CN114460839A - Distributed model-free adaptive control technology for indoor heating ventilation and air conditioning of building - Google Patents

Distributed model-free adaptive control technology for indoor heating ventilation and air conditioning of building Download PDF

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CN114460839A
CN114460839A CN202210142821.3A CN202210142821A CN114460839A CN 114460839 A CN114460839 A CN 114460839A CN 202210142821 A CN202210142821 A CN 202210142821A CN 114460839 A CN114460839 A CN 114460839A
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林娜
池荣虎
徐鉴
张慧敏
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Qingdao University of Science and Technology
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Abstract

The invention discloses a distributed model-free self-adaptive control technology for a building indoor heating ventilation air conditioner, and belongs to the field of intelligent control. Aiming at the problem of building indoor multi-zone temperature control with complex topological information and external disturbance, the control scheme is as follows: establishing a dynamic model of the multi-region heating ventilation air conditioner, writing the dynamic model into a matrix form, and discretizing; expressing a single room physical model as a general non-affine nonlinear system, and converting a linear data model containing a pseudo gradient through a differential median theorem; designing a distributed model-free adaptive control law based on a linear data model and in combination with topological information; and (4) combining a linear data model design parameter estimation index function to estimate the unknown pseudo gradient in the control method. In the distributed model-free self-adaptive control technology of the indoor heating ventilation air conditioner of the building, disclosed by the invention, a data-driven method is used, so that the temperature regulation performance of the heating ventilation air conditioner is improved and the requirement of the indoor temperature regulation of the building is met by only using online and offline data and related topological information without depending on model information.

Description

Distributed model-free adaptive control technology for indoor heating ventilation and air conditioning of building
Technical Field
The invention relates to the technical field of intelligent control, in particular to a distributed model-free self-adaptive control technology for a building indoor heating ventilation air conditioner.
Background
With the development of human social science and technology, energy problems are more and more valued by scientists. In terms of energy use, the building energy consumption ratio is high, and the heating, ventilation and air conditioning system is more critical as an important temperature regulation system. Therefore, designing a related control algorithm to improve the control performance of the heating, ventilating and air conditioning so as to reduce energy consumption is a good idea.
For a heating, ventilating and air conditioning system, the following points are provided: a1: has strong nonlinearity; a2: with internal uncertainty and external interference; a3: there are complex topological relationships between different regions. Among them, a1 and a2 mean that the system is difficult to obtain or accurately model, which poses a challenge to the traditional control method requiring a model, and a more effective and applicable method needs to be found. A3 is a control information of a room itself, and it is obvious that the control performance is impaired to some extent when the temperature control of the room is considered. Therefore, when designing the algorithm, the topological relationship between different rooms needs to be considered.
Through analysis, it can be known that the heating, ventilating and air conditioning system has strong nonlinearity, and a specific dynamic model is difficult to obtain. Most studies are typically linear systems, or control schemes that require a priori structural information of the system will be difficult to implement. Data-driven control has become a current focus of research in recent years due to its unique nature that can still accomplish controller design and analysis without explicit model information.
Among these data-driven Control schemes, Model Free Adaptive Control (MFAC), which was proposed by hou-loyal in 1994, has been vigorously developed in recent years. In MFAC, a non-linear, non-affine system is transformed by a differential form into a new linearized form. All dynamic information of the system is integrated as input-output data and parameters. The controller designed on the basis of the linearization model not only has the characteristic of data driving, but also is simple and easy to realize. Meanwhile, the linearized model does not ignore any original system information and is completely equivalent to the original system, thereby greatly improving the universality and applicability of the MFAC.
Formation control and consistency control in coordinated control of multi-agent systems are two main research directions. The former is a coordination problem that keeps a certain geometry between each agent to achieve a specific control goal; the latter refers to the coordination problem where each agent asymptotically achieves a certain agreement value by using information from the local neighborhood. The consistency control of the multi-agent can meet the relevant requirements of the multi-area temperature control in the building. Therefore, it is reasonable to combine the related control ideas of the multiple agents to control the temperature of multiple areas.
