Limited control set model predictive control method with guaranteed limit cycle stability

Abstract

The application claims a limited control set model predictive control method with limit cycle stability guarantee, belonging to the technical field of switching systems and model predictive control. The method comprises: solving optimal steady-state limit cycle sequences satisfying constraints for discrete-time switching affine systems; constructing a limited control set predictive control optimization problem with limit cycle tracking as the target, including periodic terminal cost and terminal set constraints; systematically designing a quadratic periodic terminal cost satisfying Lyapunov decreasing condition, and two types of periodic invariant terminal sets of ellipsoid and polyhedron; based on terminal constraint guaranteeing recursive feasibility and asymptotic stability of tracking error, realizing online rolling optimization control. Through the control architecture of "off-line terminal component pre-design + online limited set rolling optimization", the application effectively solves the defects of unpredictable steady-state behavior and lack of strict stability guarantee of traditional limited control set predictive control, while considering multi-constraint processing capability and steady-state performance certainty, and can be widely adapted to various switching affine system scenes such as power electronic converters.

Description

Technical Field

[0001] This invention belongs to the field of switching systems and model predictive control technology, and relates to the stability design of finite control set model predictive control (FCS-MPC). Specifically, it relates to a finite control set predictive control method for discrete-time switched affine systems that has limit cycle stability guarantees and recursive feasibility. Background Technology

[0002] Switched affine systems consist of a finite number of subsystems, each corresponding to a constant state matrix and affine terms. Switching between subsystems is regulated by switching rules, and these systems are widely used in engineering applications such as power electronic converters, hybrid powertrains, and industrial automation. Finite set model predictive control, due to its inherent adaptability to discrete switching inputs, fast dynamic response, and explicit constraint handling, has become one of the mainstream control methods in the field of power electronics.

[0003] Most existing predictive control methods based on finite control sets can only provide practical stability guarantees, namely, ensuring that the state converges to a bounded, invariant set containing the desired steady state. Because the switching between finite control inputs is arbitrary, the steady-state switching behavior of the system is unpredictable, making it impossible to guarantee a fixed switching frequency and steady-state ripple performance. This makes it difficult to meet the stringent requirements of power electronics scenarios for total harmonic distortion and switching losses. Furthermore, traditional methods treat quantized inputs as disturbances, failing to provide a rigorous asymptotic stability proof under finite control sets.

[0004] In recent years, limit cycle stabilization methods have been proposed for switching affine systems. These methods involve designing periodic switching sequences to converge the system to a fixed-period trajectory, thereby achieving predictable steady-state performance. However, existing limit cycle controls are mostly state feedback switching laws, which cannot handle multi-constraint and multi-objective optimization. Furthermore, the terminal components of existing periodic tracking model predictive control are designed for continuous control sets, making them unsuitable for direct transfer to finite control set scenarios. Additionally, the lack of systematic terminal set construction methods and recursive feasibility proofs limits their engineering applications. Summary of the Invention

[0005] This invention aims to solve the problems of the prior art. It proposes a finite control set model predictive control method with limit cycle stability guarantees. Under finite control set constraints, it achieves limit cycle asymptotic tracking of a switched affine system, while possessing strict recursive feasibility and asymptotic stability theoretical guarantees, balancing dynamic constraint handling capability with steady-state performance determinism.

[0006] The technical solution of the present invention is as follows:

[0007] A predictive control method for a finite control set model with limit cycle stability guarantee includes the following steps:

[0008] Steady-state limit cycle solution: For discrete-time switched affine systems, based on the desired output reference and system constraints, solve for the optimal state limit cycle sequence and the corresponding input limit cycle sequence that satisfy the periodicity condition;

[0009] Predictive control problem construction: With the target tracking limit cycle as the objective, a finite control set model containing stage cost and periodic terminal cost is constructed to predict the control cost function, and the periodic terminal set is embedded as the terminal constraint into the optimization problem;

[0010] Periodic terminal component design: Design a component that satisfies the Lyapunov diminishing condition. Periodic terminal cost function, and its periodic invariance. A periodic set of terminals constitutes a terminal constraint pair that guarantees stability;

[0011] Online rolling optimization and control: At each control moment, the finite control set optimization problem is solved based on the current system state, and the first term of the optimal control sequence is applied to the system to achieve asymptotic stability tracking of the limit cycle.

