Data-driven predictive control method for anti-interference control of nonlinear system

Abstract

The invention provides a data-driven predictive control method for anti-interference control of a nonlinear system, relates to Koopman fine modeling, interference accurate estimation and MPC accurate control, and can remarkably improve the control accuracy and robustness of the system. In the method, firstly, a dimension raising function is designed based on a time delay variable, so that a Koopman model of a nonlinear system is finely constructed; on the basis, non-linear and external interferences which are difficult to model are uniformly regarded as lumped interferences, an interference model is established, and an interference observer is designed to realize interference estimation; furthermore, interference estimation is embedded into a rolling time domain optimization framework based on an active anti-interference thought, and unbiased MPC control is realized. According to the method, the nonlinear control design process is simplified, and the anti-interference capability of the system in an uncertain environment is remarkably enhanced. Therefore, the method provides an efficient and reliable solution for the field of anti-interference control of a nonlinear system, and has a wide application prospect and a remarkable practical value.

Description

Technical Field

[0001] The present invention belongs to the technical field of nonlinear system control, and in particular relates to a data-driven predictive control method for anti-interference control of a nonlinear system under uncertain conditions. Background Art

[0002] The basic idea of ​​modeling and control of complex nonlinear systems is usually: first, build a nonlinear analytical model based on the physical laws of the system or mechanism analysis; then, design a nonlinear controller based on the model to achieve system stability. Among them, mechanism modeling and nonlinear control design are often complicated and cumbersome, and require a high theoretical level of engineering and technical personnel. In recent years, data-driven predictive control methods based on Koopman operator theory have been proposed and widely used in nonlinear system control, such as soft robots, rigid manipulators, mobile robots, etc. By designing the Koopman dimensionality-raising function, this method can map the nonlinear system to a high-dimensional linear space, realize the global linearization of the nonlinear system, and enable the application of advanced linear control theories such as model predictive control (MPC). Although this method has good versatility and simplifies control design, it has shortcomings in dealing with external disturbances and model uncertainties. The robustness of this method in practical applications needs to be improved, and it is difficult to achieve high-performance anti-interference control.

[0003] In order to enhance the anti-interference performance of the data-driven predictive control method based on the Koopman operator in an uncertain environment, it is necessary to improve the classical method from three aspects: Koopman fine modeling, accurate interference estimation and MPC precise control. Specifically: (1) It is challenging to accurately establish the Koopman model of a nonlinear system under disturbance-free conditions. The key lies in optimizing the design of the dimensionality-raising function; (2) There is a lack of consideration for the influence of nonlinearities that are difficult to model and external interference. The interference observer technology can be used to achieve interference estimation; (3) The lumped interference is difficult to be completely eliminated by the MPC feedback mechanism. Based on the idea of ​​active anti-interference, unbiased MPC control can be achieved to enhance the robustness of the system.

[0004] In summary, the application of data-driven predictive control methods based on the Koopman operator to nonlinear systems is still an open topic. In particular, the realization of anti-disturbance control in uncertain environments faces challenges and requires further in-depth research and innovation. Summary of the invention

[0005] To solve the above problems, the present invention discloses a data-driven predictive control method for anti-interference control of nonlinear systems, which involves Koopman fine modeling, accurate interference estimation and MPC precise control to enhance the anti-interference control performance, and has broad application prospects and significant practical value.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] A data driven predictive control method for nonlinear system anti-disturbance control comprises the following steps:

[0008] Step S1: finely establish the Koopman model of the nonlinear system;

[0009] Step S2: Accurately estimate the aggregate interference;

[0010] Step S3: MPC precise control based on disturbance estimation.

