State and fault estimation method and system for interconnected flexible connecting rod robot network system with innovation saturation

Abstract

The invention discloses a state and fault estimation method and system for an interconnection flexible connecting rod robot network system with innovation saturation, belongs to the field of robot state estimation, and aims to solve the problem that the existing method does not consider signal transmission damage, nonlinearity, sensor faults, time-varying and time-lag, bounded random noise and innovation saturation at the same time. And the estimation effect is poor. According to the method, a dynamic model taking a flexible connecting rod robot system as a complex network system node, a dynamic model of a sensor fault, a dynamic model of a complex network system node considering the sensor fault and a dynamic model of a compensated recovery sensor measurement signal are sequentially established; obtaining an overall state and fault estimation error system, solving a gain parameter of the dynamic model of the state and fault estimator with the innovation saturation, and substituting the gain parameter into the model to obtain an overall state and fault estimation error system; and estimating states and sensor faults taking the flexible connecting rod robot system as a complex network system node.

Description

Technical Field

[0001] The present invention relates to the field of robot state estimation, and in particular to a state and fault estimation method and system for an interconnected flexible link robot network system with innovation saturation. Background Art

[0002] Complex network systems, composed of a large number of interconnected nodes, can be used to describe the World Wide Web, citation networks, social networks, and more. Generally speaking, real-world complex network systems exhibit nonlinear characteristics, information delays, and are subject to external perturbations. These characteristics are characterized by considering nonlinear functions, time-varying delays, and bounded random noise, respectively. Understanding the evolution of complex networks requires monitoring the states of network nodes. Node states cannot typically be directly obtained; state estimates can only be obtained indirectly by constructing an estimator from available sensor measurement signals. During the transmission of sensor measurement signals across the network to a remote estimator, signal transmission impairments due to binary bit flips can occur, causing the estimator's estimated value to deviate from the ideal value. Consequently, an innovation saturation function must be incorporated into the estimator to mitigate signal transmission impairments and ensure good estimation performance. Furthermore, sensor aging, battery depletion, harsh operating environments, and vandalism can cause sensor failures, impacting the estimator's accurate estimation performance. Therefore, it is essential to account for and estimate sensor failures. Consequently, methods for simultaneously estimating the state and faults of complex network systems are needed.

[0003] At present, the state estimation methods of complex network systems have not yet simultaneously considered signal transmission impairment, nonlinearity, sensor failure, time-varying delay, bounded random noise and information saturation, resulting in poor estimation results. Summary of the Invention

[0004] The technical problems to be solved by the present invention are:

[0005] Existing state estimation methods for complex network systems do not simultaneously consider signal transmission impairment, nonlinearity, sensor failure, time-varying delay, bounded random noise, and information saturation, resulting in poor estimation results.

[0006] The present invention is to solve the above technical problems using the following technical solutions:

[0007] The present invention provides a state and fault estimation method for an interconnected flexible link robot network system with innovation saturation, comprising the following steps:

[0008] S100. Establish a dynamic model of a complex network system with a flexible link robot system as a node, which has nonlinearity, sensor failure, time-varying delay, and bounded random noise;

[0009] S200, establishing a dynamic model of sensor failure with random deviation and first-order difference;

[0010] S300, establishing a dynamic model of the complex network system node considering the sensor failure based on the dynamic model of the sensor failure obtained in step S200 and the dynamic model of the complex network system node with the flexible link robot system obtained in step S100;

[0011] S400, under a given coding mechanism, establishing a dynamic model of the compensated restored sensor measurement signal according to the statistical characteristics of the decoded sensor measurement signal;

[0012] S500, establishing a dynamic model of a state and fault estimator with innovation saturation based on the dynamic model of the complex network system node considering sensor failure obtained in step S300 and the dynamic model of recovering sensor measurement signals obtained in step S400;

[0013] S600, obtaining an overall state and fault estimation error system based on the dynamic model of the state and fault estimator with innovation saturation obtained in step S500 and the dynamic model of the complex network system node considering sensor failure obtained in step S300;

[0014] S700, using system stability determination theory, based on the overall state and fault estimation error system obtained in step S600, solve the gain parameters of the dynamic model of the state and fault estimator with innovation saturation obtained in step S500;

[0015] S800 , substituting the gain parameters obtained in step S700 into the dynamic model of the state and fault estimator with innovation saturation obtained in step S500 , and estimating the state and sensor faults of the complex network system with the flexible link robot system as a node.

