precision indirect signal reconstruction. According to the method, under the interference of external noise, a wheeled robot system containing an unknown system state and an actuator fault is established, a system output function of the wheeled robot system is given, indirect variables are constructed based on the unknown system state and the actuator fault, and an estimation error system is obtained. In addition, a distributed fault-tolerant controller containing an estimation state and a fault is designed to act on the continuous moment of the system, and it is ensured that the consistency of an estimation error system is finally bounded, so that synchronization of the error system is achieved.

Description

Technical Field

[0001] The invention relates to a fault-tolerant control method, and in particular to a high-precision indirect signal reconstruction method based on a wheeled robot system. Background Art

[0002] Many dynamic models used in wheeled robot control systems are only established under known system states and known actuator failures. In actual applications, the actual state of the system and the actual value of the actuator failure are unknown. In addition, the information interaction topology between the wheeled robot system and its subsystems needs to change the interaction structure for self-repair under different failure situations. Therefore, the discussion on the synchronization of switching wheeled robot systems is crucial to ensure the stability of the system. Based on this idea, researchers have conducted a lot of research on the synchronization of switching wheeled robot systems in continuous time and achieved a series of results. Summary of the invention

[0003] The purpose of the present invention is to propose a fault-tolerant control method for a wheeled robot system based on high-precision indirect signal reconstruction, which can effectively improve the performance of the wheeled robot system.

[0004] The specific technical solution of the present invention is as follows: A fault-tolerant control method for a wheeled robot system based on high-precision indirect signal reconstruction comprises the following steps:

[0005] The Kronecker product technique is used to obtain a wheeled robot system with unknown system states and actuator fault signals, and an indirect signal is constructed to estimate the actual value of the system fault.

[0006] Design a distributed fault-tolerant controller with estimated states and faults

[0007] The uniform final bounded conditions based on Lyapunov stability theorem and Young inequality are given to achieve synchronization state

[0008] Under the interference of external noise, for the wheeled robot system model with unknown system state and actuator failure:

[0009] f(x)=1.5tanh(x),ɑ 1 =1.2,α 2 =0.4, L=[9.9041 179.3490 9.9041], L I =[3.6010 3.6010 3.6010],

[0010] Where p represents the number of nodes, ζ(t) represents the known system state, and x p (t) represents the unknown state of the pth node, x j (t) represents the unknown state of the jth node, A, B, C, G, D represent the known parameter matrices, f(ζ(t)) represents the composite function with ζ(t) as the independent variable, and f(x p (t)) represents the p (t) is a composite function of the independent variable, u p (t) represents the control input, r p (t) represents unknown system failure, τ p (t) represents external input, ɑ σ(t) >0 indicates coupling strength, represents the external coupling matrix, Γ σ(t) represents the internal coupling matrix; for t∈[t i , t i+1 ), the system switching signal σ(t) = ω: [0, +∞) → Z is defined by ω (ω represents the system mode, Z represents an integer), where ( represents a natural number) is the mode switching instant, and its switching time sequence satisfies t0<t1<t2<…, and for any ( represents a positive integer) has t i+1 -t i ≥μ1>0;

[0011] Assume that time t∈[t i , t i+1 ), the corresponding switching signal mode is σ(t) = ω, and the variable is defined and T i，h =[t i，h , t i，h+1 ), where h∈{0, 1, 2, ..., H-1}, H∈N + ;

[0012] Definition p (t) = x p (t)-ζ(t), we can get the error system

[0013] where e j (t) is the synchronization error of the jth node, F(e p (t)) = f(x p (t))-f(ζ(t)).

[0014] In addition, its output system is given:

[0015] y p (t)=De p (t)

[0016] Where D is a known matrix;

[0017] With the help of Kronecker product, the system can be further written as:

[0018]

[0019] Where e(t) is the error variable e p (t) in matrix form, G σ(t) is the external coupling matrix In matrix form, F(e(t)) is F(e p (t)) is the matrix form, u(t) is the control input u p (t), R(t) is the matrix form of the unknown system fault r p (t), τ(t) is the matrix form of the external input τ p (t), y(t) is the matrix form of the system output y p The matrix form of (t)

[0020] Due to x p (t) is an unknown state, then the error variable e p (t) is also unknown; to solve this problem, an indirect signal is introduced;

[0021]

[0022] Where L R is the estimated gain.

