Novel self-adaptive control and synchronization method for nonlinear dynamic behavior of sodium ion battery

Abstract

The invention relates to the technical field of battery management, in particular to a novel self-adaptive control and synchronization method for nonlinear dynamic behaviors of a sodium-ion battery, which comprises the following steps: designing a controller by combining a self-adaptive inversion technology, and constructing a strategy by adopting a multi-step Lyapunov function; in order to ensure that a system state error and a parameter estimation error can be converged to zero within free intention time pre-specified by a user, a self-adaptive parameter adjustment rate is designed to ensure the continuity and the bounded property of a control signal, and in order to cope with parameter uncertainty caused by battery aging and environment change, a self-adaptive parameter adjustment rate is designed. The method further introduces a real-time monitoring and dynamic adjusting mechanism. According to the method, the control capability of a highly-uncertain and highly-nonlinear system is remarkably enhanced, the control flexibility is improved through setting of free intention time, the global stability is enhanced through multi-step inversion design, the control precision and robustness are remarkably improved, and the method can be widely applied to various scenes such as fixed energy storage and electric automobiles and is prominent in practical value.

Description

Technical Field

[0001] This invention relates to the field of battery management technology, specifically to a novel adaptive control and synchronization method for the nonlinear dynamic behavior of sodium-ion batteries. Background Technology

[0002] Sodium-ion batteries, as an emerging electrochemical energy storage technology, have shown broad application prospects in large-scale energy storage and low-speed electric vehicles due to their abundant resources, low cost, and environmental friendliness. Compared with lithium-ion batteries, the internal electrochemical processes of sodium-ion batteries exhibit stronger nonlinearity, time-varying characteristics, and uncertainties, and their kinetic behavior displays highly complex nonlinear system characteristics.

[0003] Current sodium-ion battery management systems (BMS) mainly employ methods based on traditional linear control theory (such as PID control) or model predictive control (MPC). These methods have significant limitations in dealing with the strong nonlinearity and uncertain dynamic characteristics of sodium-ion batteries. 1. Slow convergence speed: Traditional linear control methods rely on local linearization approximations when dealing with highly nonlinear battery dynamics, resulting in slow convergence of the system state to the equilibrium point, which cannot meet the rapid response requirements of high-dynamic application scenarios. Especially when dealing with conditions such as high-current charging and discharging and sudden temperature changes, the system adjustment process exhibits significant lag.

[0004] 2. Complex control laws and heavy computational burden: Existing nonlinear control methods, such as backstepping control and sliding mode control, can handle certain nonlinear characteristics, but they usually require accurate system models and parameter information. When faced with the uncertainty of time-varying parameters inside sodium-ion batteries (such as diffusion coefficient, reaction rate, internal resistance, etc.), the design of the controller becomes extremely complex, resulting in cumbersome control law structures, a significant increase in computational load, and difficulty in implementing real-time control on embedded BMS hardware platforms.

[0005] 3. Settlement time depends on initial conditions: While existing fixed-time or finite-time control methods can achieve fast convergence, their convergence time is heavily dependent on the initial state of the system and the magnitude of parameter uncertainties. Designers cannot freely specify the convergence time according to actual application requirements (such as safety deadlines, operating condition switching times, etc.), resulting in a lack of flexibility.

[0006] (4) Poor parameter adaptability: The parameters of sodium-ion batteries (such as internal resistance and capacity) change significantly with factors such as the number of cycles, temperature, and aging. Existing control methods lack effective online parameter identification and adaptive mechanisms, making it difficult to maintain consistent control performance throughout the entire life cycle, resulting in insufficient system robustness.

[0007] (5) Lack of rigorous theoretical guarantees: Although some existing methods attempt to introduce adaptive mechanisms, they usually rely on strong assumptions (such as slow parameter changes, bounded uncertainty, etc.) and lack a rigorous theoretical framework to guarantee stability within the user-specified time, making it difficult to meet the needs of high reliability applications.