In the document "data-driven multi-agent system consistency tracking based on model-free adaptive control", buxu shin et al successfully converts the algorithm into a distributed algorithm by replacing the error term in the control input in the original MFAC with a distributed measurement output. Therefore, the advantages of the MFAC are combined, and meanwhile, the control information of the adjacent agents is contained in the control law due to the addition of the distributed measurement output, so that the control law has excellent performance in the consistency tracking task of the multi-agent system. Further analysis of the distributed controller design described above, however, shows that the design is based on Compact Form Dynamic Linearization (CFDL) technology. In CFDL, only the first median differential theorem is used. This allows only one moment of data in the linearized data model to be processed simply for the remaining non-linear terms.
The above processing method results in that if the complex system is sensitive to some state responses of the system within a certain time window, the control law cannot respond in time, thereby reducing the control performance. The influence of the historical time temperature change of different areas on the control performance of the heating, ventilating and air conditioning system is extremely critical. It is logical to further consider these factors to improve the control performance of the algorithm. The Partial Form Dynamic Linearization (PFDL) uses the multiple median differential theorem to convert the Pseudo Partial Derivative (PPD) under CFDL into a Pseudo Gradient (PG). Compared to the CFDL, where the data model only contains information at one time, the data model obtained by using PFDL contains information within a time window of variable length. Formally, PFDL is more generic than CFDL. The control method designed by the PFDL data model increases more control information of previous time, thereby increasing the space for improving the control performance of the whole method.
Disclosure of Invention
The invention discloses a distributed model-free adaptive control technology for building indoor heating ventilation and air conditioning, which solves the problem that the temperature of each indoor area can track the expected temperature with better control performance under the condition that a complex topological relation and an unknown external environment exist in a building room.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention discloses a distributed model-free adaptive control technology for building indoor heating ventilation air conditioners, which mainly aims at a multi-zone indoor temperature system containing complex topological relation and unknown disturbance, takes partial form dynamic linearization as a research basis under the framework of model-free adaptive control, adds topological information into a control scheme, enables the temperature of each zone to better track expected temperature without depending on model information, and has better control performance in the aspects of overshoot, regulation time and the like.
The invention discloses a distributed model-free adaptive control technology for building indoor heating ventilation air-conditioning, which comprises the following steps:
step 1, establishing a dynamic model of a multi-region heating and ventilation air conditioner, writing the dynamic model into a matrix form, and discretizing:
T(t+1)＝(I+ΔtC-R)T(t)+ΔtC-U(t)+ΔtC-ω(t)
wherein T (T) ═ T1(t),T2(t),…Tz(t)]TEach element in the vector represents the temperature of each room at time t, and z represents the number of rooms; i is as large as RzRepresenting an identity matrix; Δ t represents a sampling time; c ═ diag { C ═ C1,C2…CzThe heat capacity of each element in the matrix is represented by kJ/K; c-Represents the inverse of the C matrix; u (t) ═ u1(t),u2(t),…uz(t)]TEach element in the vector represents the control input of each room at time t; ω (t) ═ ω1(t),ω2(t),…ωz(t)]TEach element in the vector represents unknown disturbance of each room at time t;
Figure BDA0003507118800000041
rijrepresenting the thermal resistance between two rooms;
step 2, representing the single room physical model as a general non-affine nonlinear model, and converting the model into a linear data model containing a pseudo gradient through a median theorem of differentiation:
Figure BDA0003507118800000042
wherein, Δ Ti(t+1)＝Ti(t+1)-Ti(t), i is the number of the room; delta Ui,L(t)＝Ui,L(t)-Ui,L(t-1)，Ui(t)＝[ui(t),ui(t-1)…,ui(t-L+1)]TL is the time window length; phi is ai,p,L(t)＝[φi,1(t),…,φi,L(t)]TIs the pseudo-gradient, L is the time window length;
Figure BDA0003507118800000043
represents a vector phii,p,L(t) transposing;
step 3, designing a distributed model-free self-adaptive control law based on a linear data model and in combination with topological information:
Figure BDA0003507118800000044
wherein ξi(t) is the distributed measurement output at the time of the tth time of the ith room; lambda i0 is the weight factor of the adaptive control law of the ith room; rho i,j0, j is 1,2, …, L is the step factor of the adaptive control law of the ith room, L is the time window length;
Figure BDA0003507118800000045
represents the t-th time phi of the ith roomi,j(t), L is the time window length;
and 4, designing a parameter estimation index function by combining a linear data model, and estimating unknown pseudo gradients in the algorithm:
Figure BDA0003507118800000051
wherein the content of the first and second substances,
Figure BDA0003507118800000052
is indicative of phii,p,L(t) estimation; mu.si> 0 is the parameter estimation weight factor for the ith room; eta of 0iThe parameter estimation step size factor of the ith room is less than or equal to 2;
Figure BDA0003507118800000053
an initial parameter estimate representing a first iteration; ε is a small positive number.
