Joint optimization method for probabilistic scheduling and resource allocation of wireless networked control systems

Abstract

The present application relates to wireless networked control system technology, in particular to a kind of probability scheduling and resource allocation joint optimization method of wireless networked control system.The present application is applicable to the wireless networked control system formed by multiple discrete linear subsystems and shared 5G network.In particular, the linear quadratic Gaussian (LQG) control cost of wireless networked control system is modeled as the closed-form expression of subsystem activation probability, uplink and downlink transmission reliability;With the goal of minimizing LQG control cost, a joint optimization problem of probability scheduling and resource allocation is established;Alternating optimization is used to solve the problem, and the optimal network parameter setting is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless networked control systems, in particular to a joint optimization method for probability scheduling and resource allocation of a wireless networked control system. BACKGROUND

[0002] Industrial Internet of Things and industrial control systems are expanding in scale, which promotes the development of wireless networked control systems. It is generally believed in the field of industrial manufacturing that wireless networked control systems will become an important part of smart factories. Compared with traditional control systems, wireless networked control systems have the advantages of low cost, high flexibility, easy installation and maintenance, etc. However, due to limited spectrum resources and poor radio frequency environment, real-time and reliable transmission of industrial wireless networks cannot be guaranteed, which leads to the difficulty of meeting the control performance of wireless networked control systems.

[0003] Resource scheduling methods are crucial for improving the control performance of wireless networked control systems. However, existing resource scheduling methods are mainly centralized scheduling methods, which generate a large amount of calculation and communication overhead. A small number of distributed methods only focus on the scheduling process and do not consider optimizing network resource allocation, resulting in low efficiency of network resource use and poor control performance of the system. SUMMARY

[0004] In view of the problem that the control performance of resource-limited wireless networked control systems in poor factory environments is difficult to meet, the present application proposes a joint optimization method for probability scheduling and resource allocation of a wireless networked control system. This method is applicable to a wireless networked control system composed of multiple discrete linear subsystems and a shared 5G network. Specifically, the linear quadratic Gaussian (LQG) control cost of the wireless networked control system is modeled as a closed-form expression of the subsystem activation probability, uplink and downlink transmission reliability; a joint optimization problem of probability scheduling and resource allocation is established with the goal of minimizing the LQG control cost; and the optimal network parameter settings are obtained by solving the problem using alternating optimization.

[0005] The technical solution adopted by the present application to achieve the above-mentioned purposes is as follows:

[0006] The joint optimization method for probability scheduling and resource allocation of a wireless networked control system comprises the following steps:

[0007] 1) Model the linear quadratic Gaussian (LQG) control cost of the wireless networked control system as a closed-form expression between the subsystem activation probability, uplink and downlink transmission reliability;

[0008] 2) Establish a joint optimization problem of probability scheduling and resource allocation with the goal of minimizing the LQG control cost;

[0009] 3) solving the joint optimization problem by using alternating optimization to obtain the optimal network parameter settings, and scheduling and resource allocation of the wireless network according to the obtained network parameters.

[0010] The wireless networked control system comprises a central controller, a 5G base station and m discrete linear subsystems, wherein the central controller is connected with the 5G base station through a wired connection, the m discrete linear subsystems are connected through a shared 5G network, and the discrete linear subsystems share the same sampling period or control period and are time-synchronized with the 5G base station.

[0011] The discrete-time state-space equation of the discrete linear subsystem i is:

[0012]

[0013] wherein k is the control period number, x i,k is a state vector, is a control input, A i is a system matrix, B i is an input matrix, w i,k is a Gaussian white noise with a mean of 0 and a covariance matrix of W i .

[0014] The discrete linear subsystem i adopts closed-loop control, specifically:

[0015] In the kth control period, the scheduler of the discrete linear subsystem i decides whether to send the state vector information x i,k to the central controller according to the implementation of Bernoulli variable α i,k ~ B(p a ), if α i,k = 1, x i,k is sent to the central controller; otherwise, x i,k is prevented from being sent by the scheduler, wherein B(p a ) represents a Bernoulli distribution with an activation probability of p a .

[0016] The available information of the central controller about the discrete linear subsystem i is z i,k = α i,k γ i,k x i,k , the controller calculates the control variable u i,k based on z i,k , and sends u i,k to the actuator of the discrete linear subsystem i through the 5G base station, and the control input received by the actuator of the discrete linear subsystem i is wherein the random variable γ i,k ∈ {0, 1} and v i,k∈{0,1} respectively represent uplink and downlink transmission results of the discrete linear subsystem i, and the value of 1 indicates successful transmission, and vice versa indicates packet loss.