[0012] Furthermore, the solution to the steady-state limit cycle specifically includes:

[0013] For discrete-time switched affine systems:

[0014] (1.1)

[0015] in, for Constantly control the input. for Time-corresponding control input The system state matrix, for Time-corresponding control input The system state affine term, for Time-corresponding control input The system output matrix, for Time-corresponding control input The system output affine terms; For system status, For control inputs within a finite control set. For system output; select period length Construct an input sequence of length p. , The first input sequence of the limit cycle Each element (the control input at the last moment of a cycle); the corresponding element is obtained by solving the periodic state equation. Periodic state limit cycle ,in The first state in the limit cycle sequence Each state point (the system state at the last moment of a cycle) satisfies... With the goal of minimizing the output reference tracking error, the optimization problem is solved under state and input constraints to obtain the optimal steady-state limit cycle sequence and the corresponding input sequence.

[0016] Furthermore, the periodic state equation is expressed in augmented matrix form as follows:

[0017] (1.2)

[0018] in, For the augmented state vector, For a block-based cyclic system matrix, For augmented input term vectors; if and only if the single-valued matrix When the eigenvalues ​​of any power of are not 1, there exists a unique steady-state limit cycle. The state matrix of the subsystem at "time 0 (the start of the period)" within one period of the limit cycle. It is determined by the control input at the initial time of the period. Decision, that is The corresponding state recursive relationship This describes the linear evolution of the state in the first step of the cycle. Within one period of the limiting cycle, "the first The subsystem state matrix corresponding to "each time point (the last time point of the cycle)". Furthermore, the construction of the predictive control problem specifically includes:

[0019] Define the prediction time domain as The predicted state sequence at time step is The predicted input sequence is ,in This represents the current measured state; where, express Predict the state at step 0 of time; express The first moment Predict the state step by step; express The control input at step 0 of time, i.e., the current time. The control input must be constantly and actually applied to the system; express The first moment The step control input is the last control input in the prediction time domain.

[0020] Construct the cost function:

[0021] (1.3)

[0022] in, As a stage cost, , They are respectively The limit cycle reference state and reference input at each moment; The time-varying periodic terminal cost; the constraints include system dynamics constraints, state constraints, input constraints, and terminal set constraints.

[0023] Furthermore, the stage cost is in quadratic form:

[0024] (1.4)

[0025] Where Q and R are the state error weight matrix and the input error weight matrix, respectively, both of which are positive definite matrices.

[0026] Furthermore, the periodic terminal cost is A periodic quadratic function, in the form of:

[0027] (1.5)

[0028] in, for A set of periodic positive definite weight matrices This represents the positive definite weight matrix of terminal cost corresponding to "step 0 (the start time of the cycle)" within one cycle of the limiting cycle; The term "the first" in a limit cycle refers to the period of a limit cycle. The terminal cost positive definite weight matrix corresponding to "step (the last moment of the cycle)".

[0029] By solving the system of linear matrix inequalities, the terminal cost diminishing condition is satisfied:

[0030] (1.6)

[0031] in Indicates the limit cycle of the 1st The state matrix of the steady-state subsystem corresponding to the step.

[0032] Furthermore, the aforementioned Periodic terminal set is Periodically invariant tube, by The sets are formed sequentially, satisfying: for any i-th set... Given a set of states, after applying the input corresponding to a limit cycle, the state will fall into the set of states. Within a set; the terminal set is in ellipsoidal or polyhedral form.

[0033] Furthermore, the method for constructing the ellipsoidal periodic terminal set is as follows:

[0034] Define error state ,structure ellipsoid set The positive definite matrix is ​​obtained by solving a convex optimization problem. This ensures that the error system satisfies the invariance condition. Each ellipsoid is contained within the state constraint feasible region at the corresponding time; the error space ellipsoid is mapped back to the original state space through the Minkowski addition method to obtain the p-period invariant terminal tube of the original system.

[0035] Furthermore, the method for constructing the polyhedral periodic terminal set is as follows:

[0036] Using the Pontryagin difference set between the feasible region of the state constraints at each time step and the reference state of the limit cycle as the initial set, the set is recursively processed by iterating through the backward reachable set and performing set intersection operations until the set converges, resulting in a polyhedral form. Periodically invariant error tubes; then mapped back to the original state space to obtain the terminal set.

[0037] Furthermore, the guarantees of recursive feasibility and asymptotic stability are specifically as follows:

[0038] If the initial state is within the feasible region, a feasible solution for the next time step can be constructed by shifting the optimal control sequence of the previous time step and supplementing the terminal limit cycle control law, thus ensuring the recursive feasibility of the algorithm.