[0011] Preferably, in step S1:

[0012] Based on the design of the dimensionality-raising function optimized by time-delay variables, the extended dynamic mode decomposition algorithm is used to approximate the Koopman operator in a data-driven manner, and the Koopman model of the nonlinear system is finely constructed;

[0013] Step S11: optimizing the design of the dimension-raising function based on time-lag variables, wherein the time-lag variables include state time-lag variables and input time-lag variables;

[0014] Assume that the discrete dynamic equation of the nonlinear system is expressed as:

[0015] x(k+1)=f(x(k),u(k))

[0016] Among them, x(k),u(k) are the state and input of the system at time step k, and f represents the nonlinear dynamics of the system;

[0017] The dimension-raising function Ψ designed based on time-delay variables can be expressed as:

[0018] Ψ=[x(k) x(k-1) x(k-2) … x(ki) u(k) u(k-1) u(k-2) … u(kj) 1]

[0019] Among them, x(ki) is the i-th time lag of the system state at the k-th time step, u(kj) is the j-th time lag of the system input at the k-th time step, and 1 is the bias term;

[0020] Introducing the state time-delay variable x(ki) into the dimension-raising function can infer the higher-order derivatives of the state according to the sampling period, so that the dimension-raising state has the potential to describe a higher-order system; in addition, introducing the input time-delay variable can also infer the rate of change of the input, thereby reflecting the rate-dependent nonlinearity of the system;

[0021] Step S12: data-driven acquisition of the Koopman model, according to the above-mentioned dimensionality-raising function designed based on the time-delay variable, the extended dynamic mode decomposition algorithm is used to approximate the Koopman operator in a data-driven manner, and the Koopman model of the nonlinear system is finely constructed;

[0022] Use random input to stimulate the system or simulation model to fully stimulate the nonlinear dynamics of the system, collect input and state data, and organize the state data into two matrices with one sampling step evolution relationship:

[0023] X1=[x(1) x(2) … x(p)]

[0024] X2=[x(2) x(3) … x(p+1)]

[0025] Based on the dimension-raising function Ψ designed in step S11, X1 and X2 are improved:

[0026] X 1lift =[Ψ(x(1),u(1)) Ψ(x(2),u(2)) … Ψ(x(p),u(p))]

[0027] X 2lift =[Ψ(x(2),u(2)) Ψ(x(3),u(3)) … Ψ(x(p+1),u(p+1))]

[0028] Further introducing the input term, X 1lift ,X 2lift Expand to

[0029] Y 1lift =[X 1lift U] Τ

[0030] Y 2lift =[X 2lift U] Τ

[0031] Where U=[u[1] u[2] ··· u[p]];

[0032] Solve the following minimization problem to obtain a finite-dimensional approximation of the Koopman operator:

[0033]

[0034] Further, from The Koopman model is isolated and divided into:

[0035]

[0036] z(k+1)=Az(k)+Bu u(k)

[0037] y(k)=Cz(k)

[0038] Where z(k)=Ψ(x(k),u(k)) represents the increased-dimensional state at k time steps, and y(k)=x(k),C=[IO] is defined, allowing mapping from the increased-dimensional state space back to the original state space.

[0039] Preferably, in step S2:

[0040] The nonlinear and external interferences that are difficult to model are uniformly regarded as lumped interferences, the interference characteristics are analyzed and the interference model is constructed, and the interference observer is designed to realize interference estimation;

[0041] S21: Analyze interference characteristics and build interference models;

[0042] Taking into account model uncertainty and external disturbances, the disturbed Koopman model can be used to describe the actual working conditions of the nonlinear system:

[0043] z(k+1)=Az(k)+B u u(k)+B d d(k)

[0044] y(k)=Cz(k)

[0045] Where d(k) is the total disturbance to the Koopman model, including model uncertainty and external disturbance, and B d The channels with interference and interference gain in the dimensional state are determined, usually designed as unit arrays;

[0046] In actual working conditions, nonlinear systems are usually subject to unpredictable time-varying disturbances. The time-varying disturbance model is defined as:

[0047]

[0048] where h j (k) is the jth-order derivative of the aggregate interference d(k) at the kth time step, T s represents the sampling time. The interference model assumes that the j+1 order derivative of the interference remains constant. The above time-varying interference model is written in matrix form:

[0049] D(k+1)=A w D(k)

[0050] d(k)=C w D(k)

[0051] in C w = [I 0 - 0 0];

[0052] S22: Based on the above interference model, the following interference observer is designed:

[0053] q(k+1)=(A w -L w B d C w )(q(k)+L w z(k))-L w (Az(k)+B u u(k))

[0054]

[0055] in is an auxiliary variable, L w is the observer gain. By designing the observer gain, (A w -L w B d C w ) is configured within the unit circle, which can achieve asymptotic convergence of the estimation error.

