CN112987561A - Robust filter type iterative learning control method for finite time trajectory tracking - Google Patents

Robust filter type iterative learning control method for finite time trajectory tracking Download PDF

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CN112987561A
CN112987561A CN201911308075.5A CN201911308075A CN112987561A CN 112987561 A CN112987561 A CN 112987561A CN 201911308075 A CN201911308075 A CN 201911308075A CN 112987561 A CN112987561 A CN 112987561A
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iterative learning
filter
discrete
tracking
track
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CN112987561B (en
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马晓贤
朱凤增
彭力
乔伟豪
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Wuxi Electronics & Instruments Industry Co ltd
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract

A robust filter type iterative learning control method for finite time trajectory tracking provides a distributed filter type iterative learning control method for finite time expected trajectory tracking, and track tracking errors possibly generated during target trajectory tracking are reduced by the method, so that the target trajectory is accurately tracked.

Description

Robust filter type iterative learning control method for finite time trajectory tracking
Technical Field
The invention relates to a distributed filter type iterative learning control method for finite time expectation trajectory tracking, and belongs to the field of communication information processing.
Background
Iterative learning control is a process of imitating human behavior extraction experience, adopts a strategy of 'learning in repetition', corrects an undesired control signal according to the deviation of the actual output and the expected output of a system, generates a new control signal, improves the tracking performance of the system, and approaches to an ideal expected track after iteration for a plurality of times. Because the iterative learning control method does not depend on an accurate mathematical model of the system, can realize the control of a nonlinear strong coupling dynamic system with high uncertainty by a very simple algorithm in a given time range, and tracks a given expected track with high precision, the iterative learning control method has very strong engineering background, such as manipulator track tracking, mobile robot track tracking and the like, and the track of a moving target has time-varying, strong coupling and nonlinear dynamic characteristics in an actual scene, so that an accurate and complete moving model of the moving target cannot be obtained in many times, and therefore, the iterative learning control based on distributed filtering provides a feasible solution for reducing tracking track errors generated during target track tracking.
Disclosure of Invention
The invention aims to provide a distributed filter type iterative learning control method for the limited-time expected trajectory tracking, which reduces the possible trajectory tracking error generated during the target trajectory tracking and achieves more accurate tracking of the target trajectory.
The invention adopts the following technical scheme for solving the technical problems:
1. a robust filter type iterative learning control method for finite time trajectory tracking comprises the following steps:
step 1: establish a discrete system and determine parameters A, B, Ci、M
Figure RE-GDA0002525196210000011
Wherein k is a discrete time parameter, x (k +1) is a state variable of the discrete random system at the moment k +1, x (k) is a state variable of the discrete random system at the moment k, yi (k) is an input value of different filters at the moment k, A, Ci is a transfer matrix and an output matrix of the discrete random system respectively, and w (k) is process noise of the discrete random system at the moment k;
step 2: designing a distributed filter:
Figure RE-GDA0002525196210000021
wherein
Figure RE-GDA0002525196210000022
Is the state variable of the discrete random system of filter i at time k,
Figure RE-GDA0002525196210000023
and
Figure RE-GDA0002525196210000024
is the filter parameter to be designed, aijIs the topology of the distributed filter;
the augmented state and the filtering error are defined as:
Figure RE-GDA0002525196210000025
the system for obtaining the filtering error is as follows:
Figure RE-GDA0002525196210000026
wherein:
Figure RE-GDA0002525196210000027
Figure RE-GDA0002525196210000028
Figure RE-GDA0002525196210000029
Figure RE-GDA00025251962100000210
Figure RE-GDA00025251962100000211
Figure RE-GDA00025251962100000212
if the equations (3) and (4) hold, the distributed filter has a given performance, and the filter has parameters of
Figure RE-GDA00025251962100000213
And
Figure RE-GDA00025251962100000214
and step 3: solving the LMI equations shown in the formulas (3) and (4) to obtain the parameters of the distributed filter
Figure RE-GDA00025251962100000215
And
Figure RE-GDA00025251962100000216
and 4, step 4:
the discrete linear system is:
Figure RE-GDA0002525196210000031
in the formula (5), k is the iteration number of the iterative learning algorithm, and T belongs to [0T ]]Is the iteration time, xk(t) is the state vector of the discrete time system, wk(t) is the repetitive external disturbance in the iterative learning process, yk(t) is the output of the system, yd(t) is the desired trajectory of the target, u(k,i)(t) is the iterative learning rate of the different filter feeds back to the system, assuming the desired trajectory yd(T) in the time interval T ∈ [0T ]]Is differentiable by controlling the iterative learning rate uk(T) such that for all T ∈ [0T ]]When k → ∞ is reached, yk(t) convergence to yd(t)；
