Event-triggered predictive control method in networked control systems

Abstract

The present invention belongs to the field of automatic control technology, specifically, an event-triggered predictive control method in a networked control system, comprising the following steps: constructing a networked control system model based on a state space; constructing an event-triggered mechanism to determine whether to update current sampled data; constructing a Kalman filter based on the current actual output value; constructing a predictive control method for the networked control system model, and performing predictions based on a prediction algorithm; and achieving Schur stability of the system by forming a closed-loop system with the networked control system model, the event-triggered mechanism, the Kalman filter, and the predictive control method. The present invention not only adopts a predictive control method but also combines the event-triggered mechanism with the Kalman filter, thereby significantly reducing control costs, improving resource utilization, and ensuring the stability of the networked control system, while also solving the system's time delay and noise interference problems.

Description

Technical Field

[0001] The present invention belongs to the technical field of automatic control, and in particular relates to an event-triggered predictive control method in a networked control system. Background Art

[0002] With the advent of the information age and the rapid development of computer and network technologies, networked control systems (NCSs) have garnered widespread attention. Compared to traditional control systems, NCSs enable resource sharing, remote operation, and control, reducing system complexity, weight, power consumption, and costs, simplifying installation and maintenance, and improving system flexibility and reliability. Network bandwidth in NCSs is limited. Therefore, to reduce network resource usage, bandwidth pressure, and control costs, many researchers have employed event-triggered mechanisms to reduce data transmission times. Compared to traditional periodic sampling control, event-triggered control is a discontinuous, non-periodic communication control protocol. Information in the system feedback loop is transmitted only when the trigger condition is met. Therefore, event-triggered mechanisms are undoubtedly an effective implementation method for improving resource utilization. Since the use of state-based schedulers in closed-loop systems can result in dual effects, the existence of dual effects complicates the design of optimal controllers. Consequently, some output-based event-triggered control methods have emerged.

[0003] NCSs transmit data over the network. However, the presence of unreliable communication networks with limited bandwidth can lead to network delays between wireless transmitters and receivers, and between receivers and terminal devices. Therefore, network delays are unavoidable in real life and can also lead to adverse effects such as system stability and performance degradation. Predictive control is an effective approach to addressing network delays. Currently, many researchers are combining event-triggered mechanisms with predictive control strategies. Existing technologies utilize event-triggered mechanisms to study output-based predictive control for networked control systems with sensor-to-controller delays, and provide sufficient conditions for ensuring closed-loop system stability. For networked control systems subject to two types of DoS attacks, combining model-based predictive control schemes with event-triggered control schemes not only reduces network bandwidth pressure but also effectively compensates for the negative impact of DoS attacks on system performance.

[0004] In addition to unreliable communication channels, actual communication processes are often affected by channel noise, which can cause signal distortion and bit errors, making it impossible to obtain complete system status information. Existing technologies have not considered this. Although existing technologies have proposed output-feedback collaborative distributed model predictive control methods to handle bounded disturbances and communication delays in certain networked systems, they do not utilize event-triggered mechanisms, which can result in a waste of communication resources. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention discloses an event-triggered predictive control method in a networked control system. The method is based on a Kalman filter, wherein the Kalman filter optimally estimates the system state from a series of noisy data when the measurement variance is known.

[0006] The specific technical solutions adopted in the present invention are as follows:

[0007] An event-triggered predictive control method in a networked control system comprises the following steps:

[0008] Step 1: Build a networked control system model based on the state space:

[0009]

[0010] Among them, x k ∈R n ,u k ∈R l ,y k ∈R m Represent the system state, control input and measurement output respectively. k ∈R m represents the measurement noise, which obeys the normal distribution of (0,Q); k ∈R m represents process noise, obeying A, B, C are constant matrices of known appropriate dimensions, Q and is the variance of the noise.

[0011] Step 2: In order to ensure the performance of the closed-loop system and reduce the occupation of computing resources, network bandwidth resources, etc., an event trigger mechanism (ETM) is constructed to select y k , to decide whether to update the current sampling data, define

[0012] like but

[0013] like but

[0014] in, Indicates the current actual state of the system. Indicates the current actual transmitted output value, y k Indicates the current measured output value. Represents the output value actually transmitted at the last moment, σ is an adjustable parameter, represents process noise, obeying The next triggering time is:

[0015]

[0016] in, It is non-periodic.

[0017] Step 3: From the current actual output value We start by constructing a Kalman filter to achieve the optimal estimation of the state of a networked control system containing noise. The Kalman filter is:

[0018]

[0019] in, Represents the state of the Kalman filter, using the actual output value renew, Represents the measured output value of the Kalman filter, M k is the gain matrix of the Kalman filter, which is an adaptive quantity rather than a fixed value. is the covariance matrix of the Kalman filter prediction error, is the covariance matrix of the Kalman filter estimation error.

