An integrated energy system distributed fault-tolerant control method based on an intermediate observer

Abstract

The application discloses a kind of based on intermediate observer's integrated energy system distributed fault-tolerant control method, it is related to integrated energy system collaborative control and safe operation technical field.The application establishes integrated energy system unified dynamics model containing concurrent fault and external disturbance, and then constructs singular augmented system and introduces intermediate variable design distributed intermediate observer, avoids the strict observer matching condition required by traditional observer, realizes the joint accurate estimation of system state and sensor, concurrent fault of actuator;Then, design the compound fault-tolerant control law containing feedforward compensation term and active fault cancellation term;Subsequently, combined with unilateral Lipschitz condition and singular value decomposition technology, the robust stability condition of closed-loop system is converted into linear matrix inequality condition for solving, and the observer and controller gain are obtained;Finally, the gain obtained is configured in each energy subnetwork node, and online active fault-tolerant control of integrated energy system is realized.

Description

Technical Field

[0001] This invention relates to the field of integrated energy system collaborative control and safe operation technology, specifically a distributed fault-tolerant control method for integrated energy systems based on an intermediate observer. Background Technology

[0002] Against the backdrop of advancing the "dual carbon" goals, integrated energy systems, through the coupling and complementarity of multiple energy sources such as electricity, gas, and heat, achieve coordinated energy conversion, transmission, and utilization, serving as a crucial pathway to improve energy efficiency and promote the consumption of renewable energy. With the development of distributed collaborative control, integrated energy systems are gradually evolving from centralized dispatch to distributed control. However, sensors and actuators are prone to malfunctions such as deviations, jamming, and gain attenuation under complex operating conditions, equipment aging, and external disturbances, affecting the safe and stable operation of the system and endangering people's lives and property.

[0003] Existing methods for ensuring the safety of integrated energy systems primarily rely on data-driven fault diagnosis technologies. These technologies utilize historical operational data and algorithms such as machine learning and deep learning to classify faults, detect anomalies, or predict states. However, integrated energy systems comprise multiple physical subsystems, including electricity, natural gas, and heat. The operating mechanisms, dynamic time scales, and fault behaviors of these subsystems differ significantly, making it difficult to obtain accurately labeled data samples covering all operating conditions and all types of faults in engineering practice. Furthermore, data-driven models lack physical mechanism constraints and interpretability, making it difficult to provide rigorous mathematical proofs for the stability, convergence, and safety boundaries of closed-loop systems. Their diagnostic results often remain at the level of fault alarms, classification, or health status assessments, failing to output fault reconstruction signals with accurate amplitudes and dynamic trajectories, thus hindering their direct application to control compensation.

[0004] To address the aforementioned issues, some existing technologies employ model-driven methods such as unknown input observers, sliding mode observers, adaptive observers, or robust observers to estimate system states, unknown inputs, or fault signals. These methods can estimate faults using the system's mathematical model, but typically require the system to meet strict algebraic matching conditions. For example, the output matrix and fault distribution matrix must satisfy specific rank constraints, or the fault channel must be directly decoupled from the observed output. However, integrated energy systems have large node scales and complex topologies, and sensor deployment is limited by cost, space, and communication conditions. Real-world systems often struggle to meet these conditions, making it difficult for traditional observers to obtain feasible solutions. Furthermore, existing observers are mostly designed for single sensor or single actuator faults, making it difficult to achieve simultaneous estimation and accurate reconstruction of system states, sensor faults, and actuator faults.

[0005] Integrated energy systems also exhibit significant heterogeneity and nonlinearity. The state dimensions, response speeds, and physical constraints of the power subsystem, natural gas pipeline network, and heating network differ, and coupling components such as combined heat and power (CHP) units create strong coupling relationships between different energy flows. Existing distributed cooperative control methods are mostly based on assumptions of isomorphic agents, linear models, or consistent dimensions, making it difficult to handle state estimation and consistency control problems among multi-dimensional heterogeneous agents. For components with nonlinear dissipation and transmission characteristics, such as gas and heating networks, traditional linearization methods can easily introduce model errors, affecting the stability of the closed-loop system under fault conditions.

[0006] In terms of fault-tolerant control, passive fault-tolerant control relies on a pre-designed robust controller to resist faults and disturbances within a certain range, but its compensation capability is limited and it is difficult to accurately offset specific fault amplitudes. Although active fault-tolerant control can adjust the control law in real time based on fault estimation results, existing technologies mostly focus on closed-loop stability or asymptotic stabilization after a fault, lacking a control structure that combines steady-state feedforward, state feedback, and active fault compensation. When the system simultaneously experiences external disturbances, nonlinear dynamics, sensor faults, and actuator faults, traditional control strategies struggle to simultaneously achieve dynamic disturbance rejection, fault compensation, and steady-state zero-steady-state tracking performance.

[0007] Therefore, there is an urgent need in this field for a distributed fault-tolerant control scheme for integrated energy systems that is adapted to the integrated energy system architecture, overcomes the limitations of observer matching conditions, and has the ability to reconstruct and actively fault-tolerant control in the event of concurrent failures of actuators and sensors. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the present invention aims to propose a distributed fault-tolerant control method for integrated energy systems based on intermediate observers, comprising:

[0009] Step 1: Construct a collaborative communication network for the integrated energy system, thereby obtaining the adjacency matrix and Laplace matrix, and constructing a unified dynamic model for the integrated energy system;

[0010] Step 2: Transform the unified dynamics model to obtain the standard dynamics model;

[0011] Step 3: Based on the standard dynamics model and adjacency matrix, construct a distributed intermediate observer and a composite fault-tolerant control law;

[0012] Step 4: Based on the Laplace matrix, unified dynamics model, standard dynamics model, distributed intermediate observer, and composite fault-tolerant control law, construct the estimation error dynamics equation and the augmented closed-loop system dynamics equation;

[0013] Step 5: Based on the estimation error dynamic equation and the augmented closed-loop system dynamic equation, construct the stability conditions in the form of LMI;

[0014] Step 6: Solve the stability conditions in the form of LMI to obtain the parameter values ​​in the distributed intermediate observer and the parameter values ​​in the composite fault-tolerant control law;

[0015] Step 7: Run the distributed intermediate observer and the composite fault-tolerant control law based on the parameter values ​​in the distributed intermediate observer and the composite fault-tolerant control law.

[0016] Optionally, step 1 specifically includes:

[0017] Step 1.1: Construct a collaborative communication network for the integrated energy system , ,in, Represents a set of nodes. N represents the total number of nodes, where each node is a smart grid agent, a smart gas network agent, or a smart heating network agent within the integrated energy system. Denotes the set of edges. The edge set includes communication links between nodes. For any node i, its set of adjacent nodes is denoted as . , It is an adjacency matrix. , This represents the adjacency state value between node i and node j, when there is a communication connection between node i and node j. When there is no communication connection between node i and node j, ;

[0018] The Laplace matrix is ​​defined based on the adjacency matrix. , Among them, the Laplace matrix elements in Represented as:

[0019] ;

[0020] in, Represented as the adjacency state value between node i and node k;

[0021] Step 1.2: Construct a unified dynamic model for the integrated energy system.

