A State Feedback Control Method for a Distributed Radar System with Time-Varying Delay

Abstract

This invention discloses a state feedback control method for a distributed radar system with time-varying delay. The method includes: constructing a distributed radar system model with time-varying delay; constructing a state feedback control law based on the distributed radar system model and determining system stability conditions; calculating the state feedback control law based on the stability conditions; designing a controller using the state feedback control law; and using the controller to perform feedback control on the state of the distributed radar system with time-varying delay. The system state feedback control method provided by this invention avoids the masking or loss of some important characteristics of the distributed radar system and solves the time delay problem.

Description

Technical Field

[0001] This invention relates to the field of distributed radar control, and more specifically to a state feedback control method for a distributed radar system with time-varying delay. Background Technology

[0002] In a distributed radar system, each local radar station first processes the raw echo, sharing the computational load with the fusion center to acquire target information with a smaller data volume. The target information is then transmitted to the fusion center via wireless communication. The fusion center performs fusion detection. Due to the use of wireless communication, the geographical distance between local radar stations and the fusion center can be set to a considerable distance, and mobile platforms can be networked, improving wartime survivability. Distributed radar has become the development trend of networked radar systems.

[0003] A distributed radar system consists of a joint processing and control center and several transmitting and receiving stations connected by a communication network. The communication network is the central nervous system of the distributed radar. The transmission of radar signals and control information depend entirely on the support of the communication network. The quality of network communication directly affects the performance of the entire system. To study the stability control of broadband communication networks in distributed radar systems, existing methods approximate the space-based distributed communication network control system as a decoupled lumped parameter model. However, approximating the distributed radar system as a weakly correlated lumped parameter model can obscure or cause the loss of some important characteristics of the distributed radar system. Summary of the Invention

[0004] In view of the above-mentioned shortcomings in the prior art, the present invention provides a state feedback control method for a distributed radar system with time-varying delay, which avoids the masking or loss of some important characteristics of the distributed radar system and solves the time delay problem.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0006] A state feedback control method for a distributed radar system with time-varying delay includes the following steps:

[0007] S1. Construct a distributed radar system model with time-varying delay;

[0008] S2. Based on the distributed radar system model with time-varying delay in step S1, construct the state feedback control law and determine the system stability conditions.

[0009] S3. Calculate the state feedback control law in step S2 based on the stability condition in step S2.

[0010] S4. Design a controller using the state feedback control law in step S3, and use the controller to perform feedback control on the state of the distributed radar system with time-varying delay.

[0011] Further, in step S1, the distributed radar system with time-varying delay is modeled as a 2D linear discrete system with time-varying delay, expressed as:

[0012]

[0013] Where: x h (k+1,l) represents the first state component of the l-th radar system at discrete time k+1, x v (k, l+1) represents the second state component of the (l+1)th radar system at discrete time k, A is the known first real coefficient matrix, and x h (k,l) represents the first state component of the l-th radar system at discrete time k, x v (k,l) represents the second state component of the l-th radar system at discrete time k, A d Given the second real coefficient matrix, x h (kd(k),l) represents the first state component of the l-th radar system at discrete time kd(k), d(k) represents the first time delay at discrete time k, and x v (k,lh(k)) represents the second state component of the lh(k)-th radar system at discrete time k, h(k) represents the second time delay at discrete time k, B is the known third real coefficient matrix, and u(k,l) is the input vector of the l-th radar system at discrete time k.

[0014] Furthermore, step S2 includes the following sub-steps:

[0015] S21. Based on the distributed radar system model with time-varying delay in step S1, construct the state feedback control law;

[0016] S22. Substitute the state feedback control law in step S21 into the distributed radar system model with time-varying delay in step S1 to obtain a distributed radar system model with time-varying delay including the state feedback control law.

[0017] S23. Based on the distributed radar system model with time-varying delay that includes the state feedback control law in step S22, determine the system stability conditions.

[0018] Furthermore, in step S21, a state feedback control law is constructed, expressed as:

[0019] u(k,l)=Kx(k,l)

[0020] Where u(k,l) is the input vector of the l-th radar system at discrete time k, K is the designed control gain, and x(k,l) is the state vector of the l-th radar system at discrete time k.

