Random model predictive control method and device triggered by self-adaptive event

Abstract

The invention discloses the field of automatic control systems, and particularly relates to a random model predictive control method and equipment triggered by a self-adaptive event. The method comprises the following steps: S1, dynamically adjusting the sampling time of a control system and the updating frequency of control input through a self-adaptive event triggering mechanism; the self-adaptive event triggering mechanism is adjusted according to a system state and a change condition of control input; s2, using a distributed robust optimization method to convert a prediction control problem of the random model with opportunity constraint into a second-order conic convex optimization problem for solving; and S3, at each sampling time, determining the optimal control input by solving the second-order cone convex optimization problem, performing feedback control on the state of the control system, and adjusting the communication sampling frequency. According to the method, unnecessary sampling and communication costs are reduced, the feasibility and robustness of the optimization problem are improved, the calculation burden of the system is reduced, and meanwhile, the stability of the control system is ensured.

Description

Technical Field

[0001] The present invention relates to the field of automatic control systems, and particularly to an adaptive event-triggered stochastic model predictive control method and device. Background Art

[0002] Model Predictive Control (MPC) has been widely applied in the field of industrial control, such as power electronic systems, automatic control systems, and networked control systems, due to its ability to handle system hard constraints. In the actual industrial production environment, the system is often affected by uncertain factors such as external disturbances and unknown parameters, resulting in a decline or even failure of control performance. Therefore, in order to effectively reduce the influence of uncertain factors, Robust Model Predictive Control (RMPC) has been widely studied.

[0003] However, when dealing with the coupling of system states and controller constraints, the feasible region of the initial state in RMPC is small, and it may even lead to no solution to the optimization problem, which limits its effectiveness in practical applications. In the existing technology, Stochastic Model Predictive Control (SMPC) can improve the limitations of RMPC and improve the feasible set of the optimization problem. The main feature of SMPC is the introduction of chance constraints to measure the control performance of the system and system constraints. Currently, there are mainly two methods for dealing with chance constraints: stochastic methods and analytical approximation methods. The stochastic method proposed in "Jorge A D, Santoro B F, Anderson A, et al. Stochastic model predictive control for tracking linear systems[J]. Optimal Control Applications and Methods, 2020, 41(1)" approximates the SMPC optimization problem based on a large number of random noise data samples. The analytical approximation method proposed in "Dai L, Gao Y, Xie L, et al. Stochastic self-triggered model predictive control for linear systems with probabilistic constraints[J]. Automatica, 2018, 92: 9-17. DOI: 10.1016" reconstructs the chance constraint as a hard constraint according to the distribution law of the noise, and then solves the SMPC optimization problem. Although SMPC has achieved certain results in theory and applications, there are significant limitations in practical applications. First of all, the effectiveness of the analytical approximation method depends on the accurate description of the noise distribution. However, due to the complexity of the actual environment, it is difficult to accurately obtain the distribution law of the noise, resulting in certain limitations of this method.On this basis, "Tan Y, Yang J, Chen WH, et al. A Distributionally Robust Optimization Approach to Two-Sided Chance-Constrained Stochastic Model Predictive Control With Unknown Noise Distribution[J]. IEEE Transactions on Automatic Control, 2024(1):69." proposed an SMPC based on the Distributionally Robust Optimization (DRO) method, which transforms the SMPC problem with chance constraints into the form of a second-order cone (SOC) optimization problem, converting the original optimization problem into a second-order cone convex optimization problem, thereby enhancing the robustness of the system. This method does not require the distribution law of random perturbations, and compared with RMPC, it does not require quantifying the boundaries of random perturbations.

[0004] Since SMPC updates the control input at each sampling and is affected by constraint conditions, it may cause a large communication cost and computational burden. "Y.H. Liu, J. Fu. Dynamic event-triggered model predictive control with guaranteed rigorous satisfaction of probabilistic path constraints[J]. IEEE Trans. Syst. Man Cybern.: Syst, vol. 53, no. 12, pp. 7681-7692, 2023" introduced the Event-Triggered Mechanism (ETM) into the SMPC problem, thus effectively saving the computational resources and communication costs of the control system. In actual industrial control systems, static ETM depends on preset thresholds, making the results too conservative to adapt to the rapidly changing external environment. On this basis, "L.Xu, X.L.Yi,, et al. Distributed nonconvex optimization with event-triggered communication[J]. IEEE Trans. Autom. Control, pp. 1-8, 2023" further proposed the Adaptive Event-Triggered Mechanism (AETM) to address the limitations of ETM. AETM can dynamically adjust the triggering interval according to external conditions, reduce computational and communication costs, and adapt to changes in the system's external conditions, thereby reducing computational and communication costs. However, the research on SMPC based on AETM is still preliminary, especially when dealing with linear discrete systems with unknown noise distributions, which is rarely involved in the existing technologies. Summary of the Invention

[0005] For a linear discrete system with unknown noise distribution, the present invention proposes an adaptive event-triggered stochastic model predictive control method (AET-SMPC) and device. Stochastic model predictive control has been widely studied, but almost all studies are based on periodic stochastic model predictive control (PSMPC) and self-triggered stochastic model predictive control. Little consideration has been given to the exact sampling time and system computational burden. An adaptive event-triggered mechanism (AETM) is introduced to reduce unnecessary sampling and lower the update frequency of control inputs, thereby alleviating the system's computational burden. To reduce the violation of chance constraints, a distributionally robust optimization (DRO) method is adopted. By means of second-order cone (SOC) equivalence, the optimization problem of chance constraints is transformed into a second-order cone convex optimization problem, and the recursive feasibility and stability of the optimal control algorithm are strictly established. The effectiveness and advancement of the proposed algorithm are demonstrated through numerical simulations.

[0006] To achieve the above-mentioned invention objectives, the present invention provides the following technical solutions:

[0007] An adaptive event-triggered stochastic model predictive control method, comprising the following steps:

[0008] S1. Dynamically adjust the sampling time of the control system and the update frequency of the control input through an adaptive event-triggered mechanism; the adaptive event-triggered mechanism is adjusted according to the changes in the system state and the control input;

[0009] S2. Use a distributionally robust optimization method to transform the predictive control problem of a stochastic model with chance constraints into a second-order cone convex optimization problem for solution;

[0010] S3. At each sampling time, determine the optimal control input by solving the second-order cone convex optimization problem, and perform feedback control on the state of the control system to adjust the communication sampling frequency.