[0022] Optionally, step 1.2 specifically includes:

[0023] Step 1.2.1: Construct the physical dynamics model of the power grid intelligent agent, represented as:

[0024] ;

[0025] in, For the speed regulating valve position increment, for The time derivative, The time constant of the speed controller, This is the governor droop coefficient. For frequency deviation, For governor control command input. For mechanical power increment, for The time derivative, This is the gain coefficient. The time constant of the steam turbine. for The time derivative, This is the gain coefficient. The time constant of the generator. The change in electrical power This refers to the generator rotor phase angle deviation. for The time derivative;

[0026] Step 1.2.2: Construct the physical dynamics model of the air network intelligent agent, represented as:

[0027] ;

[0028] in, Due to export pressure, for The time derivative, The gas constant is... The cross-sectional area of ​​the pipe. For the length of the pipe, For inlet quality flow, For export quality flow rate, for The time derivative, Where g is the inlet pressure and g is the gravitational constant. The angle of inclination. For the speed of sound, The coefficient of friction, The diameter of the pipe;

[0029] Step 1.2.3: Construct the physical dynamics model of the heating network intelligent agent, represented as:

[0030] ;

[0031] in, For heating temperature, for The time derivative, This is the inlet water supply temperature control quantity. For inlet quality flow, For the volume of the pipe, For specific heat capacity, For user heat load power, For fluid density;

[0032] Step 1.2.4: Define the state vector Control input Measurement output and continuous nonlinear terms Combined with actuator failure Sensor malfunction and external disturbances ,in, , , , , , , These are the dimensions of the state vector, the control input, the measurement output, the continuous nonlinear term, the actuator fault, and the sensor fault, respectively.

[0033] The physical dynamics models of the power grid intelligent agent, the gas network intelligent agent, and the heating network intelligent agent are constructed into a unified dynamic model, which is represented as:

[0034] ;

[0035] in, for The time derivative, The actuator fault distribution matrix, The external disturbance distribution matrix, For the measurement matrix, This is the sensor fault distribution matrix; , , , All are coefficient matrices. For a power grid agent, the definition is... , The coefficient matrix is ​​represented as follows:

[0036] ;

[0037] For air network intelligent agents, the definition , ,in, , All are 0. , Represented as:

[0038] ;

[0039] For a heating network intelligent agent, the definition is... , ,in, =0, , , Represented as:

[0040] .

[0041] Optionally, step 2 specifically includes:

[0042] Define augmented state vector ,in, To increase the dimension of the state vector, , The number of dimensions of the state vector. Let be the dimension of the sensor fault vector;

[0043] Construct a block matrix, including , , , , , , , , , , is represented as:

[0044] ;

[0045] ;

[0046] ;

[0047] in, for An identity matrix of dimension 1 It is a p-dimensional identity matrix;

[0048] Transforming the unified dynamics model using a block matrix yields the singular augmented equation, expressed as:

[0049] ;

[0050] in, for The time derivative;

[0051] By processing the singular augmented equation, we obtain Substituting this into the first line of the singular augmented equation, we obtain the equation that eliminates explicit dependencies, expressed as:

[0052] ;

[0053] Get , The full-rank condition is expressed as: ,in, , A matrix that satisfies the full rank condition. for An identity matrix of 3D;

[0054] Multiply both sides of the equation that eliminates explicit dependencies by the left side. Substituting the full-rank condition and rearranging the terms, we obtain the standard dynamic model:

[0055] ;

[0056] in, for The time derivative, , , , , , , The transformed matrix is ​​represented as follows:

[0057] ;

[0058] .

[0059] Optionally, step 3 specifically includes:

[0060] Step 3.1: Introduce intermediate variables , is represented as:

[0061] ;

[0062] in, The constant learning gain matrix to be designed; The dimension of the actuator fault vector;

[0063] Based on intermediate variables Using the standard dynamic model and adjacency matrix, a distributed intermediate observer is constructed, represented as:

[0064] ;

[0065] in, These are the reconstruction estimates for the augmented state, actuator fault, sensor fault, and measurement output, respectively. and These are the auxiliary state estimation variables for the augmented state estimate and the auxiliary state estimation variables for the actuator fault estimate, respectively. for The time derivative, for The time derivative; The relative output error of the neighbor obtained through the communication topology; This represents the local absolute output error. For the measurement output of node j, The reconstructed estimate of the output for node j; Let be the distributed observer gain matrix to be solved;

[0066] Step 3.2: Construct the physical equilibrium equations, expressed as:

[0067] ;

[0068] in, As the steady-state reference point, This is a feedforward compensation term;

[0069] definition The Moore-Penrose generalized inverse matrix is ​​represented as:

[0070] ;

[0071] in, represents the Moore-Penrose pseudoinverse of the matrix, and T represents the transpose of the matrix;

[0072] According to the physical equilibrium equation and The Moore-Penrose generalized inverse matrix is ​​used to solve for the feedforward compensation term. , is represented as:

[0073] ;

[0074] Define the state extraction matrix , The dimension is The zero matrix, The dimension is The identity matrix, based on the state extraction matrix right Perform the restoration to obtain the restored state estimate. , is represented as: Therefore, a composite fault-tolerant control law is designed. , is represented as:

[0075] ;

[0076] in, This is the gain matrix for the state feedback control to be designed.

[0077] Optionally, step 4 specifically includes:

[0078] Step 4.1: Define the augmented state estimation error , is represented as:

[0079] ;

[0080] Extract the matrix based on the state and augmented state estimation error Calculate the state estimation error , is represented as:

[0081] ;

[0082] Calculate the estimation error of intermediate variables Specifically, this is achieved through the following formula:

[0083] ;

[0084] Define the constant value of the continuous nonlinear term at the steady-state reference point as: Furthermore, nonlinear state deviation is defined. , is represented as:

[0085] ;

[0086] Define the nonlinear estimation error of the observer , is represented as:

[0087] ;

[0088] Constructing actuator fault reconstructing error and sensor reconstruction error , is represented as:

[0089] ;

[0090] ;

[0091] in, For the intermediate matrix, , The dimension is The zero matrix, The dimension is The identity matrix;

[0092] Based on the standard dynamics model, distributed intermediate observers, and the Laplace matrix ,right and Rewrite to get algebraic sums The algebraic sum is expressed as:

[0093] ;

[0094] ;