[0020] The following assumptions are made for the coefficient matrix of the networked control system and the Kalman filter:

[0021] Assumption 1. (A, B) is controllable and (A, C) is observable;

[0022] Assumption 2. There exists a reversible matrix C such that M k-d C≥0.

[0023] According to assumptions 1 and 2, the event trigger mechanism and Kalman filter obtain the Kalman filter gain matrix M k New update method:

[0024]

[0025] Step 4: Construct a predictive control method for the networked control system model and perform predictions based on the prediction algorithm. The d-step state prediction estimate is constructed using the following formula:

[0026]

[0027] in, represents the state prediction at time k-d+i based on the information at time kd, and By recursion we get:

[0028]

[0029] The delay of the present invention takes d steps as an example, d∈Z + , so in the actual network control system, the control input information received by the controller at time k is In order to ensure the normal operation of the system, the predictive controller should predict the output information of the controller at time k based on the input information at time kd, that is, set the controller:

[0030]

[0031] Step 5: By combining the networked control system model with the event trigger mechanism, Kalman filter, and predictive control method to form a closed-loop system, the Schur stability of the system is obtained: for a given event trigger parameter σ and time delay d, under assumptions 1 and 2, when e(A+BK) is Schur stable (i.e., the modulus of the largest eigenvalue of T and e(A+BK) is less than 1). The networked control system composed of the event trigger mechanism, Kalman filter, and predictive control strategy is stable, where the closed-loop system is:

[0032]

[0033] in, Let X k =e k x k ,

[0034] Beneficial effects of the present invention:

[0035] (1) The present invention constructs an output-based event triggering mechanism, which reduces unnecessary measurement transmission, greatly saves control costs, and improves resource utilization;

[0036] (2) The present invention constructs a predictive control method based on the Kalman filter, which solves the time delay and noise interference problems of the networked control system;

[0037] (3) The present invention combines the event triggering mechanism with the predictive control method based on the Kalman filter to obtain the Schur stability of the networked control system model. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the networked control system of the present invention, where ETM represents event triggering mechanism and Observe represents Kalman filter.

[0039] Figure 2 is the predictive control u in the present invention k State trajectory diagram.

[0040] Figure 3 The networked control system in the present invention is used for predictive control u k The state trajectory diagram below. DETAILED DESCRIPTION

[0041] In order to deepen the understanding of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The embodiments are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0042] Example: Figure 1 As shown, an event-triggered predictive control method in a networked control system includes the following steps:

[0043] Step 1: Build a networked control system model based on the state space:

[0044]

[0045] Among them, x k ∈R n ,u k ∈R l ,y k ∈R m Represent the system state, control input and measurement output respectively. k ∈R m represents the measurement noise, which obeys the normal distribution of (0,Q); k ∈R m represents process noise, obeying A, B, C are constant matrices of known appropriate dimensions, Q and is the variance of the noise.

[0046] Step 2: In order to ensure the performance of the closed-loop system and reduce the occupation of computing resources, network bandwidth resources, etc., an event trigger mechanism (ETM) is constructed to select y k , to decide whether to update the current sampling data, define

[0047] like but

[0048] like but

[0049] in, Indicates the current actual state of the system. Indicates the current actual transmitted output value, y k Indicates the current measured output value. Represents the output value actually transmitted at the last moment, σ is an adjustable parameter, represents process noise, obeying The next triggering time is:

[0050]

[0051] in, It is non-periodic.

[0052] Step 3: From the current actual output value We start by constructing a Kalman filter to achieve the optimal estimation of the state of a networked control system containing noise. The Kalman filter is:

[0053]

[0054] in, Represents the state of the Kalman filter, using the actual output value renew, Represents the measured output value of the Kalman filter, M k is the gain matrix of the Kalman filter, which is an adaptive quantity rather than a fixed value. is the covariance matrix of the Kalman filter prediction error, is the covariance matrix of the Kalman filter estimation error.

[0055] The following assumptions are made for the coefficient matrix of the networked control system and the Kalman filter:

[0056] Assumption 1. (A, B) is controllable and (A, C) is observable;

[0057] Assumption 2. There exists a reversible matrix C such that M k-d C≥0.

[0058] According to assumptions 1 and 2, the event trigger mechanism and Kalman filter obtain the Kalman filter gain matrix M k New update method:

[0059]

[0060] Step 4: Construct a predictive control method for the networked control system model and perform predictions based on the prediction algorithm. The d-step state prediction estimate is constructed using the following formula:

[0061]

[0062] in, represents the state prediction at time k-d+i based on the information at time kd, and By recursion we get:

[0063]

[0064] The delay of the present invention takes d steps as an example, d∈Z + , so in the actual network control system, the control input information received by the controller at time k is In order to ensure the normal operation of the system, the predictive controller should predict the output information of the controller at time k based on the input information at time kd, that is, set the controller:

[0065]