[0039] The optimal value function constitutes the time-varying Lyapunov function of the error system, which satisfies the conditions of being positive definite, bounded and monotonically decreasing, ensuring that the tracking error origin is asymptotically stable, that is, the system state asymptotically converges to the target limit cycle.

[0040] The advantages and beneficial effects of this invention are as follows:

[0041] 1. Controllable steady-state performance: This invention uses a limit cycle tracking framework to enable the finite control set system to converge to a pre-designed periodic steady-state trajectory, solving the problems of unpredictable steady-state switching behavior and uncertain harmonic characteristics in traditional FCS-MPC, and can accurately meet the steady-state performance indicators of power electronics and other scenarios.

[0042] 2. Rigorous theoretical guarantee: This invention designs a systematic method for periodic terminal cost and terminal set construction for finite control set scenarios. Under the FCS-MPC framework, it simultaneously proves the recursive feasibility and the asymptotic stability of the limit cycle tracking error, making up for the lack of theoretical guarantee in existing methods.

[0043] 3. Strong engineering adaptability: This invention supports two terminal set forms, ellipsoids and polyhedra, which can be flexibly selected according to the system dimension and constraint type; the optimization problem is naturally adapted to finite switching inputs and can be directly applied to power electronic systems such as DC-DC converters and motor drives;

[0044] 4. Strong constraint handling capability: Based on the model predictive control framework, it can explicitly handle state constraints, input constraints and safety constraints, ensuring that the system operates within the feasible domain during dynamic processes.

[0045] 5. The innovation of this invention is mainly the innovation of the top-level architecture (claim 1), which corresponds to the complete combination of methods: "solution of steady-state limit cycle → construction of FCS-MPC with periodic terminal constraints → systematic design of periodic terminal components → online rolling optimization".

[0046] There are two parallel and independent technical routes in the existing technology: ① Traditional FCS-MPC only pursues "practical stability (ultimately bounded)" and improves steady state through superimposed switching frequency penalty heuristic. It is generally believed in the industry that finite control sets cannot achieve strict asymptotic stability by nature; ② Limit cycle control of switching systems only adopts pure state feedback switching law, which cannot explicitly handle multiple constraints.

[0047] Conventional approaches would not combine the "limit cycle steady-state objective" with the "FCS-MPC constrained optimization framework," let alone consider using periodic terminal components to compensate for stability shortcomings; this is a non-obvious combination across technical branches. Attached Figure Description

[0048] Figure 1 This is an overall technical roadmap of the method of the present invention, which provides a preferred embodiment;

[0049] Figure 2 is a schematic diagram of the behavior of the closed-loop limit cycle FCS-MPC system;

[0050] Figure 3 shows the behavior of the closed-loop system; a schematic diagram comparing standard predictive control and limit loop predictive control with a stable model predictive control.

[0051] Figure 4 is a schematic diagram of the topology of a non-inverting Buck-Boost converter. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0053] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0054] Example 1: Overall Method Flow

[0055] As shown in Figure 1, the finite control set model predictive control method with limit cycle stability guarantee described in this embodiment is divided into two main parts: offline design and online control. The offline part completes the limit cycle solution and terminal component design, while the online part completes the rolling optimization and control output.

[0056] Step S1: Solving for the steady-state limit cycle

[0057] First, establish a discrete-time switching affine system model:

[0058] (1.1)

[0059] In the formula, For system status, For a finite set of control inputs, This is the system output. The continuous state matrix is ​​also included. Continuous affine terms Continuous state matrix Continuous affine terms Output matrix ,

[0060] For the selected period length Construct the input sequence ,remember , If the input sequence generates a unique value... Periodic state limit cycle It needs to meet the periodic conditions. The corresponding system of equations:

[0061] (1.2)

[0062] Write the system of equations in augmented matrix form , in The necessary and sufficient condition for the existence of a limit cycle is that the single-valued matrix... The eigenvalues ​​of any positive integer power of are not 1.

[0063] To obtain the optimal limiting cycle, the following optimization problem is constructed:

[0064] (1.3.1)

[0065] (1.3.2)

[0066] in, The cost function is the desired output reference sequence. The error norm between the steady-state output mean and the reference value is used to measure the tracking accuracy of the limit cycle. Solving this problem yields the optimal steady-state limit cycle. With the corresponding input sequence Optimal input sequence ,

[0067] Step S2: Problem Construction of Limit Cycle FCS-MPC

[0068] definition The time domain for time prediction is Predicting state sequence Predict the input sequence ,in This is the current measured state, the initial state. The reference limit cycle sequence extended periodically is as follows: .

