CN108008632B - State estimation method and system of time-lag Markov system based on protocol - Google Patents
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Abstract
The invention discloses a state estimation method of a time-lag Markov system based on a protocol, which comprises the following steps: establishing a dynamic model of a neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag and random interference; under a given protocol, establishing an updating matrix according to the sensor selected to transmit data; establishing a dynamic model of the neural network system under a protocol according to the update matrix and the dynamic model of the neural network system; constructing an estimator according to a dynamic model of the neural network system under the protocol; calculating a state estimation error according to the estimated state vector of the estimator and the state vector of the neural network system under the protocol; obtaining an estimation augmentation system by using the state estimation error; solving a gain matrix of the estimator according to an estimation augmentation system by using a system stability judgment theorem; and substituting the gain matrix into the estimator to complete the estimation of the dynamic model of the neural network system. And a system.
Description
Technical Field
The invention relates to the field of signal processing, in particular to a state estimation method and a state estimation system of a time-lag Markov system based on a protocol.
Background
For decades, the state estimation problem of the artificial neural network has been paid extensive attention because the extraordinary parallel information processing capability, adaptive capability and self-learning capability of the artificial neural network have been widely applied to the fields of brain science, cognitive science, computer science and the like. It is noted that due to the operating environment and other factors, the structure and parameters of the system may change indefinitely, so the markov parameter is a topic that has been favored in recent years. More notably, in the existing research on state estimation of the neural network system, the problem of limited communication is rarely considered, so the problem of limited communication is considered herein in an important way, and a Round-Robin protocol is introduced to schedule the sensor for transmitting the measurement data.
The existing state estimation method can not consider communication limitation, Markov parameters, sensor nonlinearity, modal dependence time lag and random interference at the same time, and further influences the state estimation performance.
Disclosure of Invention
In view of this, the invention provides a state estimation method and system of a time-lag markov system based on a protocol, so as to solve the problem that the existing state estimation method cannot simultaneously consider communication limitation, markov parameters, sensor nonlinearity, mode-dependent time lag and random interference, thereby affecting the state estimation performance.
In a first aspect, the present invention provides a state estimation method for a protocol-based time-lag markov system, including:
establishing a dynamic model of a neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag and random interference;
under a given protocol, establishing an updating matrix according to the sensor selected to transmit data;
establishing a dynamic model of the neural network system under a protocol according to the update matrix and the dynamic model of the neural network system;
constructing an estimator according to a dynamic model of the neural network system under the protocol;
calculating a state estimation error according to the estimated state vector of the estimator and the state vector of the neural network system under the protocol;
obtaining an estimation augmentation system by using the state estimation error;
solving a gain matrix of the estimator according to the estimation augmentation system by using a system stability judgment theorem;
and substituting the gain matrix into the estimator to complete the estimation of the dynamic model of the neural network system.
Preferably, the given protocol is a Round-Robin protocol;
and under the Round-Robin protocol, establishing an update matrix according to the sensor selected to transmit data.
Preferably, the K + 1-step state vector of the dynamic model of the neural network system with markov parameters, sensor non-linearity, modality dependent time lag and stochastic disturbances is established as a linear combination of the K-step state vector, the excitation function with markov parameters, the excitation function with modality dependent time lag and the stochastic disturbances.
Preferably, the K-step measurement output of the dynamic model of the neural network system with markov parameters, sensor non-linearity, modal-dependent time lag and stochastic interference is a linear combination of the K-step state vector and the sensor non-linearity.
Preferably, the excitation function satisfies a fan constraint condition.
Preferably, the K + 1-step protocol state vector of the dynamic model of the neural network system under the protocol is a linear combination of a K-step augmented protocol state vector, a markov parameter excitation function with an extended dimension, a modal-dependent time-lag excitation function with an extended dimension, protocol sensor nonlinearity and extended dimension random interference;
and the K-step protocol measurement output of the dynamic model of the neural network system under the protocol is a linear combination of the K-step augmentation protocol state vector and the nonlinearity of the protocol sensor.
Preferably, the K-1 step protocol measurement output of the dynamic model of the neural network system under the protocol is used as an augmentation matrix of the K step state vector of the dynamic model of the neural network system to form the K step augmentation protocol state vector.