[0095] in, Let j be the block matrix corresponding to node j. The augmented state estimation error corresponding to node j;

[0096] right Taking the derivative and combining the standard dynamic model and the distributed intermediate observer, the augmented state error dynamic equation is generated, expressed as:

[0097] ;

[0098] in, for The time derivative;

[0099] right Differentiate and set the prefix term Combined with intermediate variables With distributed intermediate observers, the error dynamics equation for intermediate variables is generated, expressed as:

[0100] ;

[0101] in, for The time derivative, for The time derivative;

[0102] Define a unified error vector , is represented as:

[0103] ;

[0104] Define the external synthesis perturbation vector , is represented as:

[0105] ;

[0106] Introducing local feedback gain Topology gain and local measurement mapping Define the neighbor measurement mapping matrix ;

[0107] Extract the underlying error matrix without injected feedback, including , , , is represented as:

[0108] ;

[0109] Where I is the identity matrix;

[0110] Combining the augmented state error dynamics equation and the intermediate variable error dynamics equation, the estimation error dynamics equation is constructed as follows:

[0111] ;

[0112] in, for The time derivative;

[0113] Step 4.2: Define the adjustment error , is represented as:

[0114] ;

[0115] Composite fault-tolerant control law Substituting into the unified dynamics model and apply algebraic relations and ,get:

[0116] ;

[0117] Subtracting the physical equilibrium equation from the above formula yields the closed-loop regulation error dynamic equation, expressed as:

[0118] ;

[0119] in, for The time derivative;

[0120] Define the closed-loop cross-coupling gain matrix ;

[0121] Define the global closed-loop joint augmented state vector as The augmented closed-loop system dynamic equations are constructed as follows:

[0122] ;

[0123] in, for The time derivative, Let be the unified error vector corresponding to node j.

[0124] Optionally, step 5 specifically includes:

[0125] Step 5.1: Define a positive definite symmetric matrix and Lyapunov functions are constructed using the estimation error dynamics equation and the augmented closed-loop system dynamics equation. , is represented as:

[0126] ;

[0127] Based on the augmented closed-loop system dynamics equations, Differentiate and rearrange to obtain the Lyapunov function. Expanded to:

[0128] ;

[0129] in, for The time derivative;

[0130] Introducing auxiliary scalars and mapping matrix Construct the following four nonnegativity constraints , , , , is represented as:

[0131] ;

[0132] ;

[0133] ;

[0134] ;

[0135] in, It is a real constant;

[0136] Define the evaluation index vector as ,Will Substituting into the definition of the evaluation index vector, we get: ;in, ;

[0137] Define a performance function that includes evaluation metrics. , is represented as:

[0138] ;

[0139] in, For suppression performance indicators;

[0140] Adding the four non-negativity constraint terms to the performance function yields the sufficient condition expressed as follows:

[0141] ;

[0142] against By performing SVD, we obtain:

[0143] ;

[0144] in, , For the reason The known orthogonal matrix obtained from the singular value decomposition. for A diagonal matrix composed of the positive singular values;

[0145] right Applying structured constraints is represented as follows:

[0146] ;

[0147] in, and Let be the symmetric positive definite matrix to be solved;

[0148] bilinear nonconvex coupling terms Transform into:

[0149] ;

[0150] Define the auxiliary constant matrix ,in, Indicates a dimension of m i The identity matrix is ​​obtained, and linearized free variables are introduced. For bilinear nonconvex coupling terms After simplification, we get:

[0151] ;

[0152] Define the integrated distribution matrix for LMI block description. , , is represented as:

[0153] ;

[0154] Will , Substitute the cross-coupling term ,get:

[0155] ;

[0156] Define the variable substitution and integrated perturbation distribution matrix on the observer side. , , , is represented as:

[0157] ;

[0158] Define extended state vector After combining the performance function with the four nonnegativity constraints, the global system stability condition is obtained, expressed as:

[0159] ;

[0160] in, It is a quadratic matrix;

[0161] Step 5.2: Process using Schur's supplementary lemma The term will include the quadratic form matrix in the global system stability condition. Transforming into LMI constraints yields stability conditions in LMI form. ,express:

[0162] ;

[0163] in, As a diagonal main block, it is represented as:

[0164] ;

[0165] in, , , , , , , The definition is as follows:

[0166] ;

[0167] ;

[0168] ;

[0169] ;

[0170] ;

[0171] ;

[0172] ;

[0173] For non-diagonal pieces Defined as:

[0174] .

[0175] Optionally, step 6 specifically includes:

[0176] Solving for the stability condition of the LMI form yields... The solution;

[0177] Calculation via matrix inverse operation The value of is achieved through the following formula:

[0178] ;

[0179] Computing distributed intermediate observers , The value of is achieved through the following formula:

[0180] ;

[0181] ;

[0182] The distributed intermediate observer is calculated using a block extraction technique. , , and The value is represented as:

[0183] .

[0184] Optionally, step 7 specifically includes:

[0185] according to , , , , and Configure a distributed intermediate observer, and collect data from node i in real time based on the configured distributed intermediate observer. , as well as Real-time solution through numerical integration and ;

[0186] right and The real-time and accurate reconstruction is achieved through the following formula:

[0187] ;

[0188] ;

[0189] according to value and The specific composite fault-tolerant control law is calculated and executed.

[0190] The beneficial effects of adopting the above technical solution are as follows:

[0191] 1. Achieving zero steady-state error active fault-tolerant tracking under concurrent faults in integrated energy systems. This invention constructs a composite fault-tolerant control law that integrates steady-state feedforward, state feedback, and active fault cancellation. This control law directly compensates for deviations caused by actuator faults at the physical terminal, while actively eliminating steady-state errors caused by inherent nonlinearities in the system. Compared to the limitations of traditional fault-tolerant control, which can only maintain system stability, this control law can drive the heterogeneous electrical, gas, and thermal states to accurately track the safety benchmark point even under complex operating conditions.

[0192] 2. Overcoming the Challenge of Cooperative Fault-Tolerant Control under Heterogeneous Multi-Energy Flow with Strong Nonlinearity. Addressing the physical characteristics of spatially heterogeneous electrical, gaseous, and thermal subsystems exhibiting strong nonlinear dynamics, this invention establishes a unified state-space model for heterogeneous multi-agent systems and utilizes the one-sided Lipschitz condition to rigorously enclose the nonlinear dynamics. This scheme successfully extends traditional cooperative fault-tolerant control theory from isomorphic linear ideal models to spatially heterogeneous and highly nonlinear integrated energy systems, significantly improving the engineering applicability of the control architecture.