[0017] The uplink and downlink transmission processes are as follows:

[0018] For the activated discrete linear subsystem, contention-based uplink transmission is adopted, each data packet is transmitted β times, β≥1, and each transmission randomly selects a RU from all available resource units RUs; for the discrete linear subsystem with successful uplink transmission, the polling method is used for downlink transmission.

[0019] Uplink transmission reliability and downlink transmission reliability are as follows:

[0020]

[0021]

[0022] wherein C is a permutation combination symbol, is a combination number, j is an intermediate variable, represents that the data packet is transmitted j times, j=1~β, m is the number of discrete linear subsystems, p u and p d are the uplink and downlink packet loss rates respectively, is the number of discrete linear subsystems with successful uplink transmission, and respectively represent the floor function and the ceiling function, N1=L1M and N2=L2M are the available RU numbers for uplink and downlink transmission respectively, L1 and L2 are the TTI numbers for uplink and downlink transmission respectively, M is the available RU number in each TTI, and mod(·) represents the remainder function.

[0023] The step 1) is specifically:

[0024] Based on the infinite time domain scenario, the LQG performance of the discrete linear subsystem i is measured by the cost function J i :

[0025]

[0026] wherein Q i and R i are intermediate variable matrices, Q i is a non-negative definite matrix, R i is a positive definite matrix, represents taking expectation, and N is the length of the time domain.

[0027] The optimal feedback control is as follows:

[0028] u i,k = K i,∞ z i,k = a i,k y i,k K i,∞ x i,k

[0029] where K i,∞ is the state feedback gain matrix, which is given by

[0030]

[0031] where P i,∞ is the solution of the following modified algebraic Riccati equation:

[0032]

[0033] where X is the solution of the equation, is an intermediate variable;

[0034] The LQG control cost of the discrete linear subsystem i is given by

[0035] J i (p a , β, L1, L2) = Tr(P i,∞ W i )

[0036] The LQG control cost J(p a , β, L1, L2) of the wireless networked control system is the sum of the LQG control costs of the m discrete linear subsystems, i.e.,

[0037]

[0038] The step 2) is specifically given by

[0039] By optimizing {p a , β, L1, L2}, the LQG control cost of the wireless networked control system is minimized, i.e.,

[0040]

[0041] s.t. 0 < p a ≤ 1

[0042]

[0043] L1 + L2 = L

[0044] 1 ≤ L1, L2 ≤ L - 1

[0045] where p * is the optimal activation probability, and β* for optimal uplink repetition transmission number, and are the optimal uplink and downlink TTI numbers, respectively, and L is the number of TTIs within each control period;

[0046] According to the LQG control cost closed-form expression of the wireless networked control system, the optimization problem is equivalent to:

[0047]

[0048] s.t.0<p a ≤1

[0049]

[0050] L1+L2=L

[0051] 1≤L1,L2≤L-1

[0052] where, is the end-to-end transmission reliability.

[0053] The step 3) comprises the following steps:

[0054] 3.1) input parameters m, p u , p d , the maximum number of iteration steps n max , the threshold σ;

[0055] 3.2) initialize parameters, let β * = 1, the intermediate variable take infinity, the intermediate variable delta = 0, the iteration step n = 0;

[0056] 3.3) let

[0057] 3.4) fix Solve optimization problem 1 by exhaustive method:

[0058]

[0059]

[0060] L1+L2=L

[0061] 1≤L1,L2≤L-1

[0062] 3.5) fix Solve optimization problem 2 by MATLAB fmincon solver:

[0063]

[0064] s.t.0<p a ≤1

[0065] 3.6) Let

[0066] 3.7) Let n = n + 1;

[0067] 3.8) Repeat steps 3.3) ~ 3.7) until the condition

[0068] 3.9) Output the optimal parameters

[0069] The present application has the following beneficial effects and advantages:

[0070] 1. The LQG control cost of the wireless networked control system is modeled as a closed-form expression of the subsystem activation probability, uplink and downlink transmission reliability, and a joint optimization problem of probability scheduling and resource allocation is established to minimize the LQG control cost.

[0071] 2. The optimization problem is solved by alternating optimization to obtain the optimal settings of the subsystem activation probability, uplink transmission repetition number, uplink and downlink transmission phase duration, thereby minimizing the LQG control cost of the wireless networked control system. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 The wireless networked control system is;

[0073] Figure 2 The subsystem control closed loop diagram is;

[0074] Figure 3 The 5G transmission frame structure diagram is. DETAILED DESCRIPTION

[0075] The present application will be further described in detail below with reference to the accompanying drawings and examples.