[0008] Therefore, there is an urgent need for a new control method that can achieve fast and accurate convergence under relaxed assumptions, and whose convergence time can be freely specified, in order to solve the above-mentioned defects of existing technologies in practical applications. Summary of the Invention

[0009] The purpose of this invention is to provide a novel adaptive control and synchronization method for the nonlinear dynamic behavior of sodium-ion batteries, in order to solve the problems of slow convergence speed, complex control law, and stability time dependence on initial conditions in traditional control methods such as PID or model predictive control mentioned in the background art.

[0010] To achieve the above objectives, the present invention provides the following technical solution: A novel adaptive control and synchronization method for the nonlinear dynamic behavior of sodium-ion batteries, specifically including the following steps: (1) Establish a nonlinear dynamic model of sodium-ion battery with unknown parameters and generalize it to an uncertain Lorentz system; (2) Based on the theory of free will time stability, construct an adaptive control law that satisfies more relaxed constraints; (3) Design a controller by combining the adaptive inversion method to realize the system convergence to the equilibrium point within a preset free will time; (4) Design the corresponding adaptive parameter adjustment rate to make the control signal and parameter estimation continuous and bounded; (5) The effectiveness of the control law is verified by simulation, so that the sodium-ion battery dynamic system can be stable, synchronized and maintain a convergent state within any set time.

[0011] Preferably, the uncertain Lorentz system is: ; The above formula can be summarized as follows: ,in, , and These represent the system state, control input, and unknown parameters, respectively. It is the initial state of the system, mapping It satisfies the Lipschitz condition with respect to the state, where the state is continuous in time.

[0012] Preferably, the free will time stability includes weak free will time stability and strong free will time stability; wherein, weak free will time stability requires the system convergence time to be not less than a specified time, and strong free will time stability requires the system convergence time to be equal to the specified time, and the stability guarantee is enhanced by relaxing the Lyapunov inequality conditions.

[0013] Preferably, the adaptive inversion controller is designed using a multi-step Lyapunov function construction strategy. Each step designs a local Lyapunov function based on the result of the previous step, and by deriving the control law and adaptive rate, it is ensured that the system state error and parameter estimation error converge to zero within the free-will time. Preferably, the adaptive inversion method specifically includes the following steps: S1: Establish the coordinate transformation as follows: ; in It is the virtual control of free will time in the first step; Represented as: ; The design of the Lyapunov function is as follows: ; in, , ; S2: Based on the above formula, the following result can be obtained: Lyapunov function The design is as follows: ; Control Law The design is as follows: The adaptive rate design is as follows: ; ; Substituting the above formula, it can be written in the following form: ; S3: Through coordinate transformation and the uncertain Lorentz system, we can obtain... for: Lyapunov function The design is as follows: ; Free Will Time Control Law and adaptive rate The design is as follows: ; Substituting the above formula, we get: .

[0014] Preferably, the proof of the free-will time stability includes two parts: Part A proves that the system state and adaptive parameters are bounded during the control process, and Part B proves that the system converges within a specified time. Part A is achieved through the monotonically decreasing property of the Lyapunov function, and Part B uses the integral divergence lemma to ensure global stability.

[0015] Preferably, the specific steps of the simulation verification are as follows: simulate the dynamic behavior of sodium-ion batteries through numerical simulation and compare the system performance under different free will time settings; in the simulation, the system model adopts the Lorentz system as a representative, the initial state is set as a non-equilibrium point, and the controller parameters are adjusted according to the specified time.

[0016] Preferably, the parameters of the Lorentz system are selected as follows: , and The initial state of the system is set to .

[0017] As a preferred option, it also includes a real-time monitoring and dynamic adjustment mechanism for the time-varying characteristics of the internal parameters of the sodium-ion battery. This mechanism estimates unknown parameters online and feeds them back to the controller to achieve dynamic optimization of the control strategy, so as to cope with the impact of external factors such as battery aging and temperature changes on system performance.

[0018] Preferably, the real-time monitoring and dynamic adjustment mechanism uses recursive least squares or extended Kalman filter algorithm for parameter estimation. By continuously updating the parameter estimates, the control accuracy and the system's adaptability to complex working environments are improved.