[0193] 3. Overcoming the strict observer matching condition constraint, this invention constructs an easily solvable closed-loop fault-tolerant control framework. By constructing a singular augmented system and introducing intermediate variables, this invention completely circumvents the strict observer matching condition relied upon by traditional unknown input observer design at the analytical algebra level, providing a high-precision fault reconstruction signal for the fault-tolerant controller to achieve compensatory control. Simultaneously, it utilizes SVD technology to solve the bilinear non-convex coupling problem in the control gain solution and transforms it into an LMI condition, rigorously ensuring the robustness of the integrated energy system. Fault-tolerant control performance. Attached Figure Description

[0194] Figure 1 This is a flowchart illustrating a distributed fault-tolerant control method for an integrated energy system based on an intermediate observer, as described in an embodiment of the present invention.

[0195] Figure 2 This is a control closed-loop block diagram of the integrated energy system in an embodiment of the present invention. Detailed Implementation

[0196] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0197] To address the problems existing in the prior art, this invention provides a distributed fault-tolerant control method for integrated energy systems based on intermediate observers. This method aims to solve the problem of accurately estimating concurrent faults of sensors and actuators in integrated energy systems, and to achieve active fault tolerance and steady-state consistency tracking of heterogeneous systems under the condition of external disturbances.

[0198] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0199] A distributed fault-tolerant control method for an integrated energy system based on an intermediate observer is proposed. First, a dynamic model and communication topology for the integrated energy system considering concurrent sensor and actuator faults and external disturbances are established. Second, a singular augmented system is used to transform sensor faults into augmented state variables, and intermediate variables are introduced to construct a distributed intermediate observer, achieving joint estimation of faults and states. Next, a composite control law incorporating steady-state feedforward and active fault tolerance is designed, and the observer error and the dynamic equations of the closed-loop system are derived. Subsequently, by combining singular value decomposition (SVD) and one-sided Lipschitz conditions, the originally non-convex nonlinear coupling terms are transformed into linear constraints. Finally, the controller gain and observer gain are obtained by solving the linear matrix inequality (LMI) conditions, enabling online reconstruction of concurrent faults and fault-tolerant control of the integrated energy system.

[0200] This invention provides a distributed fault-tolerant control method for integrated energy systems based on intermediate observers, combined with... Figure 1 and Figure 2 This may include the following steps:

[0201] Step 1: Construct a collaborative communication network for the integrated energy system, thereby obtaining the adjacency matrix and Laplace matrix, and constructing a unified dynamic model of the integrated energy system with unilateral Lipschitz conditions, including concurrent sensor and actuator failures and external disturbances;

[0202] Step 1.1: Construct a collaborative communication network for the integrated energy system , ,in, Represents a set of nodes. N represents the total number of nodes, where each node is a smart grid agent, a smart gas network agent, or a smart heating network agent within the integrated energy system. Denotes the set of edges. The edge set includes communication links between nodes. For any node i, its set of adjacent nodes is denoted as . , It is an adjacency matrix. , This represents the adjacency state value between node i and node j, when there is a communication connection between node i and node j. When there is no communication connection between node i and node j, Since the agent only needs to communicate collaboratively with other energy subnet nodes, and its own state can be directly obtained through local sensing and computation without establishing a communication link from the node to itself, a loop-free topology is adopted. .

[0203] The Laplace matrix is ​​defined based on the adjacency matrix. , Among them, the Laplace matrix elements in Represented as:

[0204] ;

[0205] in, Represented as the adjacency state value between node i and node k;

[0206] Step 1.2: Construct a unified dynamic model for the integrated energy system;

[0207] For the power grid intelligent agent, based on the physical characteristics of the governor, turbine, and generator rotor of the steam turbine generator set, the speed regulating valve position increment is... Mechanical power increment Frequency deviation Phase angle deviation of generator rotor The dynamic evolution process between them is described by the physical dynamics model of the power grid agent.

[0208] Step 1.2.1: Construct the physical dynamics model of the power grid intelligent agent, represented as:

[0209] ;

[0210] in, For the speed regulating valve position increment, for The time derivative, The time constant of the speed controller, This is the governor droop coefficient. For frequency deviation, For governor control command input. For mechanical power increment, for The time derivative, This is the gain coefficient. The time constant of the steam turbine. for The time derivative, This is the gain coefficient. The time constant of the generator. The change in electrical power This refers to the generator rotor phase angle deviation. for The time derivative;

[0211] For a gas network intelligent agent, considering the frictional resistance, gravity effect, and pressure wave propagation characteristics of natural gas during pipeline transmission, its node outlet pressure... With pipeline inlet flow The dynamic change process is described by the physical dynamics model of the gas network agent.

[0212] Step 1.2.2: Construct the physical dynamics model of the air network intelligent agent, represented as:

[0213] ;

[0214] in, Due to export pressure, for The time derivative, The gas constant is... The cross-sectional area of ​​the pipe. For the length of the pipe, For inlet quality flow, For export quality flow rate, for The time derivative, Where g is the inlet pressure and g is the gravitational constant. The angle of inclination. For the speed of sound, The coefficient of friction, The diameter of the pipe;

[0215] For a heating network intelligent system, considering the thermal inertia and heat loss characteristics of the heating pipes, the node heating temperature... The dynamic change process is described by the physical dynamics model of the heating network intelligent agent.

[0216] Step 1.2.3: Construct the physical dynamics model of the heating network intelligent agent, represented as:

[0217] ;

[0218] in, For heating temperature, for The time derivative, This is the inlet water supply temperature control quantity. For inlet quality flow, For the volume of the pipe, For specific heat capacity, For user heat load power, For fluid density;

[0219] The integrated energy system achieves multi-energy flow coupling through combined heat and power (CHP) units. The thermal power demand of the CHP units inversely constrains the reference inlet flow rate of the gas grid intelligent agent, expressed as... ,in, This refers to the heat and power demand of a combined heat and power (CHP) unit; obj represents a reference value. Indicates and Relevant functions; actual outlet flow rate of the gas network The electricity generated is produced by combustion in a combined heat and power unit. The frequency dynamics affecting the power grid are represented as ,in, To and The relevant function. Net power change on the grid side. Defined as:

[0220] ;

[0221] in, For changes in user heat load power, The change in electrical power generated by the combined heat and power unit;

[0222] Step 1.2.4: Define the state vector Control input Measurement output and continuous nonlinear terms Combined with actuator failure Sensor malfunction and external disturbances ,in, , , , , , , These are the dimensions of the state vector, the control input, the measurement output, the continuous nonlinear term, the actuator fault, and the sensor fault, respectively.

