A saturation optimization model-free adaptive control method, system, device and storage medium for a MIMO system

Abstract

The application discloses a kind of saturated optimization model-free adaptive control methods, systems, equipment and storage medium for MIMO system, obtain the input data and output data of MIMO system, establish the dynamic linearization data model containing pseudo-gradient matrix;Using projection algorithm with penalty mechanism and reset mechanism to update the pseudo-gradient matrix online;According to discrete quasi-sliding surface and backstepping method, combine the dynamic linearization data model, solve the unconstrained ideal control increment by reverse algebra;According to the amplitude constraint and rate constraint of MIMO system actuator, establish a linear inequality constraint set about control increment, use the unconstrained control increment as reference quantity, construct the quadratic objective function containing tracking error term and control increment weighting term;Using Hildreth algorithm to solve iteratively, obtain the actual control increment that satisfies constraint;According to actual control increment, update control input and apply to MIMO system.

Description

Technical Field

[0001] This invention belongs to the field of automatic control and data-driven control technology, and relates to a saturation optimization model-free adaptive control method, system, device and storage medium for MIMO systems. Background Technology

[0002] In modern industrial and engineering fields (such as aerospace, petrochemicals, multi-joint robots, and power systems), controlled objects often exhibit typical multiple-input multiple-output (MIMO) nonlinear systems. A significant characteristic of these systems is the complex dynamic coupling between different channels within the system (e.g., the interaction between temperature and pressure in a chemical reactor, or the motion coupling of a multi-joint robot), and the fact that system model parameters are often difficult to obtain accurately or change over time. Furthermore, actuators in practical engineering systems (such as valves, motors, and thrusters) are generally subject to physical constraints, exhibiting saturation constraints on output amplitude and rate of change.

[0003] Therefore, Model-Free Adaptive Control (MFAC), as a method that uses only system input / output (I / O) data for online learning and control, offers a new approach to solving the stabilization control problem of such complex systems due to its advantages such as not relying on the physical model of the controlled object, low computational burden, and strong robustness.

[0004] However, existing methods struggle to effectively handle strong coupling characteristics: most current model-free control methods are based on the single-input single-output (SISO) framework, simplifying the MIMO system into multiple independent single-loop control. This approach ignores the cross-coupling terms between the input and output channels (i.e., ignores the influence of one control input on other output channels), leading to a significant decrease in control accuracy under strong coupling conditions, and even causing system instability.

[0005] Existing control schemes lack optimization mechanisms for handling physical saturation constraints of actuators, and commonly employ hard limiting, which directly truncates the over-limit portion of the command. While this approach protects the hardware, it undermines the theoretical consistency of the closed-loop control system, causing a severe mismatch between the actual control quantity applied to the object and the expected value calculated by the algorithm. This not only leads to severe integral saturation, resulting in system response lag and increased overshoot, but also causes the control command to exhibit abrupt changes at the saturation boundary. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a saturation optimization model-free adaptive control method, system, device and storage medium for MIMO systems, which achieves stable control of MIMO systems under the premise of satisfying actuator amplitude and rate saturation constraints.

[0007] To achieve the above objectives, the present invention employs the following technical solution: A model-free adaptive control method for saturation optimization of MIMO systems includes the following steps: The input and output data of the MIMO system at adjacent sampling times are obtained, and a dynamic linearized data model containing a pseudo-gradient matrix is ​​established accordingly. Based on the input increment, output increment, and pseudo-gradient matrix estimate from the previous time step, the pseudo-gradient matrix is ​​updated online using an update algorithm with a penalty mechanism and a reset mechanism. Based on the discrete quasi-sliding surface and the backstepping method, combined with this dynamic linearized data model, the unconstrained ideal control increment is calculated by inverse algebra. Based on the amplitude and rate constraints of the MIMO system actuator, a set of linear inequality constraints about the control increment is established. Taking the unconstrained control increment as a reference, a quadratic objective function containing a tracking error term and a control increment weighting term is constructed. The Hildreth algorithm is used to iteratively solve the quadratic objective function under the set of linear inequalities to obtain the actual control increment that satisfies the constraints. The control input is updated based on the actual control increment and applied to the MIMO system.

[0008] Optionally, establishing a dynamically linearized data model that includes a pseudo-gradient matrix includes: Extract the input signal vector and output signal vector of a multi-input multi-output nonlinear controlled object at two consecutive discrete sampling times; Perform differential operations on signals at adjacent discrete sampling times to generate input and output increments; Construct a linear algebraic equation between the input increment and the output increment at the next time step. Internally, this linear algebraic equation treats the pseudo-gradient matrix as a time-varying parameter matrix.

[0009] Optionally, online updates of the pseudo-gradient matrix using projection algorithms with penalty and reset mechanisms include: Extract the historical input increment data, historical output increment data, and historical pseudo gradient matrix estimate saved from the previous control cycle; Calculate the residual between the actual measured output change and the output change predicted using historical parameters; The historical pseudo-gradient matrix estimates are iteratively corrected along the negative gradient direction of the residual to generate the pseudo-gradient matrix estimates at the current time. This penalty mechanism is activated when the input increment norm is lower than a set threshold to prevent division by zero errors in division operations. The reset mechanism is activated when there is a sudden, impulsive change in the pseudo-gradient matrix estimate, restoring it to the initial setting.

[0010] Optionally, the inverse algebraic solution for the unconstrained ideal control increment includes: Extract the position tracking error between the current actual state of the system and the desired trajectory; By combining historical error data, a discrete quasi-sliding surface with Hurwitz stability is constructed. Based on the backstepping calculation logic, the boundary conditions for the system state to reach the discrete quasi-sliding surface at the next moment are set; Under these boundary conditions, the unconstrained ideal control increment under any physical limitations is derived and calculated in reverse.