[0076] The joint optimization method of probability scheduling and resource allocation for the wireless networked control system models the LQG control cost of the wireless networked control system as a closed-form expression of the subsystem activation probability, uplink and downlink transmission reliability; establishes a joint optimization problem of probability scheduling and resource allocation to minimize the LQG control cost; and solves the problem by alternating optimization to obtain the optimal network parameter settings.

[0077] The wireless networked control system, in particular:

[0078] The considered wireless networked control system is composed of m discrete linear subsystems connected through a shared 5G network. A central controller is connected to the 5G base station through a wired connection, and each subsystem shares the same sampling period (or control period) and is time-synchronized with the base station. The discrete-time state-space equation of the subsystem i is:

[0079]

[0080] where k is the control period index, x i,k is the state vector, is the control input, A i is the system matrix, B i is the input matrix, w i,k is a Gaussian white noise with mean 0 and covariance matrix W i .

[0081] The control loop of the subsystem i is as follows:

[0082] At the kth control period, the scheduler of the subsystem i decides whether to send the state information x i,k to the controller according to the realization of the Bernoulli variable α a ~ B(p i,k ), where B(p a ) denotes a Bernoulli distribution with the activation probability p a . If α i,k = 1 (with probability p a ), x i,k is sent to the controller; otherwise, x i,k is prevented from being sent by the scheduler. Then the available information of the controller about the subsystem i is z i,k = α i,k γ i,k x i,k , and the controller calculates the control u i,k based on z i,k and sends u i,k to the actuator of the subsystem i through the base station, and the control input received by the actuator of the subsystem i is The random variables γ i,k ∈ {0, 1} and ν i,k ∈ {0, 1} represent the uplink and downlink transmission results of the subsystem i, respectively, and take the value 1 to represent successful transmission, and otherwise represent packet loss, and are the uplink and downlink transmission reliabilities of the subsystem i, respectively.

[0083] The uplink and downlink transmission reliabilities are specifically:

[0084] For activated subsystems, contention-based uplink transmission is adopted, each data packet is transmitted β(β≥1) times, and each transmission randomly selects a RU from all available RUs; for the activated subsystems with successful uplink transmission, polling-based downlink transmission is adopted. and The specific expressions are as follows:

[0085]

[0086]

[0087] wherein, is the number of combinations, m is the number of subsystems, p u and p d are the uplink and downlink packet loss rates respectively, is the number of activated subsystems with successful uplink transmission, and respectively represent the floor and ceiling functions, N1=L1M and N2=L2M are the available RU numbers for uplink and downlink transmission respectively, L1 and L2 are the uplink and downlink transmission time interval (TTI) numbers respectively, M is the available RU number in each TTI, and mod(·) represents the remainder function.

[0088] The LQG control cost of the wireless networked control system is modeled as a closed-form expression of the subsystem activation probability, uplink and downlink transmission reliability, specifically:

[0089] Considering the infinite time domain scenario, the LQG performance of subsystem i is measured by the following cost function:

[0090]

[0091] wherein, Q i and R i are intermediate variable matrices, Q i is a non-negative definite matrix, and R i is a positive definite matrix.

[0092] The optimal feedback control is as follows:

[0093] u i,k = K i,∞ z i,k = α i,k γ i,k K i,∞ x i,k

[0094] wherein, K i,∞ is the state feedback gain matrix, and specifically:

[0095]

[0096] where P i,∞ is the solution of the following modified algebraic Riccati equation:

[0097]

[0098] where X is the solution of the equation, is an intermediate variable.

[0099] The LQG control cost of subsystem i is:

[0100] J i (p a ,β,L1,L2)=Tr(P i,∞ W i )

[0101] The LQG control cost of the considered wireless networked control system is the sum of the LQG control costs of the m subsystems:

[0102]

[0103] The joint optimization problem of probabilistic scheduling and resource allocation is established to minimize the LQG control cost, which is specifically:

[0104] By optimizing {p a ,β,L1,L2}, the LQG control cost of the wireless networked control system is minimized:

[0105]

[0106] s.t.0<p a ≤1

[0107]

[0108] L1+L2=L

[0109] 1≤L1,L2≤L-1

[0110] where is the optimal activation probability, β * is the optimal uplink repetition transmission number, and are the optimal uplink and downlink TTI numbers, respectively, and L is the TTI number within each control period.