[0021] Furthermore, in step S22, a distributed radar system model with time-varying delay, including a state feedback control law, is obtained, represented as:

[0022]

[0023] Where: x h (k+1,l) represents the first state component of the l-th radar system at discrete time k+1, x v (k, l+1) represents the second state component of the (l+1)th radar system at discrete time k, A is the known first real coefficient matrix, B is the known third real coefficient matrix, K is the designed control gain, and x h (k,l) represents the first state component of the l-th radar system at discrete time k, x v (k,l) represents the second state component of the l-th radar system at discrete time k, A d Given the second real coefficient matrix, x h (kd(k),l) represents the first state component of the l-th radar system at discrete time kd(k), d(k) represents the first time delay at discrete time k, and x v (k,lh(k)) represents the second state component of the lh(k)-th radar system at discrete time k, and h(k) represents the second time delay at discrete time k.

[0024] Furthermore, in step S23, the system stability condition is determined, expressed as:

[0025]

[0026] in: T is the transpose symbol. P1 is the first diagonal element of the first positive definite symmetric matrix, and P2 is the second diagonal element of the first positive definite symmetric matrix.

[0027] Furthermore, step S3 includes the following sub-steps:

[0028] S31. Based on the stability condition in step S2, calculate the second diagonal elements of the first positive definite symmetric matrix and the second positive definite symmetric matrix using linear matrix inequalities.

[0029] S32. Calculate the design control gain based on the second diagonal elements of the first positive definite symmetric matrix and the second positive definite symmetric matrix in step S31.

[0030] S33. Determine the state feedback control law based on the control gain designed in step S32.

[0031] Further, in step S31, the second diagonal elements of the first positive definite symmetric matrix and the second positive definite symmetric matrix are calculated using linear matrix inequalities, and are expressed as:

[0032]

[0033] Where: P1 is the first diagonal element of the first positive definite symmetric matrix, P2 is the second diagonal element of the first positive definite symmetric matrix, A is the known first real coefficient matrix, B is the known third real coefficient matrix, G is the second positive definite symmetric matrix, and A d Let be the known second real coefficient matrix.

[0034] Further, in step S32, the control gain of the design is calculated, expressed as:

[0035]

[0036] Where: K is the control gain of the design.

[0037] The beneficial effects of this invention are as follows:

[0038] (1) This invention models a distributed radar system with time-varying delay as a 2D linear discrete system with time-varying delay, thereby avoiding the obscuring or loss of some important characteristics of the distributed radar system and thus enhancing the accuracy of the system model.

[0039] (2) This invention obtains the stability condition of the mean square asymptotic stability of the two-dimensional system through the linear matrix inequality, and calculates the state feedback control law based on the stability condition, thus solving the influence of time-varying delay on system stability in a simple way. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of a state feedback control method for a distributed radar system with time-varying delay. Detailed Implementation

[0041] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0042] like Figure 1As shown, a state feedback control method for a distributed radar system with time-varying delay includes steps S1-S4:

[0043] S1. Construct a distributed radar system model with time-varying delay.

[0044] In an optional embodiment of the present invention, a distributed radar system model with time-varying delay is constructed. Considering that approximating the distributed radar system as a lumped parameter model with weak correlation would mask or lose some important characteristics of the distributed radar system, the present invention transforms the state feedback control design into analyzing the stability of a 2D linear discrete system with time-varying delay.

[0045] This invention models a distributed radar system with time-varying delay as a 2D linear discrete system with time-varying delay, expressed as:

[0046]

[0047] Where: x h (k+1,l) represents the first state component of the l-th radar system at discrete time k+1, x v (k, l+1) represents the second state component of the (l+1)th radar system at discrete time k, A is the known first real coefficient matrix, and x h (k,l) represents the first state component of the l-th radar system at discrete time k, x v (k,l) represents the second state component of the l-th radar system at discrete time k, A d Given the second real coefficient matrix, x h (kd(k),l) represents the first state component of the l-th radar system at discrete time kd(k), where d(k) is the first time delay at discrete time k, and is a time-independent random function. v (k,lh(k)) is the second state component of the lh(k)th radar system at discrete time k, h(k) is the second time delay at discrete time k, which is a time-independent random function, B is the known third real coefficient matrix, and u(k,l) is the input vector of the lth radar system at discrete time k.

[0048] Specifically, the condition for satisfying the first time delay is expressed as follows:

[0049] d m ≤d(k)≤d M

[0050] Where: d m d is the lower bound of the first time delay. M This is the upper bound of the first time delay.

[0051] The condition for satisfying the second time delay is expressed as follows:

[0052] h m ≤h(k)≤h M

[0053] Where: h m h is the lower bound of the second time delay. M This is the upper bound of the second time delay.

[0054] S2. Based on the distributed radar system model with time-varying delay in step S1, construct the state feedback control law and determine the system stability conditions.

[0055] In an optional embodiment of the present invention, the present invention constructs a corresponding state feedback control law based on a distributed radar system model with time-varying delay, and determines the stability conditions that need to be satisfied to make the distributed radar system with time-varying delay stable.