[0069] Construct the cost function:

[0070] (1.4)

[0071] in, As a stage cost, , They are respectively The limit cycle reference state and reference input at each moment; This is the cost of a time-varying periodic terminal.

[0072] Among them, the stage cost Adopting a quadratic form:

[0073] (1.5)

[0074] The positive definite weight matrix is ​​used to adjust the state tracking accuracy and input smoothness, respectively. For time-varying periodic terminal costs, This represents the periodic terminal set at the corresponding time.

[0075] The constraints of the optimization problem are:

[0076] (1.6)

[0077] Solving the optimization problem yields the optimal input sequence. According to the rolling time domain principle, the first term is taken.

[0078] It acts on the system.

[0079] Step S3: Design of Periodic Terminal Components

[0080] The terminal components, including terminal costs and terminal sets, are the core of ensuring stability and feasibility.

[0081] S3.1 Periodic Terminal Cost Design

[0082] Terminal cost adopts Periodic quadratic form:

[0083] (1.7)

[0084] in, for A set of periodic positive definite matrices.

[0085] To ensure that the terminal cost decreases along the limit cycle control law, the following linear matrix inequality (LMI) constraint must be satisfied:

[0086] (1.8)

[0087] Solving this LMI problem yields the periodic terminal cost weight matrix that satisfies the stability condition.

[0088] S3.2 Periodic Terminal Set Design

[0089] Define error state Then the error system is The terminal set design is transformed into an error system. The periodically invariant transistor is designed, and then mapped back to the original state space using the Minkowski addition method.

[0090] Ellipsoidal periodic terminal set: construction ellipsoidal error set The following convex optimization problem is obtained by solving it. :

[0091] (1.9.1)

[0092] (1.9.2)

[0093] in , Let be the hyperplane matrix of the state-constrained polyhedron. The resulting ellipsoid set satisfies the invariance and constraint inclusion conditions.

[0094] The polyhedral periodic terminal set is constructed using a set recursive algorithm, with the following steps:

[0095] 1. Initialization: Let That is, the Pontryagin difference between the state constraint set and the reference state;

[0096] The Pontryagin set difference is defined as follows: .

[0097] 2. Reverse iteration: For each Calculate the one-step backward reachable set and intersect with the previous set;

[0098] 3. Convergence criterion: If all sets are equal before and after the iteration, then the iteration is terminated, and the polyhedral invariant error tube is obtained.

[0099] Map the error set back to the original state space: That is, to obtain the original system The periodic terminal tube remains unchanged.

[0100] in This is the Minkowski set addition method.

[0101] Step S4: Stability and Feasibility Analysis

[0102] S4.1 Proof of Recursive Feasibility

[0103] like If the time-limited optimization problem is feasible, i.e., if there exists an input sequence that satisfies all constraints, then construct... Candidate input sequence at time:

[0104] Due to the terminal state at time k Apply limit cycle input Then, the next state falls into The terminal constraint is satisfied. Therefore, this candidate sequence is... Since there is a feasible solution at any given time, the optimization problem is recursively feasible.

[0105] S4.2 Proof of asymptotic stability

[0106] Define tracking error Optimal value function From the positive definiteness of stage cost, we can obtain... From the boundedness of terminal cost, we can obtain It can be derived from the condition of diminishing terminal costs. Therefore, the optimal value function is the time-varying Lyapunov function of the error system, and the error origin is asymptotically stable, meaning that the system state asymptotically converges to the target limit cycle.

[0107] Figure 2 For Example 1: Closed-loop limit cycle FCS-MPC system behavior, from the state trajectory diagram ( and From the perspective of changes over time, although the two subsystems that make up the system are inherently unstable, under the action of the controller, the state variables (solid blue line) converge rapidly and completely coincide with the preset 3-period limit cycle reference trajectory (dashed red line) after about 2 seconds. Afterwards, and It strictly follows the law of the limit cycle to perform periodic oscillations on the phase plane, and the entire process always remains at... Within the state constraint boundaries, no boundary violations occurred. The solid blue line in the lower left of the figure gradually approaches the dashed red line after the initial transient state and completely overlaps it after approximately 2 seconds, indicating that the actual state successfully entered the preset periodic trajectory; the lower right figure shows the optimal cost function (logarithmic coordinates). From the evolution curve of the function, it can be seen that the function is strictly monotonically decreasing from the initial moment, and stabilizes at a certain low logarithmic level after the state enters the steady-state period.