Preferably, the gain matrix of the estimator is obtained by solving a set of convex optimization problems using the system stability judgment theorem.
Preferably, the convex optimization problem is a linear matrix inequality condition when the system reaches exponential final bounding.
In a second aspect, the present invention provides a state estimation system for a protocol-based time-lapse markov system, comprising:
a memory and a processor and a computer program stored on the memory and executable on the processor, the computer program being a method of state estimation for a protocol-based time-lapse markov system as described above, the processor when executing the program implementing the steps of:
establishing a dynamic model of a neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag and random interference;
under a given protocol, establishing an updating matrix according to the sensor selected to transmit data;
establishing a dynamic model of the neural network system under a protocol according to the update matrix and the dynamic model of the neural network system;
constructing an estimator according to a dynamic model of the neural network system under the protocol;
calculating a state estimation error according to the estimated state vector of the estimator and the state vector of the neural network system under the protocol;
obtaining an estimation augmentation system by using the state estimation error;
solving a gain matrix of the estimator according to the estimation augmentation system by using a system stability judgment theorem;
and substituting the gain matrix into the estimator to complete the estimation of the dynamic model of the neural network system.
The invention has at least the following beneficial effects:
the invention provides a state estimation method and a state estimation system of a time-lag Markov system based on a protocol, which simultaneously consider the influence of communication limitation, Markov parameters, sensor nonlinearity, mode dependence time lag and random interference on state estimation performance, and a stability criterion completely utilizes effective information of the time lag. The method solves the problem that the existing state estimation method can not simultaneously consider communication limitation, Markov parameters, sensor nonlinearity, modal dependence time lag and random interference, thereby influencing the state estimation performance.
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The above and other objects, features and advantages of the present invention will become more apparent from the following description of the embodiments of the present invention with reference to the accompanying drawings, in which:
FIG. 1 is a schematic flow chart of a state estimation method for a protocol-based time-lapse Markov system according to an embodiment of the present invention;
figure 2 is a schematic diagram of a state estimation method of a protocol-based time-lapse markov system and an evolution process of a markov chain of the system according to an embodiment of the present invention;
FIG. 3 shows an actual state trajectory x of a method and system for state estimation of a skewed Markov system based on a protocol according to an embodiment of the present invention1(k) And its state estimation trajectory
Comparing the images;
FIG. 4 shows an actual state trajectory x of a method and system for state estimation of a skewed Markov system based on a protocol according to an embodiment of the present invention2(k) And its state estimation trajectory
Comparing the images;
FIG. 5 shows a state x of a method and system for estimating a state of a skewed Markov system based on a protocol according to an embodiment of the present invention1(k) Is estimated error trajectory e1(k)；
FIG. 6 shows a state x of a method and system for estimating a state of a skewed Markov system based on a protocol according to an embodiment of the present invention2(k) Is estimated error trajectory e2(k)。
Detailed Description
The present invention will be described below based on examples, but it should be noted that the present invention is not limited to these examples. In the following detailed description of the present invention, certain specific details are set forth. However, the present invention may be fully understood by those skilled in the art for those parts not described in detail.
Furthermore, those skilled in the art will appreciate that the drawings are provided solely for the purposes of illustrating the invention, features and advantages thereof, and are not necessarily drawn to scale.
Also, unless the context clearly requires otherwise, throughout the description and the claims, the words "comprise", "comprising", and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is, the meaning of "includes but is not limited to".
In the present invention, MTRepresenting the transpose of the matrix M, M-1Representing the inverse of matrix M.
Representing an n-dimensional euclidean space,
representing the set of all real matrices of order n x m.
Representing a set of integers. I and 0 denote an identity matrix and a zero matrix, respectively. Matrix P>0 denotes that P is a real symmetric positive definite matrix,
and
respectively representing the mathematical expectation of the random variable x and the mathematical expectation of the random variable x under the condition of y. | x | | represents the euclidean norm of the vector x. diag { A1,A2,…,AnDenotes that the diagonal block is the matrix A1,A2,…,AnThe symbol indicates the omission of the symmetric term in the symmetric block matrix. If M represents a symmetric matrix, then λmax(M),λmin(M) represents the maximum and minimum eigenvalues of M, respectively. mod (a, b) represents the remainder operation. δ (a) represents a binary function, which has a value of 1 when a is 0 and 0 otherwise. Symbol
Representing a kronecker multiplication operation.
