Gain-adjusted complex system adaptive anti-windup output feedback control method
The adaptive anti-saturation output feedback control method with gain adjustment solves the input saturation problem in the output feedback scenario by using a state observer and a planning function, thereby improving the reliability and stability of the system, simplifying the controller structure, and enabling precise tracking of the reference signal.
Patent Information
- Application Number
- CN202610345982.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-20
- Publication Date
- 2026-05-15
- Estimated Expiration
- 2046-03-20
AI Technical Summary
Existing output feedback adaptive anti-saturation control schemes cannot completely avoid input saturation, which may affect system reliability and have the problem of complex recursive calculations. In particular, in output feedback scenarios, there is a lack of full-state information, and the gain adjustment method may lead to excessive transient control amplitude when compensating for uncertainties.
An adaptive anti-saturation output feedback control method based on gain adjustment is adopted. The unmeasurable internal state is estimated in real time by a state observer. Combined with the dynamic gain update law and the planning function, an adaptive anti-saturation output feedback control signal is generated to ensure that the control signal does not exceed the actuator saturation limit. An input planning mechanism is designed to avoid saturation limitations.
It achieves complete avoidance of input saturation in complex systems, improves system reliability, simplifies controller structure, can accurately track reference signals, compensate for system nonlinearity and external disturbances, and prevents Zeno's phenomenon.
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Figure CN121879161B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of adaptive control, and particularly relates to an adaptive anti-saturation output feedback control method for complex systems based on gain adjustment. Background Technology
[0002] In practical control systems, the physical saturation limitation of actuators is a common problem. If the control signal amplitude becomes too large, exceeding the actuator's physical limits, it will adversely affect control performance or system stability, and may even lead to system instability. Significant progress has been made in state feedback adaptive anti-saturation control based on backstepping. Its core idea is to use Nussbaum-type functions or auxiliary compensation systems, combined with smooth approximation functions, to compensate for the effects of input saturation. However, in practical engineering, output feedback scenarios are more common, and the lack of full-state information makes the design of adaptive anti-saturation control more challenging. Most existing output feedback adaptive anti-saturation control schemes follow the technical approach of state feedback. Overall, while existing backstepping-based schemes can compensate for the effects of input saturation to some extent, they cannot completely avoid input saturation, potentially affecting system reliability, and they also suffer from complex recursive calculations.
[0003] Gain adjustment, as another effective adaptive control strategy, has shown significant advantages in trajectory tracking, fault-tolerant control, and event triggering. However, how to use this method to solve the input saturation problem is still unclear, and the dynamic gain may lead to excessive transient control amplitude when compensating for uncertainties.
[0004] Therefore, researching an adaptive anti-saturation output feedback tracking control method based on gain adjustment that can completely avoid input saturation and has a simple and practical structure still has potential application value. Summary of the Invention
[0005] The technical objective of this application is to propose a practical adaptive anti-saturation output feedback tracking scheme based on gain adjustment for a class of uncertain nonlinear systems with input saturation constraints.
[0006] To achieve the above-mentioned technical objectives, the present application adopts the following technical solution.
[0007] This invention provides an adaptive anti-saturation output feedback control method for complex systems based on gain adjustment, comprising:
[0008] Step 1: Based on the real-time output signal of the controlled object, the preset reference signal, and the constraints of the preset dynamic model of the controlled object, the unmeasurable internal state of the controlled object is estimated in real time through the state observer to obtain the estimation result;
[0009] Step 2: Based on the preset dynamic model of the controlled object and the saturation limit of the actuator, combined with the real-time output signal of the controlled object, the preset reference signal, the initial dynamic gain and the estimation results, the initial control signal is calculated and generated; the optimized initial control signal is obtained through the preset dynamic gain update law.
[0010] Step 3: Based on the optimized initial control signal, determine if the preset monitoring conditions are met, trigger the preset planning time, and use the preset planning function to adjust the amplitude of the optimized initial control signal to a safe range that does not exceed the saturation limit of the actuator, thereby generating an adaptive anti-saturation output feedback control signal.
[0011] Step 4: Output the output feedback control signal to the actuator of the controlled object;
[0012] Repeat steps 1 through 4 above.
