CN112269318B

CN112269318B - Finite time remote safety state estimation method for time delay uncertain system

Info

Publication number: CN112269318B
Application number: CN202011236055.4A
Authority: CN
Inventors: 陈海洋
Original assignee: Nanjing Institute of Technology
Current assignee: Nanjing Institute of Technology
Priority date: 2020-11-09
Filing date: 2020-11-09
Publication date: 2022-06-10
Anticipated expiration: 2040-11-09
Also published as: CN112269318A

Abstract

The invention discloses a finite time remote safety state estimation method of a time delay uncertain system, which comprises the following steps: establishing a state space model of the controlled system; establishing a state estimator system model and a calculation center, and developing a state estimation task; establishing an extended state estimation model of an extended state estimation system; providing existence conditions of a finite time remote safety state estimator by combining an energy function with a bounded decision auxiliary equation; a state estimator algorithm is designed through the steps of giving system parameters, initializing parameters, solving an inequality group, modifying the initializing parameters and the like, a remote safety state estimation strategy is generated, and the limited time remote safety state estimation of a delay uncertain system is realized. The invention can ensure the robust finite time safety state estimation of the time delay uncertain system based on the remote transmission data, and realize the timeliness and reliability of the state estimation under the remote data transmission mode with network attack.

Description

Finite time remote safety state estimation method for time delay uncertain system

Technical Field

The invention belongs to the field of control of a system with time delay and model uncertainty, and particularly relates to a finite time remote safety state estimation method of a time delay uncertainty system.

Background

The system state is an important parameter for understanding the internal dynamics of the system and realizing key control tasks (such as positioning, tracking and synchronization). However, it is not easy to directly acquire the state of the controlled system under the limitation of objective conditions such as measurement technique or cost input. Therefore, how to effectively estimate the unknown system state has been a hot issue in the control field.

In developing state estimation, the main challenges come from two areas: on one hand, the accuracy of the controlled system model is high, and in an actual system, the nonlinearity of electronic components, the hysteresis of signal transmission and the destructiveness of external unknown interference bring great difficulty to the construction of a reasonable and real controlled system model. On the other hand, the validity of the measurement information required by the state estimation is essentially the process of filtering the system state from the measurement information acquired by the sensor, and as can be seen from the intrinsic mechanism, the validity of the measurement information directly relates to the reliability of the state estimation result. With the continuous development of computer and communication technologies, the network-based data transmission mode gradually replaces the traditional wired communication mode due to its advantages of low cost, easy maintenance, high flexibility, etc., and has received more and more attention in the fields including signal processing and automatic control. It should be noted that the network transmission mode brings many conveniences to the implementation of the automatic control, and also causes a series of new technical problems, including the current hot network attack problem. By means of network attack, a malicious attacker can not directly damage a target system any more, but starts with key information required by normal operation of the target system, and takes illegal action to block information transmission or tamper data information, so that the target system is in failure or even paralysis due to failure in receiving normal input, and the purpose of being unable to be notified is achieved. Especially in the distributed design, which is more and more favored today, the data acquisition system, the data processing system and the controller/estimator system are often not in one area, and information exchange is needed to be realized through remote data transmission. In the process of remote data transmission, although designers can take necessary security measures, the diversity and complexity of network attack modes still increase the difficulty of state estimation. Both of the aforementioned challenges pose a serious threat to estimation performance, and inaccuracy in the estimated state may result in significant economic loss or even personal safety. Therefore, by constructing a more objective and actual controlled system model and improving the effectiveness of the measurement information as much as possible, two major problems to be solved urgently in state estimation are solved.

Meanwhile, in a large number of scientific and technological industries such as target tracking, rocket launching, robot control, chemical reaction kettle temperature control and the like, the system state acquisition teaches stronger timeliness, namely, the estimation process is required to be completed within a limited time and a reliable result is given. Therefore, asymptotically stable control targets have great limitations in the use of practical systems. In contrast, the finite time state estimation shows better utility because it can ensure the designer to obtain the required system state within a given finite time, and thus to complete the corresponding control task in time.

In conclusion, it can be seen that how to effectively overcome adverse effects of time delay, model uncertainty and network attack in the context of engineering application of remote data transmission, an estimated state that is as accurate and reliable as possible is provided by designing a finite time state estimator, and the method has important research value.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the problem of state estimation of a controlled system with uncertain time delay and model in given time in the engineering application background of remote data transmission in the prior art, the invention discloses a finite time remote safety state estimation method of a time delay uncertain system, which improves the tolerance of a state estimator to time delay, effectively reduces the damage of time delay to state estimation performance, enhances the robustness of the state estimation process to the model uncertain and unknown external interference, and realizes the timeliness and reliability of state estimation in a remote data transmission mode with network attack.