[0011] Preferably, the adaptive event-triggered mechanism comprises the following steps:

[0012] S101. Monitor the system state deviation between the current state and the most recent triggered state;

[0013] S102. When the system state deviation exceeds a preset threshold, the preset adaptive event-triggered condition is reached, triggering sampling and updating the control input.

[0014] By monitoring the system state deviation between the current state and the most recent triggered state and dynamically adjusting the sampling frequency according to the adaptive event-triggered condition, the dynamic optimization of sampling and control input update is achieved; this flexible adjustment mechanism can further reduce the system's consumption of computational and communication resources and adapt to complex and changing external environments.

[0015] Preferably, the formula for the adaptive event-triggering condition is:

[0016]

[0017] where is the triggering function, ε is the system error, ε ∈ (0, 1), is the triggering parameter, τ is the system step size, k is time, k l is the triggering moment; γ is a predetermined positive definite constant; represents the error variable from one sampling state to the latest triggering state . The specific formula of the adaptive event-triggering condition is clarified, and considering factors such as system error, triggering parameter, and step size, it ensures the accuracy and flexibility of the triggering condition, improves the real-time performance and adaptability of event triggering, and further optimizes the system performance.

[0018] Preferably, the adaptive event-triggering mechanism includes an adaptation law:

[0019]

[0020] where ζ0 is the initial value of ζ τ |k l . If then the triggering condition is a static event-triggering mechanism; if then the adaptive event-triggering condition is applicable. By introducing the adaptation law and combining static and adaptive event-triggering mechanisms, a more compatible triggering condition design is provided. This mechanism can dynamically switch triggering strategies under different conditions, retaining the stability of the static triggering mechanism and improving the flexibility of the adaptive triggering mechanism, enhancing the robustness of the system to different environments.

[0021] Preferably, step S2 further includes, through a distributionally robust optimization method, considering partial prior information of the disturbance distribution, and proving that the chance constraint is equivalent to the distributionally robust constraint and equivalent to the second-order cone convex optimization constraint; specifically, the chance constraint, the formula is as follows:

[0022]

[0023] where is the distribution of the disturbance; and are constant vectors, r and are given constants; x τ|k , u τ|k respectively represent the system state and control input at τ|k, τ|k represents k + τ; δ x , δu ∈(0,1) are the maximum probabilities of allowing constraint violations pre-specified for the system state and control input respectively;

[0024] The distributionally robust constraint is given by the following formula:

[0025]

[0026] The second-order cone convex optimization constraint is given by the following formula:

[0027]

[0028] where Φ = A + BK, is the decision variable; K is the controller gain; Σ w is the covariance matrix, is the predicted covariance matrix; is the predicted system state. By dealing with the chance constraint through the distributionally robust optimization method, it is transformed into a distributionally robust constraint and further into a second-order cone convex optimization constraint, avoiding the dependence on the precise description of the perturbation distribution; this transformation method improves the solution efficiency and robustness of the optimization problem and reduces the risk of constraint violation in the uncertain environment.

[0029] Preferably, the objective function of the adaptive triggering mechanism is:

[0030]

[0031] where is the system state deviation, is the cost of the control input, is the terminal Lyapunov state cost; is the expectation under the distribution ; N is the prediction horizon length, and are known weight matrices, F N is the terminal weighting matrix. Through the design of the objective function, the system state deviation, the cost of the control input, and the terminal state cost are incorporated into the optimization objective, comprehensively weighing the system performance and resource consumption; this design can optimize the control input and the terminal state to the greatest extent while meeting the system robustness requirements.

[0032] Preferably, the constraint conditions of the second-order cone convex optimization problem include: the chance constraints of the system state and the control input; the probabilities that the system state and the control input satisfy are not less than a preset value. By introducing the chance constraint into the second-order cone convex optimization problem, the stability of the system state and the control input under uncertain conditions is ensured; the constraint condition that the satisfaction probability is not less than the preset value helps to enhance the robustness and reliability of the system in the uncertain environment.

[0033] Preferably, in step S3, the optimal control input at each sampling time is determined by a recursive method, and it is ensured that the system state and the control input satisfy the given constraint conditions at each moment. By solving the optimal control input recursively, it is ensured that the system state and the control input at each sampling moment satisfy the constraint conditions; this recursive solution method improves the stability and real-time performance of the optimization algorithm, and further ensures the efficiency of the system during dynamic operation.

[0034] Preferably, the method is applied to the control of a buck-boost DC-DC converter, where: the adaptive event-triggered mechanism dynamically adjusts the trigger interval for updating the control input according to the state deviation of the inductor current and the output voltage and the change amount of the control input; the distributionally robust optimization method transforms the probabilistic constraint in the optimization problem of the buck-boost DC-DC converter into a second-order cone convex optimization problem, and generates the optimal control input by solving this optimization problem; the switch state is adjusted by the control input obtained through optimization to control the output voltage of the DC-DC converter and reduce the trigger frequency. In the above implementation process, the trigger interval is dynamically adjusted by the adaptive event-triggered mechanism, reducing the number of samplings and updates during the control process of the buck-boost DC-DC converter, thereby reducing the communication and computational costs. The distributionally robust optimization method is used to transform the probabilistic constraint into a second-order cone convex optimization problem, improving the solution efficiency and robustness of the optimization problem. The control input generated by optimization can accurately adjust the switch state, achieve stable control of the output voltage, reduce the trigger frequency at the same time, reduce energy consumption and extend the device life. It effectively improves the control performance of the DC-DC converter in an uncertain environment and the system resource utilization efficiency, and has significant practical application value.

[0035] The present invention also provides a device applied to an automatic control system, including a processor, a memory, a communication interface, and a computer-readable storage medium; a computer program is stored on the computer-readable storage medium; when the computer program is executed by the computer, the described adaptive event-triggered stochastic model predictive control method is implemented.