[0023] So

[0024] Based on the above formula, the actual values ​​of system status and faults are estimated as

[0025]

[0026] Where L R and L I is the estimated gain, I N is the identity matrix

[0027] make Then the estimated error system can be obtained

[0028]

[0029] Therefore, the control input u(t) is constructed as

[0030] in

[0031] At this point, the error system can be rewritten as

[0032]

[0033] This control scheme can ensure that the system is uniformly bounded and stable. The proof process is as follows:

[0034] C001: Select the energy function in the following form:

[0035] V σ(t) (t) = V1(t) + V2(t) + V3(t)

[0036] C002: In the formula, the selected energy functions V1(t), V2(t), and V3(t) are respectively expressed as

[0037]

[0038] C003:

[0039] C004: When t∈T j，h When σ(t)=ω, the first-order derivative of V1(t) is calculated as:

[0040]

[0041] C005: According to C003 The definition of , we can get:

[0042]

[0043] C006: Using Young's inequality, we can get

[0044]

[0045] C007: Taking the derivatives of V2(t) and V3(t) we get

[0046]

[0047] C008: Similar to C006

[0048]

[0049] C009: Combine C003-C008 to get

[0050]

[0051] C010:

[0052] C011: Based on Lyapunov stability theory, if have

[0053] C012: When t∈[t i，H , t i+1 ), σ(t)=ω, and combining C003 and C008, we can get

[0054]

[0055] C013:

[0056] C014: Based on Lyapunov stability theory, if have

[0057] C015: Due to V σ(t) (t) i , t i+1 ) is a continuous function, then from C011 and C014 we can get

[0058]

[0059] C016: Assume that for t∈[t i-1 ,t i )satisfy Then when hour, Indicates time t i Left continuous, C002 can be redescribed as

[0060]

[0061] C017:

[0062] C018: When hour, Indicates time t i Right continuous, B002 can be redescribed as

[0063] V σ(t) (t i )=V1(t i )+V2(ti )+V3(t i )

[0064] C019:

[0065] C020: According to the definition in C002, we can get

[0066]

[0067] C021: Combining C017 and C019, we get

[0068]

[0069] C022: Then when the condition When established, there were Therefore, the closed-loop system achieves consistent eventually bounded synchronization. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1-2 Two topological diagrams of followers;

[0071] Figure 3-7 It is the dynamic trajectory diagram of unknown error and tracking error;

[0072] Figure 8-12 Dynamic trajectory diagram for unknown fault signals and tracking fault signals; DETAILED DESCRIPTION

[0073] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0074] A fault-tolerant control method for a wheeled robot system based on high-precision indirect signal reconstruction comprises the following steps:

[0075] Step 1: Set various system parameters;

[0076] Step 2: construct an indirect signal based on the unknown state and unknown actuator failure;

[0077] Step 3: Give the actual values ​​corresponding to the unknown state and unknown actuator fault;

[0078] Step 4: Set up the estimation error system;

[0079] Step 5: Setting distributed control inputs at consecutive moments;

[0080] Step 6: Verify whether the estimated error system is consistently ultimately bounded;

[0081] Step 7: Verify whether the error system is synchronized at the continuous moment and the switching moment

[0082] An embodiment of the present invention is described below:

[0083] Consider a wheeled robot system based on high-precision indirect signal reconstruction, and its corresponding dynamic models are:

[0084] f(x)=1.5tanh(x),α 1 =1.2,α 2 =0.4, L=[9.9041 179.3490 9.9041], L I =[3.6010 3.6010 3.6010],

[0085] The two topological structures of the followers are shown in Figure 1-2. The dynamic trajectories of the unknown error and tracking error under high-precision indirect signal reconstruction are shown in Figure 1-2. Figure 3-7 As shown in the figure, the dynamic trajectories of unknown fault signals and tracked fault signals under high-precision indirect signal reconstruction are as follows: Figure 8-12 shown.

Claims

1. A fault-tolerant control method for a wheeled robot system based on high-precision indirect signal reconstruction, characterized in that: The following steps are involved: The Kronecker product technique is used to obtain the wheeled robot system with unknown system states and actuator fault signals, and an indirect signal is constructed to estimate the actual value of the system fault. Design a distributed fault-tolerant controller with estimated states and faults; The uniform ultimate boundedness conditions of the wheeled robot closed-loop system are given based on Lyapunov stability theorem and Young's inequality.