The invention provides a distributed model-free self-adaptive control technology for a building indoor heating ventilation air conditioner, which solves the problem that the temperature of each indoor area tracks the expected temperature under the condition that a complex topological relation and an unknown external environment exist in a building room. The technology of the invention has the following advantages:
1. the technology of the invention comprises the related information of the adjacent area and the control information in a time window with adjustable length, thereby further improving the control performance;
2. the technology of the invention is based on data driving and is independent of an accurate system model;
3. although the design and analysis of the present invention starts with building room temperature control, the results can be generalized to the resolution of the relevant multi-agent coherence control problem.
Other features and advantages of the present invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
Drawings
Fig. 1 is a structural diagram of an indoor heating, ventilating and air conditioning system to which the distributed model-free adaptive control technique of the present invention is applied;
FIG. 2 is a schematic diagram of a topology of an indoor HVAC system to which the distributed model-free adaptive control technique of the present invention is applied;
FIG. 3 is a diagram illustrating a disturbance variation of an indoor HVAC system to which the distributed model-free adaptive control technique of the present invention is applied;
fig. 4 shows four room temperature changes after the distributed model-free adaptive control technique proposed by the present invention is applied to the heating, ventilating and air conditioning system;
fig. 5 shows the error variation between each room and the expected temperature after the distributed model-free adaptive control technique proposed by the present invention is applied to the heating, ventilating and air conditioning system;
Detailed Description
To better illustrate the objects and advantages of the present invention, the following detailed description is given with reference to the accompanying drawings.
Step S1: and establishing a dynamic model of the multi-region heating, ventilating and air conditioning, writing the dynamic model into a matrix form, and then discretizing.
Specifically, the following single indoor temperature dynamics model is established:
Figure BDA0003507118800000061
the interaction among the rooms can be seen from the model, and the rooms have complex topological relations. External perturbations also add to the uncertainty of the system. The temperature dynamics model for each room can be written as:
Figure BDA0003507118800000062
for convenience of representation, it is represented in matrix form and discretized:
T(t+1)＝(I+ΔtC-R)T(t)+ΔtC-U(t)+ΔtC-ω(t) (a3)
wherein T (T) ═ T1(t),T2(t),…Tz(t)]TEach element in the vector represents the temperature of each room at time t, and z represents the number of rooms; i is as large as RzRepresenting an identity matrix; Δ t represents a sampling time; c ═ diag { C ═ C1,C2…CzThe heat capacity of each element in the matrix is represented by kJ/K; c-Represents the inverse of the C matrix; u (t) ═ u1(t),u2(t),…uz(t)]TEach element in the vector represents the control input of each room at time t; ω (t) ═ ω1(t),ω2(t),…ωz(t)]TEach element in the vector represents an unknown perturbation of the respective room at time t.
From the analysis of the formulas (a1) to (a3), the multi-zone hvac model has strong nonlinearity, and a general model-based control scheme is difficult to implement, so that the model needs to be further processed, and a foundation is laid for the design of a subsequent control scheme.
Step S2: the single room physical model is represented as a general non-affine non-linear system, which is converted into a linear data model containing pseudo-gradients by the differential median theorem.
Specifically, a single room temperature model is represented as a non-affine nonlinear system as follows:
Ti(t+1)＝f(Ti(t),Ti(t-1),…,Ti(t-nT),ui(t),ui(t-1),…ui(t-nu)) (a4)
wherein, Ti(t) E R represents the temperature of the ith room at the time of tth, and is the output of the system, ui(t) E R represents the control input of the ith room at time t; n isTAnd nuRespectively representing the unknown orders of the system; f (-) is an unknown non-linear function.
The formula (a4) represents the heating, ventilating and air conditioning model as a form that the current temperature is influenced by the control input and the temperature at the previous moment, and other complex topological information and unknown disturbance information are all contained in an unknown nonlinear system.
By using the differential median theorem to differentiate the temperatures of two adjacent moments, a time-varying parameter vector phi named Pseudo Gradient (PG) must existi,p,L(t)∈RLThe system is converted into a linear data model as follows:
Figure BDA0003507118800000071
wherein, Delta Ti(t+1)＝Ti(t+1)-Ti(t), i is the room number; delta Ui,L(t)＝Ui,L(t)-Ui,L(t-1)；
Figure BDA0003507118800000072
Represents a vector phii,p,LAnd (t) transposing.