[0056] Step S2 includes the following sub-steps:

[0057] S21. Based on the distributed radar system model with time-varying delay in step S1, construct the state feedback control law.

[0058] Specifically, the present invention constructs a state feedback control law, expressed as follows:

[0059] u(k,l)=Kx(k,l)

[0060] Where u(k,l) is the input vector of the l-th radar system at discrete time k, K is the designed control gain, and x(k,l) is the state vector of the l-th radar system at discrete time k.

[0061] S22. Substitute the state feedback control law from step S21 into the distributed radar system model with time-varying delay from step S1 to obtain a distributed radar system model with time-varying delay including the state feedback control law.

[0062] Specifically, the present invention obtains a distributed radar system model with time-varying delay, including a state feedback control law, as follows:

[0063]

[0064] Where: x h (k+1,l) represents the first state component of the l-th radar system at discrete time k+1, x v (k, l+1) represents the second state component of the (l+1)th radar system at discrete time k, A is the known first real coefficient matrix, B is the known third real coefficient matrix, K is the designed control gain, and x h(k,l) represents the first state component of the l-th radar system at discrete time k, x v (k,l) represents the second state component of the l-th radar system at discrete time k, A d Given the second real coefficient matrix, x h (kd(k),l) represents the first state component of the l-th radar system at discrete time kd(k), d(k) represents the first time delay at discrete time k, and x v (k,lh(k)) represents the second state component of the lh(k)-th radar system at discrete time k, and h(k) represents the second time delay at discrete time k.

[0065] S23. Based on the distributed radar system model with time-varying delay that includes the state feedback control law in step S22, determine the system stability conditions.

[0066] This invention determines the initial boundary conditions based on a distributed radar system model with time-varying delay, including a state feedback control law, as follows:

[0067] x h (k,l)=ρ kl ,

[0068]

[0069] -d M ≤k<0,

[0070] x v (k,l)=σ kl ,

[0071]

[0072] -h M ≤k<0

[0073] Where: ρ kl Let r1 be the first known boundary constant vector, r1 be the first positive integer, r1 < ∞, and σ kl Let r be the known second boundary constant vector, and r2 be the second positive integer, where r2 < ∞.

[0074] Based on the initial boundary conditions, this invention derives a first definition of a distributed radar system model with time-varying delay, including a state feedback control law, as follows:

[0075]

[0076] Where: E is a distributed radar system model with time-varying delay, including a state feedback control law.

[0077] The present invention determines the system stability condition based on the first definition above, which is expressed as:

[0078]

[0079] in: T is the transpose symbol. P1 is the first diagonal element of the first positive definite symmetric matrix, and P2 is the second diagonal element of the first positive definite symmetric matrix.

[0080] S3. Calculate the state feedback control law in step S2 based on the stability condition in step S2.

[0081] In an optional embodiment of the present invention, the present invention calculates the second diagonal elements and the second positive definite symmetric matrix of the first positive definite symmetric matrix related to the state feedback control law based on the stability condition in step S2, and then determines the specific state feedback control law.

[0082] Step S3 includes the following sub-steps:

[0083] S31. Based on the stability condition in step S2, calculate the second diagonal elements of the first positive definite symmetric matrix and the second positive definite symmetric matrix using linear matrix inequalities.

[0084] Specifically, this invention calculates the second diagonal elements of the first positive definite symmetric matrix and the second positive definite symmetric matrix using linear matrix inequalities, expressed as:

[0085]

[0086] Where: P1 is the first diagonal element of the first positive definite symmetric matrix, P2 is the second diagonal element of the first positive definite symmetric matrix, A is the known first real coefficient matrix, B is the known third real coefficient matrix, G is the second positive definite symmetric matrix, and A d Let be the known second real coefficient matrix.

[0087] S32. Calculate the control gain of the design based on the second diagonal elements of the first positive definite symmetric matrix and the second positive definite symmetric matrix in step S31.

[0088] Specifically, the control gain calculated in this invention is expressed as:

[0089]

[0090] Where: K is the control gain of the design.

[0091] S33. Determine the state feedback control law based on the control gain designed in step S32.

[0092] Specifically, the state feedback control law constructed in this invention is expressed as:

[0093] u(k,l)=Kx(k,l)

[0094] Where u(k,l) is the input vector of the l-th radar system at discrete time k, K is the designed control gain, and x(k,l) is the state vector of the l-th radar system at discrete time k.

[0095] Therefore, the present invention calculates the control gain designed in step S32, and thus can determine the specific state feedback control law.