[0016] Furthermore, in step S100, it specifically includes:

[0017] Establish a dynamic model of a complex network system with flexible linkage robot system as the node, which has nonlinearity, sensor failure, time-varying delay and bounded random noise;

[0018]

[0019] Where, is the state vector of node i, i = 1, 2, ..., M, M is the total number of nodes; d x dimensional Euclidean space; is the time-delay state vector of node i, φ k To satisfy The time-varying delay, φ and are the lower and upper bounds of the time lag; θ i，k is the initial state; is a nonlinear vector-valued function, Indicates the mapping symbol; x j，k is the state vector of node j that may be connected to node i; The sensor measurement signal has a value range of is the additive sensor fault to be estimated; To measure noise, to satisfy the mathematical expectation E{v i，k}=0 and variance is a bounded random noise sequence, v0>0 is the standard deviation of the measurement noise; is the internal coupling matrix, if It means connecting state components, is the process noise, to satisfy E{w i，k}=0 and A is a bounded random noise sequence, w0>0 is the standard deviation of the process noise; i 、B i 、F i 、E i 、C i , L i and D i is a known matrix of suitable dimension; is the external coupling configuration matrix of the complex network system, and the external coupling connection strength coefficient b ij ≥0 but not all 0, i≠j; F satisfies A symmetric matrix;

[0020] The nonlinear vector-valued function σ(·) for any vector The function satisfies:

[0021] [σ(o1)-σ(o2)-Π1(o1-o2)] T [σ(o1)-σ(o2)-Π2(o1-o2)]≤0

[0022] Where T represents the transpose, and Π1 and Π2 are any known matrices that reflect the boundaries of the sector-bounded constraints.

[0023] Furthermore, in step S100, the state vector Medium x =4, and They are motor position, motor speed, connecting rod position and connecting rod speed respectively; sensor measurement signal dy=2, and are the motor position and motor speed measured by the sensor respectively.

[0024] Furthermore, in step S200, a dynamic model of sensor failure with random deviation and first-order difference is established as follows:

[0025]

[0026] Where, Sensor failure f i，k The first-order difference of and is the random deviation, ζ i，k To satisfy E{ζ i，k}=0 and is a bounded random noise sequence, ζ0>0 is the standard deviation of the random deviation.

[0027] Furthermore, in step S300, the dynamic model of the complex network system node considering sensor failure is established as follows:

[0028]

[0029] Where,

[0030]

[0031] I and 0 represent the unit matrix and zero matrix of appropriate dimensions, respectively. The superscript “~” represents the symbol of the new vector and system parameter.

[0032] Furthermore, step S400 includes the following process:

[0033] Sensor measurement signal y i，k After being processed by the quantizer, the quantized sensor measurement signal is obtained Quantify the sensor measurement signal The length after encoding is The binary bit string of the decoded sensor measurement signal received by the estimator The statistical characteristics of are:

[0034]

[0035] and

[0036]

[0037] Where q is the crossover probability

[0038]

[0039] Establishing the compensated recovered sensor measurement signal The dynamic model is:

[0040]

[0041] Furthermore, in step S500, a dynamic model of the state and fault estimator with innovation saturation is established as follows:

[0042]

[0043] Where, For Estimates, Respectively for The estimate of H i is the gain parameter of the dynamic model of the state and fault estimator to be designed, is a saturation function, μ(·) is defined as follows:

[0044]

[0045] Where a is an arbitrary scalar, sign(·) is the sign function, min{·,·} is the minimum value of the two, a max is the saturation level, |·| is the absolute value;

[0046] for There are two diagonal matrices S1 and S2, 0≤S1<I≤S2, S1≥0 represents a semi-positive definite matrix. Decomposed into the following linear and nonlinear parts:

[0047]

[0048] Nonlinear part The following conditions must be met:

[0049]

[0050] Where,

[0051] Furthermore, in step S600, the overall state and fault estimation error system is:

[0052]