The technical scheme is as follows: the invention adopts the following technical scheme: a limited-time remote safety state estimation method of a time delay uncertain system is characterized by comprising the following steps:

s1, establishing a controlled system state space model with time delay, nonlinear dynamics, model uncertainty and unknown external disturbance;

s2, establishing a state estimator system model based on the controlled system state space model, and establishing a calculation center;

sequentially establishing communication links between a state estimator system and a computing center as well as between a controlled system and the computing center;

the state estimator system requests the computing center to send information data as external input information and carries out a state estimation task;

s3, constructing an expansion vector;

establishing an extended state estimation model of an extended state estimation system through a controlled system state space model and a state estimator system model;

the method comprises the steps of designing an energy function and applying a bounded decision auxiliary equation at the same time, and providing conditions for an extended state estimation system to obtain robust H-infinity bounded time bounded performance, namely existence conditions of a finite time remote safe state estimator;

s4, according to the existing conditions in the step S3, designing a solving algorithm of the state estimator and calculating the gain of the state estimator, generating a remote safety state estimation strategy, and realizing the limited time remote safety state estimation of the time delay uncertain system, wherein the method comprises the following steps:

giving system parameters; initializing parameters;

solving according to the linear matrix inequality group constraint, wherein the linear matrix inequality constraint is obtained by applying a scaling theorem and a Schur complement theorem under the existence condition in the step S3, and if a feasible solution exists, the gain of the state estimator is obtained; if no feasible solution exists, modifying the parameters;

if the modified parameters meet the requirements, solving again; if the modified parameters are not satisfactory, an acceptable state estimate cannot be achieved.

Preferably, in step S1, the controlled system state space model established over the finite time interval [0, N ] is as follows:

wherein, tau_kDenotes the time delay of the controlled system, [ tau ]_m,τ_M]Is a time delay interval; x is the number of_k∈RⁿRepresents the state of the system at time k, x_k+1∈RⁿRepresenting the state of the system at time k +1,

the representation system is at k-tau_kState of time, N ∈ N₀Is the dimension of the system state;

is a known system initial state; w is a_k∈R^sIs a set l₂Energy-limited external perturbation over [0, ∞) ], s ∈ N₀Is the dimension of the external disturbance; f is belonged to C (R)^F；R^F) Is a non-linear dynamic function and has a zero initial state F (0) of 0, F ∈ N₀The number of subfunctions contained in the nonlinear dynamic function f; y is_k∈R^lRepresents the measurement output of the system, L ∈ N₀Is the dimension of the measurement output of the system; z is a radical of formula_k∈R^gRepresenting the target signal to be estimated, g ∈ N₀Is the dimension of the target signal; a is an element of R^n×n、A_d∈R^n×n、B_f∈R^n×F、B_w∈R^n×s、C∈R^L×n、D∈R^L×sAnd C_z∈R^g×nAre all known matrices; Δ a ═ N_zM_kN_yIn which N is_zAnd N_yAre all known matrices, M_kIs a time-varying real-valued matrix and satisfies

Is a known positive scalar quantity; the nonlinear dynamical function f has the characteristic of 2-norm bounding

Where H is a known matrix.

Preferably, step S2 includes the steps of:

s21, establishing a state estimator system model as follows:

where K is the gain of the state estimator in the state estimator system; Σ is the external input information for the state estimator system;

representing the state estimate of the system at time k,

representing the state estimate of the system at time k +1,

the representation system is at k-tau_kEstimating the state of the moment;

representing an estimate of the target signal at time k;

the calculation center is established as follows:

wherein,

and

are two types of input data for the computation center,

is the output data of the computing center, and C is the conversion parameter of different types of data;

s22, establishing the communication relation between the state estimator system and the computing center, and between the controlled system and the computing center as follows:

s23, the computing center receives the request sent by the state estimator system and generates the innovation theta_kThe following were used:

innovation theta_kIn the process of transmitting from the computing center to the state estimator system, new information is obtained after attack

The following were used:

wherein,

χ_b,kare independent of each other and subject to Bernoulli's scoreRandom variables of cloth, where b is 1,2, …, L, defined by the interval [0,1]And satisfy mathematical expectations

Covariance

When a and b are the same, it can be simplified to

Or

S24, state estimator system and new information

As external input information, a state estimation task is performed, i.e.