If the dimension of the matrix is not specified explicitly somewhere in the text, it is assumed that the dimension is suitable for algebraic operation of the matrix.
Fig. 1 is a schematic flowchart of a state estimation method of a protocol-based time-lag markov system according to an embodiment of the present invention. As shown in fig. 1, a state estimation method of a protocol-based time-lapse markov system includes: step 101, establishing a dynamic model of a neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag and stochastic interference; 102, under a given protocol, establishing an update matrix according to the sensors selected to transmit data; 103, establishing a dynamic model of the neural network system under a protocol according to the update matrix and the dynamic model of the neural network system; 104, constructing an estimator according to a dynamic model of the neural network system under the protocol; step 105, calculating a state estimation error according to the estimation state vector of the estimator and the state vector of the neural network system under the protocol; step 106, obtaining an estimation augmentation system by using the state estimation error; step 107, solving a gain matrix of the estimator according to the estimation augmentation system by using a system stability judgment theorem; step 108 brings the gain matrix into the estimator to complete the estimation of the dynamic model of the neural network system.
Further, in fig. 1, step 101 builds a dynamic model of the neural network system with markov parameters, sensor non-linearities, modality dependent time lags and stochastic disturbances. Further, in fig. 1, the K + 1-step state vector that builds the dynamic model of the neural network system with markov parameters, sensor non-linearities, modality dependent time lags, and stochastic disturbances is a linear combination of the K-step state vector, the excitation function with markov parameters, the excitation function with modality dependent time lags, and the stochastic disturbances.
Further, in fig. 1, the K-step measurement output of the dynamic model of the neural network system with markov parameters, sensor non-linearity, modal-dependent time-lags, and stochastic interference is built as a linear combination of the K-step state vector and the sensor non-linearity.
Further, in fig. 1, the excitation function satisfies a fan constraint.
Specifically, a dynamic model of a neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag, and stochastic interference is established in the form of a state space:
the initial conditions of the system are as follows:
in the formula,
a state vector representing the system;
representing an excitation function and meeting a fan-shaped constraint condition;
in order to define the diagonal matrix positively,
in order to connect the matrices for the weights,
a matrix of known fitting circumference numbers; tau (r (k)) is modal dependent time lag and satisfies
To be aA measurement output of the system;
the sensor is nonlinear and meets the fan-shaped constraint condition; omega (k) is Gaussian white noise and satisfies the following conditions:
r (k) is a Markov chain, and the transmission probability is theta ═ thetaij]s×sWherein thetaijIs not less than 0 and
for convenience of representation, we will make the following expression r (k) ═ i (i ∈ S), i.e., Z (r (k)) will be expressed as Zi。
102, under a given protocol, establishing an update matrix according to the sensors selected to transmit data;
to update the matrix, ζ (k) e {1,2, …, m } is the sensor selected to transmit data.
Further, in fig. 1, the given protocol is a Round-Robin protocol; and under the Round-Robin protocol, establishing an update matrix according to the sensor selected to transmit data.
Specifically, according to the dynamic model in step 101 and the scheduling principle of the Round-Robin protocol, a dynamic model of the neural network system under the Round-Robin protocol is established, and a spatial model of the dynamic model is as follows:
wherein:
step 104 constructs an estimator from the dynamic model of the neural network system under the protocol.
Further, in fig. 1, the K + 1-step protocol state vector of the dynamic model of the neural network system under the protocol is a linear combination of a K-step augmented protocol state vector, a markov parameter excitation function with an extended dimension, a modality dependent time-lag excitation function with an extended dimension, a protocol sensor nonlinearity, and an extended dimension random disturbance;
and the K-step protocol measurement output of the dynamic model of the neural network system under the protocol is a linear combination of the K-step augmentation protocol state vector and the nonlinearity of the protocol sensor.