[0056] Preferably, in step S3:

[0057] The disturbance observer in step S22 is embedded in the rolling horizon optimization to achieve an unbiased MPC control effect;

[0058] In order to achieve unbiased tracking effect, the penalty function in the rolling time domain optimization is defined as:

[0059]

[0060] Among them, δu(k)=u(k)-u(k-1) represents the control increment, and e(k) is relative to the reference trajectory y r Tracking error, Q, R, F are the penalty weights for tracking error, control increment and terminal tracking error respectively;

[0061] At k time steps, solve the following optimization problem:

[0062]

[0063] y(i|k)=Cz(i|k)

[0064] e(i|k)=y(i|k)-y r (i|k)

[0065]

[0066] Where N p is the prediction time domain, and the solution of the optimization problem at k time steps can be expressed as:

[0067] δu * (k)=[δu * (k|k)δu * (k+1|k)…δu * (k+N p -1|k)]

[0068] The control input at time step k is the optimal sequence δu * The first value of (k) is summed with the k-1 time step control input:

[0069] u(k)=δu * (k|k)+u(k-1)

[0070] Beneficial technical effects of the present invention:

[0071] The present invention provides a data-driven predictive control method for anti-interference control of nonlinear systems, which significantly improves the control accuracy and robustness of the system. By introducing state lag variables and input lag variables to optimize the dimensionality-raising function, the Koopman model of the nonlinear system is finely constructed in a data-driven manner, which achieves an accurate description of the system hysteresis behavior and high-order characteristics, and ensures the high-fidelity global linearization of the nonlinear system. Furthermore, a time-varying interference model is established and an interference observer is designed to accurately estimate model uncertainty and external interference. Finally, the interference estimation is embedded in the rolling time domain optimization design of an unbiased MPC controller, which effectively eliminates the impact of lumped interference on the system. The present invention not only simplifies the nonlinear control design process, but also significantly enhances the anti-interference ability of the system in an uncertain environment. Therefore, the present invention provides an efficient and reliable solution for the field of anti-interference control of nonlinear systems, and has broad application prospects and significant practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 A control block diagram of a data-driven predictive control method for anti-interference control of a nonlinear system according to the present invention;

[0073] Figure 2 Schematic diagram of the internal structure of the robust Koopman-MPC controller of the present invention;

[0074] Figure 3 is an implementation flow chart of the robust Koopman-MPC controller of the present invention;

[0075] Figure 4 This is an implementation flow chart of the data-driven predictive control method for anti-interference control of nonlinear systems described in the present invention applied to load control of soft robots. DETAILED DESCRIPTION

[0076] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0077] Example 1

[0078] This embodiment describes a specific implementation structure of a data-driven predictive control method for nonlinear system anti-interference control. Figure 1 , Figure 1 The invention is a control block diagram of a data-driven predictive control method for anti-interference control of nonlinear systems, including a robust Koopman-MPC controller, an actuator, a nonlinear system and a sensor element. The robust Koopman-MPC controller solves the control quantity according to the reference trajectory and the actual trajectory. The solving process comprehensively considers the influence of the nonlinear system on the external interference and the internal model uncertainty, and sends the control output instruction to the actuator; common actuators include electrical proportional valves, flow valves, motors, etc., and their specific types depend on the driving mode of the nonlinear system. The actuator is responsible for transmitting power and driving the nonlinear system to achieve the preset motion or behavior; the sensor element is used to measure the kinematic or mechanical signals of the nonlinear system, including but not limited to posture, angle, output force, output torque, etc., and feeds back to the robust Koopman-MPC controller to form a closed-loop control system.

