CN117828864A - System state estimation method based on multi-cell spatial filtering and P norm - Google Patents
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Abstract
The invention discloses a system state estimation method based on multicell spatial filtering and P norms, and belongs to the technical field of state estimation. According to the method, the size of the multicellular bodies of the time-lapse system is measured by adopting the P norm, and the size of the multicellular space at the moment is measured by referring to the size of the ellipsoidal space, so that the size characteristics of the multicellular bodies are more comprehensively described. And then the state estimation problem of the time-lag system is converted into the design problem of the multi-cell space filter of the time-lag system based on the P norm, and the problem is converted into the linear matrix inequality optimization problem by constructing a multi-cell space expansion model, so that the state feasible space can more closely wrap the real state of the time-lag system, and the estimation conservation is effectively reduced. In addition, when the P norm is adopted to measure the scale of the multicellular body of the time-lapse system, the conventional mode of directly constructing the corresponding ellipsoidal shape to replace the multicellular body is not adopted, and the LMI inequality is constructed, so that the calculation complexity is reduced, the solution is faster, and the real-time performance of the system is improved.
Description
Technical Field
The invention relates to a system state estimation method based on multicell spatial filtering and P norm, and belongs to the technical field of state estimation.
Background
Industrial systems are often affected by network transmission, sensor transmission delay and other factors, and often have time lag phenomena. In order to meet the increasingly complex requirements of modern, integrated and precise industrial equipment, more accurate state estimation is required for the system state, so that the cost is reduced and the production efficiency is improved.
The traditional state estimation method mainly focuses on a Kalman filtering method based on a Bayesian theory and a derivative algorithm thereof, and the method both requires process noise and measurement noise to meet a specific distribution rule or known distribution rules, so that the posterior distribution of the state to be estimated is solved by utilizing the noise distribution characteristics. However, in practice, it is often difficult to obtain a probability distribution of noise, especially if the noise is non-gaussian. Therefore, the state estimation result is liable to be inaccurate. In addition, conventional system modeling often does not consider the influence of the system time lag amount, and when the system time lag is obvious, inaccurate system state estimation and even divergence of estimation can be caused.
In order to overcome the influence of system time lag and non-Gaussian noise and solve the problem of inaccurate estimation of the state of an estimated system, the conventional state estimation algorithm generally adopts a set operator filtering algorithm, adopts interval, ellipsoid, multicellular bodies and the like to describe measurement data, disturbance and noise, designs a proper multicellular space contraction strategy, can reduce the scale of multicellular space and obtain more accurate system state estimation.
Currently, commonly used multicellular spatial contraction strategies focus on utilizing the minimum multicellular volume or the minimum constructional F-norm as an optimization criterion for scaling the multicellular volume. The method adopting the minimum multicellular volume as the multicellular space contraction criterion has good accuracy, but the calculation complexity is obviously increased along with the increase of the iteration steps, and the calculation cost is high. The method adopting F norm minimization as a space contraction criterion has low computational complexity, but the accuracy is relatively poor because the method ignores the geometric structure information of the multicellular bodies and the directionality of the multicellular body vectors.
Disclosure of Invention
In order to solve the above problems, the present invention provides a system state estimation method based on multi-cell spatial filtering and P-norm, comprising:
step one: establishing a time-lag-containing discrete state space model of the industrial system;
step two: introducing a parameter lambda, and performing multi-cell space characterization on a state feasible set of a time delay system, namely giving a multi-cell space iterative form from the current k moment to the k+1th moment;
step three: according to two different conditions of 0<k less than or equal to h and k > h, respectively designing a multicellular space filter, namely respectively constructing an LMI inequality aiming at a state without time lag and a state with time lag of a system, and converting a solving parameter lambda (k) into an LMI optimization problem; wherein h represents the time lag of the industrial system;
step four: solving an LMI optimization problem and optimizing a parameter lambda (k);
step five: performing dimension reduction on the multicellular body feasible set obtained by solving;
step six: calculating the interval envelope to obtainAnd obtaining an optimal state estimate of the system.