[0019] Compared with the prior art, the beneficial effects of the present invention are: The core advantage of this invention's novel adaptive control and synchronization method for the nonlinear dynamic behavior of sodium-ion batteries lies in: 1. Stronger ability to cope with high uncertainty and strong nonlinearity Sodium-ion batteries exhibit complex internal electrochemical reactions during charging and discharging, influenced by factors such as temperature, aging level, and charging / discharging rate, resulting in high uncertainty and strong nonlinear dynamic characteristics. Traditional control methods often struggle to accurately model and effectively address these complex characteristics, leading to poor control performance. However, the adaptive control technology introduced in this invention can sense changes in the battery system state and parameters in real time and automatically adjust the control strategy without requiring a precise system model. This allows for more relaxed constraints while effectively handling the uncertainties in the battery's internal parameters, ensuring stable system operation.

[0020] 2. Free will time setting enhances control flexibility. Traditional fixed-time or predefined-time control methods typically have a pre-set and fixed convergence time, making it difficult to flexibly adjust according to actual needs and system states. This invention constructs a control strategy based on the free-will-time stability theorem, allowing for flexible setting and adjustment of the free-will time according to specific application scenarios and performance requirements. This means that under different operating conditions, such as fast charging, deep discharging, or different temperature environments, the system state can be quickly and accurately converged to the equilibrium point within a specified time by modifying the time parameter in the control law, greatly improving the flexibility and adaptability of control.

[0021] 3. Ensure the continuity and boundedness of control signals. In battery control systems, the continuity and boundedness of control signals are crucial for stable system operation and equipment safety. Discontinuous or unbounded control signals can lead to battery overcharging, over-discharging, or control system oscillations, and may even damage the battery and equipment. This invention fully considers this point when designing the control law and adaptive rate. By rationally selecting the control gain and adaptive gain, it ensures that the control signal remains continuous and bounded throughout the control process, effectively avoiding safety problems caused by abnormal control signals and improving the reliability and safety of the system.

[0022] 4. Multi-step inversion design enhances global stability The adaptive inversion controller of this invention employs a multi-step design process. Each step constructs a local Lyapunov function based on the result of the previous step, designs a virtual control input, and progressively modifies it until the final control law is obtained. This multi-step design method ensures the stability of each subsystem level, thereby guaranteeing the global stability of the overall system. Compared with the traditional single-step design method, multi-step inversion design can handle nonlinear and uncertain factors in the system more meticulously, gradually building a stable control system from local to global, effectively improving the system's stability and robustness.

[0023] 5. Real-time monitoring and dynamic adjustment enhance adaptability. During use, the internal parameters of sodium-ion batteries change over time due to factors such as battery aging and temperature variations. Traditional control methods often fail to detect these parameter changes in a timely manner and make corresponding adjustments, leading to a decline in control performance. This invention establishes a real-time monitoring and dynamic adjustment mechanism, which estimates unknown parameters online and feeds them back to the controller to achieve dynamic optimization of the control strategy. This mechanism employs advanced parameter estimation methods such as recursive least squares or extended Kalman filtering algorithms, enabling rapid and accurate updates of parameter estimates. This allows the control system to adapt to changes in battery parameters in a timely manner, maintaining optimal control performance and improving the system's adaptability to complex operating environments.

[0024] 6. Significantly improves control accuracy and robustness By comprehensively utilizing adaptive control technology, the free-will time stability theorem, multi-step inversion design, and real-time monitoring and dynamic adjustment mechanisms, the method of this invention exhibits superior control accuracy and robustness. Simulation experiments and actual battery system test results show that, under different free-will time settings and various operating conditions, the system state can quickly and stably converge to the desired equilibrium state within a specified time, and the control effect is significantly better than traditional fixed-time and predefined-time control methods. This indicates that the method of this invention can more accurately control the state of the battery system, effectively resist the influence of external disturbances and internal parameter changes, and improve the overall performance of the battery management system.