2. A wheeled robot system fault-tolerant control method based on high-precision indirect signal reconstruction according to claim 1, characterized in that: The Kronecker product technique is used to obtain the closed-loop system of the wheeled robot containing unknown system states and actuator fault signals, and an indirect signal is constructed to estimate the actual value of the system fault. The specific steps are as follows: The wheeled robot system model with unknown states and actuator failures under the influence of external noise is as follows: Where f(x) = 1.5tanh(x), ɑ 1 =1.2,α 2 =0.4, L=[9.9041 179.3490 9.9041], L I =[3.6010 3.6010 3.6010], Where p represents the number of nodes, which can be 1, 2, 3, 4, or 5, ζ(t) represents the known system state, and x p (t) represents the unknown state of the pth node, x j (t) represents the unknown state of the jth node, A, B, C, G, D represent the known parameter matrices, f(ζ(t)) represents the composite function with ζ(t) as the independent variable, and f(x p (t)) represents the p (t) is a composite function of the independent variable, u p (t) represents the control input, r p (t) represents unknown system failure, τ p (t) represents external input, ɑ σ(t) >0 indicates coupling strength, represents the external coupling matrix, Γ σ(t) represents the internal coupling matrix; for t∈[t i , t i+1 ), the system switching signal σ(t) = ω: [0, +∞) → Z is defined by ω, ω represents the system mode, Z represents an integer, where is the mode switching moment, represents a natural number, whose switching time sequence satisfies t0<t1<t2<…, and for any There is i+1 -t i ≥μ1>0, represents a positive integer; Assume that time t∈[t i , t i+1 ), the corresponding switching signal mode is σ(t) = ω, and the variable is defined and T i，h =[t i,h , t i，h+1 ), where h∈{0, 1, 2, ..., H-1}, H∈N + ; Define the synchronization error of the pth node as e p (t) = x p (t)-ζ(t), we can get the error system where e j (t) is the synchronization error of the jth node, F(e p (t)) = f(x p (t))-f(ζ(t)); In addition, its output system is given: and p (t)=Of p (t), Where D is a known matrix, y p (t) is the system output; With the help of Kronecker product operator The system can be further written as Where e(t) is the error variable e p (t) in matrix form, G σ(t) is the external coupling matrix In matrix form, F(e(t)) is F(e p (t)) is the matrix form, u(t) is the control input u p (t), R(t) is the matrix form of the unknown system fault r p (t), τ(t) is the matrix form of the external input τ p (t), y(t) is the matrix form of the system output y p (t) in matrix form; Due to x p (t) is an unknown state, then the error variable e p (t) is also unknown; to solve this problem, an indirect signal is introduced Where L R is the estimated gain; So Based on the above formula, the actual values ​​of system status and faults are estimated as Where L R and L I is the estimated gain, I N is the identity matrix; make Then the estimated error system can be obtained 3. The fault-tolerant control method for a wheeled robot system based on high-precision indirect signal reconstruction according to claim 1 is characterized in that: Design a distributed fault-tolerant controller with estimated states and faults. The specific steps are as follows: The control input u(t) is constructed as in 4. The method for fault-tolerant control of a wheeled robot system based on high-precision indirect signal reconstruction according to claim 1, characterized in that: The uniform final boundedness conditions of the wheeled robot closed-loop system based on Lyapunov stability theorem and Young's inequality are given: B001: Select the energy function in the following form: V σ(t) (t)=V1(t)+V2(t)+V3(t), B002: The selected energy functions V1(t), V2(t), and V3(t) are expressed as in B003: When t∈T j，h When σ(t)=ω, the first-order derivative of V1(t) is calculated as: B004: According to B002 for P1 ω The definition of (t) yields: B005: Using Young's inequality, we can get B006: Taking the derivative of V2(t) and V3(t) we get B007: Similar to B005 B008: Combine B003-B007 to get in B009: Based on Lyapunov stability theory, if [Ω] 1 5×5 <0, yes B0010: When t∈[t i,H , t i+1 ), σ(t)=ω, and combining B002 and B008, we can get: in B0011: Based on Lyapunov stability theory, if [Ω] 2 5×5 <0, yes B0012: Due to V σ(t) (t) i , t i+1 ) is a continuous function, then from B009 and B0011 we can get B0013: Assume that for t∈[t i-1 , t i )satisfy Then when hour, Indicates time t i Left continuous, B002 can be redescribed as in B0014: When hour, Indicates time t i Right continuous, B002 can be redescribed as V σ(t) (t i )=V1(t i )+V2(t i )+V3(t i ) in B0015: According to the definition in B002, we can get B0016: Combining B0013 and B0014, we get B0017: Then when the condition When established, there were Therefore, the closed-loop system achieves consistent eventually bounded synchronization.

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