A distributed adaptive fault-tolerant control method and system for nonlinear inline systems

Abstract

This invention discloses a distributed adaptive fault-tolerant control method and system for nonlinear inline systems, relating to the field of distributed control technology for nonlinear inline systems. The method includes: for each subsystem in the nonlinear inline system, constructing the actual output of each actuator in the subsystem based on the fault type of the actuator; the nonlinear inline system includes several subsystems; for each subsystem, constructing a local objective function, an error optimizer, an auxiliary system, high-gain parameters, and a control law, and generating an optimal error trajectory based on the local objective function and the error optimizer. At the upper level, this invention designs an error optimizer to generate the optimal error trajectory based on a local objective function that converges to zero; at the lower level, it designs a trajectory tracking fault-tolerant controller with the help of an auxiliary system, employing a dynamic high-gain approach to adaptively handle the effects of uncertain parameters, actuator faults, and unknown strong inline coupling.

Description

Technical Field

[0001] This invention relates to the field of distributed control technology for nonlinear inline systems, and in particular to a distributed adaptive fault-tolerant control method and system for nonlinear inline systems based on dynamic high gain in the event of actuator failure. Background Technology

[0002] In recent years, distributed control of nonlinear inline systems has attracted widespread attention due to its promising applications in power systems, transportation systems, computer network systems, and aerospace systems. Unlike centralized control, which requires information exchange between subsystems, distributed control designs a local controller for each subsystem. Each subsystem has only its own local information, thus reducing the communication burden and enhancing robustness to interactive faults. A key challenge of distributed control is relying solely on local controllers to perform stability and performance analysis of the entire closed-loop system. Since actuators are among the most vulnerable components, a failure in any subsystem can affect other subsystems due to physical interactions. Although many effective fault-tolerant control algorithms have been proposed for inline systems, existing results still have the following limitations:

[0003] (1) Regardless of the research on distributed fault-tolerant control strategies for weakly coupled or strongly coupled systems, most existing results only consider single output tracking control without considering how to improve transient performance through error optimization in the event of actuator failure, so as to reduce the impact of failure on system output performance.

[0004] (2) Most studies on fault-tolerant control of inline systems require that the first derivative of the reference output signal is known, which makes them difficult to apply to engineering systems where only the reference output is available and updated in real time, not to mention the complexity explosion problem caused by the recursive design algorithms used in these studies. Summary of the Invention

[0005] The purpose of this invention is to provide a distributed adaptive fault-tolerant control method and system for nonlinear inline systems. It can use a dynamic high-gain approach to adapt to the effects of uncertain parameters, actuator failures, and unknown strong inline coupling effects, relaxes the requirement that the derivative of the output trajectory is known, and achieves asymptotic tracking.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A distributed adaptive fault-tolerant control method for a nonlinear inline system includes:

[0008] For each subsystem in the nonlinear inline system, the actual output of each actuator in the subsystem is constructed based on the fault type of the actuator in the subsystem; the nonlinear inline system includes several subsystems;

[0009] For each subsystem, a local objective function, an error optimizer, an auxiliary system, high-gain parameters, and a control law are constructed, and an optimal error trajectory is generated based on the local objective function, the error optimizer, the auxiliary system, the high-gain parameters, and the control law; the optimal error trajectory is used to minimize the difference between the actual output signal of the subsystem and the desired reference signal in the nonlinear inline system;

[0010] Local objective function f i (∈ i )satisfy

[0011] in, Let y represent the tracking error of the i-th subsystem. i The actual output signal of the i-th subsystem. Let i be the desired reference signal output by the i-th subsystem, where i = 1, 2, 3...N, and N is the number of subsystems. f i (∈ i The global minimum value of ).

[0012] Error optimizer is

[0013] Where, p i Optimize the reference signal for the tracking error of the i-th subsystem; based on p i Design an optimized trajectory tracking controller for each subsystem to minimize the tracking error. i It asymptotically converges to p i ;

[0014] The auxiliary system is:

[0015]

[0016] Where k = 2,...,n i , Describes the first q(1,...,n) of the auxiliary system. i A vector consisting of ) states, n i Indicates the system order; Represents the set of vectors of uncertain constants; It is θ i The estimate; Represents a known set of nonlinear functions;

[0017] The high-gain parameter is automatically updated using the following formula:

[0018]

[0019] Among them, l iThe high-gain parameter of the i-th subsystem; and σ i,2 ≥1 is a positive constant; It is a diagonal matrix; e i Let be the tracking error vector of the i-th subsystem.