[0053] Where, ε k is the overall state and fault estimation error vector, is the time-delayed overall state and fault estimation error vector, is the state and fault estimation error of node i, is the Kronecker product;

[0054]

[0055]

[0056] The overall fault estimation error is:

[0057]

[0058] Where, is the fault estimation error vector of node i;

[0059]

[0060] Furthermore, step S700 includes the following process:

[0061] Minimize the final bound on the norm of the overall state and fault estimation error:

[0062]

[0063] Based on the boundedness theory of Lyapunov's stability theorem, the parameter Γ is obtained when the overall state and fault estimation error system achieves the final bounded mean square exponent. i and Ψ i , solve for the gain parameters of the dynamic model of the state and fault estimator with innovation saturation:

[0064]

[0065] Where tr{·} represents the trace of the matrix, Represents the matrix Γ i The inverse of

[0066]

[0067]

[0068] Among them, 0<α≤1 is a known scalar, and the composite variable matrix Ψ=diag{Ψ1,Ψ2,...,Ψ M}, weight matrix Γ=diag{Γ1,Γ2,...,Γ M}>0 is a positive definite matrix, and the weight matrix for the time-delay state is Φ=diag{Φ1,Φ2,...,Φ M}>0, the final bound R>0 is a matrix whose dimension matches the system parameters, and π1>0 and π2>0 are scalars.

[0069] The present invention also provides a state and fault estimation system for an interconnected flexible-link robot network system with new information saturation. The system has a program module corresponding to the steps of the method described in any one of the above technical solutions, and executes the steps in the above-mentioned state and fault estimation method for an interconnected flexible-link robot network system with new information saturation during operation.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] The present invention provides a state and fault estimation method and system for an interconnected flexible-link robot network system with new information saturation, which simultaneously considers the influence of signal transmission impairment, nonlinearity, sensor failure, time-varying lag, and bounded random noise on state estimation performance. The boundedness criterion fully utilizes the effective information of time-varying lag. Compared with the current state estimation method of complex network systems, the state and fault estimation method of the present invention can simultaneously process signal transmission impairment, nonlinearity, sensor failure, time-varying lag, and bounded random noise under new information saturation, and solves the gain parameters of the dynamic model of the state and fault estimator based on the overall state and fault estimation error system of the complex network system, thereby achieving the purpose of resisting system interference and signal transmission impairment, and has the advantages of being easy to solve and implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 Flowchart of a method for estimating state and faults of an interconnected flexible-link robot network system with innovation saturation in an embodiment of the present invention;

[0073] Figure 2 Schematic diagram of a flexible link robot system in an embodiment of the present invention;

[0074] Figure 3 Schematic diagram of a network system of interconnected flexible link robots in an embodiment of the present invention;

[0075] Figure 4 In the embodiment of the present invention, the new information Trajectory and Innovation Saturation Trajectory comparison chart;

[0076] Figure 5 is the sensor failure f in the embodiment of the present invention i，k Trajectory and its estimation Trajectory comparison chart;

[0077] Figure 6 State x in the embodiment of the present invention i，k Trajectory and its estimation Trajectory comparison chart;

[0078] Figure 7 is the sensor fault estimation error trajectory in an embodiment of the present invention;

[0079] Figure 8 is the state estimation error trajectory in an embodiment of the present invention;

[0080] Figure 9 is the overall state and fault estimation error norm E{||ε k ‖ 2}trajectory. DETAILED DESCRIPTION

[0081] In order to enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below with reference to the accompanying drawings. Obviously, the described embodiments or examples are only some of the embodiments or examples of the present invention, and not all of them. Based on the embodiments or examples of the present invention, all other embodiments or examples obtained by those skilled in the art without creative work should fall within the scope of protection of the present invention.