And 5: design parameters C, B for iterative learningiAnd D, satisfying formula (7):
the dynamic process of the controlled system is shown as the formula (5), and the given expected track is yd(t)(t∈[0T]) If the condition of the formula (7) is satisfiedCan prove yk(t) capable of converging on the desired trajectory yd(t), namely the output track of the system is close to the expected track, namely the actual target track, so as to achieve the aim of target tracking;
Figure RE-GDA0002525196210000032
step 6: the iterative learning control system of the distributed filter comprises:
Figure RE-GDA0002525196210000033
and (4) obtaining a tracking track according to the equation of the formula (6).
The invention has the advantages that: a distributed filter type iterative learning control method for expected trajectory tracking in limited time is provided, and the method reduces possible trajectory tracking errors generated during target trajectory tracking so as to achieve more accurate tracking of the target trajectory.
Description of the drawings:
fig. 1 is a block diagram of a distributed filter based iterative learning control system employing a filtered output error signal instead of a filtered output signal.
The specific implementation mode is as follows:
the invention provides a distributed filter type iterative learning control method for finite time expectation trajectory tracking, which is used for obtaining the motion trajectory of a moving target, and the design method specifically comprises the following steps:
establishing a discrete system:
Figure RE-GDA0002525196210000041
where k is a discrete time parameter, x (k +1) is a state variable of the discrete random system at time k +1, x (k) is a state variable of the discrete random system at time k, yi(k) Is the input value of the different filters at time k, A, CiRespectively is a transfer matrix and an output matrix of the discrete random system, and w (k) is process noise of the discrete random system at the moment k;
the distributed filter is designed as follows:
Figure RE-GDA0002525196210000042
wherein
Figure RE-GDA0002525196210000043
Is the state variable of the discrete random system of filter i at time k,
Figure RE-GDA0002525196210000044
and
Figure RE-GDA0002525196210000045
is the filter parameter to be designed, aijIs the topology of the distributed filter.
The augmented state and the filtering error are defined as:
Figure RE-GDA0002525196210000046
the system for obtaining the filtering error is as follows:
Figure RE-GDA0002525196210000047
wherein:
Figure RE-GDA0002525196210000048
Figure RE-GDA0002525196210000049
Figure RE-GDA0002525196210000051
Figure RE-GDA0002525196210000052
Figure RE-GDA0002525196210000053
Figure RE-GDA0002525196210000054
if the equations (3) and (4) hold, the distributed filter has a given performance, and the filter has parameters of
Figure RE-GDA0002525196210000055
And
Figure RE-GDA0002525196210000056
iterative learning controller design based on distributed filter:
fig. 1 is a block diagram of a distributed filter-based iterative learning control system, in which the iterative learning control algorithm shown in fig. 1 uses a filtered output error signal instead of a filtered output signal.
Consider a discrete linear system:
Figure RE-GDA0002525196210000057
in the formula (5), k is the iteration number of the iterative learning algorithm, and T belongs to [0T ]]Is the iteration time, xk(t) is the state vector of the discrete time system, wk(t) is the repetitive external disturbance in the iterative learning process, yk(t) is the output of the system, yd(t) is the desired trajectory of the target, u(k,i)(t) is the iterative learning rate of the different filters fed back into the system, and the distributed filter compares to but the filter contributes to the control of the iterative learning rate, assuming the desired trajectoryTrace yd(T) in the time interval T ∈ [0T ]]The purpose of the invention using iterative learning control is to control the iterative learning rate uk(T) such that for all T ∈ [0T ]]When k → ∞ is reached, yk(t) convergence to yd(t)
Therefore, the iterative learning control system of the distributed filter is as follows:
Figure RE-GDA0002525196210000058
the dynamic process of the controlled system is shown as the formula (5), and the given expected track is yd(t)(t∈[0T]) If the condition of formula (7) is satisfied, y can be verifiedk(t) capable of converging on the desired trajectory yd(t), the output track of the system is close to the expected track, namely the actual target track, and the target tracking is achieved.
Figure RE-GDA0002525196210000061
The algorithm flow is as follows:
1. a discrete system is established, as shown in equation (1), and parameters A, B, C are determinedi、M，
2. Designing a distributed filter as shown in equation (2)
3. Solving the LMI equations shown in the formulas (3) and (4) to obtain the parameters of the distributed filter
4. Determining a desired trajectory y to trackd。
5. Design parameters C, B for iterative learningiAnd D, the formula (7) is satisfied.
6. And (4) obtaining a tracking track according to the equation of the formula (6).
The above is a specific solution for controlling target trajectory tracking based on iterative learning of distributed filtering, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications and substitutions within the technical scope of the present invention are covered by the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.