Optionally, the industrial system time-lapse discrete state-containing space model is in the form of:
wherein,the state vector and the measurement vector of the system, A respectively h B, C, D and F are coefficient matrixes with proper dimensions; aiming at a three-blade variable-speed horizontal-axis wind driven generator system, x (k) is the pitch angle beta of a fan variable-pitch actuating mechanism and the angular speed beta of rotation of blades during operation of the fan a And y (k) represents the observed signal value output by the sensing device measuring the system state. />And->Respectively unknown but bounded process noise and measurement noise. When 0 is<When k is less than or equal to h, the system is zero initial value, u (k) represents an externally applied control signal applied to the system, and the setting is usually carried out according to the requirements of an industrial field.
Optionally, the centrosymmetric multicellular form is: definition of an r-order centrosymmetric multicellular in an n-dimensional spaceWherein (1)>Is the central coordinate vector of multicellular body Z, < >>A matrix is generated for multicellular Z, which determines the shape and size of the multicellular Z. B (B) r ＝[-1,1] r Is an r-order unit box.
Optionally, the noise of the industrial system is unknown but bounded, i.e. when k is greater than or equal to 0, the process noise and the measurement noise of the time-lapse system respectively satisfy:wherein G is w And G v Are all of suitableAnd generating a matrix of dimensions.
Optionally, in the step two, the state feasible set multi-cell space iterative form is as follows: estimating value of system state at given k timeThen a parameter lambda (k) is present, which makes the estimated value of the system state at time k+1 +.>Satisfy the following requirements
Optionally, in the third step, the LMI optimization problem is:
0<k.ltoreq.h, λ (k) which minimizes the P-norm of the multicell space at the current k-time is the solution to the LMI optimization problem as follows:
wherein,
and->Representing a unit box having the appropriate dimensions.
When k > h, λ (k) which minimizes the P norm of the multicell space at the current k moment is a solution to the LMI optimization problem as follows:
wherein,
α 1 ＝γ′P
α 3 ＝(DG w ) T P(DG w )
α 4 ＝(FG v ) T P(FG v ) (9)
gamma' represents a coefficient for measuring the shrinkage degree of multicellular bodies, and can be specified or adjusted and optimized according to actual requirements, wherein I is an identity matrix.
Optionally, the dimension reduction calculation method provided in the fourth step is as follows:
for multicellular body Z =<p,G>With reduced multicellular Z ↓ ＝<p,rs(G)>Make the followingWherein the reduced multicellular space generating matrix rs (G) is a diagonal matrix, and the elements of the ith row and the ith column are
Wherein G is ij Representing the elements of the ith row and jth column of matrix G.
Optionally, the interval envelope method proposed in the fifth step is: for any multicellular bodyThere is a minimum inter-zone envelope Box (Z) = [ Z - ,z + ]Make->Let->And->Z respectively - And z + Is selected from the group consisting of the (i) th element,
wherein p is i Is the i-th element of p.
Thereby obtaining multicellular bodiesMinimum inter-frame envelope Box (Z) = [ Z ] - ,z + ]And the optimal state estimation value of the system is obtained.
The time lag system also comprises a temperature control system in the chemical industry field and a mechanical industrial system with response delay of a sensor or an actuator.
The invention has the beneficial effects that:
according to the invention, the P norm is used as an optimization criterion for measuring the multicellular body size of the time lag system, and the size of the multicellular space at the moment is measured by referring to the size of the ellipsoidal space, so that the size characteristics of the multicellular body are more comprehensively described. And then the state estimation problem of the time-lag system is converted into the design problem of the multi-cell space filter of the time-lag system based on the P norm, and the problem is converted into the linear matrix inequality optimization problem by constructing a multi-cell space expansion model, so that the state feasible space can more closely wrap the real state of the time-lag system, and the estimation conservation is effectively reduced. In addition, when the P norm is adopted to measure the multicellular body scale of the time-lapse system, the conventional method of directly constructing the corresponding ellipsoidal shape to replace the multicellular body is not adopted, but the complexity of constructing the ellipsoidal is reduced by constructing the LMI inequality, the solution is faster, and the real-time performance of the system can be met. In addition, when the industrial system model is built, the system time lag phenomenon is considered, the model precision is improved, and the precision of the state estimation method is increased.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a hydraulic pitch actuator of a wind turbine disclosed in one embodiment of the present invention in the industrial field;
FIG. 2 is a graph of simulated comparison of state estimation curves for a state variable β using the methods of the present application and prior art methods, respectively, as disclosed in one embodiment of the present invention;
FIG. 3 shows the state variable β obtained by the methods of the present application and the prior art, respectively, as disclosed in one embodiment of the present invention k A state estimation curve simulation contrast diagram of (1);
fig. 4A is a simulated comparison of estimated ranges obtained at k=80 using the method of the present application and the prior art method, respectively, as disclosed in one embodiment of the present invention;
fig. 4B is a simulated comparison of estimated ranges obtained at k=130 using the method of the present application and the prior art method, respectively, as disclosed in one embodiment of the present invention;
fig. 4C is a simulated comparison of estimated ranges obtained at k=150 using the method of the present application and the prior art method, respectively, as disclosed in one embodiment of the present invention;
fig. 4D is a simulated comparison of estimated ranges obtained at k=190 using the method of the present application and the prior art method, respectively, as disclosed in one embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the accompanying drawings.