[0020] A computer system includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described distributed adaptive fault-tolerant control method for a nonlinear inline system.

[0021] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the aforementioned distributed adaptive fault-tolerant control method for a nonlinear inline system.

[0022] A computer program product includes a computer program that, when executed by a processor, implements the steps of the aforementioned distributed adaptive fault-tolerant control method for a nonlinear inline system.

[0023] According to specific embodiments provided by the present invention, the following technical effects are disclosed: The present invention provides a distributed adaptive fault-tolerant control method and system for a nonlinear inline system. For each subsystem in the nonlinear inline system, the actual output of each actuator in the subsystem is constructed according to the fault type of the actuator in the subsystem. The nonlinear inline system includes several subsystems. For each subsystem, a local objective function, an error optimizer, an auxiliary system, high-gain parameters, and a control law are constructed, and an optimal error trajectory is generated based on the local objective function, the error optimizer, the auxiliary system, the high-gain parameters, and the control law. At the upper layer, the present invention designs an error optimizer to generate the optimal error trajectory based on a local objective function that converges to zero. At the lower layer, a trajectory tracking fault-tolerant controller is designed with the help of an auxiliary system, employing a dynamic high-gain approach to adaptively address the effects of uncertain parameters, actuator faults, and unknown strong inline coupling. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 A schematic flowchart of the distributed adaptive fault-tolerant control method for a nonlinear inline system provided in Embodiment 1 of the present invention.

[0026] Figure 2This is a structural diagram of the distributed adaptive fault-tolerant control method for a nonlinear inline system provided in Embodiment 1 of the present invention;

[0027] Figure 3 This is an output tracking curve diagram for each motor provided in Embodiment 1 of the present invention;

[0028] Figure 4 This is a graph showing the output tracking error of each motor provided in Embodiment 1 of the present invention;

[0029] Figure 5 This is a control input curve diagram for each motor provided in Embodiment 1 of the present invention;

[0030] Figure 6 This is an adaptive update parameter curve provided in Embodiment 1 of the present invention;

[0031] Figure 7 An internal structural diagram of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] The purpose of this invention is to provide a distributed adaptive fault-tolerant control method and system for nonlinear inline systems. At the upper layer, an error optimizer is designed to generate the optimal error trajectory based on a local objective function that converges to zero. At the lower layer, a trajectory tracking fault-tolerant controller is designed with the help of an auxiliary system, and a dynamic high-gain approach is used to adaptively address the effects of uncertain parameters, actuator failures, and unknown strong inline coupling.

[0034] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] Example 1

[0036] like Figure 1 and Figure 2 As shown in this embodiment, a distributed adaptive fault-tolerant control method for a nonlinear inline system includes:

[0037] S1: For each subsystem in the nonlinear inline system, construct the actual output of each actuator in the subsystem based on the fault type of the actuator in the subsystem; the nonlinear inline system includes several subsystems. Consider the following redundant-driven nonlinear inline system containing N subsystems, where the dynamic system of the i-th (i∈N) subsystem is as follows:

[0038]

[0039] Where, n i Denotes the order of the system, k = 1, ..., n i -1, Represents a measurable state variable, and and These represent the output of the i-th subsystem and the output of the h-th actuator in the i-th subsystem, respectively; s i,h ∈{0,1} represents the activation function that determines whether the h-th executor is connected to the system; Represents a set of vectors of uncertain constants. d represents a known set of nonlinear functions; i Indicates satisfaction Unknown bounded perturbations, It is an unknown constant; This represents the unknown inline coupling terms between the subsystems. m i This represents the number of redundant actuators in the i-th subsystem.

[0040] Considering additive and multiplicative faults in the actuators, the actual output formula of the h-th actuator in the i-th subsystem under the condition of actuator faults is as follows:

[0041]

[0042] Among them, v i κ represents the controller output of the i-th subsystem. i,h This means that 0 ≤ κ i,h Unknown constants ≤ 1; Indicates satisfaction Unknown time-varying additive faults It is an unknown constant.

[0043] This embodiment considers the following three actuator states: 1) κ i,h =1, This indicates that the h-th actuator of the i-th subsystem has no faults; 2) 0 < κ i,h <1, This indicates that the h-th actuator of the i-th subsystem suffers from both multiplicative and additive faults simultaneously; 3)κ i,h=0 indicates that the h-th actuator of the i-th subsystem is completely faulty, and the actual output u of the h-th actuator of the i-th subsystem is then... i,h No longer subject to v i The impact.