[0036] Compared with the prior art, the beneficial effects of the present invention are:

[0037] The present invention proposes an SMPC method. By introducing an adaptive event-triggering mechanism, the sampling time and the update frequency of the control input are dynamically adjusted to reduce unnecessary sampling and communication costs. By using the distributionally robust optimization method, the optimization problem with chance constraints is transformed into a second-order cone convex optimization problem, improving the feasibility and robustness of the optimization problem. The optimal control input is recursively solved and the communication frequency is adjusted to reduce the computational burden of the system while ensuring the stability of the control system. At the same time, compared with the existing event-based SMPC algorithms, the AET-SMPC algorithm has lower conservatism and a lower risk of constraint violation based on the DRO method. Finally, the recursive feasibility of the AET-SMPC algorithm under system state and control input constraints and the stability of the closed-loop system are proven. Description of the Drawings

[0038] Figure 1 It is the flowchart of a method for an adaptive event-triggered stochastic model predictive control method according to Embodiment 1 of the present invention;

[0039] Figure 2 It is the system structure diagram of an adaptive event-triggered stochastic model predictive control (AET-SMPC) according to Embodiment 2 of the present invention;

[0040] Figure 3 It is the algorithm flowchart of an adaptive event-triggered stochastic model predictive control according to Embodiment 3 of the present invention;

[0041] Figure 4 It is the circuit schematic diagram of a buck-boost DC-DC converter according to Embodiment 4 of the present invention;

[0042] Figure 5 It is the comparison diagram of closed-loop state trajectories under different control algorithms according to Embodiment 4 of the present invention;

[0043] Figure 5 Markings in it: (a) PSMPC; (b) ET-SMPC; (c) ζ0 = 1.5; (d) ζ0 = 2;

[0044] Figure 6 It is the distribution diagram of event-triggering time points under Case a - Gaussian mixture noise according to Embodiment 4 of the present invention;

[0045] Figure 6 Markings in it: (a) PSMPC; (b) ET-SMPC; (c) ζ0 = 1.5; (d) ζ0 = 2;

[0046] Figure 7 It is the comparison diagram of closed-loop state trajectories under different control algorithms according to Embodiment 4 of the present invention;

[0047] Figure 7Markings in the figure: (a) PSMPC; (b) ET-SMPC; (c) ζ0 = 1.5; (d) ζ0 = 2;

[0048] Figure 8 This is the distribution diagram of event trigger time points in Case b - Gaussian noise for Embodiment 4 of the present invention;

[0049] Figure 8 Markings in the figure: (a) PSMPC; (b) ET-SMPC; (c) ζ0 = 1.5; (d) ζ0 = 2. Detailed implementation manners

[0050] The following further elaborates on an adaptive event-triggered stochastic model predictive control method and device provided by the present invention in conjunction with the accompanying drawings and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments. Any technology implemented based on the content of the present invention falls within the scope of the present invention. In combination with the following description, the advantages and features of the present invention will become clearer. It should be noted that the accompanying drawings are all in a very simplified form and use non-precise scales, only for the purpose of facilitating and clearly assisting in explaining the objectives of the embodiments of the present invention.

[0051] Embodiment 1

[0052] This embodiment provides a specific implementation manner of an adaptive event-triggered stochastic model predictive control method, as Figure 1 shown, including the following steps:

[0053] S1. Through an adaptive event-triggering mechanism, dynamically adjust the sampling time of the control system and the update frequency of the control input; the adaptive event-triggering mechanism is adjusted according to the changes in the system state and the control input;

[0054] S2. Use the distributionally robust optimization method to transform the predictive control problem of a stochastic model with chance constraints into a second-order cone convex optimization problem for solution;

[0055] S3. At each sampling time, by solving the second-order cone convex optimization problem, determine the optimal control input, and perform feedback control on the state of the control system to adjust the communication sampling frequency.

[0056] Preferably, the adaptive event-triggering mechanism includes the following steps:

[0057] S101. Monitor the system state deviation between the current state and the most recent triggered state;

[0058] S102. When the system state deviation exceeds a preset threshold, the preset adaptive event-triggering condition is reached, triggering sampling and updating the control input.

[0059] By monitoring the system state deviation between the current state and the last triggered state, and dynamically adjusting the sampling frequency according to the adaptive event-triggering condition, the dynamic optimization of sampling and control input update is achieved. This flexible adjustment mechanism can further reduce the system's computational and communication resource occupancy and adapt to complex and changing external environments.

[0060] Preferably, the formula for the adaptive event-triggering condition is:

[0061]

[0062] Where, is the triggering function, ε is the system error, ε ∈ (0, 1), is the triggering parameter, τ is the system step size, k is time, k l is the triggering moment; γ is a predetermined positive definite constant; represents the error variable from a sampling state to the latest triggered state . Defining the specific formula of the adaptive event-triggering condition and combining factors such as system error, triggering parameter, and step size ensures the accuracy and flexibility of the triggering condition, improves the real-time performance and adaptability of event triggering, and further optimizes the system performance.

[0063] Preferably, the adaptive event-triggering mechanism includes an adaptation law:

[0064]

[0065] Where, ζ0 is the initial value of ζ τ |k l If then the triggering condition is a static event-triggering mechanism; if then the adaptive event-triggering condition is applicable. By introducing the adaptation law and combining static and adaptive event-triggering mechanisms, a more compatible triggering condition design is provided. This mechanism can dynamically switch triggering strategies under different conditions, retaining the stability of the static triggering mechanism and improving the flexibility of the adaptive triggering mechanism, enhancing the system's robustness in dealing with different environments.