[0013] Further, step 3 specifically includes: comparing the difference between the optimized initial control signal amplitude and the maximum saturation value of the actuator in real time;
[0014] Based on the comparison results, determine whether the optimized initial control signal meets the preset monitoring conditions;
[0015] When the monitoring conditions are met, a preset planning time is triggered, and a preset planning function is started. The optimized initial control signal amplitude is adjusted to a safe range that does not exceed the actuator saturation limit through the planning function, and an adaptive anti-saturation output feedback control signal is generated.
[0016] When the monitoring conditions are not met, the adaptive anti-saturation output feedback control signal directly uses the optimized initial control signal.
[0017] Furthermore, the judgment logic for whether the preset monitoring conditions are met is as follows: when the amplitude of the optimized initial control signal reaches the difference between the maximum saturation value of the actuator and the preset small normal value, it is determined that the preset monitoring conditions are met.
[0018] Furthermore, the constraints of the dynamic model include unknown time-varying vector constraints and bounded external disturbance constraints; the unknown time-varying vector constraint is that the unknown time-varying vector is restricted to an unknown bounded convex set, and the bounded external disturbance constraint is that the amplitude of the external disturbance does not exceed an unknown positive constant.
[0019] Furthermore, the actuator saturation limit includes the maximum saturation value and the minimum saturation value of the actuator, wherein the maximum saturation value is the upper limit of the physical output of the actuator, and the minimum saturation value is the lower limit of the physical output of the actuator.
[0020] Furthermore, the planning function is defined as:
[0021] ;
[0022] in, For each interval positive numbers, ,in The absolute value of the preset amplitude. For the optimized initial control signal at the planning time The value of , where r is the preset interval duration. For a strictly decreasing smooth function, satisfying , and derivatives of each order in The value is 0.
[0023] Furthermore, the estimation basis of the state observer also includes tracking error, which is the difference between the real-time output signal of the controlled object and the preset reference signal.
[0024] Furthermore, the adjustment basis of the dynamic gain update law includes: the tracking error, the estimation result obtained by the state observer, the real-time dynamic gain, and the boundary of the preset tracking error compact set, and the dynamic gain is always non-negative.
[0025] Furthermore, the constraints of the dynamic model also include: the dynamic model contains a nonlinear function, the nonlinear function satisfies a polynomial growth condition, the polynomial growth condition is that the amplitude of the nonlinear function does not exceed a polynomial expression containing unknown constants, the real-time output signal of the controlled object and each state variable, and the nonlinear function is coupled with all unmeasurable internal states.
[0026] Furthermore, the method also includes using a sensor to acquire the real-time output signal of the controlled object; the sensor is an industrial measurement sensor, and the type of industrial measurement sensor includes at least one of position sensor, temperature sensor, pressure sensor, and voltage sensor, and the acquired real-time output signal is the actual operating parameter of the controlled object.
[0027] It should be understood that the summary section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description.
[0028] Compared with existing technologies, the adaptive anti-saturation output feedback control method for complex systems based on gain adjustment provided by this invention has the following beneficial technical effects: This invention uses an input planning mechanism consisting of monitoring conditions and a planning function to prepare the planning control signal; it utilizes gain adjustment technology and a series of planning functions to design an adaptive observer and a practical anti-saturation controller. A dynamic gain is designed to eliminate the effects of system uncertainties and the additional effects introduced by the planning function, which is responsible for planning the control signal to a pre-designed amplitude. This invention designs an output feedback adaptive anti-saturation tracking controller to compensate for system nonlinearity, input saturation limitations, and external disturbances, thereby preventing saturation constraints and enabling the system output to accurately track a given reference signal. Attached Figure Description
[0029] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of this application in any way. Furthermore, the shapes and scales of the components in the drawings are merely illustrative to aid in understanding this application and do not specifically limit the shapes and scales of the components. Those skilled in the art, guided by the teachings of this application, can select various possible shapes and scales to implement this application according to specific circumstances. In the drawings:
[0030] Figure 1 A schematic block diagram of the control flow of the adaptive anti-saturation output feedback control method based on gain adjustment provided in the embodiment. Detailed Implementation
[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 are within the scope of protection of the present invention.