Preferably, step S3 includes the steps of:

s31, constructing an extension vector of

S32, establishing an extended state estimation model of the extended state estimation system through the controlled system state space model and the state estimator system model as follows:

wherein,

s33, providing an extended state estimation system to obtain the parameter (alpha) by designing an energy function, namely Lyapunov functional and combining a bounded decision auxiliary equation₁,α₂,α₃G, N) the condition of robust H ∞ finite time-bounded performance, i.e. the existence condition of the finite time remote safe state estimator;

wherein the designed Lyapunov functional is as follows:

wherein,

wherein, V_kExpanding the Lyapunov functional of the state estimation system for the time k; p and Q_i(i ═ 1,2,3,4) is a Lyapunov matrix。

The bounded decision-assist equation is designed as follows:

wherein, V_k+1Expanding the Lyapunov functional of the state estimation system for the time k + 1; delta>0 represents the interference suppression level; mu.s>1 represents a finite time bounded design parameter;

is the estimated error of the target signal.

Preferably, in step S33, the parameter (α) is selected₁,α₂,α₃G, N) the robust H ∞ finite time-bounded satisfies the following condition:

under the condition of zero initial condition, the method can reduce the initial condition,

wherein, 0 is less than or equal to alpha₁≤α₃，α₂≥0，G>0，N∈N₀；

Is the estimated error of the target signal.

Preferably, in step S4, the linear inequalities resulting from the presence condition are as follows:

G<P<σ₀G

0<Q_i<σ_iG(i＝1,2,3,4)

wherein phi is phi^T＝[Φ_a,b]_{a,b＝1,2,3,4,5}，

Φ_2,1＝Φ_2,3＝Φ_2,4＝Φ_2,5＝Φ_3,1＝Φ_3,2＝Φ_3,4＝Φ_3,5＝0，

Φ_4,1＝Φ_4,2＝Φ_4,3＝Φ_4,5＝Φ_5,1＝Φ_5,2＝Φ_5,3＝Φ_5,4＝0，

Ψ₃＝[0_2n×8n [I_2n,0_q×2n] 0_2n×4n]，

Ψ₄＝[0_2n×8n [0_q×2n,I_2n] 0_2n×4n]，

ε＝[0 I_n]，

Wherein σ_iIs a positive scalar, i is 0,1,2,3, 4; p and Q_iIs a symmetric positive definite matrix, i is 1,2,3, 4; Λ is a diagonal positive definite matrix; for time delay interval [ tau ]_m,τ_M]Dividing to obtain q subintervals with the lengths of delta tau; m is a weighting coefficient of time delay segmentation; denotes a symmetrical element or elements of the structure,

represents the kronecker product;

col{a_b}_{b＝1,2,…,c}is c column vectors a_bA matrix of compositions; diag_a{ b } represents a diagonal matrix containing a diagonal elements b;

preferably, step S4 includes the steps of:

s41, giving system parameters, including: A. a. the_d、B_f、B_w、C、D、C_z、M_k、

And H; initial state of a controlled system

A nonlinear dynamic function f; lower time delay bound τ_mAnd upper bound τ_M(ii) a Increment Δ m ∈ (0,1) and

s42, time delay interval [ tau ]_m,τ_M]Dividing to obtain q subintervals with the lengths of delta tau;

s43, initializing parameters, including: robust H-infinity time-bounded parameter alpha₁、α₂、α₃Q and N; the weighting coefficient m of the time delay segmentation belongs to (0, 1); parameter(s)

S44, setting the design parameter with limited time

S45, solving the parameters delta, kappa and sigma under the condition of satisfying the constraint of the linear matrix inequality group_i、P、

Λ and S:

if a feasible solution exists, then the gain of the state estimator is calculated to be

A state estimator is designed to realize robust H infinity finite time remote safe state estimation; if no feasible solution exists, go to step S46;

s46, at present

Adding on the basis of the value

Obtaining new parameters

If the new parameter is

Greater than or equal to 1, then no parameter (α) is found for the current initialization₁,α₂,α₃G, N), then step S47 is performed; otherwise, return to step S44;

s47, adding delta m on the basis of the current m value to obtain a new parameter m, and if the new parameter m is smaller than 1, re-initializing the parameter

Making it identical to that initialized in step S42

Equal in value, and then return to step S44; otherwise, no feasible solution is found for all acceptable parameters, and exit is performed.