Further, in fig. 1, the K-1 step protocol measurement of the dynamic model of the neural network system under the protocol outputs an augmentation matrix as a K step state vector of the dynamic model of the neural network system, and the K step augmentation protocol state vector is formed.
Specifically, the state estimation is performed on the neural network system with Markov parameters, sensor nonlinearity, modality dependent time lag and stochastic disturbance under the protocol in step 103, and the estimator is in the form of:
in the formula,
is composed of
The state estimate at the time instant k is,
is composed of
Is determined by the estimation function of (a),
as a non-linear function
Is determined by the estimation function of (a),
the state estimation gain is to be solved.
Step 105 calculates a state estimation error based on the estimated state vector of the estimator and the state vector of the neural network system under the protocol. Calculating a state estimation error according to step 104 for a state estimation of a nonlinear dynamical model having markov parameters, sensor nonlinearities, modal-dependent time lags, and random disturbances:
where e (k) is an estimation error at time k, and e (k +1) is an estimation error at time k + 1.
in the above formula:
and 107, solving a gain matrix of the estimator according to the estimation augmentation system by using a system stability judgment theorem.
Further, in fig. 1, the gain matrix of the estimator is obtained by solving a set of convex optimization problems using the system stability judgment theorem.
Further, in fig. 1, the convex optimization problem is to obtain the gain matrix of the estimator for the matrix when the system reaches exponential final exponent bounded.
Specifically, using the state estimation augmentation system of step 106, applying the Lyapunov stability theorem and solving a set of convex optimization problems to obtain an estimator gain matrix K:
by the formula:
according to the Lyapunov stability theorem, a matrix when the system reaches the final exponent bounded is obtained
And
by the formula:
a state estimation gain matrix is calculated.
The specific form of the matrix in formulas (6) to (8):
in the formula:
Step 108 brings the gain matrix into the estimator to complete the estimation of the dynamic model of the neural network system. Specifically, the estimator gain matrix K obtained in step 107 is substituted into the state estimation formula in step three to realize state estimation of the neural network system with markov parameters, sensor nonlinearity, modal-dependent time lag and random interference.
Fig. 2 is a schematic diagram of a state estimation method of a time-lag markov system based on a protocol and an evolution process of a markov chain of the system according to an embodiment of the present invention, and it can be seen from the diagram that at different times, the mode of the system is in a jump, and after the jump, parameters of the system change accordingly.
In addition, the present invention provides a state estimation system of a protocol-based time lag markov system, comprising:
a memory and a processor and a computer program stored on the memory and executable on the processor, the computer program being a method of state estimation for a protocol-based time-lapse markov system as described above, the processor when executing the program implementing the steps of: step 101, establishing a dynamic model of a neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag and stochastic interference; 102, under a given protocol, establishing an update matrix according to the sensors selected to transmit data; 103, establishing a dynamic model of the neural network system under a protocol according to the update matrix and the dynamic model of the neural network system; 104, constructing an estimator according to a dynamic model of the neural network system under the protocol; step 105, calculating a state estimation error according to the estimation state vector of the estimator and the state vector of the neural network system under the protocol; step 106, obtaining an estimation augmentation system by using the state estimation error; step 107, solving a gain matrix of the estimator according to the estimation augmentation system by using a system stability judgment theorem; step 108 brings the gain matrix into the estimator to complete the estimation of the dynamic model of the neural network system. Detailed description of the preferred embodimentsreference is made to the description of fig. 1.
For further verification of the state estimation method and system of the time-lag Markov neural network system based on the protocol, the Lyapunov stability theory in step 107 is as follows:
wherein:
in the formula,
for the Lyapunov function at time k,
is the Lyapunov function at time k + 1,
is composed of
The transpose of (a) is performed,
is composed of
The transposing of (1).
The method of the invention is utilized for simulation: (assuming that n is 2, m is 2, i is e {1,2})
The system parameters are set as follows:
the excitation function and sensor nonlinearity are as follows:
state estimator gain solving:
solving equations (6) - (8) to obtain the gain matrix of the state estimator
In the form:
the effect of the state estimator is illustrated in fig. 3-6.