[0025] 7. It has broad application prospects and high practical value. The method of this invention is applicable to different types of sodium-ion battery systems, including stationary energy storage systems, electric vehicle battery packs, and batteries for portable electronic devices. Whether for large-scale energy storage applications or small portable devices, stable control and synchronization of battery systems in different scales and application scenarios can be achieved by adjusting control parameters. This broad applicability gives the method of this invention enormous market potential and practical value, providing strong technical support for the large-scale application of sodium-ion batteries in various fields. Attached Figure Description

[0026] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are explained in detail together with the embodiments of the invention, but do not constitute a limitation thereof.

[0027] Figure 1 This is a diagram of the chaotic motion of the uncontrolled Lorentz system of this invention. Figure 2 This is a state performance diagram when the present invention is configured; Figure 3 This is a state performance diagram when the present invention is configured; Figure 4This is a comparison diagram of the system state evolution under four time-based control schemes of the present invention. Detailed Implementation

[0028] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0029] This invention primarily investigates the convergence of Lorentz systems with uncertain parameters to an equilibrium point within a free-will time under more relaxed constraints. Traditional battery management systems struggle to achieve rapid and precise state control when dealing with the highly uncertain and strongly nonlinear internal parameters of sodium-ion batteries (such as time-varying internal resistance, diffusion coefficient, and reaction rate), and suffer from slow convergence speeds and complex control laws. The core of this invention lies in researching how to stabilize such battery dynamic systems with uncertain parameters to a desired equilibrium state within a pre-specified free-will time under more relaxed constraints. First, for nonlinear systems with unknown parameters, a free-will time stability theorem based on adaptive techniques is defined. This theorem extends the traditional free-will time theorem and provides broader stability guarantees by relaxing the conditions of Lyapunov's inequality. Furthermore, based on this theorem and combined with an adaptive inversion method, a novel adaptive free-will time control strategy is proposed. Compared to existing control methods, the proposed strategy requires fewer assumptions and has a simpler controller form. This strategy ensures that the system's transformation error and state converge to zero and remain at zero within a specified free-will time, while also ensuring the continuity and boundedness of the control signal and the adaptive rate.

[0030] Specifically as follows: 1. Consider the following uncertain Lorentz system: (1) We can summarize the above system as follows: (2) in, , and These represent the system state, control input, and unknown parameters, respectively. This is the initial state of the system. Mapping The Lipschitz condition with respect to the state is satisfied, where the state is continuous in time. Therefore, for all System (2) has a unique solution.

[0031] Definition 1: Consider the following nonlinear system: if , It is the stability of free will at any time. (a) It is time-stable. (b) It is independent of system parameters and initial conditions and can be predefined; (c) can establish (1) (Weak free will, stable at any time) or (2) (Strong free will and arbitrary time stability), where is the true fixed time.

[0032] Consider the following nonlinear system: (3) in Assumption set , Including the origin, and also... There is a smooth positive function. and Suppose there exists a piecewise, real-valued, continuously differentiable function: ,in, Considering the convergence time .if The following conditions must be met.

[0033] (2) So the system It is a free will with weak time stability, and its stability time is .

[0034] Definition 2: For system (2), if the following control law and adaptive rate exist: , (4) , (5) in, It is an estimate of the unknown parameter B. , , This represents the parameter estimation error. For any system initial values... ,in As a positive constant, under the influence of the controller (4) and the adaptive rate (5), and The trajectory is bounded. right Established, among which It is a positive constant. The equilibrium point of system (2) is at free will time. The point below is called the local free will time-stability point (denoted as ). -ATS), which is independent of the system's initial conditions. It is the attraction domain of the system (2). If If true, then the equilibrium point of system (1) is called the global free will time-stability (denoted as global). -ATS).

[0035] For in The above-defined defective Continuous functions If it satisfies: (6) in Is it a positive number or Then inappropriate integration It is divergent.

[0036] (12) if If is a normal constant, then the equilibrium point of system (2) is globally free will time stable.