[0066] Step 5: By combining the networked control system model with the event trigger mechanism, Kalman filter, and predictive control method to form a closed-loop system, the Schur stability of the system is obtained: for a given event trigger parameter σ and time delay d, under assumptions 1 and 2, when e(A+BK) is Schur stable (i.e., the modulus of the largest eigenvalue of T and e(A+BK) is less than 1). The networked control system composed of the event trigger mechanism, Kalman filter, and predictive control strategy is stable, where the closed-loop system is:

[0067]

[0068] in, Let X k =e k x k ,

[0069] For networked control systems, the following parameters are used:

[0070]

[0071] Using the pole placement principle, we obtain: K = [3.19575.0324]. Assume that the delay d = 3 on the sensor-to-controller channel, the time length k = 200, the event trigger parameter σ = 0.125, and the initial state of the system x0 = [2.50] T , the initial control input u0=0, the noise ωk 、υ k 、 They are all random number sequences that obey a uniform distribution in the interval (0,1).

[0072] Let G = [B, AB, ..., A n-1 B],H=[C,CA,...,CA n-1 ] T From Matlab calculation, we know that the rank of G and H are both 2, that is, G and H are full rank, so (A, B) is controllable and (A, C) is observable, satisfying assumption 1; for all k∈N, M k-d C≥0 is true, satisfying assumption 2; the modulus of the largest characteristic root of e(A+BK) is 0.998<1; The modulus of the largest eigenvalue is 0.9669<1, so the moduli of all eigenvalues ​​of e(A+BK) and T are less than 1, that is, both are Schur stable.

[0073] Figure 2 Given the predictive control u k The state trajectory of Figure 3 The networked control system is given in the predictive control u k From the state trajectory of the Kalman filter, it can be seen that the state trajectory gradually tends to 0 after k = 30. Therefore, it can be shown that when e(A+BK) and T are Schur stable, the networked control system is stable under the predictive control based on the Kalman filter.

[0074] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. An event-triggered predictive control method in a networked control system, characterized in that: The following steps are involved: Step 1: Construct a networked control system model based on the state space; Step 2: Build an event trigger mechanism to decide whether to update the current sampling data; Step 3: Construct a Kalman filter based on the current actual output value; Step 4: Construct a predictive control method for the networked control system model and perform predictions based on the prediction algorithm; Step 5: The networked control system model is combined with the event trigger mechanism, Kalman filter, and predictive control method to form a closed-loop system, and the Schur stability of the system is achieved. In step 3, the actual output value is We start by constructing a Kalman filter to achieve the optimal estimation of the state of a networked control system containing noise. The Kalman filter is: ， in, Indicates the moment, Represents the state of the Kalman filter, using the actual output value renew, represents the measured output value of the Kalman filter, is the gain matrix of the Kalman filter, is the covariance matrix of the Kalman filter prediction error, is the covariance matrix of the Kalman filter estimation error, Represents the system control input; In step 3, the coefficient matrices of the networked control system and the Kalman filter are set as follows: Setting 1. It is controllable. is observable; Assumption 2. There exists an invertible matrix C such that ; According to setting 1 and setting 2, the event trigger mechanism and Kalman filter obtain the Kalman filter gain matrix New update method: , In step 5, for a given event trigger parameter and delay d, under settings 1 and 2, when 、 It is Schur stable, and the closed-loop system is: ， in, , ,make , , , In the above formula, A, B, and C are constant matrices of known appropriate dimensions.

2. The event-triggered predictive control method in a networked control system according to claim 1, characterized in that: In the step 1, the networked control system model is constructed based on the state space as follows: , in, , respectively represent the system state, control input and measurement output, represents the measurement noise, obeying Normal distribution; represents process noise, obeying The normal distribution of , and the measurement noise and process noise are independent of each other, A, B, C are constant matrices of known appropriate dimensions, and is the variance of the noise.

3. The event-triggered predictive control method in a networked control system according to claim 2, characterized in that: In step 2, construct an event trigger mechanism to select , to decide whether to update the current sampling data, define , like ,but , like ,but , in, Indicates the current actual state of the system. Indicates the output value actually transmitted at present. Indicates the current measured output value. Indicates the output value actually transmitted at the last moment, is an adjustable parameter, represents process noise, obeying Normal distribution.

4. The event-triggered predictive control method in a networked control system according to claim 3, characterized in that: In step 2, the next triggering moment is: , in, It is non-periodic.

5. The event-triggered predictive control method in a networked control system according to claim 4, characterized in that: In step 4, a predictive control method for a networked control system model is constructed, and prediction is performed according to a prediction algorithm: The step state prediction estimate is constructed using the following formula: , in, Indicates time-based The information in The state prediction at the moment, and , obtained by recursion: , in, , The control input information received by the controller at this moment is , the predictive controller is based on The input information at the moment is predicted to obtain the controller Output information at each moment, that is, setting the controller: .

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