[0011] Optionally, the Hildreth algorithm can be used to iteratively optimize the quadratic objective function, including: Initialize a set of Lagrange multiplier variables; Update each multiplier component in the group of Lagrange multiplier variables one by one along the multidimensional coordinate axis; Perform a zero-boundary truncation operation on the updated multiplier components, and force the negative components to be set to zero; The iteration stops when all changes in multipliers fall below a set convergence threshold, and the converged set of multipliers is output. Substitute the convergent set of multipliers back into the equation and solve for the optimal actual control increment.

[0012] Optionally, constructing a quadratic objective function that combines tracking error and control energy includes: Extract the tracking error minimization term according to the system settings; Extract control energy limiting terms based on controller parameters; By introducing weighting coefficients to adjust the ratio of the tracking error minimization term to the control energy constraint term, a positive definite quadratic objective function is synthesized.

[0013] Optionally, this method is executed in a controller that internally contains a cascading structure, and the execution flow includes: The virtual expected velocity calculator included in the controller receives external position tracking error signals, actual position feedback signals, and actual velocity feedback signals, and plans and outputs virtual expected velocity signals to the inner loop dynamics layer; The parameter estimator contained in the controller extracts the changes in control input and velocity through differential delay, and calculates and sends out the estimated value of the pseudo gradient matrix at the current moment online; The saturation optimization module included in the controller receives the virtual desired speed signal, the actual speed feedback from the previous moment, the control input from the previous moment, and the estimated value of the pseudo gradient matrix at the current moment. It then performs quadratic programming of the control input and anti-saturation processing, and outputs the optimal actual control increment.

[0014] A saturation optimization model-free adaptive control system for MIMO systems includes: The dynamic linearized data model building module is used to acquire the input and output data of the MIMO system at adjacent sampling times, and to build a dynamic linearized data model containing a pseudo-gradient matrix based on this data. The update module is used to update the pseudo-gradient matrix online based on the input increment, output increment, and pseudo-gradient matrix estimate from the previous time step, using an update algorithm with a penalty mechanism and a reset mechanism. The inverse algebraic solution module is used to calculate the unconstrained ideal control increment by inverse algebraic solution based on the discrete quasi-sliding surface and the backstepping method, combined with the dynamic linearized data model. The quadratic objective function construction module is used to establish a set of linear inequality constraints on the control increment based on the amplitude and rate constraints of the MIMO system actuator, and to construct a quadratic objective function containing a tracking error term and a control increment weighting term using the unconstrained control increment as a reference. The optimal actual control increment solution module is used to iteratively solve the quadratic objective function under the set of linear inequality constraints using the Hildreth algorithm to obtain the actual control increment that satisfies the constraints. An application module is used to update the control input according to the actual control increment and apply it to the MIMO system.

[0015] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the saturation optimization model-free adaptive control method for MIMO systems.

[0016] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the saturation optimization model-free adaptive control method for MIMO systems.

[0017] Compared with the prior art, the present invention has the following beneficial effects: This invention first introduces compact-form dynamic linearization based on the generalized partial differential mean value theorem. This transforms complex dynamic systems containing high-order nonlinear terms into a concise linear data model without losing local dynamic coupling information. This natively handles multi-channel cross-coupling effects, eliminating unmodeled dynamic disturbances caused by forced independent decoupling in traditional control methods and preventing system instability. Secondly, addressing the physical limits of actuators in practical engineering, it abandons traditional hard-limiting methods that disrupt closed-loop theoretical consistency and easily lead to integral saturation. By combining the Hildreth quadratic programming algorithm, it acts as a safety filter when multi-dimensional control channels approach physical saturation limits. It proactively and smoothly adjusts the control output ratios of each dimension, effectively avoiding distortion of the synthesized control vector, system deviation from the flight path, and high-frequency chatter caused by direct peak clipping. This maximizes the system's trajectory tracking accuracy while ensuring hardware safety. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the model-free quasi-sliding mode predictive controller of the present invention; Figure 2 The flowchart shows the saturation optimization model-free adaptive control method for MIMO systems in multi-input multi-output nonlinear systems according to the present invention. Detailed Implementation

[0019] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of 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 skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0020] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0021] Example 1 This embodiment provides a saturation optimization model-free adaptive control method for MIMO systems, which includes the following process: The input and output data of the MIMO system at adjacent sampling times are obtained, and a dynamic linearized data model containing a pseudo-gradient matrix is ​​established based on this.

[0022] Based on the input increment, output increment, and pseudo-gradient matrix estimate from the previous time step, the pseudo-gradient matrix is ​​updated online using an update algorithm with a penalty and reset mechanism.

[0023] Based on the discrete quasi-sliding surface and the backstepping method, combined with the dynamic linearized data model, the unconstrained ideal control increment is calculated by inverse algebraic solution.

[0024] Based on the amplitude and rate constraints of the MIMO system actuator, a set of linear inequality constraints regarding the control increment is established. Using the unconstrained control increment as a reference, a quadratic objective function containing a tracking error term and a control increment weighting term is constructed.

[0025] The Hildreth algorithm is used to iteratively solve the quadratic objective function under the set of linear inequalities to obtain the actual control increment that satisfies the constraints.

[0026] The control input is updated based on the actual control increment and applied to the MIMO system.

[0027] Specifically, establishing a dynamically linearized data model that includes a pseudo-gradient matrix includes: Extract the input signal vector and output signal vector of a multi-input multi-output nonlinear controlled object at two consecutive discrete sampling times; perform differential operation on the signals at adjacent discrete sampling times to generate input increment and output increment; construct a linear algebraic equation between the input increment and the output increment at the next time step, and internally treat the pseudo-gradient matrix as a time-varying parameter matrix in the linear algebraic equation.