Embodiment one:
the embodiment provides a system state estimation method based on multi-cell spatial filtering and P norm, which comprises the following steps:
step one: aiming at a specific industrial system, considering time lag, and establishing a discrete state space model containing time lag;
step two: state estimation for time-lapse systemsPerforming multi-cell space characterization, namely giving a multi-cell space iterative form from the current k moment to the k+1th moment; the time lag system is an industrial system containing time lag;
step three: according to two different conditions of 0<k less than or equal to h and k > h, respectively designing a multicellular space filter, namely respectively constructing an LMI inequality aiming at a state without time lag and a state with time lag of a system, and converting a solving parameter lambda (k) into an LMI optimization problem; wherein h represents the time lag of the industrial system;
step four: solving an LMI optimization problem and optimizing a parameter lambda (k);
step five: performing dimension reduction on the multicellular body feasible set obtained by solving;
step six: calculating the interval envelope to obtainAnd obtaining an optimal state estimate of the system.
Embodiment two:
the embodiment provides a system state estimation method based on multi-cell spatial filtering and P norm, which is illustrated by taking a three-blade variable speed horizontal axis wind driven generator system as an example, as shown in fig. 1, the three-blade variable speed horizontal axis wind driven generator system comprises a power converter, a generator, a gearbox, a transmission shaft, a variable pitch actuating mechanism and a transformer, in the working process of the system, the wind power drives the variable pitch actuating mechanism to rotate, torque generated by rotation of the variable pitch actuating mechanism is transmitted to the gearbox through the transmission shaft to change speed, the rotation speed is converted into a rotation speed suitable for generating power by the generator, the converted rotation speed torque drives the generator to generate power, and the power generated by the generator is converted into alternating current suitable for a power grid after being converted by the power converter; the alternating current is converted into a proper one by a transformerAfter the voltage of the power grid is integrated, the voltage is transmitted to the power grid for users to use; the method is based on the pitch angle beta of the variable pitch actuator of the fan and the angular speed beta of the rotation of the blades during the operation of the fan a And (3) estimating the value of the next moment.
The method comprises the following steps:
step one: aiming at a specific industrial system, considering time lag, and establishing a discrete state space model containing time lag;
specifically, the embodiment establishes an industrial system mathematical model of a hydraulic variable pitch actuator of a wind driven generator aiming at a three-blade variable speed horizontal axis wind driven generator system:
wherein, beta is the pitch angle of the variable pitch actuating mechanism of the fan, and beta is the pitch angle of the variable pitch actuating mechanism of the fan a For the angular velocity of rotation of the blades, beta, during operation of the fan r Reference value of beta, natural frequency omega n And damping ratio xi is a system parameter.Representing derivation of pitch angle beta->Represents the angular velocity beta of the opposite fan a And (5) deriving.
In order to establish a time-lag-containing discrete state space model of the variable pitch actuator, discretizing a mathematical model of the power generation system shown in the formula (1):
wherein,
will becomeParameter ω of pitch actuator n ,ξ,A h Substituting the D, F and the parameter C of the sensing measurement mechanism to obtain a time-lag-containing discrete state space model of the variable pitch actuating mechanism:
wherein,in the three-blade variable speed horizontal axis wind driven generator system, x (k) is the pitch angle beta of a fan variable pitch actuator and the angular velocity beta of the rotation of the blades during the operation of the fan a And y (k) represents the signal value, A, outputted by the sensing device measuring the system state h B, C, D and F are all corresponding coefficient matrices. />And->Respectively unknown but bounded process noise and measurement noise. When 0 is<When k is less than or equal to h, the system is zero initial value, and u (k) represents an input signal applied to the system and is generally designated according to the requirements of an industrial field.