Claims (1)

1. A robust filter type iterative learning control method for finite time trajectory tracking is characterized in that: the method comprises the following steps:
step 1: establish a discrete system and determine parameters A, B, Ci、M
Figure RE-FDA0002525196200000011
Wherein k is a discrete time parameter, x (k +1) is a state variable of the discrete random system at the moment k +1, x (k) is a state variable of the discrete random system at the moment k, yi (k) is an input value of different filters at the moment k, A, Ci is a transfer matrix and an output matrix of the discrete random system respectively, and w (k) is process noise of the discrete random system at the moment k;
step 2: designing a distributed filter:
Figure RE-FDA0002525196200000012
wherein
Figure RE-FDA0002525196200000013
Is the state variable of the discrete random system of filter i at time k,
Figure RE-FDA0002525196200000014
and
Figure RE-FDA0002525196200000015
is the filter parameter to be designed, aijIs the topology of the distributed filter;
the augmented state and the filtering error are defined as:
Figure RE-FDA0002525196200000016
the system for obtaining the filtering error is as follows:
Figure RE-FDA0002525196200000017
wherein:
Figure RE-FDA0002525196200000018
Figure RE-FDA0002525196200000019
Figure RE-FDA00025251962000000110
Figure RE-FDA0002525196200000021
Figure RE-FDA0002525196200000022
Figure RE-FDA0002525196200000023
if the equations (3) and (4) hold, the distributed filter has a given performance, and the filter has parameters of
Figure RE-FDA0002525196200000026
And
Figure RE-FDA0002525196200000027
and step 3: solving the LMI equations shown in the formulas (3) and (4) to obtain the parameters of the distributed filter
Figure RE-FDA0002525196200000028
And
Figure RE-FDA0002525196200000029
and 4, step 4:
the discrete linear system is:
Figure RE-FDA0002525196200000024
in the formula (5), k is the iteration number of the iterative learning algorithm, and T belongs to [0T ]]Is the iteration time, xk(t) is the state vector of the discrete time system, wk(t) is the repetitive external disturbance in the iterative learning process, yk(t) is the output of the system, yd(t) is the desired trajectory of the target, u(k,i)(t) is the iterative learning rate of the different filter feeds back to the system, assuming the desired trajectory yd(T) in the time interval T ∈ [0T ]]Is differentiable by controlling the iterative learning rate uk(T) such that for all T ∈ [0T ]]When k → ∞ is reached, yk(t) convergence to yd(t)；
And 5: design parameters C, B for iterative learningiAnd D, satisfying formula (7):
the dynamic process of the controlled system is shown as the formula (5), and the given expected track is yd(t)(t∈[0 T]) If the condition of formula (7) is satisfied, y can be verifiedk(t) capable of converging on the desired trajectory yd(t), namely the output track of the system is close to the expected track, namely the actual target track, so as to achieve the aim of target tracking;
Figure RE-FDA0002525196200000025
step 6: the iterative learning control system of the distributed filter comprises:
Figure RE-FDA0002525196200000031
and (4) obtaining a tracking track according to the equation of the formula (6).
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101846979A (en) * 2010-06-29 2010-09-29 北京航空航天大学 Advanced iterative learning control method for accurate target tracking
CN103631142A (en) * 2013-12-09 2014-03-12 天津工业大学 Iterative learning algorithm for trajectory tracking of wheeled robot
CN105549598A (en) * 2016-02-16 2016-05-04 江南大学 Iterative learning trajectory tracking control and robust optimization method for two-dimensional motion mobile robot
CN108319144A (en) * 2018-02-21 2018-07-24 湘潭大学 A kind of robotic tracking control method and system
CN108536007A (en) * 2018-03-01 2018-09-14 江苏经贸职业技术学院 A kind of adaptive iterative learning control method based on non-critical repetition

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101846979A (en) * 2010-06-29 2010-09-29 北京航空航天大学 Advanced iterative learning control method for accurate target tracking
CN103631142A (en) * 2013-12-09 2014-03-12 天津工业大学 Iterative learning algorithm for trajectory tracking of wheeled robot
CN105549598A (en) * 2016-02-16 2016-05-04 江南大学 Iterative learning trajectory tracking control and robust optimization method for two-dimensional motion mobile robot
CN108319144A (en) * 2018-02-21 2018-07-24 湘潭大学 A kind of robotic tracking control method and system
CN108536007A (en) * 2018-03-01 2018-09-14 江苏经贸职业技术学院 A kind of adaptive iterative learning control method based on non-critical repetition

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