[0028] A linear mapping relationship is established between the output increment and input increment of the previous time step through a pseudo-gradient matrix, realizing the dimensionality reduction and transformation of complex unknown physical systems into standardized mathematical data models. By performing differential operations on the input and output signals of adjacent discrete sampling time steps and introducing a time-varying pseudo-gradient matrix that implicitly includes cross-coupling gains, the risks of multiple solutions and divergence caused by directly designing global control laws for multivariable nonlinear functions can be effectively avoided. This provides a solid and extremely concise mathematical equation framework for all subsequent model-free controller designs and online parameter learning.

[0029] Specifically, the online update of the pseudo-gradient matrix using a projection algorithm with penalty and reset mechanisms includes: Extract the historical input increment data, historical output increment data, and historical pseudo-gradient matrix estimate saved from the previous control cycle; calculate the residual between the actual measured output change and the output change predicted using historical parameters; iteratively correct the historical pseudo-gradient matrix estimate along the negative gradient direction of the residual to generate the pseudo-gradient matrix estimate at the current moment; activate the penalty mechanism to avoid division by zero errors when the input increment norm is lower than a set threshold; activate the reset mechanism to restore the pseudo-gradient matrix estimate to its initial set value when a pulse-like change occurs.

[0030] The online update of the pseudo-gradient matrix employs an estimation method with a penalty term, and a reset operation is performed when the norm of the estimated pseudo-gradient matrix exceeds a preset threshold or the change between adjacent time steps exceeds a preset threshold. This endows the entire control algorithm with self-learning ability and extremely high numerical computation robustness in response to changes in the working environment. By minimizing the prediction residual to approximate the local partial derivatives of the real system in real time, the control system no longer relies on prior physical parameters and can intrinsically adapt to the drift of physical characteristics (such as inertia and damping) caused by factors such as temperature and load. At the same time, the penalty mechanism effectively avoids division-by-zero collapse when the input increment is extremely small, while the anti-divergence reset mechanism ensures that the algorithm can quickly discard extreme singular values ​​that have lost physical meaning when encountering strong non-Gaussian noise or hard physical shocks, guaranteeing the timeliness and accuracy of parameter identification.

[0031] Specifically, the inverse algebraic solution for the unconstrained ideal control increment includes: Extract the position tracking error between the current actual state of the system and the desired trajectory; construct the discrete quasi-sliding surface with Hurwitz stability by combining historical error data; set the boundary conditions for the system state to reach the discrete quasi-sliding surface at the next moment according to the backstepping method calculation logic; and derive and solve the unconstrained ideal control increment under the boundary conditions without any physical restrictions.

[0032] This approach significantly overcomes the shortcomings of purely data-driven control in terms of robustness against unknown external environmental disturbances (such as gusts of wind and water flow). By introducing a discrete quasi-sliding mode surface that satisfies the Hurwitz stability condition, this scheme forces the system's closed-loop error to converge dynamically within a finite number of sampling periods and maintain its sliding within a predefined manifold space. Utilizing the inherent disturbance resistance characteristics of sliding mode control, it ensures rapid and asymptotic convergence of the tracking error. This design smoothly transforms the abstract trajectory tracking error into a concrete actuator action tendency without increasing model complexity.

[0033] Specifically, the optimization iteration of the quadratic objective function using the Hildreth algorithm includes: Initialize a set of Lagrange multiplier variables; update each multiplier component in the set of Lagrange multiplier variables one by one along the multidimensional coordinate axis; perform a zero boundary truncation operation on the updated multiplier components, forcing the negative components to zero; stop iterating when all multiplier changes are lower than the set convergence threshold, and output the converged multiplier set; substitute the converged multiplier set back into the equation and solve for the optimal actual control increment.

[0034] Real-time online anti-saturation optimization is achieved on microprocessor hardware with extremely low computational power consumption. Traditional quadratic programming solvers (such as interior-point methods) require high-dimensional Hessian matrix inversion operations, which are prone to numerical computational crashes and consume large amounts of memory due to matrix condition number differences. The Hildreth algorithm, based on the duality principle and sequential coordinate descent method, retains only basic scalar multiplication and addition operations and non-negative projection in one dimension (zero boundary truncation), completely avoiding the matrix inversion process. This makes it not only computationally inefficient but also extremely numerically stable, making it very suitable for low-level control deployment in embedded systems.

[0035] Specifically, constructing a quadratic objective function that combines tracking error and control energy includes: Extract the tracking error minimization term based on the system settings; extract the control energy limitation term based on the controller parameters; introduce weighting coefficients to adjust the ratio of the tracking error minimization term to the control energy limitation term, and synthesize the positive definite quadratic objective function.

[0036] An optimal dynamic balance between tracking accuracy and control energy consumption is achieved. By combining minimizing the tracking error term with limiting the control energy term, and adjusting it with weighting coefficients, this objective function effectively constrains the energy output of the actuator while ensuring that the system closely follows the desired trajectory. This prevents saturation distortion caused by excessive energy demand from individual channels during multivariate synthesis of control commands, thereby ensuring the physical realizability of control commands and the long-term stable operation of the system.

[0037] Specifically, the method described in this embodiment is executed in a controller that internally contains a cascaded structure, and the execution flow includes: The virtual desired velocity calculator included in the controller receives external position tracking error signals, actual position feedback signals, and actual velocity feedback signals, and plans and outputs virtual desired velocity signals to the inner loop dynamics level. The parameter estimator included in the controller extracts the changes in control input and velocity through differential delay, calculates and sends out the estimated value of the pseudo gradient matrix at the current moment online. The saturation optimization module included in the controller receives the virtual desired velocity signal, the actual velocity feedback at the previous moment, the control input at the previous moment, and the estimated value of the pseudo gradient matrix at the current moment, performs quadratic programming of the control quantity and anti-saturation processing, and outputs the optimal actual control increment.