[0066] Preferably, step S2 also includes, through the distributionally robust optimization method, considering partial prior information of the disturbance distribution, and proving that the chance constraint is equivalent to the distributionally robust constraint and equivalent to the second-order cone convex optimization constraint. Specifically, the chance constraint has the following formula:

[0067]

[0068] Where, is the distribution of the disturbance; and is a constant vector, r and are given constants; x τ|k , u τ|k represent the system state and control input at τ|k respectively, where τ|k represents k + τ; δ x , δ u ∈(0, 1) are the maximum probabilities of pre-specified allowable violations of the system state and control input constraints respectively;

[0069] The distributionally robust constraint is as follows:

[0070]

[0071] The second-order cone convex optimization constraint is as follows:

[0072]

[0073] where Φ = A + BK, is a decision variable; K is the controller gain; Σ w is the covariance matrix, is the predicted covariance matrix; is the predicted system state. By dealing with the chance constraint through the distributionally robust optimization method, it is transformed into a distributionally robust constraint and further into a second-order cone convex optimization constraint, avoiding the dependence on the precise description of the perturbation distribution; this transformation method improves the solution efficiency and robustness of the optimization problem and reduces the risk of constraint violation in the uncertain environment.

[0074] Preferably, the objective function of the adaptive triggering mechanism is:

[0075]

[0076] where is the system state deviation, is the cost of the control input, is the terminal Lyapunov state cost; is the expectation under the distribution ; N is the prediction horizon length, and are known weight matrices, F N is the terminal weighting matrix. Through the design of the objective function, the system state deviation, the cost of the control input, and the terminal state cost are incorporated into the optimization objective to comprehensively balance the system performance and resource consumption; this design can optimize the control input and the terminal state to the greatest extent while meeting the system robustness requirements.

[0077] Preferably, the constraint conditions of the second-order cone convex optimization problem include: chance constraints on system states and control inputs; the probability that the system states and control inputs satisfy is not lower than a preset value. By introducing chance constraints into the second-order cone convex optimization problem, the stability of system states and control inputs under uncertain conditions is ensured; the constraint condition that the satisfaction probability is not lower than the preset value helps to enhance the robustness and reliability of the system in an uncertain environment.

[0078] Preferably, in step S3, the optimal control input at each sampling time is determined by a recursive method, and it is ensured that the system states and control inputs satisfy the given constraint conditions at each moment. By solving the optimal control input recursively, it is ensured that the system states and control inputs at each sampling moment satisfy the constraint conditions; this recursive solution method improves the stability and real-time performance of the optimization algorithm, and further ensures the efficiency of the system during dynamic operation.

[0079] Preferably, the method is applied to the control of a buck-boost DC-DC converter, where: the adaptive event-triggering mechanism dynamically adjusts the triggering interval for updating the control input according to the state deviation of the inductor current and output voltage and the change amount of the control input; the distributionally robust optimization method transforms the probability constraint in the optimization problem of the buck-boost DC-DC converter into a second-order cone convex optimization problem, and generates the optimal control input by solving this optimization problem; the control input obtained by optimization adjusts the switch state to control the output voltage of the DC-DC converter and reduce the triggering frequency. In the above implementation process, by dynamically adjusting the triggering interval through the adaptive event-triggering mechanism, the number of samplings and updates in the control process of the buck-boost DC-DC converter is reduced, thereby reducing the communication and computational costs. The distributionally robust optimization method is used to transform the probability constraint into a second-order cone convex optimization problem, which improves the solution efficiency and robustness of the optimization problem. The optimized generated control input can accurately adjust the switch state to achieve stable control of the output voltage, while reducing the triggering frequency, reducing energy consumption and extending the device life. It effectively improves the control performance of the DC-DC converter in an uncertain environment and the utilization efficiency of system resources, and has significant practical application value.

[0080] This embodiment also provides a device applied to an automatic control system, including a processor, a memory, a communication interface, and a computer-readable storage medium; a computer program is stored on the computer-readable storage medium; when the computer program is executed by the computer, the described adaptive event-triggered stochastic model predictive control method is implemented.

[0081] Embodiment 2

[0082] As a further optimization of Embodiment 1, Embodiment 2 provides a specific implementation manner of the adaptive event-triggered stochastic model predictive control method, and the system structure is as Figure 2As shown. Specifically, this embodiment includes the following steps:

[0083] 1.1. Problem description

[0084] Consider a linear discrete-time system with random noise as follows:

[0085] x k+1 = Ax k + Bu k + Dw k (1)

[0086] where k represents time, and are the system state and control input respectively. w is a random perturbation, represents the random perturbation suffered by the system, with the known mean value μ w = 0 and covariance matrix Σ w > 0, is a constant matrix. Additionally, assume that (A, B) is stabilizable. Given the system state x k , the forward prediction model of the system (1) with step size is:

[0087] x τ+1|k = Ax τ|k + Bu τ|k + Dw τ|k (2)

[0088] The control objective is to adaptively reduce the flow rate and solve the problem with chance constraints. At the same time, strictly establish the recursive feasibility and stability of the optimization problem, thereby greatly reducing the sampling time of the system, saving communication resources, well ensuring the control performance, reducing the risk of violating constraints, and proving the recursive feasibility of the AET-SMPC algorithm under system state and control input constraints and the stability of the closed-loop system.

[0089] Assume that the control system (2) follows the system state and control input chance constraints as follows:

[0090]

[0091] where, is the distribution of the perturbation, and are constant vectors, r and are given constants; δ x and δ u ∈(0, 1) are the maximum probabilities of pre-specified allowable constraint violations for the system state and control input respectively. More generally, only partial distribution information of the perturbation is known in this embodiment, and the fuzzy set of the perturbation is defined as follows:

[0092]

[0093] where is the expectation under the distribution and is the n w dimensional zero vector All probability distributions containing the perturbation w k Since the specific distribution of the probability distribution is unknown, but the mean and variance of the distribution must satisfy (5). Therefore, the system state and control input chance constraints (3), (4) are equivalent to the following distributionally robust constraints

[0094]

[0095] Lemma 1: For any system error ε, ε ∈ (0, 1), the chance constraint

[0096]

[0097] where κ is a constant, equation (8) is equivalent to the following SOC constraint

[0098]

[0099] where is the set of random perturbations, Σ is the variance of various perturbation distributions

[0100]

[0101] According to the definition in "Deng L, Shu Z, Chen T. Event-triggered robust model predictive control with stochastic event verification[J]. Automatica, 2022", if there exist θ ∈ (0, 1) and σ > 0 such that then the system (2) has a feasible region X N and the exponential mean-square stability of the initial state x(0) ∈ X N 1.2. Adaptive event-triggered mechanism

[0102]

[0103] To relieve the communication pressure of the communication network, AETM is introduced. The adaptive event-triggered condition is as follows

[0104]

[0105] ​​where is the triggering parameter; in the formula represents the error variable from a sampling state to the latest triggering state . l is the number of triggerings, k l is the triggering moment of the l-th time, and γ is a predetermined positive definite constant.