[0044] S2: For each subsystem, construct a local objective function, an error optimizer, an auxiliary system, high-gain parameters, and a control law, and generate an optimal error trajectory based on the local objective function, the error optimizer, the auxiliary system, the high-gain parameters, and the control law; the optimal error trajectory is used to minimize the difference between the actual output signal of the subsystem and the desired reference signal in the nonlinear inline system.

[0045] The control objective of this embodiment is to design a distributed adaptive fault-tolerant asymptotic tracking control strategy based on dynamic high gain, such that all signals of the closed-loop system are bounded, and the output y of each subsystem is constant. i They can all progressively track the desired reference signal of their output. Right now Considering the lag in fault diagnosis and location in actual engineering, in order to ensure the stability and security of the system from the occurrence of a fault to the completion of fault isolation, this embodiment treats the unknown activation function and actuator fault as system uncertainty without requiring any prior knowledge about the number of actuators connected to the system and the number of failed actuators, and adopts a passive compensation method to compensate for the unknown actuator fault.

[0046] This embodiment incorporates optimization principles, introducing a differentiable local objective function f for each subsystem. i (∈ i ), which satisfies

[0047]

[0048] in, Let y represent the tracking error of the i-th subsystem; i The actual output signal of the i-th subsystem. Let i be the desired reference signal output by the i-th subsystem, where i = 1, 2, 3...N, and N is the number of subsystems. f i (∈ i The global minimum of f; in addition, f i (∈ i ) is ω-strongly convex, and its gradient satisfies yes of which ω i >0, The control objective in step 3 can be equivalent to the tracking error ∈ i The solution converges to the above optimization problem, i.e.

[0049] In this embodiment, an error optimizer is constructed for each subsystem as follows:

[0050]

[0051] Where, p i Optimize the reference signal for the tracking error of the i-th subsystem; based on p i Design an optimized trajectory tracking controller for each subsystem to minimize the tracking error. i It asymptotically converges to p i ,Right now In other words, at any given time, the ideal output of the i-th subsystem should be equal to

[0052] An auxiliary system is also constructed for each subsystem, specifically:

[0053]

[0054] in, This represents the state signal of the i-th auxiliary system, k = 2, ..., n i , This represents the vector formed by the first q state estimates of the auxiliary system. The range of values ​​for q is q = 1, ..., n i n i Indicates the system order; Represents the set of vectors of uncertain constants; It is θ i The estimate; Represents a known set of nonlinear functions; Let represent the desired input signal of the i-th auxiliary system.

[0055] This embodiment also constructs filters as shown in formulas (6) and (7), and uses the filters to address the components included in the auxiliary system. The derivative is estimated, specifically including:

[0056]

[0057] In this context, a dot on the parameter sign indicates the derivative of that parameter, for example... for The derivative; l i For the design of dynamic high-gain parameters; τ i and η is a given positive constant; i It is a bounded, smooth, strictly positive function that satisfies It is a bounded positive number; The variable M is uncertain. i,q The estimate.

[0058] Combining the dynamic system of formula (1) and the auxiliary system of formula (5), the tracking error vector is defined. The following error dynamic equation can be obtained:

[0059]

[0060] in, Represents the tracking error vector e i The components in; Represents a known set of nonlinear functions; k = 1, ..., n i -1, Let s represent the input signal of the i-th subsystem. i,h ∈{0,1} indicates whether the h-th actuator of the i-th subsystem is connected to the system's activation function. This represents a vector consisting of the first k errors. This represents a vector consisting of the first k errors and the first k auxiliary system state estimates. Indicates the first n i The error and the first n i A vector consisting of state estimates of the auxiliary system. Rewrite it in matrix form as follows:

[0061]

[0062] in, B i =[0,...,0,1] T ,

[0063] In this embodiment, a high-gain parameter l is designed for each subsystem. i And it updates automatically using the following formula:

[0064]

[0065] Among them, l i Let l be the high-gain parameter of the i-th subsystem; i (0)≥1, γ li and σ i,2 ≥1 is a positive constant; It is a diagonal matrix; e i Let be the tracking error of the i-th subsystem.