Has the advantages that: the invention has the following beneficial effects:

the invention improves the time delay tolerance of the state estimator, effectively reduces the damage of time delay to the state estimation performance, enhances the robustness of the state estimation process to the uncertain model and the unknown external interference and realizes the timeliness and the reliability of the state estimation in the remote data transmission mode with network attack by combining a finite time state estimation method of an energy function and an auxiliary equation based on weighted time delay segmentation.

Drawings

FIG. 1 is a general flow diagram of the method of the present invention;

FIG. 2 is a system block diagram of the method of the present invention;

FIG. 3 is a flowchart of the method for solving the state estimator algorithm in step S4 according to the present invention;

fig. 4 shows the expanded state γ under the effect of different bounded design parameters μ in the example of implementation_kUpper bound of constraint c₃(ii) a change in (c);

FIG. 5 is a trace of the evolution of the H ∞ performance metric J within a finite time interval [0,6] under the action of the optimally bounded design parameter μ in the example of implementation;

FIG. 6 is c₃Fixed at 400, the optimum interference suppression level δ_minAnd a bounded design parameter;

FIG. 7 shows the optimal interference suppression level δ under two different state estimation algorithms (weighted delay splitting and unweighted delay splitting)_minA comparative graph of (a).

Detailed Description

The present invention will be further described with reference to the accompanying drawings.

The invention discloses a finite time remote safety state estimation method of a time delay uncertain system, which aims to solve the problems of finite time state estimation and robust safety control of a time delay uncertain system and a model uncertain system in the background of remote data transmission, and comprises the following steps as shown in figures 1 and 2:

the method comprises the following steps: establishing a controlled system state space model with time delay, nonlinear dynamics, model uncertainty and unknown external disturbance, wherein the controlled system state space model with time delay, nonlinear dynamics, model uncertainty and unknown external disturbance defined in a finite time interval [0, N ] has the following form:

wherein N +1 is the length of a given time interval, i.e. the number of times when counted from time 0; tau is_kRepresenting the time delay, tau, of the system being controlled_k∈[τ_m,τ_M]Is the variation interval of time delay, and is the time delay interval [ tau_m,τ_M]Dividing to obtain q subintervals with the lengths of delta tau; x is the number of_k∈RⁿRepresents the state of the system at time k, x_k+1∈RⁿRepresenting the state of the system at time k +1,

is a known system initial state; w is a_k∈R^sIs a set l₂Energy-limited external perturbation over [0, ∞) ], s ∈ N₀Is the dimension of the external disturbance; f is belonged to C (R)^F；R^F) Is a nonlinear dynamic function and has a zero initial state F (0) 0, F ∈ N₀The number of subfunctions contained in the nonlinear dynamic function f; y is_k∈R^LRepresents the measurement output of the system, L ∈ N₀Is the dimension of the measurement output of the system; z is a radical of formula_k∈R^gRepresenting the target signal to be estimated, g ∈ N₀Is the dimension of the target signal; a is an element of R^n×n、A_d∈R^n×n、B_f∈R^n×F、B_w∈R^n×s、C∈R^L×n、D∈R^L×sAnd C_z∈R^g×nAre all known matrices with suitable dimensions; rⁿIs an n-dimensional Euclidean space, R^n×mIs the set of all n x m real matrices.

The model is not determined to have time-varying characteristics and satisfies the following relationship:

ΔA＝N_zM_kN_y (2)

wherein N is_z∈R^n×pAnd N_y∈R^q×nAre all known matrices, M_k∈R^p×qIs a time-varying real-valued matrix and satisfies the following relationship:

wherein,

is a known positive scalar quantity.

The nonlinear dynamical function f in the state space model used has the following 2-norm bounded characteristics:

where H is a known matrix.

Step two: designing a state estimator based on a state space model; establishing a data exchange and calculation center (hereinafter referred to as a calculation center) to realize the unified management and conversion of different types of data and calculate and provide related data as required; constructing a remote communication model based on a transmission network, formulating a communication protocol, and then establishing a communication link between a state estimator system and a computing center, and between a controlled system and the computing center, wherein the state estimator system comprises a state estimator; and the state estimator system requests the computing center to send estimation innovation data so as to carry out a state estimation task.

Designing a state estimator system model based on a state space model as follows:

where K is the gain of the state estimator in the state estimator system; sigma is an external input signal for a state estimator systemInformation;

representing the state estimate of the system at time k,

representing the state estimate of the system at time k +1,

the representation system is at k-tau_kEstimating the state of the moment;

representing an estimate of the target signal at time k.