[0223] The physical dynamics models of the power grid intelligent agent, the gas network intelligent agent, and the heating network intelligent agent are constructed into a unified dynamic model, which is represented as:

[0224] ;

[0225] in, for The time derivative, The actuator fault distribution matrix, The external disturbance distribution matrix, For the measurement matrix, This is the sensor fault distribution matrix; , , , All are coefficient matrices. For a power grid agent, the definition is... , The coefficient matrix is ​​represented as follows:

[0226] ;

[0227] For air network intelligent agents, the definition , ,in, , All are 0. , Represented as:

[0228] ;

[0229] For a heating network intelligent agent, the definition is... , ,in, =0, , , Represented as:

[0230] ;

[0231] Each agent configures an actuator fault distribution matrix according to the fault occurrence channel. Configure the measurement matrix according to the measured physical quantity. and sensor fault distribution matrix Configure the external disturbance distribution matrix based on the entry point of the external environmental disturbance. .

[0232] Nonlinear terms It satisfies the one-sided Lipschitz condition and the quadratic inner bounded condition, i.e., it has a real constant. This allows for any state within the interval (the reachable operating state interval of the system in practical engineering applications). Strictly meet:

[0233] ;

[0234] ;

[0235] The aforementioned system inherently possesses corresponding objective constraints in its physical operation and mathematically satisfies the strict prerequisites for fault-tolerant control solutions. Firstly, limited by the mechanical inertia of the physical actuators, the rate of change of actuator faults naturally has physical limits, satisfying… ,in The upper bound is unknown; secondly, based on the law of conservation of energy, the steady-state operating benchmark point of the integrated energy system is set. Satisfy the physical manifold constraints that allow for the equilibrium point, i.e. ,in Represents the coefficient matrix The image space; simultaneously, the physical configuration of the system's measurement and control must satisfy the structural rank constraint, that is, for all complex numbers located in the closed right half-plane of the complex plane... The observation matching condition is met. And must meet control matching conditions. .

[0236] Step 2: Transform the unified dynamics model to obtain the standard dynamics model;

[0237] To simultaneously estimate state and sensor faults, an augmented state vector is defined. ,in, To increase the dimension of the state vector, , The number of dimensions of the state vector. Let be the dimension of the sensor fault vector;

[0238] Construct a block matrix, including , , , , , , , , , , is represented as:

[0239] ;

[0240] ;

[0241] ;

[0242] in, for An identity matrix of dimension 1 It is a p-dimensional identity matrix;

[0243] Transforming the unified dynamics model using a block matrix yields the singular augmented equation, expressed as:

[0244] ;

[0245] in, for The time derivative;

[0246] By processing the singular augmented equation, we obtain Substituting this into the first line of the singular augmented equation, we obtain the equation that eliminates explicit dependencies, expressed as:

[0247] ;

[0248] Due to stacking matrix The following structural rank conditions must be met:

[0249] ;

[0250] This indicates that the matrix has full column rank. Therefore, there must exist a matrix pair with full row rank. This makes the following algebraic constraints hold:

[0251] ;

[0252] Based on this, obtain , The full-rank condition is expressed as: ,in, , A matrix that satisfies the full rank condition. for An identity matrix of 3D;

[0253] Multiply both sides of the equation that eliminates explicit dependencies by the left side. Substituting the full-rank condition and rearranging the terms, we obtain the standard dynamic model:

[0254] ;

[0255] in, for The time derivative, , , , , , , The transformed matrix is ​​represented as follows:

[0256] ;

[0257] ;

[0258] Furthermore, based on the properties of generalized inverse matrices, matrix pairs that satisfy the constraints The general solution is:

[0259] ;

[0260] in, For any dimensionally compatible matrix, the symbol is... Represents the Moore-Penrose pseudoinverse of a matrix;

[0261] Step 3: Based on the standard dynamics model and adjacency matrix, construct a distributed intermediate observer and a composite fault-tolerant control law;

[0262] Step 3.1: Introduce intermediate variables , is represented as:

[0263] ;

[0264] in, The constant learning gain matrix to be designed; The dimension of the actuator fault vector;

[0265] Based on intermediate variables Using the standard dynamic model and adjacency matrix, a distributed intermediate observer is constructed, represented as:

[0266] ;

[0267] in, These are the reconstruction estimates for the augmented state, actuator fault, sensor fault, and measurement output, respectively. and These are the auxiliary state estimation variables for the augmented state estimate and the auxiliary state estimation variables for the actuator fault estimate, respectively. for The time derivative, for The time derivative; The relative output error of the neighbor obtained through the communication topology; This represents the local absolute output error. For the measurement output of node j, The reconstructed estimate of the output for node j; Let be the distributed observer gain matrix to be solved;

[0268] After obtaining accurate reconstructed signals of system state and actuator faults using a distributed intermediate observer, an active fault-tolerant control law for the system is designed. This is to achieve a steady-state reference point for the integrated energy system with respect to a given constant. Zero steady-state error tracking, considering fault-free operation and reaching steady state (i.e.) The system physical equilibrium equations under ().

[0269] Step 3.2: Construct the physical equilibrium equations, expressed as:

[0270] ;

[0271] in, As the steady-state reference point, This is a feedforward compensation term;

[0272] definition The Moore-Penrose generalized inverse matrix is ​​represented as:

[0273] ;

[0274] in, represents the Moore-Penrose pseudoinverse of the matrix, and T represents the transpose of the matrix;

[0275] According to the physical equilibrium equation and The Moore-Penrose generalized inverse matrix is ​​obtained by explicitly solving for the feedforward compensation term based on the equilibrium point admissibility condition. , is represented as:

[0276] ;

[0277] Define the state extraction matrix , The dimension is The zero matrix, The dimension is The identity matrix, based on the state extraction matrix right Perform the restoration to obtain the restored state estimate. , is represented as: Furthermore, by integrating feedforward compensation terms, state feedback terms, and active fault cancellation terms, a composite fault-tolerant control law is designed. , is represented as:

[0278] ;

[0279] in, Here is the state feedback control gain matrix to be designed; the working mechanism of this control law is: utilizing... The feedforward compensation term generates an equal-sized and opposite physical compensation signal within the original system's control input channel to actively counteract the effects of actuator malfunctions; To offset the steady-state shift caused by the inherent nonlinear dynamics and physical dissipation of the integrated energy system; through state feedback terms. It dynamically suppresses external environmental disturbances and ultimately maintains the global stability and consistent regulation of the heterogeneous multi-agent closed-loop system.

[0280] Step 4: Based on the Laplace matrix Using a unified dynamic model, a standard dynamic model, a distributed intermediate observer, and a composite fault-tolerant control law, we construct the estimation error dynamic equation and the augmented closed-loop system dynamic equation.