[0082] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0083] Combine Figures 1 to 4 As shown, the present invention provides a state and fault estimation method for an interconnected flexible link robot network system with innovation saturation, comprising the following steps:

[0084] S100. Establish a dynamic model of a complex network system with a flexible link robot system as a node, which has nonlinearity, sensor failure, time-varying delay, and bounded random noise;

[0085] S200, establishing a dynamic model of sensor failure with random deviation and first-order difference;

[0086] S300, establishing a dynamic model of the complex network system node considering the sensor failure based on the dynamic model of the sensor failure obtained in step S200 and the dynamic model of the complex network system node with the flexible link robot system obtained in step S100;

[0087] S400, under a given coding mechanism, establishing a dynamic model of the compensated restored sensor measurement signal according to the statistical characteristics of the decoded sensor measurement signal;

[0088] S500, establishing a dynamic model of a state and fault estimator with innovation saturation based on the dynamic model of the complex network system node considering sensor failure obtained in step S300 and the dynamic model of recovering sensor measurement signals obtained in step S400;

[0089] S600, obtaining an overall state and fault estimation error system based on the dynamic model of the state and fault estimator with innovation saturation obtained in step S500 and the dynamic model of the complex network system node considering sensor failure obtained in step S300;

[0090] S700, using system stability determination theory, based on the overall state and fault estimation error system obtained in step S600, solve the gain parameters of the dynamic model of the state and fault estimator with innovation saturation obtained in step S500;

[0091] S800 , substituting the gain parameters obtained in step S700 into the dynamic model of the state and fault estimator with innovation saturation obtained in step S500 , and estimating the state and sensor faults of the complex network system with the flexible link robot system as a node.

[0092] In step S100, it specifically includes:

[0093] The k+1-step state vector of the dynamic model of a complex network system node with nonlinearity, sensor failure, time-varying delay, and bounded random noise is established, and the k+1-step state vector is the k-step state vector, k-φ k The linear combination of the k-step state vector, nonlinear function, k-step state vectors of other nodes connected to it, and bounded random noise is established; the k-step sensor measurement signal of the dynamic model of the complex network system node with nonlinearity, sensor failure, time-varying delay, and bounded random noise is established, which is a linear combination of the k-step state vector, k-step sensor failure, and bounded random noise, including:

[0094] Establish a dynamic model of a complex network system with flexible linkage robot system as the node, which has nonlinearity, sensor failure, time-varying delay and bounded random noise;

[0095]

[0096] Where, for node i, is the state vector of node i, i = 1, 2, ..., M, M is the total number of nodes; d x dimensional Euclidean space; is the time-delay state vector of node i, φ k To satisfy The time-varying lag, φ and are the lower and upper bounds of the time lag; θ i，k is the initial state; is a nonlinear vector-valued function, Indicates the mapping symbol; x j，k is the state vector of node j that may be connected to node i, j = 1, 2, ..., M is the node number connected to node i; The sensor measurement signal has a value range of is the additive sensor fault to be estimated; To measure noise, to satisfy the mathematical expectation E{v i，k}=0 and variance is a bounded random noise sequence, v0>0 is the standard deviation of the measurement noise; is the internal coupling matrix, if It means connecting state components, is the process noise, to satisfy E{w i，k}=0 and A is a bounded random noise sequence, w0>0 is the standard deviation of the process noise; i 、B i 、F i 、E i 、C i 、L i and D i is a known matrix of suitable dimension; is the external coupling configuration matrix of the complex network system, and the external coupling connection strength coefficient b ij ≥0 but not all 0, i≠j; F satisfies A symmetric matrix;

[0097] The nonlinear vector-valued function σ(·)(σ(0)=0) for any vector The function satisfies:

[0098] [σ(o1)-σ(o2)-Π1(o1-o2)] T [σ(o1)-σ(o2)-Π2(o1-o2)]≤0

[0099] Where T represents the transpose, and Π1 and Π2 are any known matrices that reflect the boundaries of the sector-bounded constraints.

[0100] In step S100, the state vector Medium x =4, and They are motor position, motor speed, connecting rod position and connecting rod speed respectively; sensor measurement signal Medium y =2, and are the motor position and motor speed measured by the sensor respectively.

[0101] Combine Figure 2 and 3 As shown, taking three nodes as an example. In step S200, the sensor fault is a fault with a second-order difference of zero; under the fault with a second-order difference of zero, the dynamic model of the sensor fault with random deviation and first-order difference is established as follows:

[0102]

[0103] Where, Sensor failure f i，k The first-order difference of and is the random deviation, ζ i，k To satisfy E{ζ i，k}=0 and is a bounded random noise sequence, ζ0>0 is the standard deviation of the random deviation.