[0038] Structural decoupling significantly enhances engineering feasibility and software reliability. The virtual velocity signal planned at the outer-loop kinematic level provides a smooth and physically consistent reference for the inner-loop dynamic controller, reducing the probability of severe command oscillations. Simultaneously, the explicit signal transmission relationships and fixed-time discrete control loop scheduling ensure that the output of preceding steps (such as parameter estimation) is stabilized before being used as input for subsequent steps (such as optimization), maintaining the unidirectional flow and causal consistency of the entire closed-loop data link and meeting the stringent real-time and continuous requirements of modern industrial control systems.

[0039] Example 2 This embodiment provides a saturation optimization model-free adaptive control method for MIMO systems in multi-input multi-output nonlinear systems, which includes the following process: Step 1: Construct a dynamic linearized data model for the MIMO system.

[0040] For any having Input and A discrete-time nonlinear system with outputs, at the current time... Let the system input vector be The system output vector is Using the compact format dynamic linearization (CFDL) technique, the following equivalent data model is established:

[0041] in, Defined as a pseudo gradient matrix (PJM).

[0042] In this embodiment, this step is implemented by obtaining the input signal vector and output signal vector of the multi-input multi-output nonlinear controlled object at two consecutive discrete sampling times, performing differential operations on the above signals to obtain the input increment and output increment, and then introducing a time-varying parameter matrix, i.e., a pseudo-gradient matrix, to construct a linear algebraic equation between the input increment and the output increment at the next time step.

[0043] This step, based on the generalized partial differential mean value theorem in multivariable calculus, performs a local equivalent expansion of a discrete-time dynamic system with unknown structure and high-order nonlinear terms near its current operating point. In the overall process, this step serves to reduce the dimensionality of the complex, unknown physical system into a standardized mathematical data model, providing a fundamental mathematical equation framework for all subsequent model-free controller design and online parameter learning.

[0044] This step directly addresses the issue of multiple solutions and divergence risks in designing global control laws for multivariable nonlinear functions with cross-coupling. However, by utilizing the compact scheme dynamic linearization technique, it is possible to transform the system into a linear time-varying difference equation with extremely simple form without losing the local dynamic coupling information of the system.

[0045] In this step, each off-diagonal element in the pseudo-gradient matrix implicitly contains the cross-coupling gain between different channels within the controlled object, enabling the algorithm to natively handle multi-channel coupling effects in subsequent calculations. This eliminates the unmodeled dynamic interference caused by forced independent decoupling in traditional control methods, and improves the system's ability to represent complex internal dynamics.

[0046] Step 2: Online estimation of the pseudo gradient matrix (PJM) based on data-driven methods.

[0047] In order to obtain without a model This invention designs an online estimation law based on a projection algorithm. Using only the input and output data from the previous time step, the matrix parameters are updated by minimizing the estimation error. The estimation algorithm is as follows:

[0048] in yes Valuation, Step size factor As a penalty factor, a reset mechanism exists: to prevent estimation divergence, when If the value is too small or there is a sudden, impulsive change, reset it to its initial value. .

[0049] In this embodiment, this step is implemented as follows: within each sampling control cycle, the control system extracts the input increment data, output increment data, and pseudo gradient matrix estimate from the previous control cycle, substitutes them into the adaptive projection update equation with penalty mechanism, calculates the pseudo gradient matrix estimate at the current moment, and sends it to the subsequent control solution module.

[0050] This step constructs a cost functional minimization process with historical data prediction error as the core. The algorithm calculates the residual between the actual measured change in system output and the change in output predicted using the old parameter matrix, and iteratively corrects the matrix parameters along the negative gradient direction of the residual.

[0051] This step acts as a real-time observer and environmental adaptation center for the unknown dynamic characteristics within the system, freeing the control system from dependence on prior physical parameters. Because the physical characteristics of a real physical system, such as inertia, damping, or stiffness, change with factors like temperature and load during operation, fixed control parameters cannot adapt to this drift. The step size factor in the formula is used to adjust the convergence speed of the parameters, and the penalty factor is set to prevent division errors that could lead to program crashes when the system input increment norm is extremely small or even close to zero. Simultaneously, an anti-divergence reset mechanism is included because when sensors detect strong non-Gaussian environmental noise or the system encounters a hard physical impact, the estimation algorithm based on the least squares concept may calculate extreme singular values ​​that have lost their physical meaning.

[0052] This step endows the entire control algorithm with the ability to learn independently as the working environment changes, ensuring that the pseudo gradient matrix can approximate the true local partial derivatives of the system, ensuring the timeliness and accuracy of the basic data on which the subsequent control law solution depends, and improving the reliability of numerical calculations in harsh industrial electromagnetic interference environments.

[0053] Step 3: Design a model-free quasi-sliding mode predictive controller.

[0054] By combining the backstepping method with quasi-sliding mode control, an ideal control law under unconstrained conditions is designed.

[0055] 1. Define tracking error: ,in This represents the desired trajectory.

[0056] 2. Designing the sliding surface: To enhance the robustness of the system, a discrete sliding mode function is defined:

[0057] Where K is the gain matrix that satisfies the Hurwitz condition.

[0058] 3. Construct the prediction equation: Based on the model from step one, predict the sliding surface value at the next time step. and order To achieve rapid convergence.

[0059] 4. Derive the unconstrained control law: Without considering saturation, the ideal control input increment can be obtained. However, directly applying this control law may exceed the actuator's limitations, so optimization is required in step four.

[0060] The controller's specific structure is as follows: like Figure 1As shown in the dashed box, the MIMO-SOSM-MFABSC controller proposed in this invention aims to effectively solve the problems of dynamic coupling and actuator amplitude and rate saturation in the system. In its overall structure, the controller is connected in series between the system's given input and the controlled object, forming a closed-loop control loop. Internally, the controller mainly consists of three core functional modules: a virtual desired velocity calculator based on quasi-sliding mode control, a saturation-optimized MIMO-CFDL-MFAC module, and a PJM parameter estimator. The specific composition and signal transmission relationships of each module are described below: The first step is acquiring the external error signal. The system receives the desired position signal from an external input. And compare it with the actual position signal obtained after delay through the feedback loop. By performing a difference comparison, the position tracking error signal at the current time can be calculated. This error signal serves as the basic input for subsequent control calculations.