[0037] Proof: This proof consists of two parts, namely Part A and Part B.

[0038] A) First, it was proven that under the action of controller (4), the state and fitness rate The trajectory is bounded.

[0039] B) In system (2), state The trajectory in free will time It converges to the equilibrium point and remains at the equilibrium point thereafter.

[0040] Part A: From formula (12), we can obtain: therefore, right Monotonically decreasing, from formula (9) we can obtain: (13) Then, according to formulas (10), (11) and (13), we can obtain: Therefore, state and adaptive parameter estimation error It is bounded. Because It is easy to conclude exist The conclusion is that it is bounded internally.

[0041] And assume (15) in, It is a normal constant.

[0042] 2. Controller Design Process and Stability Analysis A) Controller Design Process Based on Theorem 1, a theoretical adaptive inversion method is designed. The controller design includes three steps. First, the coordinate transformation is established as follows: (16) in It is the virtual control of free will time in the first step.

[0043] Step 1 is based on formulas (1) and (16). It can be represented as: (17) Lyapunov function The design is as follows: (twenty one) in, , Step 2, based on formulas (1) and (15), yields the following results: (twenty two) Lyapunov function The design is as follows: Control Law The design is as follows: (twenty four) (25) Adaptive rate and The design is as follows: (26) (27) Substitute (25)-(27) into equation (24). It can be written in the following form: (28) Step 3, through coordinate transformation (16) and system (1), yields the following results: for: (29) Lyapunov function The design is as follows: Free Will Time Control Law and adaptive rate The design is as follows: (31) (32) (33) Substituting (32) and (33) into (31), we get: (34) The design of the free will time controller has been completed.

[0044] 3. Simulation Verification In this section, we conducted simulations to further verify the effectiveness of the proposed free-will-time adaptive control scheme with parameter uncertainties. To verify the effectiveness of the proposed scheme, two sets of experiments with different free-will time intervals were compared.

[0045] The parameters for the Lorentz system are selected as follows: , and The initial state of the system is set to .from Figure 1 It can be seen that the Lorentz system exhibits chaotic behavior when no control input is applied.

[0046] To obtain better simulation results, the controller parameters are selected as follows: , , , , , , , The initial conditions are set as follows: .

[0047] 3.1 Comparative Analysis of System Response under Different Time Settings like Figure 2 and Figure 3As shown, all system states converge to zero within the specified convergence time of 1 second, indicating that the proposed controller effectively guarantees free-will convergence at any time, where the terminal time can be flexibly specified by the designer. Overall, the proposed control strategy ensures that system states and errors converge within a user-defined time range, achieving the theoretical goal of free-will convergence while maintaining low control workload and accurate parameter identification.

[0048] Comparative experiments of different settling time schemes: like Figure 4 System state under fixed-time adaptive backstepping control scheme, predefined-time adaptive backstepping control scheme, and novel adaptive free-will time backstepping control strategy , and The evolution of.

[0049] For fixed-time and predefined-time control schemes, the parameter selection is as follows: For fixed-time schemes For a predefined time scheme .

[0050] The core advantage of this invention's novel adaptive control and synchronization method for the nonlinear dynamic behavior of sodium-ion batteries lies in: 1. Stronger ability to cope with high uncertainty and strong nonlinearity Sodium-ion batteries exhibit complex internal electrochemical reactions during charging and discharging, influenced by factors such as temperature, aging level, and charging / discharging rate, resulting in high uncertainty and strong nonlinear dynamic characteristics. Traditional control methods often struggle to accurately model and effectively address these complex characteristics, leading to poor control performance. However, the adaptive control technology introduced in this invention can sense changes in the battery system state and parameters in real time and automatically adjust the control strategy without requiring a precise system model. This allows for more relaxed constraints while effectively handling the uncertainties in the battery's internal parameters, ensuring stable system operation.