[0104] In step S300, the k+1-step augmented state vector of the dynamic model of the complex network system node considering sensor failure is the k-step augmented state vector, k-φ k k-step augmented state vector, k-step augmented state vectors of other nodes connected to itself, nonlinear function, random deviation, and linear combination of bounded random noise; the k-step sensor measurement signal of the dynamic model of the complex network system node considering sensor failure is a linear combination of the k-step augmented state vector and bounded random noise; in the dynamic model of the complex network system node considering sensor failure, the k-step self-state vector, the k-step sensor failure and the first-order difference of the k-step sensor failure constitute the k-step augmented state vector, and the dynamic model of the complex network system node considering sensor failure is established as:

[0105]

[0106] Where,

[0107]

[0108] I and 0 represent the unit matrix and zero matrix of appropriate dimensions respectively, and the superscript “~” represents the sign of the new vector and system parameter.

[0109] In step S400, the encoding mechanism adopts a binary encoding mechanism. Under the binary encoding mechanism, a dynamic model of the compensated restored sensor measurement signal is established according to the statistical characteristics of the decoded sensor measurement signal, specifically including:

[0110] Sensor measurement signal y i，k After being processed by the quantizer, the quantized sensor measurement signal is obtained Quantify the sensor measurement signal The length after encoding is The binary bit string of the decoded sensor measurement signal received by the estimator The statistical characteristics of are:

[0111]

[0112] and

[0113]

[0114] Where q is the crossover probability

[0115]

[0116] From formula (4), we can see that due to the existence of random binary bit flipping, the amplitude of the decoded sensor measurement signal received by the estimator deviates from the amplitude of the original sensor measurement signal, resulting in signal transmission damage. The compensated recovery sensor measurement signal is established. The dynamic model is:

[0117]

[0118] In step S500, the k+1-step estimated state and fault vector of the state and fault estimator with innovation saturation is the k-step estimated state and fault vector, k-φ k k-step estimated state and fault vector, estimated state and fault vector of other nodes connected to itself in k steps, estimated nonlinear function and innovation saturation function. The innovation is the difference between the restored sensor measurement signal and the estimated state and fault vector. The nonlinear part of the saturation function follows the sector bounded constraint, specifically including:

[0119] In steps S300 and S400, the state and fault estimation is performed on the flexible link robot system as a node of the complex network system under the condition of innovation saturation, considering nonlinearity, sensor failure, time-varying delay, and bounded random noise. The dynamic model of the state and fault estimator with innovation saturation is established as follows:

[0120]

[0121] Where, For Estimates, Respectively for The estimate of H i is the gain parameter of the dynamic model of the state and fault estimator to be designed, is a saturation function, μ(·) is defined as follows:

[0122]

[0123] Where a is an arbitrary scalar, sign(·) is the sign function, min{·,·} is the minimum value of the two, a max is the saturation level, |·| is the absolute value;

[0124] for There are two diagonal matrices S1 and S2, 0≤S1<I≤S2, S1≥0 represents a semi-positive definite matrix. Decomposed into the following linear and nonlinear parts:

[0125]

[0126] Nonlinear part The following conditions must be met:

[0127]

[0128] Where,

[0129] In step S600, it specifically includes:

[0130] The overall state and fault estimation error system is:

[0131]

[0132] Where, ε k is the overall state and fault estimation error vector, is the time-delayed overall state and fault estimation error vector, is the state and fault estimation error of node i (i=1, 2, ..., M), Kronecker product

[0133]

[0134] The overall fault estimation error is:

[0135]

[0136] Where, is the fault estimation error vector of node i (i=1, 2, ..., M)

[0137]

[0138] In step S700, the system stability determination theory is applied to obtain the gain parameters of the dynamic model of the state and fault estimator with innovation saturation by solving an optimization problem under the constraints of a linear matrix inequality. The optimization problem under the constraints of the linear matrix inequality is to minimize the final bound when the mean square exponent of the overall state and fault estimation error system is finally bounded, and specifically includes:

[0139] Using the overall state and fault estimation error system of step S600, the boundedness theory based on Lyapunov stability theorem is adopted, and a problem of minimizing the ultimate bound of the norm of the overall state and fault estimation error is solved to obtain the gain parameter H of the dynamic model of the state and fault estimator. i .