[0108] Example 2: Buck-Boost Converter Application

[0109] This embodiment applies the described method to a non-inverting Buck-Boost converter to verify the control effect. The converter topology is shown in Figure 4, which includes two independent switches. There are a total of 4 switching modes.

[0110] The system status is These are the capacitor voltage and inductor current, respectively; the output is the capacitor voltage. .

[0111] System sampling frequency Sampling time The state constraints are Input voltage Input current Inductor internal resistance ,inductance ,capacitance Reference output voltage .

[0112] Selecting the period of the limit cycle The optimal limit cycle sequence and its corresponding switching sequence are obtained by solving the problem. Prediction in the time domain. Stage cost weight The periodic terminal cost weights are solved using LMI, and a polyhedral terminal set is constructed.

[0113] Simulation results show that the average error of the steady-state output voltage of the proposed limiting-loop FCS-MPC method is: Significantly superior to traditional FCS-MPC The steady-state switching sequence is fixed in a periodic mode, the switching frequency is stable, and the output ripple is controllable. The state trajectory asymptotically converges to the target limit cycle, satisfying the state and input constraints throughout the process, verifying the effectiveness of the method and the correctness of the theoretical guarantee.

[0114] Figure 3 In the top-left subgraph, the voltage waveforms of both the polyhedral terminal (blue dashed line) and the ellipsoidal terminal (green dashed line) stabilize on a periodic trajectory centered at 18.2V after approximately 0.1ms. While the standard no-terminal scheme (red dashed line) converges faster, its steady-state ripple is significantly larger. This indicates that the terminal set, by constraining the state into a periodic invariant channel, trades a slightly slower response speed for the predictable steady-state behavior emphasized in the paper. In the top-right subgraph, the current ripple of the standard scheme (red dashed line) is significantly greater than that of the scheme with terminals, and the fluctuation amplitude is irregular; while the current trajectory of the polyhedral / ellipsoidal terminal scheme exhibits a clear, repeating periodic waveform in steady state. This directly confirms the paper's argument that "terminal sets can regulate the system state trajectory"—by restricting the state within a periodic channel, the current fluctuation range is effectively constrained. In the bottom-left subgraph, the switching modes of the scheme with terminal sets (polyhedral / ellipsoidal) strictly follow the optimal sequence of offline optimization. The period is 6, which indicates that the terminal control law The system was indeed successfully "anchored" to the preset limit cycle, while the standard scheme (red) exhibited a chaotic switching pattern. In the lower right subplot, all three curves exhibit a strictly monotonically decreasing trend and tend towards constant values ​​in steady state.

[0115] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions.

[0116] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0117] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A predictive control method for a finite control set model with limit cycle stability guarantee, characterized in that, Includes the following steps: Steady-state limit cycle solution: For discrete-time switched affine systems, based on the desired output reference and system constraints, solve for the optimal state limit cycle sequence and the corresponding input limit cycle sequence that satisfy the periodicity condition; Predictive control problem construction: With the target tracking limit cycle as the objective, a finite control set model containing stage cost and periodic terminal cost is constructed to predict the control cost function, and the periodic terminal set is embedded as the terminal constraint into the optimization problem; Periodic terminal component design: Design a component that satisfies the Lyapunov diminishing condition. Periodic terminal cost function, and its periodic invariance. A periodic set of terminals constitutes a terminal constraint pair that guarantees stability; Online rolling optimization and control: At each control moment, the finite control set optimization problem is solved based on the current system state, and the first term of the optimal control sequence is applied to the system to achieve asymptotic stability tracking of the limit cycle.

2. The finite control set model predictive control method with limit cycle stability guarantee according to claim 1, characterized in that, The solution to the steady-state limit cycle specifically includes: For discrete-time switched affine systems: (1.1)； in, for Constantly control the input. for Time-corresponding control input The system state matrix, for Time-corresponding control input The system state affine term, for Time-corresponding control input The system output matrix, for Time-corresponding control input The system output affine terms; For system status, For control inputs within a finite control set. For system output; select period length Construct an input sequence of length p. ,in The first input sequence of the limit cycle Each element (the control input at the last moment of a cycle) is obtained by solving the periodic state equation. Periodic state limit cycle ,in The first state in the limit cycle sequence There are several state points (the system state at the last moment of a cycle), and they satisfy the following conditions: With the goal of minimizing the output reference tracking error, the optimization problem is solved under state and input constraints to obtain the optimal steady-state limit cycle sequence and the corresponding input sequence.

