CN107092193A - Tracking and controlling method independent of the non-linear pure time delay system of ideal trajectory - Google Patents

Tracking and controlling method independent of the non-linear pure time delay system of ideal trajectory Download PDF

Info

Publication number
CN107092193A
CN107092193A CN201710500697.2A CN201710500697A CN107092193A CN 107092193 A CN107092193 A CN 107092193A CN 201710500697 A CN201710500697 A CN 201710500697A CN 107092193 A CN107092193 A CN 107092193A
Authority
CN
China
Prior art keywords
msub
mrow
mover
msubsup
mtr
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201710500697.2A
Other languages
Chinese (zh)
Inventor
宋永端
张贝贝
赖俊峰
高辉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Star Institute of Intelligent Systems
Original Assignee
Star Institute of Intelligent Systems
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Star Institute of Intelligent Systems filed Critical Star Institute of Intelligent Systems
Priority to CN201710500697.2A priority Critical patent/CN107092193A/en
Publication of CN107092193A publication Critical patent/CN107092193A/en
Pending legal-status Critical Current

Links

Classifications

    • 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
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)

Abstract

Include the invention discloses a kind of tracking and controlling method of the non-linear pure time delay system independent of ideal trajectory：Step 1: setting up the mathematical modeling of the controlled uncertain pure-feedback systems with time delay；Step 2: using the parametrization linear combination of basic function, unknown ideal trajectory is reconstructed and estimated；Step 3: design is controlled the controller of non-linear pure time delay system；Step 4: controlled quentity controlled variable u is realized into system output is tracked to the default capabilities of unknown ideal trajectory as the control input of the actuator of controlled nonlinear system.The present invention independent of ideal trajectory non-linear pure time delay system tracking and controlling method, its realize system it is close to unknown ideal trajectory cut tracking, while also ensure that the transient state and steady-state behaviour of system and the stability of closed-loop system.