[0140] Minimize the final bound on the norm of the overall state and fault estimation error:

[0141]

[0142]

[0143] Based on the boundedness theory of Lyapunov's stability theorem, the parameter Γ is obtained when the overall state and fault estimation error system achieves the final bounded mean square exponent. i and Ψ i , solve for the gain parameters of the dynamic model of the state and fault estimator with innovation saturation:

[0144]

[0145] Where tr{·} represents the trace of the matrix, Represents the matrix Γ i The inverse

[0146]

[0147] Among them, 0<α≤1 is a known scalar, and the composite variable matrix Ψ=diag{Ψ1,Ψ2,...,Ψ M}, weight matrix Γ=diag{Γ1,Γ2,...,Γ M}>0 is a positive definite matrix, and the weight matrix for the time-delay state is Φ=diag{Φ1,Φ2,...,Φ M}>0, the final bound R>0 is a matrix whose dimension matches the system parameters, and π1>0 and π2>0 are scalars.

[0148] The state and fault estimation method (algorithm) of the interconnected flexible link robot network system with new information saturation proposed in the present invention is the underlying technical core of the present invention, and various products can be derived based on the algorithm.

[0149] Based on the method proposed in the present invention, a state and fault estimation system for an interconnected flexible-link robot network system with new information saturation is developed using a programming language. The system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned state and fault estimation method for an interconnected flexible-link robot network system with new information saturation during operation.

[0150] The developed system (software) computer program is stored on a computer-readable storage medium. When called by a processor, the computer program is configured to implement the steps of the aforementioned method for estimating the state and faults of an interconnected flexible-link robot network system with innovation saturation. This materializes the present invention on a carrier, becoming a computer program product.

[0151] Various implementations of the systems and techniques described herein can be realized in digital electronic circuitry, integrated circuitry, dedicated ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include being implemented in one or more computer programs that are executable and / or interpreted on a programmable system comprising at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0152] The computer programs (also referred to as programs, software, software applications, or code) of the present invention include machine instructions for a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., a magnetic disk, an optical disk, a memory, a programmable logic device (PLD)) for providing machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0153] The beneficial effects of the present invention will be described below with reference to specific embodiments.

[0154] Example 1

[0155] This embodiment performs state estimation on the physical quantities of motor position, motor speed, connecting rod position and connecting rod speed in the interconnected flexible link robot network system, and performs fault estimation on the physical quantities of motor position and motor speed.

[0156] The system stability determination theory described in step S700 of the above embodiment is a boundedness theory based on Lyapunov's stability theorem:

[0157]

[0158] Conclusion

[0159]

[0160] In the formula, sup represents the upper bound,

[0161]

[0162] Among them, λ max (·) represents the maximum eigenvalue, is the Lyapunov functional at time k, is the Lyapunov functional at time k+1;

[0163] The following system parameters are given for simulation:

[0164] M=3,d x =2,q=0.011,T=6, w0=0.3, v0=0.012, ζ0=0.6, φ =2

[0165] S=0.4I,S1=0.7I,a max =0.05,φ k =3+(-1) k , Λ=diag{0.7, 0.34,0.5,0.69}, α=0.2

[0166]

[0167] Π1=diag{0, 0, 0, 0.04}, Π2=diag{0, 0, 0, -0.09}, F1=F2=F3=I

[0168]

[0169] Select fault signal

[0170]

[0171] and nonlinear functions

[0172]

[0173] Where x i3，k is x i，k The third element of .

[0174] The initial states of complex network system nodes, sensor faults and estimators are:

[0175] x i，-4 =[0.20 0.12 0.20 0.12] T , x i，-3=[0.11 0.02 0.11 0.02] T

[0176] x i，-2 =[0.15 0.24 0.15 0.24] T , x i，-1 =[0.1 0.15 0.1 0.15] T

[0177] x i，0 =[0.08 0.03 0.08 0.03] T , f i，-4 =f i，-3 =f i，-2 =f i，-1 =f i，0 =[0 0] T

[0178]

[0179] Solve the optimization problem of formula (12) to obtain the gain parameter H of the dynamic model of the state and fault estimator i as follows:

[0180]

[0181] like Figure 5 As shown, sensor fault estimation and The trajectory can track the sensor failure f i1，k and f i2，k Trajectory. Figure 6 As shown, the node state estimation and The trajectory can track the node state x i1,k 、x i2,k 、x i3，k and x i4,k trajectory.