[0061] Secondly, there is a virtual desired velocity calculator based on quasi-sliding mode control. This module mainly functions as an outer-loop kinematics planner. Its input also receives the aforementioned position tracking error signal. Feedback of actual position signal and the actual speed signal fed back This calculator, based on a quasi-sliding mode control algorithm, processes the aforementioned state information to calculate and output the virtual desired velocity signal that the system must achieve to track the desired trajectory. .

[0062] Next is the core execution part of the controller, namely the saturation-optimized MIMO-CFDL-MFAC module. This module acts as an inner-loop dynamics controller, using a virtual desired velocity signal. As its direct tracking target. During operation, the module's input not only receives... It also incorporates the actual speed feedback from the previous moment. The control input quantity at the previous moment The module also includes real-time updated parameters from the parameter estimator. Combining the model-free adaptive control algorithm of compact-format dynamic linearization (CFDL) with a saturation optimization mechanism, this module solves for and anti-saturation processing of the control input, ultimately outputting the current actual control command. It acts on the controlled object.

[0063] Finally, it is used to achieve adaptive adjustment. Parameter estimator. To enable model-free adaptive control algorithms to track the dynamic characteristics of the controlled object in real time, this parameter estimator needs to compute the pseudo-Jacobi matrix online. The system incorporates a differential delay element in the feedback loop (i.e., shown in the diagram). (Module) used to extract changes in control input. and velocity change . The parameter estimator receives these two incremental signals and dynamically estimates the system's parameters online. The parameters are updated and then transmitted in real time to the saturated optimization MIMO-CFDL-MFAC module, thereby completing the data-driven closed-loop parameter update.

[0064] In addition, the controlled object in the control instructions Under its influence, output the position at the next moment. and speed and through The delay element is converted into the feedback quantity at the current moment, maintaining the continuous operation of the entire control system.

[0065] In this embodiment, this step is implemented by constructing a control calculation path containing an inner and outer double-loop cascade structure within the controller. At the outer loop kinematic level, the deviation is calculated by comparing the current actual state of the system with the desired trajectory. Combined with a discrete sliding surface containing historical error information, a virtual reference motion velocity signal is planned. At the inner loop dynamic level, this virtual velocity signal is used as the control target. Using the time-varying pseudo-gradient matrix obtained in the previous steps, and based on the boundary conditions that force the system to reach the sliding surface at the next moment, the ideal control quantity increment under no physical constraints is calculated algebraically in reverse.

[0066] This step integrates the recursive logic of backstepping design with the invariance characteristics of variable structure control. By reducing the order of the complex high-order system to two low-order subsystems, position loop and velocity loop, the virtual control law of each subsystem is calculated sequentially using backstepping. At the same time, a quasi-sliding surface is introduced in each derivation step to replace the conventional linear proportional-integral state, so that the dynamic behavior of the closed-loop error of the system is strictly constrained by the gain matrix that satisfies the Hurwitz stability condition.

[0067] This step achieves preliminary quantification of the control objective and coarse calculation of commands, transforming the abstract trajectory tracking error into a specific actuator action tendency, thus playing a crucial mathematical transformation role. Because purely data-driven control is insufficient in its disturbance rejection capability when faced with drastic perturbations of internal system parameters or unknown external environmental disturbances such as gusts of wind or water flow, introducing a discrete quasi-sliding mode surface forces the system state to converge to a preset manifold space within a finite number of sampling periods and maintain a sliding state within this space. This utilizes the inherent disturbance rejection characteristics of sliding mode control to compensate for the shortcomings of model-free control in robustness.

[0068] This step significantly improves the robustness of the closed-loop system to external time-varying disturbances without increasing model complexity, ensuring rapid and asymptotic convergence of the system tracking error in the absence of physical constraints. At the same time, the virtual velocity signal generated by the outer loop provides a smooth and physically consistent reference benchmark for the inner loop dynamic controller, reducing the probability of severe oscillations in the control command solution.

[0069] Step 4: Solve the saturation optimization of the control quantity based on the Hildreth method.

[0070] This step is the core innovation of this invention. Addressing the amplitude and rate saturation issues of the actuator, the control problem is transformed into a constrained quadratic programming problem.

[0071] 1. Define constraints: Amplitude constraints: .

[0072] Rate constraints: .

[0073] The above constraints are combined into a unified inequality constraint form: .

[0074] 2. Construct the optimization objective function:

[0075] The objective function aims to minimize the tracking error while limiting the control energy. (These are weighting coefficients).

[0076] 3. Solve using Hildreth's algorithm: This algorithm is based on the duality principle and finds the Lagrange multiplier vectors through a simple iterative process. Thus, the optimal control increment is obtained. The Hildreth algorithm is characterized by not involving matrix inversion, low computational cost, and high numerical stability, making it very suitable for embedded systems. The specific iterative process is as follows: 1) Initialize the Lagrange multiplier vectors .

[0077] 2) In each iteration, update the multiplier components one by one. If a component is less than 0, it is truncated to 0 (because the multipliers of the inequality constraint must be non-negative).

[0078] 3) After iterative convergence, utilize the final... Calculate the optimal control .