Y (k) is the result of a system that can be directly observed or measured, and can be the result of directly measuring the pitch angle beta of the fan variable pitch actuator and the angular velocity beta of the blade rotation during the operation of the fan a Or indirectly measuring other variables of the two values through some sensors, such as current, voltage and the like, and further obtaining the pitch angle beta of the variable pitch actuator of the fan and the angular speed beta of the rotation of the blades during the operation of the fan through the current and voltage measurement values a 。
The process noise and the measurement noise respectively satisfy:
wherein,and->Representing a unit box having the appropriate dimensions.
Step two: introducing parameter lambda, and estimating state of time delay systemMulti-cell space characterization is performed, namely, a multi-cell space iterative form from the current k time to the k+1st time is given:
estimating value of system state at given k timeThen a parameter lambda (k) is present, which makes the estimated value of the system state at time k+1 +.>The method meets the following conditions:
aiming at a three-blade variable speed horizontal axis wind driven generator system,center point coordinate vector of multicellular bodies representing system state at package time k +.>Shape moment of multicellular bodies representing system state at time k of packageAn array; />And->Is an intermediate parameter; g v Multi-cell generator matrix representing measurement noise of wrapping system, G w A multicellular generator matrix representing the process noise of the wrapping system.
Step three: according to two different conditions of 0<k less than or equal to h and k > h, respectively designing a multi-cell spatial filter, namely respectively constructing an LMI inequality aiming at a state of a system without time lag and a state with time lag, and converting a solving parameter lambda (k) into an LMI optimization problem:
0<k.ltoreq.h, λ (k) which minimizes the P-norm of the multicell space at the current k-time is the solution to the LMI optimization problem as follows:
wherein,
and P is a P norm coefficient matrix corresponding to the multicell space at the k moment, and the superscript T is transposition operation.
When k > h, λ (k) which minimizes the P norm of the multicell space at the current k moment is a solution to the LMI optimization problem as follows:
wherein,
α 1 ＝γ′P
α 3 ＝(DG w ) T P(DG w )
α 4 ＝(FG v ) T P(FG v ) (9)
gamma' represents a coefficient for measuring the degree of shrinkage of multicellular bodies, and I is an identity matrix.
Step four: solving an LMI optimization problem to obtain an optimal parameter lambda (k);
step five: and (3) performing dimension reduction on the multi-cell feasible set obtained by solving:
for multicellular body Z =<p,G>With reduced multicellular Z ↓ ＝<p,rs(G)>Make the followingp represents the center coordinate vector of the multicellular body, and G represents the generator matrix of the multicellular body. Wherein, the reduced generating matrix rs (G) of the multicell space is a diagonal matrix, and the elements of the ith row and the ith column are as follows:
wherein G is ij Representing the elements of the ith row and jth column of matrix G.
Step six: calculating the interval envelope to obtainObtaining an optimal state estimate for the system:
for any multicellular bodyThere is a minimum inter-zone envelope Box (Z) = [ Z - ,z + ]Make->Order theAnd->Z respectively - And z + I-th element of (c), then:
wherein p is i Is the i-th element of p.
Thereby obtaining multicellular bodiesMinimum inter-frame envelope Box (Z) = [ Z ] - ,z + ]And the optimal state estimation value of the system is obtained.
In order to verify the effectiveness of the method, the method is compared with the prior method, and experimental simulation results are shown in fig. 2 and 3, wherein fig. 2 is a state estimation curve of a state variable beta of a three-blade variable speed horizontal axis wind turbine system, and fig. 3 is the state variable beta k State estimation curves of (2). In fig. 2 and 3, the solid line is a true value, the dotted line is an estimated upper and lower boundary obtained by the method provided by the invention, and the dotted line and the cross line are estimated upper and lower boundaries of other existing methods. It can be seen that the algorithm disclosed by the invention has more accurate estimation, and the algorithm effect is smooth and compact and is close to the true value.
The prior art method PRad-A for comparison in experiments is described in Althoff M, jagat J R. Comparison of guaranteed state estimators for linear time-invariant systems [ J ]. Automatics, 2021,130:109662 "which adopts a method utilizing the problem of optimizing a multi-cell structure observer, and the result is less accurate than the method of the present application because the influence of system time lag is not fully considered.