[0182] like Figure 7 As shown in , the estimation error of sensor failure is bounded and is within the interval [-0.49,1.43]. Figure 8 As shown in , the estimation error of the node state is bounded and is within the interval [-0.1127, 0.09314], which shows that the estimation effect of the invented state and fault estimator is good. Figure 9 As shown, the overall state and fault estimation error system achieves a bounded mean square exponent, which further verifies that the invented state and fault estimation method is effective.

[0183] Depend on Figures 5 to 9It can be seen that under the condition of new information saturation, for the interconnected flexible link robot network system considering nonlinearity, sensor failure, time-varying delay, and bounded random noise, the state and fault estimator design method of the present invention can accurately estimate the node state and sensor failure.

[0184] Although the present invention is disclosed as above, the scope of protection disclosed by the present invention is not limited thereto. Those skilled in the art of the present invention may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A state and fault estimation method for an interconnected flexible link robot network system with innovation saturation, characterized in that: The steps include: S100. Establish a dynamic model of a complex network system with a flexible link robot system as a node, which has nonlinearity, sensor failure, time-varying delay, and bounded random noise; S200, establishing a dynamic model of sensor failure with random deviation and first-order difference; S300, establishing a dynamic model of the complex network system node considering the sensor failure based on the dynamic model of the sensor failure obtained in step S200 and the dynamic model of the complex network system node with the flexible link robot system obtained in step S100; S400, under a given coding mechanism, establishing a dynamic model of the compensated restored sensor measurement signal according to the statistical characteristics of the decoded sensor measurement signal; S500, establishing a dynamic model of a state and fault estimator with innovation saturation based on the dynamic model of the complex network system node considering sensor failure obtained in step S300 and the dynamic model of recovering sensor measurement signals obtained in step S400; S600, obtaining an overall state and fault estimation error system based on the dynamic model of the state and fault estimator with innovation saturation obtained in step S500 and the dynamic model of the complex network system node considering sensor failure obtained in step S300; S700, using system stability determination theory, based on the overall state and fault estimation error system obtained in step S600, solve the gain parameters of the dynamic model of the state and fault estimator with innovation saturation obtained in step S500; S800 , substituting the gain parameters obtained in step S700 into the dynamic model of the state and fault estimator with innovation saturation obtained in step S500 , and estimating the state and sensor faults of the complex network system with the flexible link robot system as a node.

2. The method for estimating the state and fault of an interconnected flexible link machine network system with innovation saturation according to claim 1, characterized in that: In step S100, it specifically includes: Establish a dynamic model of a complex network system with flexible linkage robot system as the node, which has nonlinearity, sensor failure, time-varying delay and bounded random noise; Where, is the state vector of node i, i = 1, 2, ..., M, M is the total number of nodes; d x dimensional Euclidean space; is the time-delay state vector of node i, φ k To satisfy The time-varying delay, φ and are the lower and upper bounds of the time lag; θ i，k is the initial state; is a nonlinear vector-valued function, Indicates the mapping symbol; x j，k is the state vector of node j that may be connected to node i; The sensor measurement signal has a value range of is the additive sensor fault to be estimated; To measure noise, to satisfy the mathematical expectation E{v i，k }=0 and variance is a bounded random noise sequence, v0>0 is the standard deviation of the measurement noise; is the internal coupling matrix, if It means connecting state components, is the process noise, to satisfy E{w i，k }=0 and A is a bounded random noise sequence, w0>0 is the standard deviation of the process noise; i 、B i 、F i 、E i 、C i 、L i and D i is a known matrix of suitable dimension; is the external coupling configuration matrix of the complex network system, and the external coupling connection strength coefficient b ij ≥0 but not all 0, i≠j; F satisfies A symmetric matrix; The nonlinear vector-valued function σ(·) for any vector The function satisfies: [σ(o1)-σ(o2)-Π1(o1-o2)] T [σ(o1)-σ(o2)-Π2(o1-o2)]≤0 Where T represents the transpose, and Π1 and Π2 are any known matrices that reflect the boundaries of the sector-bounded constraints.