[0281] Step 4.1: Define the augmented state estimation error , is represented as:

[0282] ;

[0283] Extract the matrix based on the state and augmented state estimation error Calculate the state estimation error , is represented as:

[0284] ;

[0285] Calculate the estimation error of intermediate variables Specifically, this is achieved through the following formula:

[0286] ;

[0287] Define the constant value of the continuous nonlinear term at the steady-state reference point as: Furthermore, nonlinear state deviation is defined. , is represented as:

[0288] ;

[0289] Define the nonlinear estimation error of the observer , is represented as:

[0290] ;

[0291] By utilizing the definition and reconstruction relationship of intermediate variables, an actuator fault reconstruction error is constructed. and sensor reconstruction error , is represented as:

[0292] ;

[0293] ;

[0294] in, For the intermediate matrix, , The dimension is The zero matrix, The dimension is The identity matrix;

[0295] Based on the standard dynamics model, distributed intermediate observers, and the Laplace matrix ,right and Rewrite to get algebraic sums The algebraic sum is expressed as:

[0296] ;

[0297] ;

[0298] in, Let j be the block matrix corresponding to node j. The augmented state estimation error corresponding to node j;

[0299] right Taking the derivative and combining the standard dynamic model and the distributed intermediate observer, the augmented state error dynamic equation is generated, expressed as:

[0300] ;

[0301] in, for The time derivative;

[0302] right Differentiate and set the prefix term Combined with intermediate variables With distributed intermediate observers, the error dynamics equation for intermediate variables is generated, expressed as:

[0303] ;

[0304] in, for The time derivative, for The time derivative;

[0305] Define a unified error vector , is represented as:

[0306] ;

[0307] Define the external synthesis perturbation vector , is represented as:

[0308] ;

[0309] Introducing local feedback gain Topology gain and local measurement mapping Define the neighbor measurement mapping matrix ;

[0310] Extract the underlying error matrix without injected feedback, including , , , is represented as:

[0311] ;

[0312] Where I is the identity matrix;

[0313] Combining the augmented state error dynamics equation and the intermediate variable error dynamics equation, the estimation error dynamics equation is constructed as follows:

[0314] ;

[0315] in, for The time derivative;

[0316] Step 4.2: Define the adjustment error , is represented as:

[0317] ;

[0318] Composite fault-tolerant control law Substituting into the unified dynamics model and apply algebraic relations and ,get:

[0319] ;

[0320] Subtracting the physical equilibrium equation from the above formula yields the closed-loop regulation error dynamic equation, expressed as:

[0321] ;

[0322] in, for Time derivative; feedforward compensation term The steady-state offset of the system at the reference point was explicitly eliminated.

[0323] Define the closed-loop cross-coupling gain matrix ;

[0324] Define the global closed-loop joint augmented state vector as The augmented closed-loop system dynamic equations are constructed as follows:

[0325] ;

[0326] in, for The time derivative, This is the unified error vector corresponding to node j;

[0327] Therefore, the design objective of this invention is to determine the observer gain matrix. and controller gain matrix The system must satisfy the following conditions:

[0328] ;

[0329] in, For given Suppression performance indicators.

[0330] Step 5: Based on the estimation error dynamic equation and the augmented closed-loop system dynamic equation, construct the stability conditions in the form of LMI;

[0331] Step 5.1: Define a positive definite symmetric matrix and Lyapunov functions are constructed using the estimation error dynamics equation and the augmented closed-loop system dynamics equation. , is represented as:

[0332] ;

[0333] Based on the augmented closed-loop system dynamics equations, Differentiate and rearrange to obtain the Lyapunov function. Expanded to:

[0334] ;

[0335] in, for The time derivative;

[0336] To process The nonlinear dynamics present in the expansion are addressed by introducing an auxiliary scalar. and mapping matrix Based on the one-sided Lipschitz condition satisfied by the system model, the following four non-negativity constraints are constructed. , , , , is represented as:

[0337] ;

[0338] ;

[0339] ;

[0340] ;

[0341] in, It is a real constant;

[0342] To ensure the joint convergence of system state estimation and actuator fault estimation, the evaluation index vector is defined as follows: ,Will Substituting into the definition of the evaluation index vector, we get: ;in, ;

[0343] Furthermore, in order to integrate external disturbances In the presence of [condition], simultaneously ensuring the asymptotic stability of the closed-loop system and [other conditions]. Disturbance suppression performance is defined as a performance function that includes evaluation metrics. , is represented as:

[0344] ;

[0345] in, For given Suppression performance indicators;

[0346] Adding the four non-negativity constraint terms to the performance function yields the sufficient condition expressed as follows:

[0347] ;

[0348] against By performing SVD, we obtain:

[0349] ;

[0350] in, , For the reason The known orthogonal matrix obtained from the singular value decomposition. for A diagonal matrix composed of the positive singular values;

[0351] right Applying structured constraints is represented as follows:

[0352] ;

[0353] in, and Let be the symmetric positive definite matrix to be solved;

[0354] bilinear nonconvex coupling terms Transform into:

[0355] ;

[0356] Define the auxiliary constant matrix ,in, Indicates a dimension of m i The identity matrix is ​​obtained, and linearized free variables are introduced. For bilinear nonconvex coupling terms After simplification, we get:

[0357] ;

[0358] Define the integrated distribution matrix for LMI block description. , , is represented as:

[0359] ;

[0360] Will , Substitute the cross-coupling term ,get:

[0361] ;

[0362] Define the variable substitution and integrated perturbation distribution matrix on the observer side. , , , is represented as:

[0363] ;

[0364] Define extended state vector After combining the performance function with the four nonnegativity constraints, the global system stability condition is obtained, expressed as:

[0365] ;

[0366] in, It is a quadratic matrix;

[0367] Step 5.2: Process using Schur's supplementary lemma The term will include the quadratic form matrix in the global system stability condition. Transforming into LMI constraints yields stability conditions in LMI form. ,express:

[0368] ;

[0369] in, As a diagonal main block, it is represented as:

[0370] ;

[0371] in, , , , , , , The definition is as follows:

[0372] ;

[0373] ;

[0374] ;

[0375] ;

[0376] ;

[0377] ;

[0378] ;

[0379] For non-diagonal pieces Defined as:

[0380] ;

[0381] This rigorously proves that if the above global LMI conditions are met... If true, it means that the global performance function satisfies... This ensures Under zero initial conditions, for From both ends arrive Integrating, we get:

[0382] ;

[0383] This integral inequality shows that, under zero initial conditions, the closed-loop system is robustly stable and satisfies... Performance indicators .

[0384] Step 6: Solve the stability conditions in the form of LMI to obtain the parameter values ​​in the distributed intermediate observer and the parameter values ​​in the composite fault-tolerant control law;

[0385] The stability conditions of the LMI form are solved using MATLAB's LMI toolbox. Within the feasible solution space satisfying the criterion, the following results are obtained. The solution;

[0386] Calculation via matrix inverse operation The value of is achieved through the following formula:

[0387] ;

[0388] Computing distributed intermediate observers , The value of is achieved through the following formula:

[0389] ;

[0390] ;

[0391] The distributed intermediate observer is calculated using a block extraction technique. , , and The value is represented as:

[0392] ;

[0393] Step 7: Run the distributed intermediate observer and the composite fault-tolerant control law based on the parameter values ​​in the distributed intermediate observer and the composite fault-tolerant control law.