[0079] In this embodiment, this step is implemented as follows: after obtaining the unconstrained ideal control increment calculated in step three, the controller does not directly send it to the controlled object, but instead uses it as a reference input for the quadratic programming optimization engine. The system first reads the maximum output power boundary and maximum action rate boundary recorded in the physical usage instructions of the current actuator, and uses matrix concatenation operations to uniformly map these multidimensional physical constraints into a set of linear inequalities about the current control increment vector. Next, the algorithm calls the pre-compiled Hildreth action iteration subroutine, which iteratively updates a set of Lagrange multiplier variables and truncates them to zero boundaries until all multiplier changes are below a set threshold, at which point the iteration ends. Finally, this converged set of multipliers is substituted back into the equation to calculate the optimal actual control increment that satisfies all physical boundaries.

[0080] This step utilizes the dual transformation and sequential coordinate descent method from convex optimization theory. By constructing a positive definite quadratic objective function, the original minimization problem with boundary constraints is transformed into a multiplier maximization problem with only non-negativity constraints in the dual space using the Lagrangian function. The Hildreth algorithm does not operate using the traditional method of solving simultaneous equations globally; instead, it employs a one-dimensional search along the multidimensional coordinate axes, performing a non-negativity projection after each direction update until the KKT conditional saddle point where the global optimum is located is reached.

[0081] This step acts as a safety filter and energy allocation center before control commands are issued, ensuring consistency between the algorithm's logical space and the hardware's physical space. In multi-input multi-output systems, when control commands for one or more channels are truncated due to exceeding hardware limits, the commands for the remaining unsaturated channels retain their original values. This directly distorts the direction of the synthesized control vector, causing the controlled object to deviate from its intended path and accumulate significant integral errors. Furthermore, conventional quadratic programming solvers such as the interior-point method or the effective set method require high-dimensional Hessian matrix inversion, which not only consumes a large amount of chip memory but also easily leads to numerical computational crashes when the matrix condition number is poor. The Hildreth algorithm is chosen precisely to avoid matrix inversion, retaining only basic scalar multiplication and addition operations.

[0082] This step enables real-time online anti-saturation optimization on microprocessor hardware with limited computing power in industrial settings. This allows the controller to proactively and smoothly adjust the control output ratios in various dimensions under extreme operating conditions that approach physical limits. This effectively avoids system integral divergence and high-frequency vibration of the actuator caused by actuator saturation, ensuring the operational safety and trajectory tracking accuracy of the entire electromechanical system.

[0083] Step 5: As Figure 2 As shown, the overall operation flow of the control loop execution process system is as follows: 1. Initialization: Setting controller parameters Expected trajectory And the initial value of the PG matrix.

[0084] 2. Measurement: Sample the input data of the MIMO system at the current moment. In this embodiment, a multi-joint space robot is used as an example. The input data are joint angles and base posture data. .

[0085] 3. Estimation: Using the formula from step two, update the pseudo-gradient matrix based on historical data. .

[0086] 4. Optimization Solution: Substitute the current state into the Hildreth optimization algorithm in step four, and iteratively calculate the optimal control torque that satisfies all saturation constraints. .

[0087] 5. Execution: Will Send to the motor or actuator. Cycle: Command Return to step 2.

[0088] In this embodiment, this step is implemented by constructing an infinite loop task scheduling thread driven by a fixed hardware timer interrupt signal in the main program architecture of the control system. During the system power-on startup phase, the step size factor, penalty factor, and initialization matrix parameter configuration stored in non-volatile memory are read. As the timer triggers and enters the discrete control cycle, the system sequentially calls the analog-to-digital conversion interface to collect feedback signals from external sensors according to a fixed timing sequence, triggers the parameter estimation subroutine to update the coupling matrix, calls the quadratic programming library function to complete instruction optimization, and outputs the final instruction code to the servo driver through the digital-to-analog conversion interface or pulse width modulation channel. Subsequently, the system automatically increments the time sequence number and enters sleep mode to wait until the next timer interrupt arrives and repeats the above process.

[0089] This step is based on the time-slice rotation and time-series causal scheduling logic of discrete-time digital control systems. By forcibly defining the execution order of data acquisition, parameter identification, state estimation, instruction calculation and hardware output, it ensures that the output data of the preceding steps are stably stored in the memory buffer before being used as the input for subsequent steps, thus maintaining the unidirectional flow and causal consistency of the entire closed-loop data link.

[0090] This step provides a lifecycle management framework for the continuous and stable operation of the entire control algorithm at the computer hardware level, transforming isolated mathematical formulas into time-sensitive engineering execution code. Because in complex time-varying multivariable control tasks, the controller's input data is a constantly changing dynamic data stream, any timing errors or data races in any step can lead to severely lagging estimates of the pseudo-gradient matrix or the control law using outdated state information, resulting in system instability. Employing a strictly sequential single-threaded architecture or a timed loop structure with strong synchronization mechanisms can minimize system bus latency and data uncertainty.

[0091] This step endows the entire saturated optimization model-free adaptive control method for MIMO systems with strong engineering feasibility and operational reliability. This clearly structured execution flow results in low software coupling between the various algorithm modules, facilitating portability and code refactoring on different underlying microcontroller platforms. It also ensures that the system can perform high-frequency, periodic, stabilizing control of nonlinear, multi-coupled objects over extended periods without manual intervention, meeting the stringent requirements of modern industry for the real-time performance, stability, and continuity of control systems.

[0092] This embodiment proposes a control method that integrates dynamic linearization and Hildreth optimization for a class of general multiple-input multiple-output (MIMO) nonlinear discrete-time systems. This method uses a data-driven approach to estimate the system's dynamic coupling parameters (pseudo-gradient matrix) online using input and output data. Combined with quasi-sliding mode control and the Hildreth quadratic programming algorithm, it achieves stable control of the MIMO system while satisfying actuator amplitude and rate saturation constraints.