Establishing a data exchange and calculation center (hereinafter referred to as a calculation center) to realize the unified management and conversion of different types of data and calculate and provide related data as required, wherein the specific method comprises the following steps:

wherein,

and

are two types of input data for the computing center,

is the output data of the calculation center, and C is the conversion parameter of different types of data, namely the matrix C in formula (1).

The method comprises the following steps of constructing a remote communication model based on a transmission network, formulating a communication protocol, and then establishing communication links between a state estimator system and a computing center and between a controlled system and the computing center, wherein the specific process is as follows:

the state estimator system requests the computing center to send estimated 'innovation' data so as to carry out a state estimation task, and specifically, the computing center generates innovation theta after receiving a request instruction sent by the state estimator system_kThe following were used:

innovation theta_kDuring transmission from the computing center to the state estimator system, a denial of service attack or an error data injection attack is encountered, and distortion occurs. New information after attack

Has the following form:

wherein,

reflects the distortion characteristic of the innovation under the action of network attack, chi_b,k(b ═ 1,2, …, L) are random variables which are independent of one another and obey a bernoulli distribution, and which are defined in the interval [0,1 [ ]]Is characterized by a discrete-time probability distribution of (c), and satisfies

(a and b being the same can be simplified to

Or

) E { a } represents the mathematical expectation of a, and Cov { a, b } represents the covariance of a and b, definitions

State estimator system for attack-inflicted innovation

As the data actually requested, and running a dynamic estimation process, namely:

substituting equation (10) into the state estimator system of equation (5) above yields:

step three: constructing an expansion vector based on the real state and the estimated state, and establishing an expansion state estimation model of an expansion state estimation system through the controlled system state space model and the state estimator system model obtained in the first step and the second step; aiming at the extended state estimation model, the existence condition of the finite time remote safety state estimator is given by designing an energy function and applying an auxiliary equation at the same time.

Taking the spread vector as

And establishing an extended state estimation model of the following extended state estimation system:

wherein,

if the finite-time remote security state estimation under model uncertainty and network attack is to be realized, the extended state estimation system needs to be ensured to be robust and bounded within finite time. Robust time-bounded requirements satisfy two conditions: first, in a given time interval [0, N]Inner, expansion vector gamma_kExhibits the rule shown in formula (13):

wherein alpha is₁，α₂，α₃G and N are given parameters and satisfy 0 ≦ α₁≤α₃，α₂≥0，G>0，N∈N₀；

Second, the estimation error of the target signal

And an external disturbance w_kThe following relationship is satisfied under zero initial conditions:

then the extended state estimation system is said to be (α)₁,α₂,α₃G, N) robust H ∞ finite time bounded and having a metric value δ>Interference suppression level of 0.

To ensure the above robust H ∞ finite time-bounded performance, the lyapunov functional is constructed as follows:

wherein,

wherein, V_kLyapunov functional, P and Q, for a time-k extended state estimation system_i(i ═ 1,2,3,4) is a lyapunov matrix; m is a weighting coefficient of the time delay segmentation, is an arbitrary number between 0 and 1, is given in advance and can be adjusted according to the effect of the time delay segmentation.

At the same time, to verify limited-time bounded performance, a bounded decision-assist equation of the form:

wherein, V_k+1Lyapunov functional, delta, of an extended state estimation system for the k +1 time instant>0 denotes the interference suppression level, μ>1 denotes a time-bounded design parameter.

Based on the aforementioned Lyapunov functional and bounded decision auxiliary equation, the existence condition of the robust H ∞ finite time-bounded performance of the extended state estimation system can be given as shown in equations (17) to (20):

G<P<σ₀G (18)