The existing method ES-SME compared in the experiment can refer to the introduction in Liu Y S, zhao Y, wu F L.elinipoid state-bound-based set-membership estimation for linear system with unknown-but-bounded disturbances [ J ]. IET Control Theory & Applications,2016,10 (4): 431-442', which adopts a method of wrapping system state estimation by using ellipsoids as a feasible set, because the method brings larger spatial redundancy, a compact state estimation set is difficult to obtain, and the result conservation is larger.
Fig. 4A-4D show graphs of estimated ranges obtained when k=80, k=130, k=150, and k=190 using the method of the present application and the prior method, respectively, at k=190, where the "×" point in fig. 4A-4D is the actual value at the current time, the solid line wraps the estimated ranges obtained using the method of the present application, and the dotted and dashed lines are the estimated ranges obtained using the prior methods PRad-a and ES-SME, respectively. It can be seen that the algorithm estimation disclosed by the invention is more close to the true value.
Some steps in the embodiments of the present invention may be implemented by using software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (8)
1. A system state estimation method based on multi-cell spatial filtering and P-norm, the method comprising:
step one: aiming at a specific industrial system, considering time lag, and establishing a discrete state space model containing time lag;
step two: state estimation for time-lapse systemsPerforming multi-cell space characterization, namely giving a multi-cell space iterative form from the current k moment to the k+1th moment; the time lag system is an industrial system containing time lag;
step three: according to two different conditions of 0<k less than or equal to h and k > h, respectively designing a multicellular space filter, namely respectively constructing an LMI inequality aiming at a state without time lag and a state with time lag of a system, and converting a solving parameter lambda (k) into an LMI optimization problem; wherein h represents the time lag of the industrial system;
step four: solving an LMI optimization problem and optimizing a parameter lambda (k);
step five: performing dimension reduction on the multicellular body feasible set obtained by solving;
step six: calculating the interval envelope to obtainAnd obtaining an optimal state estimate of the system.
2. The method of claim 1, wherein when the industrial system is a three-bladed variable speed horizontal axis wind turbine system, the step 1 comprises:
step 1.1, establishing an industrial system mathematical model of a hydraulic variable pitch actuator of a wind driven generator:
wherein, beta is the pitch angle of the variable pitch actuating mechanism of the fan, and beta is the pitch angle of the variable pitch actuating mechanism of the fan a For the angular velocity of rotation of the blades, beta, during operation of the fan r Reference value of beta, natural frequency omega n And damping ratio xi is a system parameter;
step 1.2, establishing a discrete state space model with time lag according to an industrial system mathematical model of a hydraulic variable pitch actuator of the wind driven generator:
wherein,state vector sum measurement of systems respectivelyVector of quantities, where x (k) is pitch angle β of the fan pitch actuator and angular velocity β of the blade rotation during operation of the fan a And y (k) represents the observed signal value, A, outputted by the sensing device for measuring the system state h B, C, D and F are corresponding coefficient matrixes; />And->The unknown but bounded process noise and measurement noise, respectively, u (k) represents the applied input to control the system.
3. The method according to claim 2, wherein the step 2 comprises:
introducing parameter lambda, and estimating state of time delay systemPerforming multicellular space characterization;
estimating value of system state at given k timeThen a parameter lambda (k) is present, which makes the estimated value of the system state at time k+1 +.>The method meets the following conditions:
aiming at a three-blade variable speed horizontal axis wind driven generator system,center of multicellular bodies representing system state at time k of packagePoint coordinate vector +.>A shape matrix of multicellular bodies representing the system state at time k of the package; />And->Is an intermediate parameter; g v Multi-cell generator matrix representing measurement noise of wrapping system, G w A multicellular generator matrix representing the process noise of the wrapping system.