FIG. 3 shows an actual state trajectory x of a method and system for state estimation of a skewed Markov system based on a protocol according to an embodiment of the present invention1(k) And its state estimation trajectory
Compare the figures. FIG. 4 shows an actual state trajectory x of a method and system for state estimation of a skewed Markov system based on a protocol according to an embodiment of the present invention2(k) And its state estimation trajectory
Compare the figures. As shown in FIGS. 3 and 4, the state estimation trajectory of the system
Can track the system status trace x1(k)，x2(k) And eventually all approach the equilibrium point of the system, illustrating that the inventive state estimator design method is effective.
FIG. 5 shows a state x of a method and system for estimating a state of a skewed Markov system based on a protocol according to an embodiment of the present invention1(k) Is estimated error trajectory e1(k) In that respect FIG. 6 shows a state x of a method and system for estimating a state of a skewed Markov system based on a protocol according to an embodiment of the present invention2(k) Is estimated error trajectory e2(k) In that respect As shown in fig. 5 and 6, the estimation error e of the system1(k)，e2(k) Is bounded with an error of [ -2,2 [)]And thus further illustrates the effectiveness and applicability of the proposed state estimation method, which can bring the system to a final bounded state.
As can be seen from fig. 3 to 6, under the communication protocol, the state estimator design method of the invention can effectively estimate the target state for the neural network system with markov parameters, sensor nonlinearity, modality dependent time lag and random disturb needles.
The invention considers the influence of communication limitation, Markov parameter, sensor nonlinearity, modal dependence time lag and random interference on the state estimation performance, constructs the Lyapunov function and completely utilizes effective information of the time lag, compared with the existing state estimation method of a neural network dynamic system, the state estimation method can process the Markov parameter, the sensor nonlinearity, the modal dependence time lag and the random interference simultaneously under a communication protocol, obtains the state estimation method depending on the linear matrix inequality solution, achieves the aim of resisting nonlinear disturbance, and has the advantages of easy solution and realization.
It will be apparent to those skilled in the art that the units or steps of the present invention described above may be implemented by a general purpose computing device, they may be centralized on a single computing device or distributed over a network of multiple computing devices, and alternatively, they may be implemented by program code executable by a computing device, such that they may be stored in a storage device and executed by a computing device, or fabricated separately as individual integrated circuit units, or fabricated as a single integrated circuit unit from multiple units or steps. Thus, the present invention is not limited to any specific combination of hardware and software.
The above-mentioned embodiments are merely embodiments for expressing the invention, and the description is specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for those skilled in the art, various changes, substitutions of equivalents, improvements and the like can be made without departing from the spirit of the invention, and these are all within the scope of the invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (8)
1. A method for estimating a state of a protocol-based time-lapse markov system, comprising:
establishing a dynamic model of a neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag and random interference;
under a given protocol, establishing an updating matrix according to the sensor selected to transmit data;
establishing a dynamic model of the neural network system under a protocol according to the update matrix and the dynamic model of the neural network system;
constructing an estimator according to a dynamic model of the neural network system under the protocol;
calculating a state estimation error according to the estimated state vector of the estimator and the state vector of the neural network system under the protocol;
obtaining an estimation augmentation system by using the state estimation error;
solving a gain matrix of the estimator according to the estimation augmentation system by using a system stability judgment theorem;
obtaining a gain matrix of the estimator by solving a group of convex optimization problems by using a system stability judgment theorem;
the convex optimization problem is a linear matrix inequality condition when the system reaches an exponential final bounded state;
by the formula:
Q＜QI，
Pi,ζ(k)<γI；
according to the Lyapunov stability theorem, a matrix X when the system reaches the final exponent bounded is obtainedi,ζ(k)And
by said formula, calculating a state estimation gain matrix
Wherein,
P1i,ζ(k)>0,P1i,ζ(k+1)>0,Q>0,Xi,ζ(k)the matrix is a suitable number of bits, gamma,
0<κ<1 is a scalar quantity, p1i,ρ2i,ρ3iIs a series of constants, H1,H2,G1,G2Is a known constant matrix; diag {. said } represents a diagonal matrix, ζ (k) ∈ {1,2, …, m } is the sensor selected to transmit data, i is the markov chain,
representing a kronecker multiplication operation, lτIs a quantity dependent on the upper and lower time lag limits;
wherein I represents an identity matrix; a. thei，BiConnecting matrix for weight value, and sigma parameter;
is a parameter matrix of the dynamic model;and substituting the gain matrix into the estimator to complete the estimation of the dynamic model of the neural network system.