[0032] To enable those skilled in the art to better understand the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0033] The embodiments provide an adaptive anti-saturation output feedback control method for complex systems based on gain adjustment, such as... Figure 1 As shown, it includes the following steps:
[0034] Step 1: Based on the real-time output signal of the controlled object, the preset reference signal, and the constraints of the preset dynamic model of the controlled object, the unmeasurable internal state of the controlled object is estimated in real time through the state observer to obtain the estimation result;
[0035] Step 2: Based on the preset dynamic model of the controlled object and the saturation limit of the actuator, combined with the acquired real-time output signal, preset reference signal, initial dynamic gain and estimation results, the initial control signal is calculated and generated; through the preset dynamic gain update law, the dynamic gain is updated in real time, and the initial control signal is adaptively compensated and optimized to obtain the optimized initial control signal.
[0036] Step 3: Based on the optimized initial control signal, if the preset monitoring conditions are met, trigger the preset planning time, use the preset planning function to adjust the amplitude of the optimized initial control signal to a safe range that does not exceed the actuator saturation limit, and generate an adaptive anti-saturation output feedback control signal.
[0037] Step 4: Output the adaptive anti-saturation output feedback control signal to the actuator of the controlled object to drive the actuator to adjust the operating state of the controlled object;
[0038] Repeat steps 1 to 4 above to ensure that the controlled object outputs a stable tracking of the preset reference signal and that the control signal is always within the saturation limit, so that the system operates stably.
[0039] In some embodiments, step 3 specifically includes: comparing the difference between the optimized initial control signal amplitude and the maximum saturation value of the actuator in real time;
[0040] Based on the comparison results, determine whether the optimized initial control signal meets the preset monitoring conditions;
[0041] When the monitoring conditions are met, the preset planning time is triggered, and the preset planning function is started. The planning function adjusts the amplitude of the optimized initial control signal to a safe range that does not exceed the actuator saturation limit, and generates an adaptive anti-saturation output feedback control signal.
[0042] When the monitoring conditions are not met, the adaptive anti-saturation output feedback control signal directly uses the optimized initial control signal.
[0043] In some embodiments, while repeatedly executing steps 1 to 4 above, a preset planning function design and dynamic gain update mechanism are used to ensure that no Zeno phenomenon occurs during system operation. Zeno phenomenon refers to the abnormal situation in which the system switches an infinite number of times within a finite time.
[0044] In the embodiments, the constraints of the dynamic model include: the dynamic model contains unknown time-varying vector constraints, bounded constraints of external disturbances, and the dynamic model contains nonlinear functions.
[0045] In the embodiments, a dynamic model of a class of output feedback uncertain nonlinear systems is established in advance, namely the dynamic model of the controlled object, and the physical saturation limit of the actuator is considered to establish an actuator saturation model.
[0046] In this embodiment, the established dynamic model of the uncertain nonlinear system is as follows:
[0047] (1);
[0048] in, Let be the system state vector. For system input, For system output; ( () is a nonlinear function that is locally Lipschitz continuous with respect to the system state; An unknown time-varying vector is restricted to an unknown bounded convex set (i.e., an unknown time-varying vector constraint). ( ) represents external interference, satisfying (i.e., bounded constraints on external disturbances, where) (Unknown positive constant); only system output. Measurable. It is the order of the system. For real numbers, yes Dimensional space; yes Dimensional space; It is the dimension of the unknown time-varying vector; It is external interference; It is both the system status and the system output; It is one of the nonlinear functions of the system.
[0049] The actuator saturation model defines the actuator saturation limits, specifically including the maximum and minimum saturation values of the actuator, as described below:
[0050] ;
[0051] in, and These are the minimum and maximum saturation values of the actuator, respectively.
[0052] In the embodiment, relevant assumptions are made regarding the nonlinear function of the system: the polynomial growth condition that the nonlinear function in the nonlinear system dynamic model must satisfy, as well as other necessary assumptions, are clarified, providing a theoretical basis for subsequent controller design and stability analysis.
[0053] Assumption 1: Nonlinear function satisfy:
[0054] ;
[0055] in For unknown constants, It is a known positive integer.
[0056] Hypothesis 1 indicates that the nonlinear function is coupled with all the unmeasurable internal states of the controlled object and satisfies the polynomial growth condition.
[0057] Assumption 2: The actuator can respond to a preset reference signal during the steady-state phase. To achieve the control objective, and with a preset reference signal. and its time derivative Both are bounded.