[0394] The system operates an online distributed intermediate observer and an active fault-tolerant controller. Based on algebraic mapping relationships, it achieves real-time and accurate reconstruction of concurrent fault signals from actuators and sensors in the integrated energy system, and drives the heterogeneous system to track to the set stable reference target without steady-state error.

[0395] according to , , , , and Configure a distributed intermediate observer, and collect data from node i in real time based on the configured distributed intermediate observer. , as well as Real-time solution through numerical integration and ;

[0396] right and The real-time and accurate reconstruction is achieved through the following formula:

[0397] ;

[0398] ;

[0399] according to value and The specific composite fault-tolerant control law is calculated and executed.

[0400] This control law utilizes compensation terms. Actively offset the fault offset on the actuator side, combined with steady-state feedforward terms. By eliminating the effects of nonlinear physical dissipation, the physical states of the integrated energy system, such as frequency deviation, node pressure, and heating temperature, can ultimately track the set stable reference target without steady-state error even under concurrent fault conditions. .

[0401] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A distributed fault-tolerant control method for an integrated energy system based on an intermediate observer, characterized in that, include: Step 1: Construct a collaborative communication network for the integrated energy system, thereby obtaining the adjacency matrix and Laplace matrix, and constructing a unified dynamic model for the integrated energy system; Step 2: Transform the unified dynamics model to obtain the standard dynamics model; Step 3: Based on the standard dynamics model and adjacency matrix, construct a distributed intermediate observer and a composite fault-tolerant control law; Step 4: Based on the Laplace matrix, unified dynamics model, standard dynamics model, distributed intermediate observer, and composite fault-tolerant control law, construct the estimation error dynamics equation and the augmented closed-loop system dynamics equation; Step 5: Based on the estimation error dynamic equation and the augmented closed-loop system dynamic equation, construct the stability conditions in the form of LMI; Step 6: Solve the stability conditions in the form of LMI to obtain the parameter values ​​in the distributed intermediate observer and the parameter values ​​in the composite fault-tolerant control law; Step 7: Run the distributed intermediate observer and the composite fault-tolerant control law based on the parameter values ​​in the distributed intermediate observer and the composite fault-tolerant control law.

2. The distributed fault-tolerant control method for an integrated energy system based on an intermediate observer according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Construct a collaborative communication network for the integrated energy system , ,in, Represents a set of nodes. N represents the total number of nodes, where each node is a smart grid agent, a smart gas network agent, or a smart heating network agent within the integrated energy system. Denotes the set of edges. The edge set includes communication links between nodes. For any node i, its set of adjacent nodes is denoted as . , It is an adjacency matrix. , This represents the adjacency state value between node i and node j, when there is a communication connection between node i and node j. When there is no communication connection between node i and node j, ; The Laplace matrix is ​​defined based on the adjacency matrix. , Among them, the Laplace matrix elements in Represented as: ； in, Represented as the adjacency state value between node i and node k; Step 1.2: Construct a unified dynamic model for the integrated energy system.

3. The distributed fault-tolerant control method for an integrated energy system based on an intermediate observer according to claim 2, characterized in that, Step 1.2 specifically includes: Step 1.2.1: Construct the physical dynamics model of the power grid intelligent agent, represented as: ； in, For the speed regulating valve position increment, for The time derivative, The time constant of the speed controller, This is the governor droop coefficient. For frequency deviation, For governor control command input. For mechanical power increment, for The time derivative, This is the gain coefficient. The time constant of the steam turbine. for The time derivative, This is the gain coefficient. The time constant of the generator. The change in electrical power This refers to the generator rotor phase angle deviation. for The time derivative; Step 1.2.2: Construct the physical dynamics model of the air network intelligent agent, represented as: ； in, Due to export pressure, for The time derivative, The gas constant is... The cross-sectional area of ​​the pipe. For the length of the pipe, For inlet quality flow, For export quality flow rate, for The time derivative, Where g is the inlet pressure and g is the gravitational constant. The angle of inclination. For the speed of sound, The coefficient of friction, The diameter of the pipe; Step 1.2.3: Construct the physical dynamics model of the heating network intelligent agent, represented as: ； in, For heating temperature, for The time derivative, This is the inlet water supply temperature control quantity. For inlet quality flow, For the volume of the pipe, For specific heat capacity, For user heat load power, For fluid density; Step 1.2.4: Define the state vector Control input Measurement output and continuous nonlinear terms Combined with actuator failure Sensor malfunction and external disturbances ,in, , , , , , , These are the dimensions of the state vector, the control input, the measurement output, the continuous nonlinear term, the actuator fault, and the sensor fault, respectively. The physical dynamics models of the power grid intelligent agent, the gas network intelligent agent, and the heating network intelligent agent are constructed into a unified dynamic model, which is represented as: ； in, for The time derivative, The actuator fault distribution matrix, The external disturbance distribution matrix, For the measurement matrix, This is the sensor fault distribution matrix; , , , All are coefficient matrices. For a power grid agent, the definition is... , The coefficient matrix is ​​represented as follows: ； For air network intelligent agents, the definition , ,in, , All are 0. , Represented as: ； For a heating network intelligent agent, the definition is... , ,in, =0, , , Represented as: 。 4. The distributed fault-tolerant control method for an integrated energy system based on an intermediate observer according to claim 3, characterized in that, Step 2 specifically includes: Define augmented state vector ,in, To increase the dimension of the state vector, , The number of dimensions of the state vector. Let be the dimension of the sensor fault vector; Construct a block matrix, including , , , , , , , , , , is represented as: ； ； ； in, for An identity matrix of dimension 1 It is a p-dimensional identity matrix; Transforming the unified dynamics model using a block matrix yields the singular augmented equation, expressed as: ； in, for The time derivative; By processing the singular augmented equation, we obtain Substituting this into the first line of the singular augmented equation, we obtain the equation that eliminates explicit dependencies, expressed as: ； Get , The full-rank condition is expressed as: ,in, , A matrix that satisfies the full rank condition. for An identity matrix of 3D; Multiply both sides of the equation that eliminates explicit dependencies by the left side. Substituting the full-rank condition and rearranging the terms, we obtain the standard dynamic model: ； in, for The time derivative, , , , , , , The transformed matrix is ​​represented as follows: ； 。 5. The distributed fault-tolerant control method for an integrated energy system based on an intermediate observer according to claim 4, characterized in that, Step 3 specifically includes: Step 3.1: Introduce intermediate variables , is represented as: ； in, The constant learning gain matrix to be designed; The dimension of the actuator fault vector; Based on intermediate variables Using the standard dynamic model and adjacency matrix, a distributed intermediate observer is constructed, represented as: ； in, These are the reconstruction estimates for the augmented state, actuator fault, sensor fault, and measurement output, respectively. and These are the auxiliary state estimation variables for the augmented state estimate and the auxiliary state estimation variables for the actuator fault estimate, respectively. for The time derivative, for The time derivative; The relative output error of the neighbor obtained through the communication topology; This represents the local absolute output error. For the measurement output of node j, The reconstructed estimate of the output for node j; Let be the distributed observer gain matrix to be solved; Step 3.2: Construct the physical equilibrium equations, expressed as: ； in, As the steady-state reference point, This is a feedforward compensation term; definition The Moore-Penrose generalized inverse matrix is ​​represented as: ； in, represents the Moore-Penrose pseudoinverse of the matrix, and T represents the transpose of the matrix; According to the physical equilibrium equation and The Moore-Penrose generalized inverse matrix is ​​used to solve for the feedforward compensation term. , is represented as: ； Define the state extraction matrix , The dimension is The zero matrix, The dimension is The identity matrix, based on the state extraction matrix right Perform the restoration to obtain the restored state estimate. , is represented as: Therefore, a composite fault-tolerant control law is designed. , is represented as: ； in, This is the gain matrix for the state feedback control to be designed.