[0096] S4. Design a controller using the state feedback control law in step S3, and use the controller to perform feedback control on the state of the distributed radar system with time-varying delay.

[0097] In an optional embodiment of the present invention, the present invention obtains the state feedback control law in step S3, and uses the control gain designed in the state feedback control law to complete the design of the controller, and then uses the controller to perform feedback control on the state of the distributed radar system with time-varying delay.

[0098] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A state feedback control method for a distributed radar system with time-varying delay, characterized in that, Includes the following steps: S1. Construct a distributed radar system model with time-varying delay; S2. Based on the distributed radar system model with time-varying delay in step S1, construct the state feedback control law and determine the system stability conditions. S3. Calculate the state feedback control law in step S2 based on the stability condition in step S2. S4. Design a controller using the state feedback control law in step S3, and use the controller to perform feedback control on the state of the distributed radar system with time-varying delay. In step S1, the distributed radar system with time-varying delay is modeled as a 2D linear discrete system with time-varying delay, expressed as: in: Discrete time Time The first state component of a radar system Discrete time Time The second state component of a radar system Given the first real coefficient matrix, Discrete time Time The first state component of a radar system Discrete time Time The second state component of a radar system Given the second real coefficient matrix, Discrete time Time The first state component of a radar system Discrete time The first time delay, Discrete time Time The second state component of a radar system Discrete time The second time delay, Given the third real coefficient matrix, Discrete time Time The input vector of a radar system.

2. The state feedback control method for a distributed radar system with time-varying delay according to claim 1, characterized in that, Step S2 includes the following sub-steps: S21. Based on the distributed radar system model with time-varying delay in step S1, construct the state feedback control law; S22. Substitute the state feedback control law in step S21 into the distributed radar system model with time-varying delay in step S1 to obtain a distributed radar system model with time-varying delay including the state feedback control law. S23. Based on the distributed radar system model with time-varying delay that includes the state feedback control law in step S22, determine the system stability conditions.

3. The state feedback control method for a distributed radar system with time-varying delay according to claim 2, characterized in that, In step S21, a state feedback control law is constructed, expressed as follows: in: Discrete time Time The input vector of a radar system For the control gain of the design, Discrete time Time The state vector of a radar system.

4. The state feedback control method for a distributed radar system with time-varying delay according to claim 2, characterized in that, In step S22, a distributed radar system model with time-varying delay, including a state feedback control law, is obtained, represented as: in: Discrete time Time The first state component of a radar system Discrete time Time The second state component of a radar system Given the first real coefficient matrix, Given the third real coefficient matrix, For the control gain of the design, Discrete time Time The first state component of a radar system Discrete time Time The second state component of a radar system Given the second real coefficient matrix, Discrete time Time The first state component of a radar system Discrete time The first time delay, Discrete time Time The second state component of a radar system Discrete time The second time delay.

5. The state feedback control method for a distributed radar system with time-varying delay according to claim 2, characterized in that, In step S23, the system stability condition is determined, expressed as: in: , Given the first real coefficient matrix, Given the third real coefficient matrix, Given the second real coefficient matrix, The control gain is denoted by T, where T is the transpose sign. , , These are the first diagonal elements of the first positive definite symmetric matrix. is the second diagonal element of the first positive definite symmetric matrix.

6. The state feedback control method for a distributed radar system with time-varying delay according to claim 2, characterized in that, Step S3 includes the following sub-steps: S31. Based on the stability condition in step S2, calculate the second diagonal elements of the first positive definite symmetric matrix and the second positive definite symmetric matrix using linear matrix inequalities. S32. Calculate the control gain of the design based on the second diagonal elements of the first positive definite symmetric matrix and the second positive definite symmetric matrix in step S31. S33. Determine the state feedback control law based on the control gain designed in step S32.

7. The state feedback control method for a distributed radar system with time-varying delay according to claim 6, characterized in that, In step S31, the second diagonal elements of the first positive definite symmetric matrix and the second positive definite symmetric matrix are calculated using linear matrix inequalities, and are expressed as follows: in: These are the first diagonal elements of the first positive definite symmetric matrix. These are the elements on the second diagonal of the first positive definite symmetric matrix. Given the first real coefficient matrix, Given the third real coefficient matrix, It is the second positive definite symmetric matrix. Let be the known second real coefficient matrix.

8. The state feedback control method for a distributed radar system with time-varying delay according to claim 6, characterized in that, In step S32, the control gain of the design is calculated and expressed as: in: For the control gain of the design, It is the second positive definite symmetric matrix. is the second diagonal element of the first positive definite symmetric matrix.

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