The data model only contains input and output data, does not depend on any explicit model of a controlled system, and is an equivalent model because any original system information is not omitted; the pseudo gradient phi is included in the modeli,p,L(t), the parameter has no physical significance, and the parameter contains complex dynamic information of the original system, compared with a pseudo partial derivative, the pseudo gradient is more complex, but the complexity of each parameter is greatly reduced, so that the parameter change is easier to capture, and the estimation difficulty is greatly reduced. Meanwhile, the control information contained in the whole data model is not only one moment, but also contains more control information in a time window with adjustable length, and the basis is provided for the excellent performance of the control performance of the controller designed later.
Step S3: a distributed model-free adaptive control law is designed based on a linear data model and combined with topological information, and the method mainly comprises the following steps.
In particular, the following distributed measurement outputs are defined:
Figure BDA0003507118800000081
where i, j is the number of the room, Ni，ai,j，diRespectively determining the neighborhood of the ith room, the communication relation between the ith room and the jth room in the neighborhood, and whether an expected signal can be received, wherein the above are topological information among all the regions; t isd(t) represents the desired temperature of the room at time t.
The distributed measurement output can be further rewritten as:
Figure BDA0003507118800000082
wherein ei(T) represents the system output temperature and the desired tracking temperature T at the T-th momentd(t) error.
Based on a linear data model, in combination with the distributed measurement output, the following distributed model-free adaptive control law is designed:
Figure BDA0003507118800000083
wherein u isi(t) represents the control input for the ith room at time t; lambda [ alpha ]i> 0 is the weighting factor for the ith room, L is the time window length; rhoi,j> 0, j-1, 2, …, L being the step factor for the ith room;
Figure BDA0003507118800000084
is an element in the pseudo gradient estimation of the ith room at time t.
The distributed control law (a8) contains the related information of adjacent agents, control input in a time window with adjustable length, and the whole method does not contain any dynamic model of heating, ventilation and air conditioning. The whole algorithm includes the main information of the heating ventilation air conditioner, and other complex information is included in the unknown pseudo-gradient, so that a related algorithm needs to be designed to estimate unknown parameters in real time, and the control performance of the algorithm is further improved.
Step S4: and (4) combining a linear data model design parameter estimation index function to estimate unknown pseudo gradients in the control method.
Specifically, firstly, an index function of parameter estimation is designed:
Figure BDA0003507118800000091
wherein the content of the first and second substances,
Figure BDA0003507118800000092
is indicative of phii,p,LEstimate of (t), μi> 0 is the weighting factor for the ith room parameter estimate;
relating the index function to
Figure BDA0003507118800000093
Is 0, thereby obtaining the following parameter estimation algorithm
Figure BDA0003507118800000094
In order to make the algorithm (a10) have stronger ability to track time-varying parameters, the following reset algorithm is designed:
Figure BDA0003507118800000095
if it is
Figure BDA0003507118800000096
Or
Figure BDA0003507118800000097
Or
Figure BDA0003507118800000098
Wherein the content of the first and second substances,
Figure BDA0003507118800000099
representing the initial parameter estimate for the first iteration,. epsilon.is a small positive number and sign (. cndot.) represents a sign function.
When the controller parameters are properly selected, the proposed distributed model-free adaptive control technique can ensure that: parameter estimation
Figure BDA00035071188000000910
Is bounded; as time t goes to infinity, per-room tracking error ei(t) converges to 0.
The indoor heating ventilation air-conditioning system of the building adopted in the embodiment is as follows:
Figure BDA00035071188000000911
wherein C is heat capacity, and the unit is kJ/K, rijIs the thermal resistance between rooms i and j, in K/W. T isiIs the temperature of the ith room. OmegaiRepresenting the perturbation, measured by K. u. ofiFor control input, the unit is KW. The structural block diagram of the heating, ventilating and air conditioning system is shown in figure 1, and the topological structure is shown in figure 2.