[0058] The embodiment also designs an input planning mechanism: constructing an input planning mechanism that includes monitoring conditions and a planning function. Step 3 monitors whether the control signal is close to the saturation limit, and adjusts the amplitude of the control signal through the planning function when necessary.
[0059] In this embodiment, the designed input planning mechanism specifically includes:
[0060] 1. Definition of planning time sequence: Let the planning time sequence be... ,Right now , This is the first planning time, i.e., the initial planning time. For the k-th planning time, the amplitude of the control signal approaches its saturation limit. Based on the planning time, the control signal is defined as follows:
[0061] ;
[0062] in, The optimized initial control signal to be designed. yes The control signals to be designed after planning, It is the planning function to be designed.
[0063] In this embodiment, an initial control signal can be calculated and generated based on a preset dynamic model of the controlled object and the actuator saturation limit, combined with the acquired real-time output signal, a preset reference signal, the initial dynamic gain, and the estimation results.
[0064] It should be noted that, where the context will not cause confusion, the time symbol and certain function arguments will be omitted, such as a function It can be represented as or .
[0065] 2. The judgment logic for whether the preset monitoring conditions are met is as follows: when the amplitude of the optimized initial control signal reaches the difference between the maximum saturation value of the actuator and the preset small normal value (i.e., the monitoring threshold), it is determined that the preset monitoring conditions are met.
[0066] Monitoring conditions are used to determine the planning time and the initial planning time. Defined as:
[0067] ;
[0068] in, To monitor the threshold, This is a preset small positive number. If the previous planning time... If this has been determined, then the next planning time... Defined as:
[0069] .
[0070] 3. Programming Function: Designing the programming function Used to adjust the amplitude of the control signal, defined as:
[0071] ;
[0072] in, For each interval positive numbers, ,in The absolute value of the preset amplitude. ; For the optimized initial control signal at the planning time The value of . For a strictly decreasing smooth function, satisfying , and derivatives of each order in The value is 0, and the candidate form is: ( and (where r is a normal number) and r is the preset interval duration.
[0073] In this embodiment, step 3 constructs a dynamic gain, a state observer, and an adaptive anti-saturation controller. Based on gain adjustment technology, a dynamic gain is designed to compensate for the system nonlinearity, external disturbances, input saturation, and additional effects introduced by the planning function; a state observer is constructed to estimate the unmeasurable state of the system; and a practical adaptive anti-saturation output feedback controller is designed by combining the input planning mechanism, dynamic gain, and observer state.
[0074] In this embodiment, the construction of the dynamic gain, state observer, and adaptive anti-saturation controller in step 3 is as follows:
[0075] Lemma 1: To determine the design parameters of the state observer and controller, the following lemma is introduced: For any positive constant... There are positive numbers and Positive definite matrix and Gain vector and gain vector This makes the following inequality hold:
[0076] ;
[0077] in, ,matrix ,vector and Defined as:
[0078] .
[0079] In some embodiments, tracking error is defined as follows: Tracking error is defined. ,in This is a preset reference signal.
[0080] State observer design: Based on Lemma 1 and tracking error, the state observer is designed as follows:
[0081] (9);
[0082] in, This refers to the observer's state, i.e., the estimation result; For dynamic gain (initial value) ), gain vector As determined by Lemma 1, and satisfying .
[0083] In the embodiment, the dynamic gain update law is: dynamic gain The update law is designed as follows:
[0084] ;
[0085] in, , and For the positive constants to be designed, This sets the boundaries for the pre-defined tracking error compactness. Dynamic gain. It satisfies the following characteristics:
[0086] .
[0087] 5. Adaptive Anti-Saturation Controller Design: Combining input planning mechanism, state observer, and dynamic gain, a practical adaptive anti-saturation output feedback controller is designed as follows:
[0088] ;
[0089] in, The gain vector K for the generated adaptive anti-saturation output feedback control signal is determined by Lemma 1. Determined by monitoring conditions, For planning functions.
[0090] In this embodiment, step 3 further includes closed-loop system stability and Zeno phenomenon analysis: using Lyapunov stability theory and proof by contradiction, the boundedness of all signals in the closed-loop system and the convergence of tracking error are proved, and the absence of Zeno phenomenon in the system is verified.