[0111] According to the closed-form expression of the LQG control cost of the wireless networked control system, the above optimization problem can be equivalent to the following optimization problem:

[0112]

[0113] st0<p a ≤1

[0114]

[0115] L1 + L2 = L

[0116] 1≤L1,L2≤L-1

[0117] in, For end-to-end transmission reliability.

[0118] Example

[0119] The wireless network control system considered in this invention is as follows: Figure 1 As shown, m discrete linear subsystems are connected via a shared 5G network. The central controller is connected to the 5G base station via a wired connection, and each subsystem shares the same sampling period (or control period) and is synchronized with the base station time.

[0120] The control closed-loop diagram of the subsystem is as follows: Figure 2 As shown, in the k-th control cycle, the scheduler of subsystem i determines the time based on α. i,k ~B(p a Decide whether to send status information to the controller. i,k If α i,k =1 (probability is p) a ), x i,k Send to the controller; otherwise x i,k The transmission is blocked by the scheduler. Therefore, the available information the controller has about subsystem i is z. i,k =α i,k γ i,k x i,k random variable γ i,k ∈{0,1} represents the uplink transmission result of subsystem i, where a value of 1 indicates successful transmission and a value of 0 indicates packet loss. The controller is based on z i,k Calculate u i,k and through the base station to u i,k The data is sent to the actuator of the subsystem. Then the state-space equation of subsystem i is:

[0121]

[0122] Among them, A i For the system matrix, B i For the input matrix, To control the input, the random variable ν i,k ∈{0,1} represents the downlink transmission result of subsystem i, where a value of 1 indicates successful transmission and a value of 0 indicates packet loss. i,k With a mean of 0 and a covariance matrix of W iGaussian white noise.

[0123] The schematic diagram of 5G transmission frame structure in a control cycle is shown in Figure 3 In the time domain direction, it contains L TTIs, and the number of uplink and downlink TTIs is L1 and L2 respectively; in the frequency domain direction, the number of available RUs in each TTI is M. In the uplink transmission process, β available RUs are randomly selected in the first L1 TTIs for transmission. In the downlink transmission process, the polling method is used in the last L2 TTIs for transmission.

[0124] By optimizing {p a , β, L1, L2}, the LQG control cost of the wireless networked control system is minimized:

[0125]

[0126] s.t.0<p a ≤1

[0127]

[0128] L1+L2=L

[0129] 1≤L1,L2≤L-1

[0130] wherein, is the optimal activation probability, β * is the optimal uplink repetition transmission number, and are the optimal uplink and downlink TTI numbers respectively, is the floor function, is the end-to-end transmission reliability, and are the uplink and downlink transmission reliabilities respectively, and The specific expressions are as follows:

[0131]

[0132]

[0133] wherein, is the combination number, m is the number of subsystems, p u and p d are the uplink and downlink transmission packet loss rates respectively, is the number of successfully transmitted subsystems in the uplink transmission, is the ceiling function, N1=L1M and N2=L2M are the available RU numbers in the uplink and downlink transmission respectively, and mod(·) is the modulo function.

[0134] The specific steps for solving the optimization problem are as follows:

[0135] (1) Input: m, p u , p d , n max , σ;

[0136] (2) Initialization: β * = 1, delta = 0, n = 0;

[0137] (3)

[0138] (4) Fix The following optimization problem is solved by exhaustive method:

[0139]

[0140]

[0141] L1+L2=L

[0142] 1≤L1,L2≤L-1

[0143] (5) Fix The following optimization problem is solved by MATLAB fmincon solver:

[0144]

[0145] s.t. 0 a ≤1

[0146] (6)

[0147] (7) n = n + 1;

[0148] (8) Repeat steps (3)-(7) until the condition is not met;