[0106] The adaptation law is

[0107]

[0108] in the formula ζ0>0 is the initial value of ζ τ |k l . According to (11), the triggering parameter is dynamically adjusted through the adaptation law. AETM has a dual nature: if then the triggering condition (10) is a traditional static event-triggering mechanism; if then the equation (11) has the ability to adaptively and dynamically adjust the triggering function (10). The dual nature of AETM is the focus of adaptive event triggering, which can not only reduce the number of samplings but also adaptively adjust the triggering function according to the actual situation. The adaptive mechanism can flexibly adjust the triggering condition and thus reduce the number of samplings and calculations; adaptive triggering is a dynamic triggering that includes the static event-triggering mechanism.

[0109] According to the above AETM, the next triggering moment can be obtained by the following two formulas:

[0110]

[0111] where is the prediction horizon length. To simplify the expression for subsequent calculation and analysis in this embodiment, define Λ l =k l+1 -k l as the interval between two adjacent triggering moments. Introducing the adaptive triggering mechanism reduces the number of samplings of the system to a certain extent and also reduces the computational load of the system. The system does not update the control sequence at every moment, and at the same time, it also reduces the transmission burden of the wireless communication network, that is, some unnecessary sampling data are filtered out due to event triggering between the sensor and the controller, and because the system uses a control sequence calculated at the triggering moment instead of the first one of the control sequence between the controller and the actuator, the channel can transmit a data packet at a time to contain the control sequence, which greatly reduces the transmission burden.

[0112] 1.3. Feedback control structure

[0113] Under AETM, the model of the prediction system (2) is rewritten as:

[0114]

[0115] Define the nominal system of the system dynamic model (14) as follows:

[0116]

[0117] where is the predicted system state; is the control input. In addition, design the controller as follows:

[0118]

[0119] where K is the controller gain, calculated offline by solving the LQR problem; is the decision variable obtained by solving the following optimization problem P1. Define the control input of system (14) as

[0120]

[0121] 1.4. Adaptive Event-Triggered Stochastic Model Predictive Control Algorithm (AET-SMPC)

[0122] Formulate the problem described in Section II into a computationally tractable SMPC optimization problem. Define the optimization problem P0 as:

[0123]

[0124]

[0125] where and are two known weight matrices, and the terminal weight matrix F N is the solution of the following Lyapunov equation:

[0126]

[0127] where Φ = A + BK.

[0128] In this subsection, P0 with chance constraints is equivalent to a second-order cone convex optimization problem based on partial prior information of the stochastic perturbation w.

[0129] Theorem 1 P0 can be equivalent to a second-order cone convex optimization problem.

[0130]

[0131]

[0132] where is the predicted covariance matrix.

[0133] Proof: Define Then

[0134]

[0135] Therefore, the expected value of the random state error and the predicted covariance matrix are calculated as follows:

[0136]

[0137] To simplify the calculations and expressions, according to the properties of the random perturbation and the state error the objective function J is simplified as follows:

[0138]

[0139] The objective function J is a quadratic objective function with respect to the system state and control input. Its meaning is that the system state converges and the control input is minimized. Physically, it means that the system state is stable (the temperature and speed do not fluctuate greatly) and the external input to it is small (fuel, control torque, etc.).

[0140] Based on the robust distribution characteristics of the random perturbation w, according to Lemma 3.1 of Theorem 3.1 in "Calafiore G C, Ghaoui L E. On Distributionally Robust Chance-Constrained Linear Programs[J]. Journal of Optimization Theory and Applications, 2006, 130(1)", this lemma uses the DRO method to transform the equivalent form of the chance constraint into an SOC. Define

[0141]

[0142] Therefore, we obtain

[0143]

[0144] where Var represents the variance.

[0145] The chance constraint (23) is equivalent to the following

[0146]

[0147] By applying the lemma, it is obtained that (41) is equivalent to (31). Re-formulating (24) into (32) in the same way, the proof is completed.

[0148] In summary, by converting the chance constraints (23) and (24) into the forms of SOC (31) and (32) respectively, P1 has been transformed into a second-order cone convex optimization problem that can be directly solved. Starting from the initial time k0 with the initial state , the sampling time interval is determined at each sampling time through (13), and then the next sampling time is determined. Note that as long as the problem P1 has a solution at k l , P1 generates a set of optimal decision variables corresponding to the control input However, given the initial conditions , the problem P1 may be infeasible. In this case, set to As will be proven later, this makes the problem P1 always feasible. This binary initialization strategy was proposed by M. Farina and R. Scattolini in the study of "Model predictive control of linear systems with multiplicative unbounded uncertainty and chance constraints". Combining AETM (10)-(13), of is used for the system (14) until the system reaches the triggering condition (10), otherwise, the controller is updated through (30).

[0149] To prove the recursive feasibility of the system under P1, the following terminal set is proposed

[0150]

[0151] where

[0152]

[0153] and X T is a positive invariant set that satisfies.

[0154]

[0155] In summary, if , the condition (31) must hold.

[0156] Theorem 2 If there exists a feasible solution at k l , then for the system (1) under Algorithm 1, the optimization problem P1 is recursively feasible at each sampling instant . Furthermore, for , the constraints (31) and (32) are satisfied.