[0079] The internal structure of the robust Koopman-MPC controller is referenced Figure 2 , including a Koopman fine modeling module, a rolling time domain optimization module and an interference observation module. The Koopman fine modeling module uses state time-delay variables and input time-delay variables to optimize the dimensionality-raising function design to accurately describe the hysteresis behavior of the nonlinear system and the high-order system characteristics, so as to construct a high-precision Koopman model through data-driven; the interference observation module comprehensively considers external interference and internal model uncertainty to construct a time-varying interference model, and designs an interference observer, which accurately estimates the lumped interference based on the control output and the actual trajectory; the rolling time domain optimization module is based on the system model constructed by the Koopman fine modeling module and the lumped interference estimated by the interference observation module, and establishes a disturbed Koopman model. The model fully considers the lumped interference caused by external interference and internal model uncertainty to achieve accurate prediction, and implements rolling time domain optimization based on the disturbed model to solve the optimal control quantity. Further, the implementation process of the robust Koopman-MPC controller refers to Figure 3 .

[0080] This embodiment describes the specific implementation structure of a data-driven predictive control method for anti-interference control of nonlinear systems, and proposes a detailed design including a system control block diagram and its internal modules. The robust Koopman-MPC controller can effectively cope with external interference and internal model uncertainty of nonlinear systems through the collaborative work of the Koopman fine modeling module, the interference observation module and the rolling time domain optimization module, and improve the control accuracy and robustness of the system. This method not only realizes the accurate modeling of the complex dynamic characteristics of nonlinear systems, but also significantly enhances the anti-interference ability of the system in uncertain environments through interference estimation and unbiased control strategies, providing an effective solution for achieving high-performance control of nonlinear systems.

[0081] Example 2

[0082] This embodiment describes the specific implementation details of a data-driven predictive control method for nonlinear system anti-interference control, specifically targeting the load control problem of a nonlinear soft robot system. The implementation flow chart of this method is as follows: Figure 4 As shown, the following steps are included:

[0083] Step S1: Establish a Koopman model of the soft robot under no-load conditions. This step specifically includes:

[0084] Step S11: optimizing the design of the dimension-raising function based on time-lag variables, wherein the time-lag variables include state time-lag variables and input time-lag variables;

[0085] The discrete dynamic equation of the soft robot system is expressed as:

[0086] x(k+1)=f(x(k),u(k))

[0087] Among them, x(k) is the state of the system at the kth time step, usually the bending angle, elongation or end position, u(k) is the input of the system at the kth time step, usually air pressure or voltage, and f represents the nonlinear dynamics of the system.

[0088] The dimension-raising function Ψ designed based on time-delay variables can be expressed as:

[0089] Ψ=[x(k) x(k-1) x(k-2) … x(ki) u(k) u(k-1) u(k-2) … u(kj) 1]

[0090] Among them, x(ki) is the i-th time lag of the system state at the k-th time step, u(kj) is the j-th time lag of the system input at the k-th time step, and 1 is the bias term.

[0091] Considering that the nonlinearity of soft robot systems is mainly reflected in hysteresis nonlinearity, which is specifically manifested as historical correlation and rate correlation, and the system dynamics usually presents second-order system characteristics. Introducing the state lag variable x(ki) in the dimensionality-raising function is equivalent to introducing the historical information of the state, thereby reflecting the historical correlation of hysteresis. At the same time, the first-order derivative of the state can be inferred based on the state single-step lag and the sampling period, and the first-order derivative in the discrete system state can reflect the second-order characteristics of the system. In addition, the introduction of input lag variables can also infer the rate of change of the input, which corresponds to the rate-related nonlinearity of the system. Therefore, the introduction of state lag variables and input lag variables enables the dimensionality-raising function to fully describe the typical nonlinear characteristics of soft robots, including the historical correlation of hysteresis, rate correlation and second-order system characteristics, which is helpful to finely construct the Koopman model of soft robots.