wherein,

Ω₁₂＝Ω₁₄＝Ω₁₅＝Ω₂₁＝Ω₂₃＝Ω₂₄＝Ω₂₅＝Ω₂₆＝Ω₂₇＝Ω₃₁＝Ω₃₂＝Ω₃₄＝Ω₃₅＝0，

Ω₄₁＝Ω₄₂＝Ω₄₃＝Ω₄₅＝Ω₄₆＝Ω₄₇＝Ω₅₁＝Ω₅₂＝Ω₅₃＝Ω₅₄＝Ω₅₅＝Ω₅₆＝Ω₅₇＝0，

Ω₆₁＝Ω₆₂＝Ω₆₃＝Ω₆₄＝Ω₆₅＝Ω₆₇＝Ω₇₁＝Ω₇₂＝Ω₇₃＝Ω₇₄＝Ω₇₅＝Ω₇₆＝0，

Ψ₃＝[0_2n×8n [I_2n,0_q×2n] 0_2n×4n]，

Ψ₄＝[0_2n×8n [0_q×2n,I_2n] 0_2n×4n]，

ε＝[0 I_n]，

wherein the positive scalar σ_i(i ═ 0,1,2,3,4), symmetric positive definite matrices P and Q_i(i ═ 1,2,3,4) and the diagonal positive definite matrix Λ are both undetermined parameters (or matrices); for time delay interval [ tau ]_m,τ_M]Dividing to obtain q subintervals with the lengths of delta tau; m is a weighting coefficient of time delay segmentation; n is the dimension of the system state; mu.s>1 is a finite time bounded design parameter which is preset and adjustable; the symbol denotes a symmetric element which is,

represents the kronecker product; I.C. A_τIs a τ -dimensional identity matrix; h is taken from equation (4) and is a known matrix.

Step four: designing a solving algorithm of the state estimator and calculating the gain of the state estimator according to the existence condition obtained in the step three; and generating a remote safety state estimation strategy to realize the limited-time remote safety state estimation of the delay uncertain system.

As shown in fig. 3, the method comprises the following steps:

step four, firstly: given the system parameters: A. a. the_d、B_f、B_w、C、D、C_z、M_k、

And H; a nonlinear dynamic function f; lower bound of delay τ_mAnd upper bound τ_M(ii) a Increment Δ m ∈ (0,1) and

initial state of a controlled system

Step four and step two: for time delay interval [ tau ]_m,τ_M]And (4) dividing to obtain q subintervals with the lengths of delta tau.

Step four and step three: initialization parameter alpha₁，α₂，α₃G, N; initializing a weighting coefficient m E (0,1) of time delay segmentation; initialization parameters

Step four: setting a time-bounded design parameter

Step four and five: solving the parameters δ, κ, σ while satisfying the linear matrix inequality group constraints shown in the following equations (21) to (25)_i(i＝0,1,2,3,4)、P、Q_i(i ═ 1,2,3,4), Λ and S.

G<P<σ₀G (23)

0<Q_i<σ_iG(i＝1,2,3,4) (24)

Wherein,

Φ_2,1＝Φ_2,3＝Φ_2,4＝Φ_2,5＝Φ_3,1＝Φ_3,2＝Φ_3,4＝Φ_3,5＝0，

Φ_4,1＝Φ_4,2＝Φ_4,3＝Φ_4,5＝Φ_5,1＝Φ_5,2＝Φ_5,3＝Φ_5,4＝0，

wherein, S ═ P₂K；col{a_b}_{b＝1,2,…,c}Is c column vectors a_bComposed matrix, diag_a{ b } denotes a diagonal matrix containing a diagonal elements b.

Equations (23) to (25) are equivalent to equations (18) to (20). The formula (22) is an 'amplification' of the formula (17), namely the formula (22) can be obtained by applying a scaling theorem and a Schur supplementary theorem on the basis of the formula (17), wherein the application of the Schur supplementary theorem does not influence the equivalence, but the original equivalence relation is changed into an inclusion relation by using the scaling theorem, namely the formula (17) is contained in the formula (22), so that the realization of the formula (22) can ensure the realization of the formula (17), and the designed state estimator can meet the robust H-infinity finite time bounded performance; k is a new parameter introduced after applying scaling theorem, and is used as a variable and needs to be solved.

Wherein, Schur supplements the theory: for a symmetric positive definite matrix S

The following items are equivalent:

(1)S<0

(2)S₁₁<0，

(3)S₂₂<0，

scaling reason: given a matrix U with suitable dimensions U ═ U^TH, V and W, then U + HWV + V^TW^TH^T<0 is true if and only if there is a scalar ε>0, such that the following linear matrix inequality holds:

if there is a feasible solution to equations (21) through (25), the gain of the state estimator is calculated as

A state estimator is designed to realize robust H infinity finite time remote safe state estimation; if no feasible solution exists, step four and six are executed.

Step four and six: at the present time

Adding on the basis of the value

Will be provided with

As new parameters

If the new parameter is

Greater than or equal to1, i.e., the time-bounded design parameter μ is less than or equal to 1, then no information is found for the current initialization (α)₁,α₂,α₃G, N), and then executing step IV; otherwise, returning to the fourth step.

Step four and seven: adding delta m on the basis of the current m value, taking m + delta m as a new parameter m, if the new parameter m<1, then re-initializing the parameters

Making it and initialised in step four or two

The values are equal, and then the fourth step is returned; otherwise, a feasible solution is not found for all acceptable parameters, and the process exits.

