CN114415504B - Unified control method based on self-adaptive control and iterative learning control - Google Patents
Unified control method based on self-adaptive control and iterative learning control Download PDFInfo
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Abstract
The application discloses a unification control method based on self-adaptive control and iterative learning control, belongs to the technical field of computer control, and has the design key points that: firstly, expanding a controller based on an adaptive observer into a formation tracking task containing a real navigator through a fully distributed communication diagram; then, according to the superposition of the linear space, adopting an adaptive observer-based control to realize formation tracking which keeps a fixed shape relative to a navigator; and thirdly, recording and storing the initialization conditions of the iterative learning control at the beginning of each test, and adopting the iterative learning control to realize the repeatable formation tracking relative to the navigator coordinate system. By adopting the method, the multi-agent system formation tracking control task containing the non-repetitive navigator can be realized.
Description
Technical Field
The present application relates to the field of computer control, and more particularly, to a unified control method based on adaptive control and iterative learning control.
Background
Most of the labor in the manufacturing industry has been replaced by machines for the 21 st century. Various related researches propose various control methods, so as to control a series of robot systems to accurately complete corresponding industrial operations. For the last two decades, there has been a long evolution of collaborative distributed control research on multi-agent systems (multi-agent systems), such as: consistency control, formation control, inclusion control, cluster control, congestion control, intersection control, and the like. Notably, in terms of consistency or synchronous control, formation control applied to target closure, cooperative positioning, loading and transportation, autonomous marine subsea testing, etc., has completed an impressive series of work, which has stimulated tremendous research into researchers' interest.
In general, there are three queuing schemes today: no pilot formation, virtual pilot formation, real pilot formation. Because there is no navigator, the follower of the convoy in the first solution cannot acquire a specific direction of travel. While in the second solution, the virtual pilot of the team usually adopts a predetermined track, the track space of the follower is limited. It follows that there are significant limitations and disadvantages to the use of the first two approaches. In the third scheme, the navigator exists truly, can move to any position in space based on a dynamics model of the navigator, and can track a target or avoid an obstacle by changing an input signal. In this scenario, to handle non-zero signal input by a real pilot, researchers typically use a nonlinear model with state-dependent boundary layers to compensate for the effects of the non-zero input, and thus also create a bounded error in formation tracking (formation tracking). To further reduce this error, rational planning and optimization of the follower trajectory becomes a direction of investigation of the heat.
According to previous studies, adaptive observer-based control (adaptive observer-based control) based controllers have been able to independently implement formation tracking. However, in the related studies the formation shape is fixed, i.e. the formation shape remains translated in space over time. The iterative learning control (iterative learning control) is a control method for improving the accuracy of performing repeated tasks. Since being proposed, iterative learning control has found relevant applications in industrial production, chemical processes, rehabilitation, and the like. There is also a close relationship between iterative learning control and formation control. In 2009, iterative learning control was first applied to multi-agent systems, and related study reports were also subsequently issued, but were limited by the repetitive design requirements of iterative learning control, in which one part of the study was formed without a pilot, and the trajectories of the pilots of the other part were repetitive, i.e., the trajectories of the pilots were static or cyclic. In recent years, research on iterative learning control has also gained a certain attention to iterative change formation shape theory. So far, no time-varying formation shape theory study of related iterative learning control has been published through retrieval.
Disclosure of Invention
The invention aims to solve the limitations of the existing research work and provides a self-adaptive and iterative learning unified control method for non-repetitive multi-agent formation, namely a fully distributed algorithm is developed by combining a self-adaptive observer control and iterative learning control technology, so that a multi-agent system formation tracking control task containing a non-repetitive navigator is realized.
The invention is realized by the following technical scheme:
the beneficial effects of this application lie in:
(1) The invention discovers the connection between the formation task with non-repeated real navigator (non-zero input and non-repeated track) and the iterative learning control, builds a uniform distributed control framework by utilizing the self-adaptive control and the iterative learning control according to the superposition of the linear space, and creatively proposes a new formation tracking mechanism. An adaptive observer-based controller is presented in detail to assist the user in establishing an iterative learning control update law that eliminates the same initial condition requirements. The self-adaptive observer control-iterative learning control algorithm is a fully distributed algorithm, so that formation tracking bounded errors in the iterative learning control test process are further reduced. In the iterative learning control test of the present invention, the formation shape is not only translatable but also rotatable, even time-varying. Compared with the existing iterative learning control formation task, the track of the navigator is non-repeatable, and the application range of iterative learning control is greatly expanded.
(2) The framework provided by the invention is formed by utilizing the superposition property of a linear system and combining self-adaptive control and iterative learning control. Based on the framework, the follower in formation can achieve non-repetitive track tracking with high precision, so that bounded errors in formation tracking are reduced. The non-repetitive track of the follower can be seen as being superimposed by the repetitive and non-repetitive tracks. For example, correlation theory suggests that in the case where the follower rotates around the navigator, the track of the follower is repetitive with respect to the navigator's own coordinate system.
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The present application is described in further detail below in conjunction with the embodiments in the drawings, but is not to be construed as limiting the present application in any way.
Fig. 1: fully distributed algorithm structure: and (5) controlling a working flow chart based on the adaptive observer and iterative learning.
Fig. 2: and forming and tracking a scene graph under a ground coordinate system and a navigator coordinate system.