[0093] In practical applications, the overall control architecture of the aforementioned multi-input multi-output nonlinear controlled system also needs to focus on the smooth transition of variable states and energy storage mechanisms in each stage. Under the combined operation of the aforementioned compact dynamic linearization model, online parameter observer, quasi-sliding mode backstepper, and quadratic programming solver, the strong coupling characteristics between multiple channels are no longer considered as interference terms that should be ignored, but are transformed into feedforward information channels to assist the system in making predictions. Since the pseudo-gradient matrix is ​​finely adjusted and corrected according to the actual output of the controlled object in each sampling period, this method has an inherent adaptive compensation capability for complex factors such as the increase in mechanical clearance caused by equipment wear, the change in fluid viscosity caused by temperature changes, or the change in system rotational inertia caused by sudden changes in external load. Under this structure, once the external changes are reflected in the difference between the position and velocity data fed back by the sensors, the projection algorithm can quickly adjust the coupling matrix parameters within several sampling periods, and the control solution module then uses the new parameters to update the gradient direction of the control signal, and issues commands in the form of the optimal path conforming to the physical boundary under the constraints of the Hildreth algorithm. The organic integration of this system has fully constructed an advanced control implementation path that does not require prior mechanistic information but has strong physical boundary compliance.

[0094] Example 3: In this embodiment, a saturated optimization model-free adaptive control system for MIMO systems is provided. This saturated optimization model-free adaptive control system for MIMO systems can be used to implement the above-mentioned saturated optimization model-free adaptive control method for MIMO systems. Specifically, the saturated optimization model-free adaptive control system for MIMO systems includes a dynamic linearization data model construction module, an update module, an inverse algebraic solution module, a quadratic objective function construction module, an optimal actual control increment solution module, and an application module.

[0095] The dynamic linearized data model construction module is used to obtain the input and output data of the MIMO system at adjacent sampling times, and to build a dynamic linearized data model containing a pseudo-gradient matrix based on this.

[0096] The update module is used to update the pseudo-gradient matrix online based on the input increment, output increment, and pseudo-gradient matrix estimate from the previous time step, using an update algorithm with a penalty mechanism and a reset mechanism.

[0097] The inverse algebraic solution module is used to calculate the unconstrained ideal control increment by inverse algebraic solution based on the discrete quasi-sliding surface and the backstepping method, combined with the dynamic linearized data model.

[0098] The quadratic objective function construction module is used to establish a set of linear inequality constraints on the control increment based on the amplitude and rate constraints of the MIMO system actuator. Using the unconstrained control increment as a reference, it constructs a quadratic objective function that includes a tracking error term and a control increment weighting term.

[0099] The optimal actual control increment solution module is used to iteratively solve the quadratic objective function under the set of linear inequality constraints using the Hildreth algorithm to obtain the actual control increment that satisfies the constraints.

[0100] The application module is used to update the control input according to the actual control increment and apply it to the MIMO system.

[0101] Example 4: This embodiment provides a terminal device, which includes a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used for the operation of a saturated optimization model-free adaptive control method for MIMO systems, including: acquiring the input and output data of the MIMO system at adjacent sampling times, and establishing a dynamic linearized data model containing a pseudo-gradient matrix; based on the input increment, output increment, and pseudo-gradient matrix estimate of the previous time step, using a... An update algorithm with penalty and reset mechanisms updates the pseudo-gradient matrix online. Based on the discrete quasi-sliding surface and the backstepping method, combined with the dynamic linearized data model, the unconstrained ideal control increment is calculated algebraically through inverse calculation. A set of linear inequality constraints regarding the control increment is established based on the amplitude and rate constraints of the MIMO system actuators. Using the unconstrained control increment as a reference, a quadratic objective function containing a tracking error term and a control increment weighting term is constructed. The Hildreth algorithm is used to iteratively solve the quadratic objective function under the set of linear inequality constraints to obtain the actual control increment that satisfies the constraints. The control input is updated based on the actual control increment and applied to the MIMO system.

[0102] Example 5: This embodiment provides a computer-readable storage medium (Memory), which is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM (Random Access Memory) or non-volatile memory, such as at least one disk storage device.

[0103] One or more instructions stored in the computer-readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the saturation optimization model-free adaptive control method for MIMO systems in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps: acquiring the input and output data of the MIMO system at adjacent sampling times, and establishing a dynamic linearized data model containing a pseudo-gradient matrix based on this; updating the pseudo-gradient matrix online using an update algorithm with a penalty mechanism and a reset mechanism based on the input increment, output increment, and pseudo-gradient matrix estimate of the previous time step. Based on the discrete quasi-sliding surface and the backstepping method, combined with the dynamic linearized data model, the unconstrained ideal control increment is calculated algebraically through inverse algebra. A set of linear inequality constraints regarding the control increment is established according to the amplitude and rate constraints of the MIMO system actuators. Using the unconstrained control increment as a reference, a quadratic objective function containing a tracking error term and a control increment weighting term is constructed. The Hildreth algorithm is used to iteratively solve the quadratic objective function under the set of linear inequality constraints to obtain the actual control increment that satisfies the constraints. The control input is updated according to the actual control increment and applied to the MIMO system.

[0104] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, etc.) containing computer-usable program code.

[0105] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0106] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0107] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0108] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0109] In the above embodiments of this application, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0110] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.

[0111] It should be understood that the above description is for illustrative purposes and not for limitation. Many embodiments and applications beyond the provided examples will be apparent to those skilled in the art upon reading the above description. Therefore, the scope of this patent should not be determined by reference to the above description, but rather by reference to the foregoing claims and the full scope of their equivalents. For purposes of completeness, all articles and references, including patent applications and publications, are incorporated herein by reference. The omission of any aspect of the subject matter disclosed herein in the foregoing claims is not intended as a waiver of that subject matter, nor should it be construed as an indication that the applicant has not considered that subject matter as part of the disclosed inventive subject matter.