[0091] In this embodiment, the stability of the closed-loop system and the Zeno phenomenon are analyzed in detail as follows:
[0092] Step 3.1: All states of the closed-loop system are bounded. Define the estimation error:
[0093] ,in , .
[0094] Introducing coordinate transformation , ( ), Derivation of the error vector and Dynamic characteristics:
[0095] ;
[0096] ;
[0097] in, , , .
[0098] For satisfying the expression normal numbers Design parameters and This has been determined by Lemma 1. Since and It is a Hurwitz matrix, and the Lyapunov function is chosen as follows:
[0099] ;
[0100] in: .
[0101] Considering (13) and , The derivative satisfies:
[0102] .
[0103] First, estimate the uncertainties caused by the programming function. Note that... ,have:
[0104] .
[0105] Considering and ,make:
[0106] ;
[0107] We can obtain: .
[0108] Furthermore, the effects of system nonlinearity and disturbances are estimated. Based on Assumption 1 and... It can be deduced that:
[0109] ;
[0110] in Using Young's inequality, we have:
[0111] ;
[0112] Selecting design parameters and for:
[0113] .
[0114] Utilization and We can obtain:
[0115] .
[0116] Finally, the formula - Substitution ,get:
[0117] ;
[0118] in It is an unknown positive number.
[0119] Utilization , and Provable variables In the maximum time interval The boundedness of the variables is well-established, and the proof includes a relatively mature method of proof by contradiction, so it is omitted here. Due to the variables... exist It is bounded above, therefore Therefore, according to Boundedness, exist There is a boundary above.
[0120] Step 3.2, prove that the control signal does not violate input saturation. From equation... , and ( The boundedness of the control signal means that the control signal It is bounded. Associative and It can be inferred that in each Location:
[0121] .
[0122] Considering the formula and Furthermore, we can obtain:
[0123] .
[0124] Therefore, the continuity of the control signal means On and ( On satisfy and Therefore, the control signal satisfies .
[0125] Step 3.3, prove the tracking error Able to converge to the preset set Note the formula Defined in On any compact set, with respect to its independent variable The Lipschitz condition is satisfied. Because... exist It is bounded above and has positive constants. , such that for any ,have:
[0126] .
[0127] Depend on Given its boundedness, It is uniformly continuous, that is, for any positive constant... There exists a positive constant. , making when At that time, there were:
[0128] .
[0129] Combined and For all ,have ,Right now exist The above is consistent and continuous. At the same time, Boundedness indicates According to Barbara's theorem, we have:
[0130] .
[0131] From the formula ,have:
[0132] ;
[0133] Combined We can obtain:
[0134] ;
[0135] That is, tracking error Can be restricted to a pre-defined compact set Inside.
[0136] Step 3.4, analyze Zeno's phenomenon, i.e., the existence of normal numbers. This makes it possible for each They all From the formula It can be seen that the planning function is in each Continuously update to reduce the amplitude of the control signal, combined with... We can obtain:
[0137] .
[0138] control signals In the interval The dynamic characteristics are as follows:
[0139] .
[0140] From the formula It can be seen that, It's about bounded signals. Therefore, there must exist positive constants. Make From this, we can deduce that:
[0141] ;
[0142] That is, there exists a constant. Therefore, the Zeno phenomenon does not exist in the system.
[0143] This invention is the first to apply the gain scaling method to adaptive anti-saturation output feedback tracking control. Compared with the existing backstepping method-based scheme, it has the following beneficial technical effects: 1. The designed quasi-linear controller structure is simpler and more practical, and the system model considered is more general, that is, the nonlinear function is coupled with all unmeasurable states and satisfies the polynomial growth condition.
[0144] 2. By designing an input planning mechanism and integrating the planning function into the anti-saturation controller, the control signal can be planned within a preset amplitude range as needed, completely avoiding triggering the actuator saturation limit. Compared with existing solutions that may have continuous input saturation, the closed-loop system has higher reliability.
[0145] 3. The reasonable range of the preset amplitude was derived in advance through theoretical analysis. The advantage of dynamic gain is that it can simultaneously compensate for system nonlinearity, input saturation, external disturbances, and the additional effects introduced by the planning function, while ensuring the control performance of the system.