Detailed Description
The invention is further described by way of examples with reference to the accompanying drawings. The following examples will assist those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present invention. The present invention will be described in detail with reference to the accompanying drawings, but the scope of the present invention is not limited to the following examples.
Example 1: a unified control method based on self-adaptive control and iterative learning control.
The basic principle of the application is as follows:
firstly, the controller based on the adaptive observer is further expanded into a formation tracking task containing a real navigator through a fully distributed communication diagram.
And then, according to the additivity of the linear space, adopting the adaptive observer control to realize formation tracking which keeps a fixed shape relative to the navigator, recording and storing the initialization condition of iterative learning control at the beginning of each test, and further adopting the iterative learning control to realize repeatable formation tracking relative to the navigator coordinate system. Note that the input to each follower is the sum of the inputs from both the adaptive observer control and the iterative learning control controller.
The workflow diagram corresponding to the unified framework provided by the invention is shown in the attached figure 1. Throughout the formation tracking task, the follower can achieve a non-repetitive trajectory following the ground coordinate system by using adaptive observer-based control. As shown in FIG. 1, in the iterative learning control initialization condition setting phaset k +T,t k+1 ]The formation application enables a relative tracking error e between follower and pilot based on adaptive observer control i aoc (t) converging to a limit such that the initial state condition of the iterative learning control is within an acceptable, further employable range. On the basis, iterative learning control is adopted to process the repetitive track, for example, each follower rotates around the navigator under the navigator coordinate system, so as to further promote [ t ] in the test k+1 ,t k+1 +T]Representation of formation tracking of time period repeatability.
A unified control method based on self-adaptive control and iterative learning control comprises the following steps:
s100, inputting parameters and initializing process
Power system A, B, C, initializing iterative learning control input u ilc,0 Formation shape component
And->
Test time T and initialization condition setting time T of selective learning control k+1 -(t k +T) and task-based formation tracking accuracy ε
S200. initializing, setting k=0
S300 at [0, t ]]Time period, at target system
Application adaptive controller
S400, learning and controlling the test time period [ t ] in the 0 th iteration 0 ,t 0 +T]The initial iteration of the adaptive controller is learned and controlled to input u ilc,0 Applied to system devices
S500 record formation tracking error
S600:
S601:
At [ t ] k +T,t k+1 ]Time period, at target system
An adaptive controller (synchronous SS 300) is applied and an iterative learning controller is used +.>
Calculating and updating the input of the next iterative learning control;
S602:
learning the control test period [ t ] at the kth iteration k+1 ,t k+1 +T]Inputs to an adaptive controller and an iterative learning controller
Applied to system devices
S603 recording formation tracking error
S604:k＝k+1
S605:end while
Table 1: physical meaning of parameters in the present application
Table 2: meaning of additional formula of parameter
The above examples are preferred embodiments of the present application, and are merely for convenience of explanation, not limitation, and any person having ordinary skill in the art shall make local changes or modifications by using the technical disclosure of the present application without departing from the technical features of the present application, and all the embodiments still fall within the scope of the technical features of the present application.
Claims (2)
1. The unified control method based on the self-adaptive control and the iterative learning control is characterized by comprising the following steps:
s100, inputting parameters and initializing;
s200, initializing, namely setting the number k=0 of iterative learning control tests;
s300 at [0, t ]]Time period, at target system
Application adaptive controller
wherein ,
the representation is: forming a first derivative of the state of agent i in the tracking task;
x i and (t) represents: the state of an agent i in a formation tracking task;
A. b, C it represents: a system state space matrix;
u i and (t) represents: input of an agent i in a formation tracking task;
y i (t) represents: calculating and outputting an agent i in the formation tracking task;
K 1 the representation is: a constant matrix to be determined;
K 2 the representation is: a constant matrix to be determined;
v i the representation is: the input of a distributed self-adaptive observer of the agent i in the formation tracking task;
f represents: a related parameter;
c i the representation is: a time-varying coupling weight associated with follower i;
ξ i the representation is: a related parameter;
ζ i the representation is: a composite signal of information from neighboring agents;
alpha represents: a related parameter;
η i the representation is: a related parameter;
z(η i ) The representation is: a nonlinear function;
β 1 the representation is: greater than 1Constant value
S400, learning and controlling the test time period [ t ] in the 0 th iteration 0 ,t 0 +T]The initial iteration of the adaptive controller is learned and controlled to input u ilc,0 Is applied to a system device;
s500 record formation tracking error
S600 when meeting
Accuracy e of formation tracking is less than or equal to execution of programs S601-S604:
S601:
at [ t ] k +T,t k+1 ]Time period, at target system
Applying an adaptive controller and using an iterative learning controller +.>
r i representing a reference signal;
calculating and updating the input of the next iterative learning control;
S602:
learning the control test period [ t ] at the kth iteration k+1 ,t k+1 +T]Inputs to an adaptive controller and an iterative learning controller
Is applied to a system device;
s603 recording formation tracking error
y 0 (t) represents the calculated output of agent 0 in the formation tracking task;
Ch i (t) represents the trajectory of agent i in the formation tracking task
And S604, assigning k to be k+1.
2. The unified control method based on adaptive control and iterative learning control according to claim 1, wherein in step S100: power system A, B, C and initialization iterative learning controlInput u ilc,0 Formation shape component
And->
Test time T and initialization condition setting time T of selective learning control k+1 -(t k +T) and task-based formation tracking accuracy E.
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