Disturbance is selected as omegai(t) ═ cos (0.02 π t) +0.3 σ, σ is a value in [ 01 ]]Random numbers within the interval. The time window length is chosen to be L-3. Defining:
Figure RE-GDA0003544265300000101
initial value set to
Figure RE-GDA0003544265300000102
Figure RE-GDA0003544265300000103
The controller parameter is set to [ rho ]i,1 ρi,2 ρi,3]＝[0.15 0.015 0.0015]，λi＝0.1，ηi＝0.01，μiThe sampling time is chosen to be 60s, and the duration is two days, i.e. N is 2880.
Selecting a topology between rooms as
Figure BDA0003507118800000105
And D-diag (1111) means that each room can receive the desired signal. Here, the desired temperatures for the four compartments are given as 24 deg.C, 25 deg.C, 26 deg.C, and 27 deg.C, respectively. The distributed model-free adaptive control technology provided by the invention controls the temperature of each room as shown in fig. 4, and the error between each room and each expected temperature is shown in fig. 5. As can be seen from fig. 4 and 5, the present invention allows the temperature of each room to track a desired temperature in a short time and allows the room to be always maintained around a set value when the desired temperature is not changed.
The above detailed description further illustrates the objects, technical solutions and advantages of the present invention, and it should be understood that the embodiments are only used for explaining the present invention and not for limiting the scope of the present invention, and modifications, equivalent substitutions, improvements and the like under the same principle and concept of the present invention should be included in the scope of the present invention.

Claims (5)

1. A distributed model-free adaptive control technology for indoor heating, ventilation and air conditioning of a building is characterized in that: the method comprises the following steps:
step 1, establishing a dynamic model of a multi-region heating and ventilation air conditioner, writing the dynamic model into a matrix form, and discretizing:
T(t+1)＝(I+ΔtC-R)T(t)+ΔtC-U(t)+ΔtC-ω(t)
wherein T (T) ═ T1(t),T2(t),…Tz(t)]TEach element in the vector represents the temperature of the respective room at time t, and z represents the number of rooms;
I∈Rzrepresenting an identity matrix;
Δ t represents a sampling time;
C＝diag{C1,C2…Czeach element in the matrix represents the heat capacity, in units ofkJ/K；
C-An inverse matrix representing the matrix C;
U(t)＝[u1(t),u2(t),…uz(t)]Teach element in the vector represents the control input of each room at time t;
ω(t)＝[ω1(t),ω2(t),…ωz(t)]Teach element in the vector represents unknown disturbance of each room at time t;
Figure FDA0003507118790000011
wherein r isijRepresenting the thermal resistance between two rooms;
step 2, representing a single room physical model as a general non-affine nonlinear model, and converting the model into a linear data model containing a pseudo gradient through a differential median theorem:
Figure FDA0003507118790000012
wherein, Delta Ti(t+1)＝Ti(t+1)-Ti(t), i is the number of the room; delta Ui,L(t)＝Ui,L(t)-Ui,L(t-1)，Ui(t)＝[ui(t),ui(t-1)…,ui(t-L+1)]TL is the time window length; phi is ai,p,L(t)＝[φi,1(t),…,φi,L(t)]TIs the pseudo-gradient at time t of the ith room, L is the time window length;
Figure FDA0003507118790000021
represents a vector phii,p,L(t) transposing;
step 3, designing a distributed model-free adaptive control law based on a linear data model and in combination with topological information:
Figure FDA0003507118790000022
wherein xi isi(t) is the distributed measurement output at time t for the ith room;
λithe weight factor of the adaptive control law of the ith room is more than 0;
ρi,j0, j is 1,2, …, L is the step factor of the adaptive control law of the ith room, L is the time window length;
Figure FDA0003507118790000023
represents the tth time phi of the ith roomi,j(t), L is the time window length;
step 4, combining a linear data model design parameter estimation index function to estimate unknown pseudo gradients in the algorithm:
Figure FDA0003507118790000024
Figure FDA0003507118790000025
if it is
Figure FDA0003507118790000026
Or | | | Δ Ui,L(t-1) | | is less than or equal to epsilon or
Figure FDA0003507118790000027
Wherein the content of the first and second substances,
Figure FDA0003507118790000028
is indicative of phii,p,L(t) estimation;
μi0 is the parameter estimation weight factor for the ith room;
0＜ηithe parameter estimation step size factor of the ith room is less than or equal to 2;
Figure FDA0003507118790000029
an initial parameter estimate representing a first iteration;
ε is a very small positive number;
sign (·) represents a sign function.