Description

Tracking and controlling method independent of the non-linear pure time delay system of ideal trajectory
Technical field
The present invention relates to Control of Nonlinear Systems technical field, more particularly to a kind of tracking control of non-linear pure time delay system Method processed.
Background technology
Most control problem, can be seen as such as Vehicular automatic driving, target tracking, missile intercept track with Track control problem.This problem has also attracted Many researchers simultaneously, therefore also has substantial amounts of and Trajectory Tracking Control to ask at present Inscribe related achievement in research.But have to explanation, most achievements in research are all based on ideal trajectory or reference Under the known such a premise of input.But in practical application, ideal trajectory or reference input are also likely to be unknown Or can not accurately obtain.Such as, in missile intercept system, be intercepted the track of guided missile may be hidden by premeditated so that Can not accurately it be obtained in ideal trajectory；In addition, can also be related to the tip of driving robot in the application problem of robot Executing agency tracks hiding track；In addition, controlling the electric power output of power system to meet electric load (user's request) In problem, the electricity needs of user is ignorant, the problem of this has still been related to unknown ideal trajectory tracing control.It is comprehensive It is above-mentioned some understand that the tracking control problem of unknown or uncertain ideal trajectory has critically important theory and practice value.But Regrettably the achievement for studying this problem at present is few.
In addition, the result on default capabilities bounded control also has a lot, these achievements are substantially by change of variable To realize, so as to ensure that the mapping and steady-state behaviour of system disclosure satisfy that default capabilities requirement.But the one of this method Individual great limitation is that requirement primary condition meets certain limitation.Therefore system transients can either be ensured and steady by being accomplished by exploration State property can again can not by primary condition limitations affect method.
Finally, it has to be mentioned that, time delay is almost present in all real systems, if when designing control program Do not consider that time delay is likely to affect control effect, system may be made unstable when serious.
The content of the invention
In view of this, it is an object of the invention to provide a kind of tracking of the non-linear pure time delay system independent of ideal trajectory Control method, to solve the unknown object tracking control problem of the uncertain pure-feedback systems with unpredictable time-delay, also simultaneously Ensure that system transients and steady-state behaviour are good.
Tracking and controlling method of the present invention independent of the non-linear pure time delay system of ideal trajectory, comprises the following steps：
Step 1: setting up the mathematical modeling of the controlled uncertain pure-feedback systems with time delay, its form is as follows：
Wherein, for i=1 ..., n, xiIt is system state variables,U ∈ R, y ∈ R are system respectively Control input and system output, τiIt is unpredictable time-delay constant,It is the state variable by time delay influence,fi() is unknown but smooth nonlinear function, Δ fi() is unknown smooth time delay function, di(·) It is uncertain disturbance, x=[x1,...,xn]T；
Definition
And have
Step 2: using the parametrization linear combination of basic function, to unknown ideal trajectory ydIt is reconstructed and estimates；
Unknown ideal trajectory ydReconstruct it is as follows：
Wherein,It is known basis function vector, cd∈ R andIt is unknown constant parameter；
Unknown ideal trajectory ydEstimationIt is as follows：
And then can obtain：
Wherein,WithIt is ω respectivelydAnd cdEstimation；
Step 3: design is controlled the controller of non-linear pure time delay system, comprise the following steps that：
1) systematic error is defined：
Wherein, αi-1, i=2 ..., n are in step 5) in firstorder filter definition in provide, system actual tracking error It is defined as ze=x1-yd, according to the reconstruct of ideal trajectory and estimator and z1And zeDefinition obtain：
2) transformed error v=η (t) z is defined1Controlled with the default capabilities for realizing system, wherein, η (t)=1/ ((1-bf) κ-1(t)+bf) it is error transfer function, κ (t) is taken from the rate function in rate function pond, bfIt is the constant parameter freely designed；
The function in wherein rate function pond meets condition：1) function is positive definite and changed to over time from 0 infinite and dull It is incremented by；2) value at t=0 is 1；3) when t ∈ [0, ∞) when, function differentiable；
3) Liapunov Krasovskii functions are introduced, with compensation system time delay；
Liapunov Krasovskii functions are：
4) a smooth preferable input is obtained according to implicit function theoremFor i=1 .., n-1 or PersonObtain
Wherein, χi(), i=1 .., n-1 is independently of xi+1Function, χn() is independently of u function；And according to The pure-feedback systems that step one is set up are converted into Affine Systems by mean value theorem, and specific reformulationses are as follows：
Wherein,
The smooth unknown function β of close approximation is carried out using neutral netn, it is shown below：
βi=Wi *TSi(Zi)+εi(Zi), i=1 ..., n
Wherein, Wi *It is the preferable weight vector of neutral net, εi(Zi) it is neural network approximate error, Si(Zi) it is Gauss Basis function vector,Had according to the characteristic of neutral net |εi(·)|≤εMi＜ ∞ are set up, εMiIt is normal number；
It is re-introduced into a virtual parameterSo as to need the adaptive ginseng of on-line tuning Number only one of which；
5) limiting bed error y is introducedi
Introduce firstorder filterWherein ζiIt is time constant；
Obtaining control strategy based on dynamic surface technology is：
Wherein Λ1It is positive definite matrix, σ1,σ2,λ1,λ2It is positive constant,It is known bounded function, ki,γi, I=1 ..., n is positive constant；
6) virtual parameter adaptive rate is
Wherein, σ3,σ4It is normal number；
Step 4: realizing system output to not as the control input of the actuator of controlled nonlinear system controlled quentity controlled variable u Know the default capabilities tracking of ideal trajectory.
Beneficial effects of the present invention：
1st, tracking and controlling method of the present invention independent of the non-linear pure time delay system of ideal trajectory, it realizes system pair The close tracking of unknown ideal trajectory, while also ensure that the transient state and steady-state behaviour of system and the stability of closed-loop system.
2nd, tracking and controlling method of the present invention independent of the non-linear pure time delay system of ideal trajectory, it is contemplated that ideal trajectory Unknown situation, and there is provided the method that unknown ideal trajectory is reconstructed.
3rd, tracking and controlling method of the present invention independent of the non-linear pure time delay system of ideal trajectory, it is by using speed Converter technique, on the one hand, the main tracking process of tracking error is tracked with accelerating rate of decay controllable when the time tending to be infinite Error goes to zero, and on the other hand, the acceleration rate of decay of tracking error and the primary condition of system are unrelated, and can arbitrarily set Put.