[0066] Construct an n for each subsystem i 1-th order matrix

[0067]

[0068] in, B i =[0,...,0,1] T , By appropriately selecting the coefficient k i,q (q=1,...,n i ) can make If the matrix is ​​a Hurwitz matrix, then a positive definite matrix can be found by solving the following Riccati equation. satisfy

[0069] make According to formula (11) and using It can be deduced that:

[0070]

[0071] The actual control input of the i-th subsystem can be written as: To compensate for actuator failures, define an uncertain variable. The control law for each subsystem is designed as follows:

[0072]

[0073] in, It is a positive number. It is g i =1 / μ i The estimate.

[0074] In formula (14) It is an auxiliary control signal, designed as follows:

[0075]

[0076] in, It is a positive number. It is an uncertain parameter ρ i The estimate.

[0077] To verify the stability of the proposed controller, this embodiment utilizes Lyapunov stability analysis theory to verify its effectiveness, specifically including the following steps:

[0078] First, regarding the definition of the error optimizer in the above steps. The error dynamics can then be expressed as:

[0079]

[0080] Define a candidate Lyapunov function as Where αi It is a positive constant for V pi Differentiating, we get:

[0081]

[0082] in, Because f i (∈ i ) is ω-strongly convex and yes Using Young's inequality, we can obtain:

[0083]

[0084]

[0085] in, σ i,1 It is a positive constant. Substituting formulas (20) and (21) into formula (19), we get:

[0086]

[0087] in,

[0088]

[0089] Based on the above formula, by choosing an appropriate α i and σ i,1 Make δ i,1 and δ i,2 It is positive. Secondly, the estimation error variable is defined for a series of uncertain variables in the controller as follows: in, Construct a system containing e for each subsystem i , l i ξ i , and Lyapunov function candidates:

[0090]

[0091] in, All are positive definite symmetric matrices. Differentiating equation (24) yields:

[0092]

[0093] After derivation and transformation, the following inequality can be obtained for each term in formula (25).

[0094]

[0095] Where, β i,1 =b i,2 n i |θ i ||P i |, Choose a positive constant τ i ≥n i +1, definition We can obtain:

[0096]

[0097] in,

[0098] definition D = diag(0, -1, ..., -n) i +1), we can get Furthermore, we can obtain:

[0099]

[0100] Where, β i,6 =(n i -1)γ li |P i |+γ li |D i ||P i |

[0101] definition The adaptive update law is We can obtain:

[0102] in,

[0103] Based on formula (15) and Young's inequality, we can obtain:

[0104]

[0105] in, Define a positive constant that satisfies We can obtain:

[0106]

[0107] in, Substituting formulas (26)-(32) into formula (25) yields:

[0108]

[0109] Where, δ i,3 =l i-2β i,1 -2β i,3 -2β i,4 -2β i,6 ;

[0110] δ i,4 =β i,5 +β i,7 +β i,8 +β i,9 +μ i >0.

[0111] In formula (33), These are residual terms related to inline terms, which cannot be eliminated using the Lyapunov function of the local system. Therefore, a global Lyapunov function is constructed as follows:

[0112]

[0113] Combining formulas (19) and (33), the derivative of formula (34) with respect to time is:

[0114]

[0115] From formula (35), it can be seen that the remaining inline terms satisfy:

[0116] based on From the definition, we can obtain

[0117]

[0118] Based on the above analysis, formula (34) can be rewritten as:

[0119]

[0120] Integrating both sides of equation (37) yields:

[0121]

[0122] e can be obtained i ξ i , and Both are bounded. Therefore, the following inequality (39) holds:

[0123]

[0124] According to formula (10), since σ i,2 ≥1, we can obtain

[0125]

[0126] Where, γ lmax =max{γ l1 ,...,γ lN Based on (39) and (40), and based on Barbalat's lemma, we can obtain:

[0127]

[0128] It can be seen that the high gain parameter l i The filtering error ξ will converge to a certain finite positive constant. i Reference tracking error e i and optimization error It is bounded and asymptotically converges to zero. Furthermore, we can obtain... Therefore, the tracking error of all subsystems The main control objective of this embodiment can be achieved by gradually converging to zero.

[0129] This embodiment uses a real power system as an example and employs Matlab 2019b software to verify the effectiveness of the proposed control algorithm. The specific verification process and results are as follows:

[0130] Consider the following nonlinear inline system containing four motors, each driven by two actuators. The dynamics (dynamic system) of the i-th (i = 1, 2, 3, 4) motor can be described as follows:

[0131]

[0132] in, λ represents the unknown inline interaction between subsystems. i,1,j =cos(ι ij -ν ij ), λ i,2,j =cos(x) i,1 -x j,1 +ι ij -ν ij );x i,1 and x i,2 These represent the absolute rotor angle and angular velocity of the motor, respectively; J i D represents the moment of inertia of the motor; i and ΔD i E represents the nominal damping coefficient and the uncertain damping coefficient, respectively. i Indicates internal voltage and Y ij The modulus of the transfer admittance between the i-th and j-th motors; d i This indicates an unknown external disturbance.