3. The finite control set model predictive control method with limit cycle stability guarantee according to claim 2, characterized in that, The periodic state equation is expressed in augmented matrix form as follows: (1.2)； in, For the augmented state vector, For a block-based cyclic system matrix, For augmented input term vectors; if and only if the single-valued matrix When the eigenvalues ​​of any power of eigenvalue are not 1, there exists a unique steady-state limit cycle. The state matrix of the subsystem corresponding to "time 0 (the start time of the period)" within one period of the limit cycle; it is determined by the control input at the initial time of the period. Decision, that is The corresponding state recursive relationship This describes the linear evolution of the state in the first step of the cycle; Within one period of the limiting cycle, "the first The subsystem state matrix corresponding to "each time point (the last time point of the cycle)"; it is composed of the control input at the last step of the cycle. Decision, that is The corresponding state recursive relationship It describes the state evolution of the last step in the cycle, which is also a key step in the formation of the periodicity of the closed loop.

4. The finite control set model predictive control method with limit cycle stability guarantee according to claim 1, characterized in that, The construction of the predictive control problem specifically includes: Define the prediction time domain as The predicted state sequence at time step is , The predicted input sequence is: , express The control input at step 0 of time, i.e., the current time. The control input must be actually applied to the system at all times; express The first moment Step control input, i.e., the last control input in the prediction time domain; Construct the cost function: (1.3)； in, As a stage cost, , They are respectively The limit cycle reference state and reference input at each moment; The time-varying periodic terminal cost; the constraints include system dynamics constraints, state constraints, input constraints, and terminal set constraints.

5. The finite control set model predictive control method with limit cycle stability guarantee according to claim 4, characterized in that, The stage cost is in quadratic form: （1.4）； Where Q and R are the state error weight matrix and the input error weight matrix, respectively, both of which are positive definite matrices.

6. The finite control set model predictive control method with limit cycle stability guarantee according to claim 1, characterized in that, The periodic terminal cost is A periodic quadratic function, in the form of: （1.5）； in, for A set of periodic positive definite weight matrices This represents the positive definite weight matrix of terminal cost corresponding to "step 0 (the start time of the cycle)" within one cycle of the limiting cycle; Indicates the "th" in one period of the limiting cycle. The positive definite weight matrix of the terminal cost corresponding to "step (the last moment of the cycle)"; By solving the system of linear matrix inequalities, the terminal cost diminishing condition is satisfied: （1.6）； in Indicates the limit cycle of the 1st The state matrix of the steady-state subsystem corresponding to the step.

7. The finite control set model predictive control method with limit cycle stability guarantee according to claim 1, characterized in that, The Periodic terminal set is Periodically invariant tube, by The sets are formed sequentially, satisfying: for any i-th set... Given a set of states, after applying the input corresponding to a limit cycle, the state will fall into the set of states. Within a set; the terminal set is in ellipsoidal or polyhedral form.

8. The finite control set model predictive control method with limit cycle stability guarantee according to claim 7, characterized in that, The method for constructing the ellipsoidal periodic terminal set is as follows: Define error state ,structure ellipsoid set The positive definite matrix is ​​obtained by solving a convex optimization problem. This ensures that the error system satisfies the invariance condition. Each ellipsoid is contained within the state constraint feasible region at the corresponding time; the error space ellipsoid is mapped back to the original state space through the Minkowski addition method to obtain the p-period invariant terminal tube of the original system.

9. The finite control set model predictive control method with limit cycle stability guarantee according to claim 7, characterized in that, The method for constructing the polyhedral periodic terminal set is as follows: Using the Pontryagin difference set between the feasible region of the state constraints at each time step and the reference state of the limit cycle as the initial set, the set is recursively processed by iterating through the backward reachable set and performing set intersection operations until the set converges, resulting in a polyhedral form. Periodically invariant error tubes; then mapped back to the original state space to obtain the terminal set.

10. The finite control set model predictive control method with limit cycle stability guarantee according to claim 1, characterized in that, The specific guarantees of recursive feasibility and asymptotic stability are as follows: If the initial state is within the feasible region, a feasible solution for the next time step can be constructed by shifting the optimal control sequence of the previous time step and supplementing the terminal limit cycle control law, thus ensuring the recursive feasibility of the algorithm. The optimal value function constitutes the time-varying Lyapunov function of the error system, which satisfies the conditions of being positive definite, bounded and monotonically decreasing, ensuring that the tracking error origin is asymptotically stable, that is, the system state asymptotically converges to the target limit cycle.

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