4. A method according to claim 3, wherein said step 3 comprises:
aiming at the state that the system does not contain time lag, namely 0<k is less than or equal to h, constructing and obtaining an LMI inequality shown in a formula (6), and enabling lambda (k) with the minimum multicellular space P norm at the current k moment to be a solution of the following LMI optimization problem:
wherein,
p represents the P norm coefficient matrix corresponding to the multicell space at the k moment, and the superscript T represents transposition operation;
aiming at the state of time lag of the system, namely when k > h, constructing and obtaining an LMI inequality shown in a formula (8), and enabling lambda (k) with the minimum P norm of the multicellular space at the current k moment to be a solution of the following LMI optimization problem:
wherein,
α 1 ＝γ′P
α 3 ＝(DG w ) T P(DG w )
α 4 ＝(FG v ) T P(FG v ) (9)
gamma' represents a coefficient for measuring the degree of shrinkage of multicellular bodies, and I is an identity matrix.
5. The method according to claim 4, wherein the step 5 comprises:
for multicellular body Z =<p,G>With reduced multicellular Z ↓ ＝<p,rs(G)>Make the followingp represents a central coordinate vector of the multicellular body, and G represents a generator matrix of the multicellular body; wherein, the reduced generating matrix rs (G) of the multicell space is a diagonal matrix, and the elements of the ith row and the ith column are as follows:
wherein G is ij Representing the elements of the ith row and jth column of matrix G.
6. The method according to claim 5, wherein the step 6 comprises:
for any multicellular bodyThere is a minimum inter-zone envelope Box (Z) = [ Z - ,z + ]Make->
Order theAnd->Z respectively - And z + I-th element of (c), then:
wherein p is i An i-th element of p;
thereby obtaining the minimum interval envelope Box (Z) = [ Z ] of the multicellular body Z - ,z + ]And the optimal state estimation value of the system is obtained.
7. The method of claim 6, wherein the process noise and the measurement noise of the time-lapse system satisfy respectively:
wherein,and->Representing a unit box.
8. The method of claim 6, wherein the time-lapse system further comprises a temperature control +system in the chemical industry, a mechanical industrial system containing a sensor or actuator response delay.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109474472A (en) * | 2018-12-03 | 2019-03-15 | 江南大学 | A kind of fault detection method based on the more cell space filtering of holohedral symmetry |
| CN112180725A (en) * | 2020-09-30 | 2021-01-05 | 山东科技大学 | Fuzzy proportional-integral state estimation method for nonlinear system with redundant time-delay channel |
| CN113236506A (en) * | 2021-05-19 | 2021-08-10 | 江南大学 | Industrial time delay system fault detection method based on filtering |
| CN114462241A (en) * | 2022-01-28 | 2022-05-10 | 杭州师范大学 | Fully-symmetrical multi-cell centralized member state estimation method for multi-rate system |
| WO2023005064A1 (en) * | 2021-07-30 | 2023-02-02 | 江南大学 | State estimation method for power battery formation process based on convex spatial filtering |
-
2023
- 2023-12-29 CN CN202311865199.XA patent/CN117828864B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109474472A (en) * | 2018-12-03 | 2019-03-15 | 江南大学 | A kind of fault detection method based on the more cell space filtering of holohedral symmetry |
| CN112180725A (en) * | 2020-09-30 | 2021-01-05 | 山东科技大学 | Fuzzy proportional-integral state estimation method for nonlinear system with redundant time-delay channel |
| CN113236506A (en) * | 2021-05-19 | 2021-08-10 | 江南大学 | Industrial time delay system fault detection method based on filtering |
| WO2023005064A1 (en) * | 2021-07-30 | 2023-02-02 | 江南大学 | State estimation method for power battery formation process based on convex spatial filtering |
| CN114462241A (en) * | 2022-01-28 | 2022-05-10 | 杭州师范大学 | Fully-symmetrical multi-cell centralized member state estimation method for multi-rate system |
Non-Patent Citations (4)
| Title |
|---|
| JIAPENG WANG: "Monotonically convergent hybrid ILC for uncertain discrete-time switched systems with state delay", TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 31 March 2016 (2016-03-31) * |
| 江明辉 等: "基于LMI方法的中立型多时滞系统稳定性分析", 三峡大学学报（自然科学版）, vol. 27, no. 6, 31 December 2005 (2005-12-31) * |
| 王子赟 等: "基于正多胞体空间扩展滤波的时变参数系统辨识方法", 控制理论与应用, vol. 37, no. 6, 30 June 2020 (2020-06-30) * |
| 王子赟 等: "基于正多胞体线性规划的滤波故障诊断方法", 控制与决策, vol. 35, no. 4, 30 April 2020 (2020-04-30) * |
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