3. The state and fault estimation method of an interconnected flexible link robot network system with innovation saturation according to claim 2, characterized in that: In step S100, the state vector Medium x =4, and They are motor position, motor speed, connecting rod position and connecting rod speed respectively; sensor measurement signal Medium y =2, and are the motor position and motor speed measured by the sensor respectively.

4. The state and fault estimation method of an interconnected flexible link robot network system with innovation saturation according to claim 2, characterized in that: In step S200, a dynamic model of sensor failure with random deviation and first-order difference is established as follows: Where, Sensor failure f i，k The first-order difference of and is the random deviation, ζ i，k To satisfy E{ζ i，k }=0 and is a bounded random noise sequence, ζ0>0 is the standard deviation of the random deviation.

5. The state and fault estimation method of an interconnected flexible link robot network system with innovation saturation according to claim 4, characterized in that: In step S300, the dynamic model of the complex network system node considering sensor failure is established as follows: Where, I and 0 represent the unit matrix and zero matrix of appropriate dimensions, respectively. The superscript “~” represents the symbol of the new vector and system parameter.

6. The state and fault estimation method of an interconnected flexible link robot network system with innovation saturation according to claim 5, characterized in that: Step S400 includes the following process: Sensor measurement signal y i，k After being processed by the quantizer, the quantized sensor measurement signal is obtained Quantify the sensor measurement signal The length after encoding is The binary bit string of the decoded sensor measurement signal received by the estimator The statistical characteristics of are: and Where q is the crossover probability Establishing the compensated recovered sensor measurement signal The dynamic model is:

7. The state and fault estimation method of an interconnected flexible link robot network system with innovation saturation according to claim 6, characterized in that: In step S500, a dynamic model of the state and fault estimator with innovation saturation is established as follows: Where, For Estimates, Respectively for The estimate of H i is the gain parameter of the dynamic model of the state and fault estimator to be designed, is a saturation function, μ(·) is defined as follows: Where a is an arbitrary scalar, sign(·) is the sign function, min{·,·} is the minimum value of the two, a max is the saturation level, |·| is the absolute value; for There are two diagonal matrices S1 and S2, 0≤S1<I≤S2, S1≥0 represents a semi-positive definite matrix. Decomposed into the following linear and nonlinear parts: Nonlinear part The following conditions are met: Where, 8. The state and fault estimation method of an interconnected flexible link robot network system with innovation saturation according to claim 7, characterized in that: In step S600, the overall state and fault estimation error system is: Where, ε k is the overall state and fault estimation error vector, is the time-delayed overall state and fault estimation error vector, is the state and fault estimation error of node i, is the Kronecker product; The overall fault estimation error is: Where, is the fault estimation error vector of node i; 9. The state and fault estimation method of an interconnected flexible link robot network system with innovation saturation according to claim 8, characterized in that: Step S700 includes the following process: Minimize the final bound on the norm of the overall state and fault estimation error: Based on the boundedness theory of Lyapunov's stability theorem, the parameter Γ is obtained when the overall state and fault estimation error system achieves the final bounded mean square exponent. i and Ψ i , solve for the gain parameters of the dynamic model of the state and fault estimator with innovation saturation: Where tr{·} represents the trace of the matrix, Represents the matrix Γ i The inverse of Among them, 0<α≤1 is a known scalar, and the composite variable matrix Ψ=diag{Ψ1,Ψ2,...,Ψ M }, weight matrix Γ=diag{Γ1,Γ2,...,Γ M }>0 is a positive definite matrix, and the weight matrix for the time-delay state is Φ=diag{Φ1,Φ2,...,Φ M }>0, the final bound R>0 is a matrix whose dimension matches the system parameters, and π1>0 and π2>0 are scalars.

10. A state and fault estimation system for an interconnected flexible link robot network system with innovation saturation, characterized in that: The system has a program module corresponding to the steps of the method described in any one of claims 1 to 9 above, and executes the steps in the state and fault estimation method of the interconnected flexible link robot network system with new information saturation during operation.

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