4th, tracking and controlling method of the present invention independent of the non-linear pure time delay system of ideal trajectory, in controller design mistake Cheng Zhong, selection neural network weight matrix norm is as estimation parameter, and this causes only one auto-adaptive parameter needs tune online It is whole, greatly reduce computation burden.
Brief description of the drawings
Fig. 1 is the step block diagram of control method of the present invention；
Fig. 2 is the system control principle block diagram of control method of the present invention；
Fig. 3 is the tracking performance of system and the biography without progress velocity transformation under the controller action designed by the present invention The tracking performance comparison diagram of system under controller action of uniting；
Fig. 4 is tracking error and the Traditional control without progress velocity transformation under the controller action designed by the present invention The lower tracking error change comparison diagram of device effect；
Fig. 5 is the control input under the controller action designed by the present invention and controlled without the tradition for carrying out velocity transformation Control input change comparison diagram under device effect processed；
Fig. 6 is system self-adaption parameter and no progress velocity transformation under the controller action designed by the present invention System self-adaption Parameters variation comparison diagram under traditional controller effect；
Fig. 7 is the estimate change curve of unknown rationality track estimation parameter vector in present invention design；
Fig. 8 is the estimate change curve of unknown rationality track evaluated error in present invention design.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
Tracking and controlling method of the present embodiment independent of the non-linear pure time delay system of ideal trajectory, comprises the following steps：
Step 1: setting up the mathematical modeling of the controlled uncertain pure-feedback systems with time delay, its form is as follows：
Wherein, for i=1 ..., n, xiIt is system state variables,U ∈ R, y ∈ R are system respectively Control input and system output, τiIt is unpredictable time-delay constant,It is the state variable by time delay influence,fi() is unknown but smooth nonlinear function, Δ fi() is unknown smooth time delay function, di(·) It is uncertain disturbance, x=[x1,...,xn]T；
Definition
And have
Step 2: using the parametrization linear combination of basic function, to unknown ideal trajectory ydIt is reconstructed and estimates；
Unknown ideal trajectory ydReconstruct it is as follows：
Wherein,It is known basis function vector, cd∈ R andIt is unknown constant parameter；
Unknown ideal trajectory ydEstimationIt is as follows：
And then can obtain：
Wherein,WithIt is ω respectivelydAnd cdEstimation；
Step 3: design is controlled the controller of non-linear pure time delay system, comprise the following steps that：
1) systematic error is defined：
Wherein, αi-1, i=2 ..., n are in step 5) in firstorder filter definition in provide, system actual tracking error It is defined as ze=x1-yd, according to the reconstruct of ideal trajectory and estimator and z1And zeDefinition obtain：
2) transformed error v=η (t) z is defined1Controlled with the default capabilities for realizing system, wherein, η (t)=1/ ((1-bf) κ-1(t)+bf) it is error transfer function, κ (t) is taken from the rate function in rate function pond, bfIt is the constant parameter freely designed；
The function in wherein rate function pond meets condition：1) function is positive definite and changed to over time from 0 infinite and dull It is incremented by；2) value at t=0 is 1；3) when t ∈ [0, ∞) when, function differentiable；
3) Liapunov Krasovskii functions are introduced, with compensation system time delay；
Liapunov Krasovskii functions are：
4) a smooth preferable input is obtained according to implicit function theoremFor i=1 .., n-1 or PersonObtain
Wherein, χi(), i=1 .., n-1 is independently of xi+1Function, χn() is independently of u function；And according to The pure-feedback systems that step one is set up are converted into Affine Systems by mean value theorem, and specific reformulationses are as follows：
Wherein,
The smooth unknown function β of close approximation is carried out using neutral netn, it is shown below：
βi=Wi *TSi(Zi)+εi(Zi), i=1 ..., n
Wherein, Wi *It is the preferable weight vector of neutral net, εi(Zi) it is neural network approximate error, Si(Zi) it is Gauss Basis function vector,Had according to the characteristic of neutral net |εi(·)|≤εMi＜ ∞ are set up, εMiIt is normal number；
It is re-introduced into a virtual parameterSo as to need the adaptive ginseng of on-line tuning Number only one of which；
5) limiting bed error y is introducedi
Introduce firstorder filterWherein ζiIt is time constant；
Obtaining control strategy based on dynamic surface technology is：
Wherein Λ1It is positive definite matrix, σ1,σ2,λ1,λ2It is positive constant,It is known bounded function, ki,γi,i =1 ..., n is positive constant；
6) virtual parameter adaptive rate is
Wherein, σ3,σ4It is normal number；
Step 4: realizing system output to not as the control input of the actuator of controlled nonlinear system controlled quentity controlled variable u Know the default capabilities tracking of ideal trajectory.
Simulating, verifying is carried out below, to prove the non-linear pure time delay system independent of ideal trajectory disclosed in the present embodiment The validity of the tracking and controlling method of system.Pure Feedback Nonlinear of the selection with unpredictable time-delay is emulated, system mould Type is as follows：
Wherein, x=[x1,x2]T.Time delay function and disturbance term are defined as follows：
Delay parameter selection therein is τ1=τ2=0.5.Selection ideal trajectory is y in simulationsd=sin (t).Emulation As a result as shown in figures 3-8, Fig. 3 illustrate the control strategy based on velocity transformation designed by the present invention tracing control effect and The tracking effect contrast of traditional control method without velocity transformation；Fig. 4 presents two kinds of strategies and acts on lower tracking respectively The convergence process of error；Fig. 5 is showing two kinds of strategies and acted on down respectively, and the change procedure of system control input can from figure To find out, under the controller action designed by the present invention, the smooth bounded of system control input；Fig. 6 shows system self-adaption parameter Renewal process, thus also confirm the boundedness of auto-adaptive parameter；Fig. 7-8 is the estimation of the reconstruction parameter of unknown ideal trajectory The change procedure of value, equally confirms the boundedness of these parameters.It was found from simulation result, control method disclosed by the invention is Validity, can realize the object of the invention.
Finally illustrate, the above embodiments are merely illustrative of the technical solutions of the present invention and it is unrestricted, although with reference to compared with The present invention is described in detail good embodiment, it will be understood by those within the art that, can be to skill of the invention Art scheme is modified or equivalent substitution, if but without departing from the objective and scope of technical solution of the present invention, just it should cover at this Among the right of invention.