[0146] The above provides a detailed description of the adaptive anti-saturation output feedback control method for complex systems based on gain adjustment provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the concept of this application and should not be construed as limiting the scope of protection of this application.
Claims
1. An adaptive anti-saturation output feedback control method for complex systems based on gain adjustment, characterized in that, include: Step 1: Based on the real-time output signal of the controlled object, the preset reference signal, and the constraints of the preset dynamic model of the controlled object, the unmeasurable internal state of the controlled object is estimated in real time through the state observer to obtain the estimation result; Step 2: Based on the preset dynamic model of the controlled object and the saturation limit of the actuator, combined with the real-time output signal of the controlled object, the preset reference signal, the initial dynamic gain and the estimation results, calculate and generate the initial control signal; The optimized initial control signal is obtained by using a preset dynamic gain update law; Step 3: Based on the optimized initial control signal, determine if the preset monitoring conditions are met, trigger the preset planning time, and use the preset planning function to adjust the amplitude of the optimized initial control signal to a safe range that does not exceed the saturation limit of the actuator, thereby generating an adaptive anti-saturation output feedback control signal. Step 4: Output the output feedback control signal to the actuator of the controlled object; Repeat steps 1 through 4 above; step 3 specifically includes: The difference between the optimized initial control signal amplitude and the maximum saturation value of the actuator is compared in real time. Based on the comparison results, determine whether the optimized initial control signal meets the preset monitoring conditions; When the monitoring conditions are met, a preset planning time is triggered, and a preset planning function is started. The optimized initial control signal amplitude is adjusted to a safe range that does not exceed the actuator saturation limit through the planning function, and an adaptive anti-saturation output feedback control signal is generated. When the monitoring conditions are not met, the adaptive anti-saturation output feedback control signal directly uses the optimized initial control signal. The planning function is defined as follows: ; in, For each interval positive numbers, ,in The absolute value of the preset amplitude. For the optimized initial control signal at the planning time The value of , where r is the preset interval duration. For a strictly decreasing smooth function, satisfying , and derivatives of each order in The value is 0; The estimation basis of the state observer also includes tracking error, which is the difference between the real-time output signal of the controlled object and the preset reference signal; The adjustment basis of the dynamic gain update law includes: tracking error, estimation results obtained by the state observer, real-time dynamic gain and the boundary of the preset tracking error compact set, and the dynamic gain is always non-negative.
2. The adaptive anti-saturation output feedback control method for complex systems based on gain adjustment according to claim 1, characterized in that, The logic for determining whether the preset monitoring conditions are met is as follows: when the amplitude of the optimized initial control signal reaches the difference between the maximum saturation value of the actuator and the preset small normal value, it is determined that the preset monitoring conditions are met.
3. The adaptive anti-saturation output feedback control method for complex systems based on gain adjustment according to claim 1, characterized in that, The constraints of the dynamic model include unknown time-varying vector constraints and bounded constraints of external disturbances; The constraint on the unknown time-varying vector is that the unknown time-varying vector is restricted to an unknown bounded convex set; The bounded constraint for external interference is that the amplitude of external interference does not exceed an unknown normal number.
4. The adaptive anti-saturation output feedback control method for complex systems based on gain adjustment according to claim 1, characterized in that, The actuator saturation limit includes the maximum saturation value and the minimum saturation value of the actuator; The maximum saturation value is the upper limit of the physical output of the actuator, and the minimum saturation value is the lower limit of the physical output of the actuator.
5. The adaptive anti-saturation output feedback control method for complex systems based on gain adjustment according to claim 1, characterized in that, The constraints of the dynamic model also include: the dynamic model contains nonlinear functions; The nonlinear function satisfies the polynomial growth condition, which is that the amplitude of the nonlinear function does not exceed the polynomial expression containing the unknown constant, the real-time output signal of the controlled object, and each state variable, and the nonlinear function is coupled with all the unmeasurable internal states of the controlled object.
6. The adaptive anti-saturation output feedback control method for complex systems based on gain adjustment according to claim 1, characterized in that, The method further includes using a sensor to acquire the real-time output signal of the controlled object; the sensor is an industrial measurement sensor, and the type of the industrial measurement sensor includes at least one of position sensor, temperature sensor, pressure sensor, and voltage sensor, and the acquired real-time output signal is the actual operating parameter of the controlled object.