[0133] The system parameters are selected as follows: E1 = 1.017, E2 = 1.005, E3 = 1.013, E4 = 1.009, J1 = 1.03, J2 = 1.25, J3 = 1.33, J4 = 1.55, D1 = 0.5, D2 = 1.2, D3 = 1.6, D4 = 2.0, Y ij =Y ji =1.98, ι ij =-ι ji =1.2, ν ij =-ν ji =1.5, ΔD i ∈[-0.6,0.6], d i =0.01sin(0.1t). The initial state of each motor is set to x1(0) = [0.02, 0]. T x2(0) = [0.04, 0] T x3(0) = [0.03, 0] T x4(0) = [0.06, 0] T In addition, the initial state of other variables is set to l. i (0) = 10, p i (0)=x i,1 (0),

[0134] In this case, assume s i,1 =s i,2 =1, meaning both actuators driving the i-th motor are connected to the system. The unknown actuator fault is set as follows: the generation u of the first motor... 1,1 The actuator was stuck at t=7s, and the second motor generated u. 2,1 The actuator loses 80% of its effectiveness at t=15s, and the third motor generates u. 3,1 The actuator experienced a bias fault at t=20s, and the fourth motor generated u. 4,1 The actuator in question experienced both effectiveness degradation and paranoia at t=30s, while the other unmentioned actuators functioned normally. These faults can be described by the following formula.

[0135]

[0136] In this embodiment, the desired output trajectory is set as formulas (44)-(47):

[0137]

[0138] The control objective is to ensure the output signal y of each motor using the control algorithm proposed in this embodiment. i Able to converge asymptotically to a given output trajectory (i.e., the desired reference signal output).

[0139] Based on the above settings, we can obtain the inline term Ψ. i satisfy:

[0140]

[0141] Among them, c i,j The coupling coefficient is unknown. The local objective function for the i-th motor is chosen as f. i (r) = 4(r-0) 2 The controller and adaptive parameters are selected as follows: k i,1 =-3,k i,2 =-4, τ i =8, η i =0.5e -0.18t α i =0.1, σ i,1 =σ i,2 =1.

[0142] This embodiment also provides simulation verification results using Matlab 2019b software.

[0143] from Figure 3 It can be seen that the output of each motor can track the desired output trajectory very well. From Figure 4 It can be seen that the tracking error gradually converges to zero. Figure 5 It is the control input curve. Figure 6 It is an adaptive parameter The curve shows that actuator failures can be effectively compensated for.

[0144] This embodiment proposes a distributed adaptive fault-tolerant asymptotic tracking control strategy. Utilizing a hierarchical control framework, an error optimizer is designed at the upper layer to generate the optimal error trajectory based on a local objective function converging to zero. At the lower layer, a trajectory tracking fault-tolerant controller is designed with the aid of an auxiliary system, employing a dynamic high-gain approach to adaptively address the effects of uncertain parameters, actuator failures, and unknown strong internal coupling. Compared to existing results, this embodiment relaxes the requirement that the derivative of the output trajectory be known, achieving asymptotic tracking. Application results on a power system demonstrate the effectiveness of the proposed control algorithm.

[0145] The advantages of this invention compared to the prior art are as follows:

[0146] (1) In terms of closed-loop system performance, this embodiment combines direct adaptive compensation with dynamic high-gain technology, which can automatically compensate for the effects of parameter uncertainty, actuator failure and strong inline effect without any prior knowledge, and ultimately ensure the gradual convergence of tracking error.

[0147] (2) The auxiliary system designed by the existing technical solution has high requirements for the accuracy of the system model and involves iterative differential calculation. In this embodiment, the influence of model uncertainty on the system is considered when designing the auxiliary system, and a set of filters is introduced to avoid iterative differential calculation of the state. This not only relaxes the requirement that the derivative of the output reference signal is known, but also reduces the computational burden.

[0148] (3) Existing technical solutions rarely study the optimization problem of inline systems. Unlike existing technical solutions that directly use tracking error to design local controllers for each subsystem, this embodiment designs an additional gradient-based error optimizer to optimize the error in order to improve transient performance before designing the local controller.