2. The method of claim 1, wherein the state estimation method comprises:
the given protocol is a Round-Robin protocol;
and under the Round-Robin protocol, establishing an update matrix according to the sensor selected to transmit data.
3. The method of claim 1, wherein the state estimation method comprises:
and establishing a K +1 step state vector of a dynamic model of the neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag and random disturbance as a linear combination of the K step state vector, an excitation function with Markov parameters and modal-dependent time lag and the random disturbance.
4. The method of claim 1, wherein the state estimation method comprises:
the K-step measurement output of the dynamic model of the neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag and random disturbance is a linear combination of the K-step state vector and the sensor nonlinearity.
5. A method of state estimation for a protocol-based time-lapse markov system according to claim 3, wherein:
the excitation function meets the fan-shaped constraint condition.
6. The method of claim 1, wherein the state estimation method comprises:
the K + 1-step protocol state vector of the dynamic model of the neural network system under the protocol is a linear combination of a K-step augmented protocol state vector, a Markov parameter excitation function with extended dimensionality, a mode dependent time-lag excitation function with extended dimensionality, protocol sensor nonlinearity and extended dimensionality random interference;
and the K-step protocol measurement output of the dynamic model of the neural network system under the protocol is a linear combination of the K-step augmentation protocol state vector and the nonlinearity of the protocol sensor.
7. The method of claim 6, wherein the state estimation method of the protocol-based time-lapse Markov system comprises:
and measuring and outputting a K-1 step protocol of the dynamic model of the neural network system under the protocol as an augmentation matrix of a K step state vector of the dynamic model of the neural network system to form the K step augmentation protocol state vector.
8. A state estimation system for a protocol-based time-lapse markov system, comprising:
memory and processor and a computer program stored on the memory and executable on the processor, the computer program being a method of state estimation for a protocol based time-lapse markov system according to any one of the claims 1 to 7, the processor when executing the computer program performing the steps of:
establishing a dynamic model of a neural network system with Markov parameters, sensor nonlinearity, modal-dependent time lag and random interference;
under a given protocol, establishing an updating matrix according to the sensor selected to transmit data;
establishing a dynamic model of the neural network system under a protocol according to the update matrix and the dynamic model of the neural network system;
constructing an estimator according to a dynamic model of the neural network system under the protocol;
calculating a state estimation error according to the estimated state vector of the estimator and the state vector of the neural network system under the protocol;
obtaining an estimation augmentation system by using the state estimation error;
solving a gain matrix of the estimator according to the estimation augmentation system by using a system stability judgment theorem;
obtaining a gain matrix of the estimator by solving a group of convex optimization problems by using a system stability judgment theorem;
the convex optimization problem is a linear matrix inequality condition when the system reaches an exponential final bounded state;
by the formula:
Q<I,
Pi,ζ(k)<γI；
according to the Lyapunov stability theorem, a matrix X when the system reaches the final exponent bounded is obtainedi,ζ(k)And
by said formula, calculating a state estimation gain matrix
Wherein,
P1i,ζ(k)>0,P1i,ζ(k+1)>0,Q>0,Xi,ζ(k)the matrix is a suitable number of bits, gamma,
0<κ<1 is a scalar quantity, p1i,ρ2i,ρ3iIs a series of constants, H1,H2,G1,G2Is a known constant matrix; diag {. said } represents a diagonal matrix, ζ (k) ∈ {1,2, …, m } is the sensor selected to transmit data, i is the markov chain,
representing a kronecker multiplication operation, lτIs a quantity dependent on the upper and lower time lag limits; wherein I represents an identity matrix; a. thei，BiConnecting matrixes for the weights; sigma is a parameter;
is a parameter matrix of the dynamic model; and substituting the gain matrix into the estimator to complete the estimation of the dynamic model of the neural network system.
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