[0051] 2. Free will time setting enhances control flexibility. Traditional fixed-time or predefined-time control methods typically have a pre-set and fixed convergence time, making it difficult to flexibly adjust according to actual needs and system states. This invention constructs a control strategy based on the free-will-time stability theorem, allowing for flexible setting and adjustment of the free-will time according to specific application scenarios and performance requirements. This means that under different operating conditions, such as fast charging, deep discharging, or different temperature environments, the system state can be quickly and accurately converged to the equilibrium point within a specified time by modifying the time parameter in the control law, greatly improving the flexibility and adaptability of control.

[0052] 3. Ensure the continuity and boundedness of control signals. In battery control systems, the continuity and boundedness of control signals are crucial for stable system operation and equipment safety. Discontinuous or unbounded control signals can lead to battery overcharging, over-discharging, or control system oscillations, and may even damage the battery and equipment. This invention fully considers this point when designing the control law and adaptive rate. By rationally selecting the control gain and adaptive gain, it ensures that the control signal remains continuous and bounded throughout the control process, effectively avoiding safety problems caused by abnormal control signals and improving the reliability and safety of the system.

[0053] 4. Multi-step inversion design enhances global stability The adaptive inversion controller of this invention employs a multi-step design process. Each step constructs a local Lyapunov function based on the result of the previous step, designs a virtual control input, and progressively modifies it until the final control law is obtained. This multi-step design method ensures the stability of each subsystem level, thereby guaranteeing the global stability of the overall system. Compared with the traditional single-step design method, multi-step inversion design can handle nonlinear and uncertain factors in the system more meticulously, gradually building a stable control system from local to global, effectively improving the system's stability and robustness.

[0054] 5. Real-time monitoring and dynamic adjustment enhance adaptability. During use, the internal parameters of sodium-ion batteries change over time due to factors such as battery aging and temperature variations. Traditional control methods often fail to detect these parameter changes in a timely manner and make corresponding adjustments, leading to a decline in control performance. This invention establishes a real-time monitoring and dynamic adjustment mechanism, which estimates unknown parameters online and feeds them back to the controller to achieve dynamic optimization of the control strategy. This mechanism employs advanced parameter estimation methods such as recursive least squares or extended Kalman filtering algorithms, enabling rapid and accurate updates of parameter estimates. This allows the control system to adapt to changes in battery parameters in a timely manner, maintaining optimal control performance and improving the system's adaptability to complex operating environments.

[0055] 6. Significantly improves control accuracy and robustness By comprehensively utilizing adaptive control technology, the free-will time stability theorem, multi-step inversion design, and real-time monitoring and dynamic adjustment mechanisms, the method of this invention exhibits superior control accuracy and robustness. Simulation experiments and actual battery system test results show that, under different free-will time settings and various operating conditions, the system state can quickly and stably converge to the desired equilibrium state within a specified time, and the control effect is significantly better than traditional fixed-time and predefined-time control methods. This indicates that the method of this invention can more accurately control the state of the battery system, effectively resist the influence of external disturbances and internal parameter changes, and improve the overall performance of the battery management system.

[0056] 7. It has broad application prospects and high practical value. The method of this invention is applicable to different types of sodium-ion battery systems, including stationary energy storage systems, electric vehicle battery packs, and batteries for portable electronic devices. Whether for large-scale energy storage applications or small portable devices, stable control and synchronization of battery systems in different scales and application scenarios can be achieved by adjusting control parameters. This broad applicability gives the method of this invention enormous market potential and practical value, providing strong technical support for the large-scale application of sodium-ion batteries in various fields.

[0057] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A novel adaptive control and synchronization method for nonlinear dynamics behavior of sodium-ion battery, specifically comprising the following steps: (1) Establish a nonlinear dynamics model of sodium-ion battery with unknown parameters, and generalize it as an uncertain Lorenz system; (2) Based on the free-will time stability theory, construct an adaptive control law that satisfies a more relaxed constraint; (3) Combine the adaptive backstepping method to design the controller, and realize the system converging to the equilibrium point within the preset free-will time; (4) Design the corresponding adaptive parameter adjustment rate, so that the control signal and parameter estimation are continuous and bounded; (5) Through simulation, verify the effectiveness of the control law, and realize the stability, synchronization and convergence of the sodium-ion battery dynamics system within any specified time.