[0157] Proof. Assume that problem P1 is feasible at time k l and the corresponding optimal solution is Then it is necessary to prove that the sub-optimal solution

[0158]

[0159] for problem P1 at time k l+1 is feasible. Therefore, the predicted control input sequence corresponding to the sub-optimal solution c τ |k l+1 can be calculated

[0160]

[0161]

[0162] Given and 's structure, it is obtained that (31) holds for and k l +τ = k ∈ [k l+1 , k l +N - 1]. Therefore, it is proved that for k ∈ [k l +N, k l +Λ l +N], c τ |k l+1 is a feasible solution of (31) at time k l+1 and the terminal constraint is satisfied Since (15) also holds when k l is replaced by k l+1 , there is

[0163]

[0164] Considering (45) and (43),

[0165]

[0166] Therefore, it can be concluded that AET-SMPC is still feasible at time step k l+1 . Further by induction, P1 is feasible at all sampling times and satisfies the constraints (31) and (32) for all . This completes the proof.

[0167]

[0168] Theorem 3 The closed-loop system (1) under Algorithm 1 satisfies the exponential mean-square stability condition. Proof. The main results regarding the convergence of the algorithm are established. In this embodiment, the objective function (18) is defined as the Lyapunov function.

[0169] Therefore, we have

[0170]

[0171] According to condition (25), we obtain:

[0172]

[0173] Combining (25) and (35), we get the following formula

[0174]

[0175] Therefore

[0176]

[0177] Combining Equation (49) and Equation (50) gives the following result

[0178]

[0179] The sub-optimal solution of P1 The corresponding objective function It should be less than or equal to the optimal solution The corresponding objective function The value of, thus, we obtain

[0180]

[0181] Based on Equation (52), we can obtain

[0182]

[0183] where β > 0. Let k l Iterate from (53) to 0, we get

[0184]

[0185] Then, we can draw a conclusion.

[0186]

[0187] where σ > 0 and θ = e -β A constant. Therefore, the system (2) is exponentially mean-square stable. The proof is complete.

[0188] Example 3

[0189] As a specific implementation of the foregoing embodiment, an optimization algorithm for a stochastic model predictive control method based on adaptive event triggering is proposed. The specific process is as follows:

[0190] First, input the initial parameters and state of the system, and initialize a discrete linear system model subject to a random disturbance ω k and ensure the feasibility of the optimization problem. If the optimization problem has no solution, re-initialize the system state and continue to solve; if the optimization problem has a solution, enter the adaptive event triggering mechanism to determine whether the current state needs to be transmitted to the controller. If the triggering condition is not satisfied, skip the current time step, increment the time step by 1, and update the control signal; if the triggering condition is satisfied, record the triggering interval and determine the next sampling time, and feedback the triggering interval, the new system state, and the control input into the optimization problem to verify its convergence and feasibility.

[0191] The algorithm flow is as Figure 3 shown, and the specific steps are as follows:

[0192] S1: The controlled object is affected by random disturbances

[0193] The state x k of the controlled object is affected by a random disturbance ω k . Its current state is measured by a sensor, and the measured system state x k is transmitted to the adaptive event triggering mechanism through the communication channel between the sensor and the controller.

[0194] S2: The adaptive event triggering mechanism determines whether to trigger an update

[0195] The adaptive event triggering mechanism determines whether to trigger the controller to update the control signal according to the system state x k transmitted in the communication channel. If the system state deviation and the change amount of the control input satisfy the triggering condition, trigger the update of the control signal; otherwise, it means that the current system state is within an acceptable range and no update is required.

[0196] S3: Handling when the triggering condition is not met

[0197] If the system state does not meet the triggering condition, it is considered that the current system state is good and there is no need to trigger the update of the control signal. At this time, the algorithm uses the predictive control sequence to generate a new system state x k+1 , and continues the next time calculation, repeating step S1.

[0198] S4: Handling when the triggering condition is met

[0199] If the system state meets the triggering condition, the system state x kwill be transmitted to the controller for generating control signals for S5.

[0200] S5: The stochastic model predictive controller generates control signals

[0201] The stochastic model predictive controller will, based on the prediction model and the system state solve the optimization problem and generate new control signals The optimization problem processes the stochastic model predictive problem with probabilistic constraints through the distributionally robust optimization method and is transformed into a second-order cone convex optimization problem to ensure the robustness and feasibility of the optimization algorithm.

[0202] S6: Storage and transmission of control signals

[0203] Control signals are stored through a zero-order hold and transmitted to the actuator.

[0204] S7: The actuator acts on the controlled object

[0205] The actuator acts on the controlled object according to the control signal to generate a new system state x k+1 . The new state is fed back to the system and the steps of S1 are repeated to form a closed-loop control process.

[0206] Since the system state x k is affected by the stochastic disturbance ω k The core of the optimization algorithm design lies in ensuring good convergence and robustness of the system through an adaptive event-triggering mechanism and the distributionally robust optimization method. By continuously feeding back the triggering interval, the new system state, and the control input into the optimization problem, the influence of stochastic disturbances on the system performance can be effectively handled, and the consistency of the system signal flow can be maintained, thereby achieving efficient control of complex uncertain environments.

[0207] This embodiment dynamically adjusts the sampling time through an adaptive event-triggering mechanism, combines distributionally robust optimization to ensure the feasibility of the optimization problem, and performs real-time adjustment of the system state through a closed-loop feedback mechanism, having the significant advantages of reducing computational and communication costs, and enhancing system stability and robustness.

[0208] Embodiment 4

[0209] As a further optimization of the foregoing embodiment, this embodiment proposes a specific implementation manner of the stochastic model predictive control method with adaptive event triggering according to the present invention.

[0210] DC-DC converters are widely used in the power supplies of electronic devices to control the energy flow between two DC systems. Buck-boost DC-DC converters are currently widely used in various related processes, including electric and hybrid vehicles, etc., and their structures are as Figure 4as shown

[0211] Figure 4 Shown is the schematic diagram of a buck - boost DC - DC converter, which is used to control the energy flow between DC systems. The main components of the circuit include the input voltage source V in , switches, inductor L, diode, capacitor C, and load R. When the switch is closed, the inductor L stores energy, and the input voltage generates current i L through the inductor, while the capacitor C supplies current to the load R; when the switch is open, the inductor releases energy, which flows through the diode to the capacitor and the load, ensuring the stability of the output voltage V out . The capacitor C smooths the output voltage, reduces fluctuations, and enables the load to obtain continuous current. This converter can adjust the relationship between the input and output voltages, being able to step up or step down the voltage.