[0092] Step S12: Data-driven acquisition of the Koopman model of the soft robot under no-load conditions. According to the above-mentioned dimensionality-raising function designed based on time-delay variables, the extended dynamic mode decomposition algorithm is used to approximate the Koopman operator in a data-driven manner, and the Koopman model of the system is extracted therefrom.

[0093] Under no-load conditions, the soft robot system is stimulated by random input to fully stimulate its nonlinear dynamics. At the same time, input and state data are collected, and the state data are organized into two matrices with one sampling step evolution relationship:

[0094] X1=[x(1) x(2) … x(p)]

[0095] X2=[x(2) x(3) … x(p+1)]

[0096] Based on the dimension-raising function Ψ designed in step S11, X1 and X2 are improved:

[0097] X 1lift =[Ψ(x(1),u(1)) Ψ(x(2),u(2)) … Ψ(x(p),u(p))]

[0098] X 2lift =[Ψ(x(2),u(2)) Ψ(x(3),u(3)) … Ψ(x(p+1),u(p+1))]

[0099] Further introducing the input term, X 1lift ,X 2lift Expand to

[0100] Y 1lift =[X 1lift U] Τ

[0101] Y2lift =[X 2lift U] Τ

[0102] Where U = [u[1] u[2] ··· u[p]]. Note that the input items do not need to be nonlinearly dimensioned to ensure that the constructed Koopman model has linear input characteristics.

[0103] The finite-dimensional approximation of the Koopman operator is obtained by solving the following minimization problem:

[0104]

[0105] Further, from The Koopman model is isolated and divided into:

[0106]

[0107] z(k+1)=Az(k)+B u u(k)

[0108] y(k)=Cz(k)

[0109] Where z(k)=Ψ(x(k),u(k)) represents the increased-dimensional state at k time steps, and y(k)=x(k),C=[IO] is defined, allowing mapping from the increased-dimensional state space back to the original state space.

[0110] Step S2: Establish a time-varying interference model and design an interference observer.

[0111] The nonlinear and external load interferences that are difficult to model are uniformly regarded as lumped interferences, the interference characteristics are analyzed and an interference model is constructed, and the interference observer is designed to realize interference estimation.

[0112] Step S21: Analyze interference characteristics and construct an interference model.

[0113] Taking into account model uncertainty and external disturbances, the disturbed Koopman model can be used to describe the actual working conditions of the soft robot system:

[0114] z(k+1)=Az(k)+B u u(k)+B d d(k)

[0115] y(k)=Cz(k)

[0116] Where d(k) is the total disturbance to the Koopman model, including model uncertainty and external load disturbance, B d The channels with interference in the increased dimensional state and the interference gains are determined, which are usually designed as unit matrices to simplify the analysis.

[0117] In actual working conditions, soft robots are usually subject to unpredictable time-varying disturbances. The time-varying disturbance model is defined as:

[0118]

[0119] where h j (k) is the jth-order derivative of the aggregate interference d(k) at the kth time step, T s represents the sampling time. The interference model assumes that the j+1 order derivative of the interference remains constant. The above time-varying interference model is written in matrix form:

[0120] D(k+1)=A w D(k)

[0121] d(k)=C w D(k)

[0122] in C w =[I 0 … 0 0];

[0123] Step S22: Based on the above interference model, the following interference observer is designed:

[0124] q(k+1)=(A w -L w B d C w )(q(k)+L w z(k))-L w (Az(k)+B u u(k))

[0125]

[0126] in is an auxiliary variable, L w is the observer gain. By designing the observer gain, (A w -L w B d C w ) is configured within the unit circle, which can achieve asymptotic convergence of the estimation error.

[0127] Step S3: Designing an unbiased MPC controller based on a disturbance observer. The disturbance observer in step S22 is embedded in the receding horizon optimization to achieve an unbiased MPC control effect.