2. The novel adaptive control and synchronization method of sodium-ion battery nonlinear dynamics behavior according to claim 1, characterized in that, The uncertain Lorenz system is: ； The above equations can be summarized as where, , and denote the state of the system, the control input and the unknown parameters, respectively, is the initial state of the system, mapping satisfies a Lipschitz condition on the state, where the state is continuous in time.

3. The novel adaptive control and synchronization method of sodium-ion battery nonlinear dynamics behavior according to claim 1, characterized in that, The free-will time stability includes weak free-will time stability and strong free-will time stability; wherein, the weak free-will time stability requires that the system convergence time is not less than the specified time, and the strong free-will time stability requires that the system convergence time is equal to the specified time, and the stability guarantee is enhanced by relaxing the Lyapunov inequality condition.

4. The novel adaptive control and synchronization method of sodium-ion battery nonlinear dynamics behavior according to claim 1, characterized in that, In the design process of the adaptive backstepping controller, a multi-step Lyapunov function construction strategy is adopted, each step is based on the results of the previous step to design a local Lyapunov function, and through the derivation of the control law and the adaptive rate, it is ensured that the system state error and parameter estimation error converge to zero within the free-will time.

5. The novel adaptive control and synchronization method of nonlinear dynamics behavior of sodium-ion battery according to claim 4, characterized in that, The adaptive backstepping method specifically comprises the following steps: S1: Establish the coordinate transformation as follows: ； wherein is the free will time virtual control in the first step; is represented as: ; The design of the Lyapunov function is as follows: ； wherein , ; S2: According to the above formula, the following results can be obtained: Lyapunov function The design is as follows: ； Control law The design of the control law is as follows: The design of the adaptive rate and is as follows: ； ； The above formula is brought into, which can be written in the following form: ； S3: By coordinate transformation and uncertain Lorentz system, we can get is: Lyapunov function The design is as follows: ； Free will time control rate and adaptive rate The design is as follows: ； The above formula is brought into, which is: 。 6. The novel adaptive control and synchronization method of sodium-ion battery nonlinear dynamics behavior according to claim 1, characterized in that, The proof of the free-will time stability includes two parts: part A proves that the system state and adaptive parameters are bounded during the control process, and part B proves that the system converges within the specified time; wherein, part A is realized by the monotonicity of the Lyapunov function, and part B utilizes the integral divergence lemma to ensure global stability.

7. The novel adaptive control and synchronization method of nonlinear dynamics behavior of sodium-ion battery according to claim 1, characterized in that, The specific steps of the simulation verification are: through numerical simulation, simulate the dynamics behavior of sodium-ion battery, and compare the system performance under different free-will time settings; in the simulation, the system model uses the Lorenz system as a representative, the initial state is set to a non-equilibrium point, and the controller parameters are adjusted according to the specified time.

8. The novel adaptive control and synchronization method of nonlinear dynamics behavior of sodium-ion battery according to claim 7, characterized in that, The parameters of the Lorentz system are chosen as follows: , and The initial state of the system is set to .

9. The novel adaptive control and synchronization method of nonlinear dynamics behavior of sodium-ion battery according to claim 1, characterized in that, It also includes a real-time monitoring and dynamic adjustment mechanism for the time-varying characteristics of the internal parameters of the sodium-ion battery, which realizes the dynamic optimization of the control strategy by online estimation of unknown parameters and feedback to the controller, to cope with the influence of battery aging, temperature changes and other external factors on the system performance.

10. The novel adaptive control and synchronization method of nonlinear dynamics behavior of sodium-ion battery according to claim 9, characterized in that, The real-time monitoring and dynamic adjustment mechanism uses the recursive least squares method or the extended Kalman filter algorithm for parameter estimation, and by constantly updating the parameter estimation value, the control precision and the adaptability of the system to complex working environment are improved.

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