The algorithm provided by the invention is specific to a group of specific parameters and initial conditions, if state estimation suitable for the current parameter set and the initial conditions cannot be found, feasible solutions can still be found by changing the parameters and the initial conditions, and therefore, limited-time remote safety state estimation is realized; if all acceptable parameters and initial conditions are tried and there is still no solution, then an acceptable state estimate is not achieved.

In order to verify the effects of the present invention, the following examples are given.

Consider the following system parameters:

D＝0,

τ_m＝2，τ_M＝8，m＝0.15，N_z＝10^-2×[30 10]，N_y＝10^-2×[20 10]^T，H＝I₂，α₁＝1,α₂＝0.5,G＝I,N＝6,δ＝1.0，

the effect of the finite time remote security state estimator obtained based on the algorithm provided by the invention is as follows:

figure 4 shows the expansion vector y under the influence of different finite time bounded design parameters mu_kIs restricted upper bound of a₃(ii) a change in (c); FIG. 5 shows the H ∞ performance metric J over a finite time interval [0,6] under the influence of the optimal finite-time-bounded design parameter μ]An inner evolution track; FIG. 6 shows a₃Fixed at 400, the optimum interference suppression level δ_minAnd a finite time bounded design parameter mu; FIG. 7 shows the optimal interference suppression level δ for two different state estimation algorithms (weighted delay splitting and unweighted delay splitting, the same below)_minA comparative graph of (a).

Fig. 4 shows that the state estimator designed based on the invention realizes the state estimation of the controlled system in a limited time, and achieves stronger timeliness. Meanwhile, the trajectory of fig. 5 shows that the dynamic response of the estimated output error already has H ∞ performance, i.e. the designed state estimator reaches a preset level of interference suppression capability. As can be seen from fig. 7, under the same conditions, compared with the finite time state estimation algorithm based on the unweighted delay partition, the finite time state estimation algorithm based on the weighted delay partition has better interference suppression capability, and enhances the robustness of the estimation system.

Table 1 shows the comparison of the maximum allowable delay upper bound for two different state estimation algorithms; table 2 shows the comparison of the feasible ranges of the bounded design parameters obtained based on two different state estimation algorithms under the condition of consistent time delay intervals.

TABLE 1

TABLE 2

The comparison results in table 1 show that, under the condition of the same delay lower bound information, the finite time state estimator based on weighted delay splitting according to the present invention has stronger capacity of accommodating delay, and thus, when the delay is larger (in this case, d is the case)_MNot less than 6) can still well complete the state estimation task, and the common finite time state estimator can not work normally; the table 2 is obtained under the condition that the time delay intervals are consistent, and the obtained comparative data show that the finite time state estimation method based on the weighted time delay segmentation has a larger feasible range. This verifies the effectiveness and superiority of the method of the invention from another point of view.

The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims

1. A limited-time remote safety state estimation method of a time delay uncertain system is characterized by comprising the following steps:

s3, constructing an expansion vector;

giving system parameters; initializing parameters;

if the modified parameters meet the requirements, re-solving; if the modified parameters do not meet the requirements, acceptable state estimation cannot be achieved;

specifically, in step S1, the state space model of the controlled system established over the finite time interval [0, N ] is as follows:

wherein, tau_kDenotes the time delay of the controlled system, [ tau ]_m，τ_M]Is a time delay interval; x is the number of_k∈RⁿRepresents the state of the system at time k, x_k+1∈RⁿRepresenting the state of the system at time k +1,

representation of the system at k-tau_kState of time, N ∈ N₀Is the dimension of the system state;

is a known systemAn initial state; w is a_k∈R^sIs a set l₂Energy-limited external perturbation over [0, ∞) ], s ∈ N₀Is the dimension of the external disturbance; f is belonged to C (R)^F；R^F) Is a non-linear dynamic function and has a zero initial state F (0) of 0, F ∈ N₀The number of subfunctions contained in the nonlinear dynamic function f; y is_k∈R^LRepresents the measurement output of the system, L ∈ N₀Is the dimension of the measurement output of the system; z is a radical of_k∈R^gRepresenting the target signal to be estimated, g ∈ N₀Is the dimension of the target signal; a is an element of Rⁿ ^×n、A_d∈R^n×n、B_f∈R^n×F、B_w∈R^n×s、C∈R^L×n、D∈R^L×sAnd C_z∈R^g×nAre all known matrices; Δ a ═ N_zM_kN_yIn which N is_zAnd N_yAre all known matrices, M_kIs a time-varying real-valued matrix and satisfies