[0212] To prove the effectiveness of the method described in this embodiment, consider a discrete buck - boost DC - DC converter. Referring to the research in "Lazar M M, Heemels W M, Roset B B, et al. Input - to - state stabilizing sub - optimal NMPC with an application to DC - DC converters[J]. International Journal of Robust & Nonlinear Control, 2010, 18(8)", the dynamic model of the DC - DC converter is as follows:

[0213]

[0214] where x k = [x 1,k x 2,k , representing the state vector, where x 1,k and x 2,k represent the current flowing through the inductor and the output voltage of the circuit respectively; u k represents the duty cycle. The parameters T, R, C, and L represent the discrete sampling time for discretizing the continuous system, the load resistance, the capacitor, and the inductor respectively.

[0215] Based on the above, referring to "Cannon M, Kouvaritakis B, V et al. Stochastic tubes in model predictive control with probabilistic constraints[C] / / American Control Conference. IEEE, 2010. The research on system linearization in it is as follows. The system state equation is established as follows:

[0216]

[0217] The chance constraints of the system state and control input of the system are as follows:

[0218]

[0219] The initial condition is \(x_0 = [2.5\ 3.2]\) T , \(\gamma = 10\). From \(F = diag\{1, 3.5\}\), \(R = 0.1\), The controller gain \(K = [-0.2632\ 0.3292]\) solved from the Ricatti equation in the LQR problem of, calculate the Lyapunov equation. The prediction horizon \(N = 8\) in this embodiment, and the simulation time is \(T\) run = 50. Consider two cases, where the system is disturbed by \(w\) following a Gaussian distribution and a non-Gaussian distribution.

[0220] Case a: The simulation results of the AET-SMPC algorithm with disturbance \(w\) k are given, following a Gaussian mixture distribution, and the probability density function distribution is as follows

[0221]

[0222] where, \(\lambda_1 = 0.4\), \(\lambda_2 = 0.6\).

[0223] Case b: Similar to most SMPC literatures, assume that \(w\) of the AET-SMPC algorithm k follows a Gaussian distribution \(N(0, 0.3)\).

[0224] This embodiment compares the Adaptive Event-Triggered Stochastic Model Predictive Control (AET-SMPC) algorithm with the Event-Triggered Stochastic Model Predictive Control (ET-SMPC) algorithm and the Periodic Stochastic Model Predictive Control (PSMPC) algorithm. The effectiveness and superiority of the AET-SMPC algorithm are demonstrated mainly from four aspects: stability, constraint violation, average sampling time, and performance. The performance metrics are calculated as follows:

[0225]

[0226] The 1000 simulation results of the system under three groups of adaptive parameters of ζ0 = 1, ζ0 = 1.5, ζ0 = 2, and PSMPC are considered. Among them, ζ0 = 1 is ET-SMPC.

[0227] The state response and control input results are as Figure 5 and Figure 7 shown. In the figure, hard constraint represents the boundary that the actual system is not allowed to cross. It can be seen that both methods can make the system state converge near 0, the system state and control input can better satisfy the chance constraint conditions, and the violation probability is much less than the preset value of 20%. From Figure 5 and Figure 7 it can be concluded that the algorithm proposed in this embodiment can not only adapt to different initial parameters but also adapt to w k subject to different distributions, and the state convergence of the system is better. In particular, when ζ0 = 2, the number of constraint violations is the least.

[0228] In addition, the last result of 1000 simulations is listed, and its trigger interval is listed. In this embodiment, the AET mechanism is used to reduce the number of triggers, thereby reducing the communication burden and the computational load of the system. Under different initial parameters, the trigger time points of case a and case b are as Figure 6 and Figure 8 shown. It can be seen that the algorithm proposed in this embodiment greatly reduces the number of samplings and communication resources.

[0229] Advantages of this algorithm compared with existing literature: As shown in Table 1 and Table 2, compared with ET-SMPC, AET-SMPC can not only reduce the communication times Γ, increase the communication step length Λ, but also has better performance metrics J perfIn addition, compared with the PSMPC studied in "B. Li, Y. Tan, A.-G. Wu and G.-R. Duan. A Distributionally Robust Optimization Based Method for Stochastic Model Predictive Control[J]. IEEE Trans. Autom. Control, vol. 67, no. 11, pp. 5762 - 5776", AET-SMPC can significantly reduce Γ from 0% to 78% and increase Λ from 0 to 4.5 while sacrificing slightly on performance metrics. Similarly, in case b, AET-SMPC can significantly reduce Γ from 0% to 64% and increase Λ from 0 to 2.77. By appropriately increasing the triggering parameter of AETM, the communication cost can be reduced.

[0230] Table 1: J perf , Λ and Γ for case a

[0231]

[0232] Table 2: J perf , Λ and Γ for case b

[0233]

[0234] In summary, the AET-SMPC algorithm proposed in this embodiment can not only reduce the sampling times of the system, reduce the number of constraint violations, save communication costs, be more robust, reduce computational costs, but also have better control performance.

[0235] Embodiment 5

[0236] This embodiment provides an adaptive event-triggered stochastic model predictive control device for implementing an adaptive event-triggered stochastic model predictive control method, which specifically includes the following structural and functional modules:

[0237] 1. Hardware composition

[0238] Processor (CPU / GPU / FPGA): Used to execute the core computational tasks of stochastic model predictive control, including state prediction, judgment of adaptive event-triggering conditions, and solution of distributionally robust optimization problems.

[0239] Memory (RAM / ROM): Used to store control algorithm programs, parameters of the adaptive event-triggering mechanism, historical state data, and intermediate results of optimization problems.

[0240] Communication module: Used for data interaction with sensors and actuators, receiving system state information and sending control inputs.

[0241] Power supply module: Provides stable power supply for the device.

[0242] 2. Software function modules

[0243] Data acquisition module: Receives system status information from sensors through the communication module, and records the current state deviation and the change amount of control input.

[0244] Event trigger judgment module: Implements an adaptive event trigger mechanism. By real-time monitoring the state deviation and input changes, it calculates whether the trigger condition is met. If it is met, it triggers the update of the control input; otherwise, it maintains the current state.