[0128] In order to achieve unbiased tracking, the penalty function in the rolling horizon optimization is defined as:

[0129]

[0130] Among them, δu(k)=u(k)-u(k-1) represents the control increment, and e(k) is relative to the reference trajectory y r The tracking error is , Q, R, and F are the penalty weights for tracking error, control increment, and terminal tracking error, respectively. Note that penalizing the control increment is conducive to achieving unbiased tracking effect.

[0131] At k time steps, solve the following optimization problem:

[0132]

[0133] y(i|k)=Cz(i|k)

[0134] e(i|k)=y(i|k)-y r (i|k)

[0135]

[0136] Where N p is the prediction time domain. To solve the optimization problem, the perturbed Koopman model is first rewritten into an incremental form:

[0137]

[0138] y[k]=Cz[k]

[0139] Where z(k)=[z i (k)u(k-1)d(k-1)] Τ ,

[0140] C=[C il×N O l×(N+m) ] l*(2N+m)

[0141] Based on the model, linear extrapolation is performed to obtain the output prediction equation

[0142]

[0143] in,

[0144]

[0145] Furthermore, the penalty function of the above optimization problem can be expressed in matrix form:

[0146]

[0147] in,

[0148] Furthermore, the above optimization problem can be transformed into a standard quadratic programming (QP) form:

[0149]

[0150] stlb≤δU k ≤ub

[0151] Among them, lb and ub represent the lower bound and upper bound of the constraint respectively. Using the standard QP algorithm to solve, the solution of this optimization problem at k time steps can be expressed as:

[0152] δu * (k)=[δu * (k|k)δu * (k+1|k)…δu * (k+N p -1|k)]

[0153] The control input at time step k is the optimal sequence δu * The first value of (k) is summed with the k-1 time step control input:

[0154] u(k)=δu * (k|k)+u(k-1)

[0155] This embodiment aims at the problem of precise control of nonlinear soft robot systems under load conditions, describes in detail the specific implementation details of a data-driven predictive control method for anti-interference control of nonlinear systems, and proposes a complete solution including fine modeling, interference estimation and unbiased control. By introducing the design of dimensionality-raising functions optimized by time-delay variables, constructing a time-varying interference model and designing an interference observer, as well as designing an unbiased MPC controller based on the interference observer, the anti-interference performance of the data-driven predictive control method based on the Koopman operator in uncertain environments is significantly improved.

[0156] It should be noted that the above content only illustrates the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications all fall within the protection scope of the claims of the present invention.

Claims

1. A data-driven predictive control method for anti-interference control of nonlinear systems, characterized in that: The following steps are involved: Step S1: finely establish the Koopman model of the nonlinear system; Step S2: Accurately estimate the aggregate interference; Step S3: MPC precise control based on disturbance estimation.