6. The distributed fault-tolerant control method for an integrated energy system based on an intermediate observer according to claim 4, characterized in that, Step 4 specifically includes: Step 4.1: Define the augmented state estimation error , is represented as: ； Extract the matrix based on the state and augmented state estimation error Calculate the state estimation error , is represented as: ； Calculate the estimation error of intermediate variables Specifically, this is achieved through the following formula: ； Define the constant value of the continuous nonlinear term at the steady-state reference point as: Furthermore, nonlinear state deviation is defined. , is represented as: ； Define the nonlinear estimation error of the observer , is represented as: ； Constructing actuator fault reconstructing error and sensor reconstruction error , is represented as: ； ； in, For the intermediate matrix, , The dimension is The zero matrix, The dimension is The identity matrix; Based on the standard dynamics model, distributed intermediate observers, and the Laplace matrix ,right and Rewrite to get algebraic sums The algebraic sum is expressed as: ； ； in, Let be the block matrix corresponding to node j. The augmented state estimation error corresponding to node j; right Taking the derivative and combining the standard dynamic model and the distributed intermediate observer, the augmented state error dynamic equation is generated, expressed as: ； in, for The time derivative; right Differentiate and set the prefix term Combined with intermediate variables With distributed intermediate observers, the error dynamics equation for intermediate variables is generated, expressed as: ； in, for The time derivative, for The time derivative; Define a unified error vector , is represented as: ； Define the external synthesis perturbation vector , is represented as: ； Introducing local feedback gain Topology gain and local measurement mapping Define the neighbor measurement mapping matrix ; Extract the underlying error matrix without injected feedback, including , , , is represented as: ； Where I is the identity matrix; Combining the augmented state error dynamics equation and the intermediate variable error dynamics equation, the estimation error dynamics equation is constructed as follows: ； in, for The time derivative; Step 4.2: Define the adjustment error , is represented as: ； Composite fault-tolerant control law Substituting into the unified dynamics model and apply algebraic relations and ,get: ； Subtracting the physical equilibrium equation from the above formula yields the closed-loop regulation error dynamic equation, expressed as: ； in, for The time derivative; Define the closed-loop cross-coupling gain matrix ; Define the global closed-loop joint augmented state vector as The augmented closed-loop system dynamic equations are constructed as follows: ； in, for The time derivative, Let be the unified error vector corresponding to node j.

7. The distributed fault-tolerant control method for an integrated energy system based on an intermediate observer according to claim 6, characterized in that, Step 5 specifically includes: Step 5.1: Define a positive definite symmetric matrix and Lyapunov functions are constructed using the estimation error dynamics equation and the augmented closed-loop system dynamics equation. , is represented as: ； Based on the augmented closed-loop system dynamics equations, Differentiate and rearrange to obtain the Lyapunov function. Expanded to: ； in, for The time derivative; Introducing auxiliary scalars and mapping matrix Construct the following four nonnegativity constraints , , , , is represented as: ； ； ； ； in, It is a real constant; Define the evaluation index vector as ,Will Substituting into the definition of the evaluation index vector, we get: ;in, ; Define a performance function that includes evaluation metrics. , is represented as: ； in, For suppression performance indicators; Adding the four non-negativity constraint terms to the performance function yields the sufficient condition expressed as follows: ； against By performing SVD, we obtain: ； in, , For the reason The known orthogonal matrix obtained from the singular value decomposition. for A diagonal matrix composed of the positive singular values; right Applying structured constraints is represented as follows: ； in, and Let be the symmetric positive definite matrix to be solved; bilinear nonconvex coupling terms Transform into: ； Define the auxiliary constant matrix ,in, Indicates a dimension of m i The identity matrix is ​​obtained, and linearized free variables are introduced. For bilinear nonconvex coupling terms After simplification, we get: ； Define the integrated distribution matrix for LMI block description. , , is represented as: ； Will , Substitute the cross-coupling term ,get: ； Define the variable substitution and integrated perturbation distribution matrix on the observer side. , , , is represented as: ； Define extended state vector After combining the performance function with the four nonnegativity constraints, the global system stability condition is obtained, expressed as: ； in, It is a quadratic matrix; Step 5.2: Process using Schur's supplementary lemma The term will include the quadratic form matrix in the global system stability condition. Transforming into LMI constraints yields stability conditions in LMI form. ,express: ； in, As a diagonal main block, it is represented as: ； in, , , , , , , The definition is as follows: ； ； ； ； ； ； ； For non-diagonal pieces Defined as: 。 8. The distributed fault-tolerant control method for an integrated energy system based on an intermediate observer according to claim 7, characterized in that, Step 6 specifically includes: Solving for the stability condition of the LMI form yields... The solution; Calculation via matrix inverse operation The value of is achieved through the following formula: ； Computing distributed intermediate observers , The value of is achieved through the following formula: ； ； The distributed intermediate observer is calculated using a block extraction technique. , , and The value is represented as: 。 9. A distributed fault-tolerant control method for an integrated energy system based on an intermediate observer according to claim 8, characterized in that, Step 7 specifically includes: according to , , , , and Configure a distributed intermediate observer, and collect data from node i in real time based on the configured distributed intermediate observer. , as well as Real-time solution through numerical integration and ; right and The real-time and accurate reconstruction is achieved through the following formula: ； ； according to value and The specific composite fault-tolerant control law is calculated and executed.

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