Claims

1. A model-free adaptive control method for saturated optimization of MIMO systems, characterized in that, Includes the following processes: The input and output data of the MIMO system at adjacent sampling times are obtained, and a dynamic linearized data model containing a pseudo-gradient matrix is ​​established accordingly. Based on the input increment, output increment, and pseudo-gradient matrix estimate from the previous time step, the pseudo-gradient matrix is ​​updated online using an update algorithm with a penalty mechanism and a reset mechanism. Based on the discrete quasi-sliding surface and the backstepping method, combined with this dynamic linearized data model, the unconstrained ideal control increment is calculated by inverse algebra. Based on the amplitude and rate constraints of the MIMO system actuator, a set of linear inequality constraints about the control increment is established. Taking the unconstrained control increment as a reference, a quadratic objective function containing a tracking error term and a control increment weighting term is constructed. The Hildreth algorithm is used to iteratively solve the quadratic objective function under the set of linear inequalities to obtain the actual control increment that satisfies the constraints. The control input is updated based on the actual control increment and applied to the MIMO system.

2. The saturation optimization model-free adaptive control method for MIMO systems according to claim 1, characterized in that, Establishing a dynamically linearized data model that includes a pseudo-gradient matrix includes: Extract the input signal vector and output signal vector of a multi-input multi-output nonlinear controlled object at two consecutive discrete sampling times; Perform differential operations on signals at adjacent discrete sampling times to generate input and output increments; Construct a linear algebraic equation between the input increment and the output increment at the next time step. Internally, this linear algebraic equation treats the pseudo-gradient matrix as a time-varying parameter matrix.

3. The saturation optimization model-free adaptive control method for MIMO systems according to claim 1, characterized in that, Online updates of the pseudo-gradient matrix using projection algorithms with penalty and reset mechanisms include: Extract the historical input increment data, historical output increment data, and historical pseudo gradient matrix estimate saved from the previous control cycle; Calculate the residual between the actual measured output change and the output change predicted using historical parameters; The historical pseudo-gradient matrix estimates are iteratively corrected along the negative gradient direction of the residual to generate the pseudo-gradient matrix estimates at the current time. This penalty mechanism is activated when the input increment norm is lower than a set threshold to prevent division by zero errors in division operations. The reset mechanism is activated when there is a sudden, impulsive change in the pseudo-gradient matrix estimate, restoring it to the initial setting.

4. The saturation optimization model-free adaptive control method for MIMO systems according to claim 1, characterized in that, The unconstrained ideal control increment is calculated by inverse algebraic solution, including: Extract the position tracking error between the current actual state of the system and the desired trajectory; By combining historical error data, a discrete quasi-sliding surface with Hurwitz stability is constructed. Based on the backstepping calculation logic, the boundary conditions for the system state to reach the discrete quasi-sliding surface at the next moment are set; Under these boundary conditions, the unconstrained ideal control increment under any physical limitations is derived and calculated in reverse.

5. The saturation optimization model-free adaptive control method for MIMO systems according to claim 1, characterized in that, The Hildreth algorithm is used to iteratively optimize the quadratic objective function, including: Initialize a set of Lagrange multiplier variables; Update each multiplier component in the group of Lagrange multiplier variables one by one along the multidimensional coordinate axis; Perform a zero-boundary truncation operation on the updated multiplier components, and force the negative components to be set to zero; The iteration stops when all changes in multipliers fall below a set convergence threshold, and the converged set of multipliers is output. Substitute the convergent set of multipliers back into the equation and solve for the optimal actual control increment.

6. The saturation optimization model-free adaptive control method for MIMO systems according to claim 1, characterized in that, Constructing a quadratic objective function that combines tracking error and control energy includes: Extract the tracking error minimization term according to the system settings; Extract control energy limiting terms based on controller parameters; By introducing weighting coefficients to adjust the ratio of the tracking error minimization term to the control energy constraint term, a positive definite quadratic objective function is synthesized.

7. The saturation optimization model-free adaptive control method for MIMO systems according to claim 1, characterized in that, This method is executed in a controller that contains a cascading structure, and the execution flow includes: The virtual expected velocity calculator included in the controller receives external position tracking error signals, actual position feedback signals, and actual velocity feedback signals, and plans and outputs virtual expected velocity signals to the inner loop dynamics layer; The parameter estimator contained in the controller extracts the changes in control input and velocity through differential delay, and calculates and sends out the estimated value of the pseudo gradient matrix at the current moment online; The saturation optimization module included in the controller receives the virtual desired speed signal, the actual speed feedback from the previous moment, the control input from the previous moment, and the estimated value of the pseudo gradient matrix at the current moment. It then performs quadratic programming of the control input and anti-saturation processing, and outputs the optimal actual control increment.

8. A saturated optimization model-free adaptive control system for MIMO systems, characterized in that, include: The dynamic linearized data model building module is used to acquire the input and output data of the MIMO system at adjacent sampling times, and to build a dynamic linearized data model containing a pseudo-gradient matrix based on this data. The update module is used to update the pseudo-gradient matrix online based on the input increment, output increment, and pseudo-gradient matrix estimate from the previous time step, using an update algorithm with a penalty mechanism and a reset mechanism. The inverse algebraic solution module is used to calculate the unconstrained ideal control increment by inverse algebraic solution based on the discrete quasi-sliding surface and the backstepping method, combined with the dynamic linearized data model. The quadratic objective function construction module is used to establish a set of linear inequality constraints on the control increment based on the amplitude and rate constraints of the MIMO system actuator, and to construct a quadratic objective function containing a tracking error term and a control increment weighting term using the unconstrained control increment as a reference. The optimal actual control increment solution module is used to iteratively solve the quadratic objective function under the set of linear inequality constraints using the Hildreth algorithm to obtain the actual control increment that satisfies the constraints. An application module is used to update the control input according to the actual control increment and apply it to the MIMO system.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the saturated optimization model-free adaptive control method for MIMO systems as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the saturated optimization model-free adaptive control method for MIMO systems as described in any one of claims 1 to 7.

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