[0245] Optimization calculation module: Adopts the distributed robust optimization method to transform the probabilistic constraints in the stochastic model predictive control into a second-order cone convex optimization problem, and calls the optimization solver to determine the optimal control input.

[0246] Feedback control module: According to the optimal control input output by the optimization calculation module, it sends control signals to the actuator through the communication module to perform closed-loop control on the system.

[0247] Storage management module: Records historical data for subsequent optimization problem solving and dynamic adjustment of trigger conditions.

[0248] 3. Working process

[0249] After the device starts, the data acquisition module receives the system status information collected by the sensors in real time and transfers the data to the event trigger judgment module.

[0250] The event trigger judgment module dynamically judges whether it is necessary to trigger the update of the control input based on the current state deviation and the change amount of the control input. If the trigger condition is met, it proceeds to the next step; otherwise, it maintains the original control signal.

[0251] The optimization calculation module calls the distributed robust optimization algorithm according to the current system state, transforms the stochastic model predictive control problem with probabilistic constraints into a second-order cone convex optimization problem, and solves to obtain the optimal control input.

[0252] The optimal control input is sent by the feedback control module to the actuator to perform real-time adjustment on the system, ensuring that the system meets the stability and performance requirements under uncertain conditions.

[0253] 4. Application scenarios

[0254] This device can be applied to scenarios such as voltage control of power electronic systems, dynamic optimization control of industrial automation equipment, and communication load management of network control systems.

[0255] Through the specific implementation of this embodiment, the device can effectively reduce the sampling frequency and communication cost, improve the computing efficiency of the control system, and at the same time maintain the robustness and stability of the system in an uncertain environment.

[0256] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects.

[0257] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0258] The above-described embodiments only represent several implementation manners of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention patent should be subject to the appended claims.

Claims

1. An adaptive event-triggered stochastic model predictive control method, characterized in that It includes the following steps: S1. Dynamically adjust the sampling time of the control system and the update frequency of the control input through an adaptive event-triggering mechanism; the adaptive event-triggering mechanism is adjusted according to the changes in the system state and the control input; S2. Use the distributionally robust optimization method to transform the predictive control problem of a stochastic model with chance constraints into a second-order cone convex optimization problem for solution; S3. At each sampling time, determine the optimal control input by solving the second-order cone convex optimization problem, and perform feedback control on the state of the control system to adjust the communication sampling frequency.

2. An adaptive event-triggered stochastic model predictive control method according to claim 1, characterized in that The adaptive event-triggering mechanism includes the following steps: S101. Monitor the system state deviation between the current state and the most recent triggered state; S102. When the system state deviation exceeds a preset threshold, the preset adaptive event-triggering condition is reached, triggering sampling and updating the control input.

3. An adaptive event-triggered stochastic model predictive control method according to claim 2, characterized in that, The formula for the adaptive event-triggering condition is: Among them, is the trigger function, ε is the system error, ε ∈ (0, 1), is the trigger parameter, τ is the step size of the system, k is the time, k l is the trigger moment; γ is a predetermined positive definite constant; represents the error variable from a sampling state to the latest trigger state ​ 4. An adaptive event-triggered stochastic model predictive control method according to claim 3, wherein The adaptive event-triggering mechanism includes an adaptation law: Among them, ζ0 > 0, where ζ0 is the initial value of ζ τ |k l ; if then the triggering condition is the static event triggering mechanism; if then the described adaptive event triggering condition is applicable.

5. An adaptive event-triggered stochastic model predictive control method according to claim 4, wherein Step S2 further includes, through the distributionally robust optimization method, considering partial prior information of the disturbance distribution, and proving that the chance constraint is equivalent to the distributionally robust constraint and equivalent to the second-order cone convex optimization constraint; specifically, the chance constraint has the following formula: wherein, is the distribution of the perturbation; and are constant vectors, r and are given constants; x τ|k , u τ|k respectively represent the system state and control input at τ|k, where τ|k represents k + τ; δ x , δ u ∈(0,1) are respectively the maximum probabilities of the pre-specified allowable violations of the system state and control input constraints; The distributionally robust constraint has the following formula: The second-order cone convex optimization constraint has the following formula: where Φ = A + BK, is the prediction horizon length; is the decision variable; K is the controller gain; Σ w is the covariance matrix, is the predicted covariance matrix; is the predicted system state.

6. An adaptive event-triggered stochastic model predictive control method according to claim 5, characterized in that The objective function of the adaptive triggering mechanism is: wherein, is the system state deviation, is the cost of the control input, is the terminal Lyapunov state cost; is the expectation under the distribution ; N is the prediction horizon length, and are known weight matrices, and F N is the terminal weighting matrix.

7. An adaptive event-triggered stochastic model predictive control method according to claim 1, characterized in that, The constraint conditions of the second-order cone convex optimization problem include: the chance constraints of the system state and the control input; the probability that the system state and the control input satisfy is not less than a preset value.

8. An adaptive event-triggered stochastic model predictive control method according to claim 1, wherein In step S3, the optimal control input at each sampling time is determined recursively, and it is ensured that the system state and the control input satisfy the given constraint conditions at each moment.

9. An adaptive event-triggered stochastic model predictive control method according to claim 1, characterized in that The method is applied to the control of a buck-boost DC-DC converter, where: the adaptive event-triggering mechanism dynamically adjusts the triggering interval for updating the control input according to the state deviation of the inductor current and the output voltage and the change amount of the control input; the distributionally robust optimization method transforms the probability constraint in the optimization problem of the buck-boost DC-DC converter into a second-order cone convex optimization problem, and generates the optimal control input by solving this optimization problem; the switch state is adjusted by the control input obtained through optimization to control the output voltage of the DC-DC converter and reduce the triggering frequency.

10. A device applied to an automatic control system, characterized in that, It includes a processor, a memory, a communication interface, and a computer-readable storage medium; a computer program is stored on the computer-readable storage medium; When the computer program is executed by a computer, it implements an adaptive event-triggered stochastic model predictive control method according to any one of claims 1 to 9.

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