[0149] Example 2

[0150] A computer system includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a distributed adaptive fault-tolerant control method for a nonlinear inline system as described in Embodiment 1.

[0151] Example 3

[0152] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a distributed adaptive fault-tolerant control method for a nonlinear inline system as described in Embodiment 1.

[0153] Example 4

[0154] A computer program product includes a computer program that, when executed by a processor, implements the steps of a distributed adaptive fault-tolerant control method for a nonlinear inline system as described in Embodiment 1.

[0155] Example 5

[0156] A computer device, which may be a database, may have an internal structure diagram as shown below. Figure 7As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The database stores pending transactions. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements a distributed adaptive fault-tolerant control method for a nonlinear inline system as described in Embodiment 1.

[0157] It should be noted that the object information (including but not limited to object device information, object personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this invention are all information and data authorized by the object or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0158] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided by this invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided by this invention may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided by this invention may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0159] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0160] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A decentralized adaptive fault-tolerant control method for nonlinear interconnected systems, characterized by, include: For each subsystem in the nonlinear inline system, the actual output of each actuator in the subsystem is constructed based on the fault type of the actuator in the subsystem. Nonlinear interconnected systems consist of several subsystems; For each subsystem, a local objective function, an error optimizer, an auxiliary system, high-gain parameters, and a control law are constructed, and an optimal error trajectory is generated based on the local objective function, the error optimizer, the auxiliary system, the high-gain parameters, and the control law; the optimal error trajectory is used to minimize the difference between the actual output signal of the subsystem and the desired reference signal in the nonlinear inline system; local objective function satisfies ; in, Indicates the first Tracking error of each subsystem; For the first The actual output signal of each subsystem For the first The expected reference signal output by each subsystem =1,2,3...N, where N is the number of subsystems; express The global minimum value; The error optimizer is ; in, For the first The tracking error optimization reference signal of each subsystem; based on Optimize the trajectory tracking controller for each subsystem to minimize tracking error. asymptotic convergence to ; The auxiliary system is: ； in, For the first The expected reference signal output by each subsystem; , Indicates the auxiliary system before A vector consisting of states, , , Indicates the system order; Represents the set of vectors of uncertain constants; yes The estimate; Represents a known set of nonlinear functions; Indicates the first The expected input signal for an auxiliary system; The high-gain parameter is automatically updated using the following formula: ； in, For the first High gain parameters of each subsystem; and It is a positive number; It is a diagonal matrix; For the first The tracking error vector of each subsystem; The control law is as follows: ； ； ； in, It is a positive number. yes The estimate; , It is a positive definite matrix; ; It is a bounded, smooth, strictly positive function; , For coefficients, ; It is an auxiliary control signal.

2. The distributed adaptive fault-tolerant control method for a nonlinear inline system according to claim 1, characterized in that, The dynamic system of the subsystem is as follows: ； in, , Represents a measurable state variable, and ; and They represent the first The output of the first subsystem and the first The output of each actuator; Indicates the decision of the first Whether each actuator is connected to the system's activation function; Represents a set of vectors of uncertain constants. Represents a known set of nonlinear functions; Indicates satisfaction Unknown bounded perturbations, It is an unknown constant; This represents the unknown inline coupling terms between the subsystems. ; Indicates the first The number of redundant actuators in each subsystem.

3. The distributed adaptive fault-tolerant control method for a nonlinear inline system according to claim 1, characterized in that, The actual output of the subsystem's actuator is: ； in, Indicates the first The controller output of each subsystem Indicates satisfaction The unknown constant; Indicates satisfaction Unknown time-varying additive faults It is an unknown constant.

4. The distributed adaptive fault-tolerant control method for a nonlinear inline system according to claim 1, characterized in that, Also includes: Construct a filter and apply the filter to the auxiliary system. The derivative is estimated, specifically including: ； ； in, , , ; For the design of dynamic high-gain parameters; and It is a given positive constant; satisfy , It is a bounded positive number; It is an uncertain variable The estimate.

5. A computer system, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the steps of a distributed adaptive fault-tolerant control method for a nonlinear inline system as described in any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the distributed adaptive fault-tolerant control method for a nonlinear inline system as described in any one of claims 1-4.

7. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the distributed adaptive fault-tolerant control method for a nonlinear inline system as described in any one of claims 1-4.

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