[0149] (9) Output: optimal parameters

Claims

1. A method for joint optimization of probabilistic scheduling and resource allocation for wireless networked control systems, characterized in that, The method comprises the following steps: 1) modeling the linear quadratic Gaussian (LQG) control cost of the wireless networked control system as a closed-form expression among the subsystem activation probability, uplink and downlink transmission reliability; 2) establishing a joint optimization problem of probabilistic scheduling and resource allocation with the objective of minimizing the LQG control cost; 3) solving the joint optimization problem by using an alternating optimization to obtain optimal network parameter settings, and scheduling and allocating resources to the wireless network according to the obtained network parameters; the step 1) is specifically: Based on the infinite time domain scenario, the cost function measures the LQG performance of a discrete linear subsystem i : ； wherein and is an intermediate variable matrix, is a non-negative definite matrix, is a positive definite matrix, denotes taking the expectation, N is the time horizon, is the state vector, is the control input, is a random variable; using the following optimal feedback control: ； wherein is the available information for the central controller about the discrete linear subsystem i is a Bernoulli variable, is a random variable, is a state feedback gain matrix, in particular:​ ； wherein is the system matrix, is the input matrix, is the solution of the following modified algebraic Riccati equation: ； wherein, is a solution of the equation, is an intermediate variable, is an activation probability, is an uplink transmission reliability, is a downlink transmission reliability; Discrete linear subsystem i The LQG control cost is: ； wherein, is the number of uplink repetitions, and are the number of uplink and downlink TTIs, respectively, is the covariance matrix; LQG control cost of a wireless networked control system is the sum of the LQG control costs of the individual discrete linear subsystems, i.e. m is the sum of the LQG control costs of the individual discrete linear subsystems, i.e. ； the step 2) is specifically: By optimizing the LQG control cost of the wireless networked control system, i.e. ； wherein, is the optimal activation probability, is the optimal number of uplink repetitions, and are the optimal number of uplink and downlink TTIs, respectively, L is the number of TTIs within each control period; equivalent to the optimization problem according to the closed-form expression of the LQG control cost of the wireless networked control system, and obtaining: ； wherein, is the end-to-end transmission reliability, is the number of available RUs for uplink transmission.

2. The method of joint optimization of probabilistic scheduling and resource allocation for wireless networked control systems according to claim 1, characterized in that, The wireless networked control system comprises a central controller, a 5G base station and m a discrete linear subsystem, wherein the central controller and the 5G base station are connected through a wired connection, m the discrete linear subsystems are connected through a shared 5G network, and the discrete linear subsystems share the same sampling period or control period and are time-synchronized with the 5G base station.

3. The method of joint optimization of probabilistic scheduling and resource allocation for wireless networked control systems according to claim 2, characterized in that, The discrete linear subsystem i The discrete-time state-space equation for the discrete linear subsystem is ； wherein, k is a control period number, is a state vector, is a control input, is a system matrix, is an input matrix, is a Gaussian white noise with mean 0 and covariance matrix W i .

4. The method of claim 2, wherein, The discrete linear subsystem i With closed loop control, in particular: In the k One control cycle, discrete linear subsystem i The scheduler is based on Bernoulli variables The implementation determines whether to send state vector information to the central controller. ,like ,but Sent to the central controller; otherwise The transmission was blocked by the scheduler, among which, Indicates the activation probability as Bernoulli distribution; Central controller has available information i about the discrete linear subsystem , computes the control variable based on , and sends it to the actuator of the discrete linear subsystem through the 5G base station i , the control input received by the actuator of the discrete linear subsystem i is , where the random variables and represent the uplink and downlink transmission results of the discrete linear subsystem i , respectively, and the value of 1 indicates successful transmission, otherwise indicates packet loss.

5. The method of claim 1, wherein, the uplink and downlink transmission processes are as follows: For activated discrete linear subsystems, contention-based uplink transmission is adopted, each data packet transmission Subsequently, , a resource unit RU is randomly selected from all available RUs; for the discrete linear subsystems with successful uplink transmission, a polling-based downlink transmission is adopted.

6. The method of joint optimization of probabilistic scheduling and resource allocation for wireless networked control systems according to claim 5, characterized in that, Uplink transmission reliability and downlink transmission reliability is: ； ； wherein, is a permutation combination symbol, , , is a combination number, is an intermediate variable representing the data packet transmission times, , m is a discrete linear subsystem number, p u and p d are uplink and downlink transmission packet loss rates, respectively, is a discrete linear subsystem number for uplink transmission success, and represent floor and ceiling functions, respectively, and are available RU numbers for uplink and downlink transmissions, respectively, L 1 and L 2 are uplink and downlink transmission time interval (TTI) numbers, respectively, M is an available RU number within each TTI, represents a remainder function.

7. The method of joint optimization of probabilistic scheduling and resource allocation for wireless networked control systems according to claim 1, characterized in that, the step 3) comprises the following steps: 3.1) input parameters m , p u , p d , maximum number of iteration steps n max , threshold σ ; 3.2) Initialize parameters, let , , , intermediate variable take infinity, intermediate variable , number of iteration steps ; 3.3) Let ; 3.4) Fixing Solve optimization problem 1 by exhaustive method: ； 3.5) Fixing Solve optimization problem 2 by the MATLAB fmincon solver: ； 3.6) Let ; 3.7) Let ; 3.8) repeat steps 3.3) - 3.7) until the condition is not met ; 3.9) Output optimal parameters .

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