2. The data-driven predictive control method for anti-interference control of nonlinear systems according to claim 1, characterized in that: In step S1: Based on the design of the dimensionality-raising function optimized by time-delay variables, the extended dynamic mode decomposition algorithm is used to approximate the Koopman operator in a data-driven manner, and the Koopman model of the nonlinear system is finely constructed; Step S11: optimizing the design of the dimension-raising function based on time-lag variables, wherein the time-lag variables include state time-lag variables and input time-lag variables; Assume that the discrete dynamic equation of the nonlinear system is expressed as: x(k+1)=f(x(k),u(k)) Among them, x(k),u(k) are the state and input of the system at time step k, and f represents the nonlinear dynamics of the system; The dimension-raising function Ψ designed based on time-delay variables is expressed as: Ψ=[x(k) x(k-1) x(k-2)…x(ki) u(k) u(k-1) u(k-2)…u(kj) 1] Among them, x(ki) is the i-th time lag of the system state at the k-th time step, u(kj) is the j-th time lag of the system input at the k-th time step, and 1 is the bias term; Introducing the state time-lag variable x(ki) in the dimension-raising function to infer the higher-order derivative of the state according to the sampling period, so that the dimension-raising state has the potential to describe a higher-order system; in addition, introducing the input time-lag variable to infer the rate of change of the input, thereby reflecting the rate-dependent nonlinearity of the system; Step S12: data-driven acquisition of the Koopman model, according to the above-mentioned dimensionality-raising function designed based on the time-delay variable, the extended dynamic mode decomposition algorithm is used to approximate the Koopman operator in a data-driven manner, and the Koopman model of the nonlinear system is finely constructed; Use random input to stimulate the system or simulation model to fully stimulate the nonlinear dynamics of the system, collect input and state data, and organize the state data into two matrices with one sampling step evolution relationship: X1=[x(1) x(2)…x(p)] X2=[x(2) x(3)…x(p+1)] Based on the dimension-raising function Ψ designed in step S11, X1 and X2 are improved: X 1lift =[Ψ(x(1),u(1)) Ψ(x(2),u(2))…Ψ(x(p),u(p))] X 2lift =[Ψ(x(2),u(2)) Ψ(x(3),u(3))…Ψ(x(p+1),u(p+1))] Further introducing the input term, X 1lift ,X 2lift Expand to Y 1lift =[X 1lift U] Τ Y 2lift =[X 2lift U] Τ Where U=[u[1] u[2]···u[p]]; Solve the following minimization problem to obtain a finite-dimensional approximation of the Koopman operator: Further, from The Koopman model is isolated and divided into: z(k+1)=Az(k)+B u u(k) y(k)=Cz(k) Where z(k)=Ψ(x(k),u(k)) represents the increased-dimensional state at k time steps, and y(k)=x(k),C=[IO] is defined, allowing mapping from the increased-dimensional state space back to the original state space.

3. The data-driven predictive control method for anti-interference control of nonlinear systems according to claim 1, characterized in that: In step S2: The nonlinear and external interferences that are difficult to model are uniformly regarded as lumped interferences, the interference characteristics are analyzed and the interference model is constructed, and the interference observer is designed to realize interference estimation; S21: Analyze interference characteristics and build interference models; Taking into account model uncertainty and external disturbances, the disturbed Koopman model is used to describe the actual working conditions of the nonlinear system: z(k+1)=Az(k)+B u u(k)+B d d(k) y(k)=Cz(k) Where d(k) is the total disturbance to the Koopman model, including model uncertainty and external disturbance, and B d The channels with interference and interference gain in the dimensional state are determined, usually designed as unit arrays; In actual working conditions, nonlinear systems are usually subject to unpredictable time-varying disturbances. The time-varying disturbance model is defined as: where h j (k) is the jth-order derivative of the aggregate interference d(k) at the kth time step, T s Represents the sampling time. The interference model assumes that the j+1-order derivative of the interference remains constant. The above time-varying interference model is written in matrix form: D(k+1)=A w D(k) d(k)=C w D(k) in S22: Based on the above interference model, the following interference observer is designed: q(k+1)=(A w -L w B d C w )(q(k)+L w z(k))-L w (Az(k)+B u u(k)) in is an auxiliary variable, L w is the observer gain. By designing the observer gain, (A w -L w B d C w )’s eigenvalues ​​are arranged within the unit circle to achieve asymptotic convergence of the estimation error.

4. The data-driven predictive control method for anti-interference control of nonlinear systems according to claim 1, characterized in that: In step S3: The disturbance observer in step S22 is embedded in the rolling horizon optimization to achieve an unbiased MPC control effect; In order to achieve unbiased tracking effect, the penalty function in the rolling time domain optimization is defined as: Among them, δu(k)=u(k)-u(k-1) represents the control increment, and e(k) is relative to the reference trajectory y r Tracking error, Q, R, F are the penalty weights for tracking error, control increment and terminal tracking error respectively; At k time steps, solve the following optimization problem: Where N p is the prediction time domain, and the solution of the optimization problem at k time steps is expressed as: The control input at time step k is the optimal sequence δu * The sum of the first value of (k) and the k-1 time step control input: u(k) = δu * (k|k)+u(k-1).

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