Wherein H is a known matrix;

step S2 includes the steps of:

s21, establishing a state estimator system model as follows:

representing the state estimate of the system at time k,

representing the state estimate of the system at time k +1,

the representation system is at k-tau_kEstimating the state of the moment;

representing an estimate of the target signal at time k;

the calculation center is established as follows:

wherein,

and

are two types of input data for the computing center,

The following were used:

wherein,

χ_b，kare random variables that are independent of one another and obey a bernoulli distribution, where b is 1,2]And satisfy mathematical expectations

Covariance

When a and b are the same, it can be simplified to

Or

S24, the state estimator system uses the new information

As external input information, a state estimation task is performed, i.e.

Step S3 includes the following steps:

s31, constructing an expansion vector of

wherein,

s33, obtaining the parameter (alpha) by the extended state estimation system by designing an energy function, namely the Lyapunov functional and combining a bounded decision auxiliary equation₁，α₂，α₃G, N) the condition of robust H ∞ finite time-bounded performance, i.e. the existence condition of the finite time remote safe state estimator;

wherein the designed Lyapunov functional is as follows:

wherein,

wherein, V_kExpanding the Lyapunov functional of the state estimation system for the time k; p and Q_i(i ═ 1,2,3,4) is a lyapunov matrix;

the bounded decision-assist equation is designed as follows:

wherein, V_k+1Expanding the Lyapunov functional of the state estimation system for the time k + 1; δ > 0 indicates a level of interference suppression; μ > 1 represents a finite time bounded design parameter;

is the estimated error of the target signal.

2. The finite-time remote security state estimator of a delay uncertainty system as claimed in claim 1The method is characterized in that in step S33, the parameter (alpha) is related to₁，α₂，α₃G, N) the robust H ∞ finite time-bounded satisfies the following condition:

wherein, 0 is less than or equal to alpha₁≤α₃，α₂≥0，G＞0，N∈N₀；

Is the estimated error of the target signal.

3. The method for estimating the finite-time remote security state of a delay uncertainty system as claimed in claim 2, wherein in step S4, the linear inequalities obtained from the existence condition are as follows:

G＜P＜σ₀G

0＜Q_i＜σ_iG(i＝1，2，3，4)

wherein phi is phi^T＝[Φ_a，b]_{a，b＝1，2，3，4，5}，

Φ_2，1＝Φ_2，3＝Φ_2，4＝Φ_2，5＝Φ_3，1＝Φ_3，2＝Φ_3，4＝Φ_3，5＝0，

Φ_4，1＝Φ_4，2＝Φ_4，3＝Φ_4，5＝Φ_5，1＝Φ_5，2＝Φ_5，3＝Φ_5，4＝0，

Ψ₃＝[0_2n×8n [I_2n，0_q×2n] 0_2n×4n]，

Ψ₄＝[0_2n×8n [0_q×2n，I_2n] 0_2n×4n]，

ε＝[0 I_n]，

Wherein σ_iIs a positive scalar, i is 0,1,2,3, 4; p and Q_iIs a symmetric positive definite matrix, i is 1,2,3, 4; Λ is a diagonal positive definite matrix; for time delay interval [ tau ]_m，τ_M]Dividing to obtain q subintervals with the lengths of delta tau; m is a weighting coefficient of time delay segmentation; the symbol denotes a symmetric element which is,

in the expression of Crohn2, product restriction;

col{a_b}_{b＝1，2，...，c}is c column vectors a_bA matrix of compositions; diag_a{ b } denotes a diagonal matrix containing a diagonal elements b.

4. The method for estimating the limited-time remote security state of the uncertainty delay system of claim 3, wherein the step S4 comprises the following steps:

And H; initial state of a controlled system

s42, time delay interval [ tau ]_m，τ_M]Dividing to obtain q subintervals with the lengths of delta tau;

s43, initializing parameters, including: robust H-infinity time-bounded parameter alpha₁、α₂、α₃G and N; the weighting coefficient m of the time delay segmentation belongs to (0, 1); parameter(s)

S44, setting the design parameter with limited time

S45, fullUnder the condition of linear matrix inequality group constraint, solving parameters delta and scaling theorem parameters kappa and sigma_i、P、Q_iΛ and S:

s46, at present

Adding on the basis of the value

Obtaining new parameters

If the new parameter is

Greater than or equal to 1, then no parameter (α) is found for the current initialization₁，α₂，α₃G, N), then step S47 is performed; otherwise, return to step S44;

Making it identical to that initialized in step S42