2. The method of claim 1, further comprising: the step 1 of establishing a dynamic model of the multi-zone heating, ventilating and air conditioning, and writing the dynamic model into a matrix form for discretization mainly comprises the following steps:
step 1.1, establishing the following dynamic temperature model in a single room:
Figure FDA0003507118790000031
step 1.2, the temperature dynamics model for each room can be written as:
Figure FDA0003507118790000032
Figure FDA0003507118790000033
Figure FDA0003507118790000034
Figure FDA0003507118790000035
step 1.3, writing the equation obtained in step 1.2 into a matrix form and discretizing:
T(t+1)＝(I+ΔtC-R)T(t)+ΔtC-U(t)+ΔtC-ω(t)
wherein T (T) ═ T1(t),T2(t),…Tz(t)]TEach element in the vector represents the temperature of each room at time t, and z represents the number of rooms; u (t) ═ u1(t),u2(t),…uz(t)]TEach element in the vector represents a respective room control input at time t; ω (t) ═ ω1(t),ω2(t),…ωz(t)]TEach element in the vector represents an unknown disturbance of the respective room at time t.
3. The method of claim 1, further comprising: the method for converting the single room physical model into the linear data model containing the pseudo gradient by the differential median theorem comprises the following steps:
step 2.1, converting the single room temperature model into the following nonlinear non-affine model:
Ti(t+1)＝f(Ti(t),Ti(t-1),…,Ti(t-nT),ui(t),ui(t-1),…ui(t-nu))
wherein, Ti(t) E R represents the temperature of the ith room at the time of tth, and is the output of the system, ui(t) E R represents the control input of the ith room at time t; n isTAnd nuRespectively representing the unknown orders of the system; f (-) is an unknown non-linear function;
step 2.2, by using the differential median theorem, a time-varying parameter vector phi named Pseudo Gradient (PG) must existi,p,L(t)∈RLSo that the system is transformed into the following linear data model:
Figure FDA0003507118790000041
wherein, Delta Ti(t+1)＝Ti(t+1)-Ti(t)；ΔUi,L(t)＝Ui,L(t)-Ui,L(t-1), i is a room number;
Figure FDA0003507118790000042
represents a vector phii,p,LAnd (t) transposing.
4. The method of claim 1, further comprising: the method for designing the distributed model-free adaptive control law based on the linear data model and combined with topological information in the step 3 mainly comprises the following steps:
step 3.1, defining the following distributed measurement outputs:
Figure FDA0003507118790000043
where i, j is the number of the room, Ni，ai,j，diThe local area is the neighborhood of the ith room, the communication relation between the ith room and the jth room in the neighborhood, and whether an expected signal can be received or not, wherein the local area and the jth room are topological information among all areas; t isd(t) represents a desired temperature of the room;
and 3.2, combining the distributed measurement output, designing the following distributed model-free adaptive control law:
Figure FDA0003507118790000044
wherein u isi(t) represents the control input at the time of the tth time of the ith room; lambda [ alpha ]i> 0 is the weighting factor for the ith room; rhoi,j> 0, j-1, 2, …, L being the step factor for the ith room, L being the time window length;
Figure FDA0003507118790000045
is an element in the pseudo gradient estimate for the ith room at the tth time.
5. The method of claim 1, further comprising: the estimation of the unknown parameters in the distributed algorithm by using the parameter estimation algorithm in the step 4 mainly comprises the following steps:
step 4.1, designing an index function of parameter estimation:
Figure FDA0003507118790000046
wherein the content of the first and second substances,
Figure FDA0003507118790000047
is indicative of phii,p,LEstimate of (t), μi> 0 is the weighting factor for the ith room parameter estimate;
step 4.2, make the above-mentioned index function be related to through optimization technique
Figure FDA0003507118790000048
Is 0, thereby obtaining the following parameter estimation algorithm
Figure FDA0003507118790000051
Wherein 0 < etaiThe step size factor of the ith room parameter estimation is less than or equal to 2;
4.3, in order to enable the algorithm to have stronger capability of tracking time-varying parameters, the following reset algorithm is designed:
Figure FDA0003507118790000052
if it is
Figure FDA0003507118790000053
Or | | | Δ Ui,L(t-1) | | is less than or equal to epsilon or
Figure FDA0003507118790000054
Wherein the content of the first and second substances,
Figure FDA0003507118790000055
representing the initial parameter estimate for the first iteration, epsilon is a small positive number.
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