Claims (1)

1. a kind of tracking and controlling method of non-linear pure time delay system independent of ideal trajectory, it is characterised in that：Including following Step：
Step 1: setting up the mathematical modeling of the controlled uncertain pure-feedback systems with time delay, its form is as follows：
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;Delta;f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>&amp;tau;</mi> <mi>i</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>f</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>,</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;Delta;f</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>d</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>=</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, for i=1 ..., n, xiIt is system state variables,U ∈ R, y ∈ R are the control of system respectively System input and system output, τiIt is unpredictable time-delay constant,It is the state variable by time delay influence,fi() is unknown but smooth nonlinear function, Δ fi() is unknown smooth time delay function, di(·) It is uncertain disturbance, x=[x1,...,xn]T；
Definition
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>g</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;part;</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>g</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>,</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;part;</mo> <msub> <mi>f</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>,</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>/</mo> <mo>&amp;part;</mo> <mi>u</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>
And have
Step 2: using the parametrization linear combination of basic function, to unknown ideal trajectory ydIt is reconstructed and estimates；
Unknown ideal trajectory ydReconstruct it is as follows：
<mrow> <msub> <mi>y</mi> <mi>d</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>q</mi> <mi>d</mi> </msub> </munderover> <msub> <mi>f</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>c</mi> <mi>d</mi> </msub> <mo>=</mo> <msubsup> <mi>f</mi> <mi>d</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>&amp;omega;</mi> <mi>d</mi> </msub> <mo>+</mo> <msub> <mi>c</mi> <mi>d</mi> </msub> </mrow>
Wherein,It is known basis function vector, cd∈ R andIt is Unknown constant parameter；
Unknown ideal trajectory ydEstimationIt is as follows：
<mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> <mo>=</mo> <msubsup> <mi>f</mi> <mi>d</mi> <mi>T</mi> </msubsup> <msub> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> <mo>+</mo> <msub> <mover> <mi>c</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> </mrow>
And then can obtain：
<mrow> <msub> <mover> <mover> <mi>y</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>=</mo> <msubsup> <mover> <mi>f</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> <mi>T</mi> </msubsup> <msub> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> <mo>+</mo> <msubsup> <mi>f</mi> <mi>d</mi> <mi>T</mi> </msubsup> <msub> <mover> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>+</mo> <msub> <mover> <mover> <mi>c</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> </mrow>
Wherein,WithIt is ω respectivelydAnd cdEstimation；
Step 3: design is controlled the controller of non-linear pure time delay system, comprise the following steps that：
1) systematic error is defined：
<mrow> <mo>{</mo> <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </mrow>
Wherein, αi-1, i=2 ..., n are in step 5) in firstorder filter definition in provide, system actual tracking error definition For ze=x1-yd, according to the reconstruct of ideal trajectory and estimator and z1And zeAnd zeDefinition obtain：
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mi>e</mi> </msub> <mo>=</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msubsup> <mi>f</mi> <mi>d</mi> <mi>T</mi> </msubsup> <msub> <mover> <mi>&amp;omega;</mi> <mo>~</mo> </mover> <mi>d</mi> </msub> <mo>-</mo> <msub> <mover> <mi>c</mi> <mo>~</mo> </mover> <mi>d</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>z</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>e</mi> </msub> <mo>=</mo> <msub> <mover> <mi>z</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <msubsup> <mover> <mi>f</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> <mi>T</mi> </msubsup> <msub> <mover> <mi>&amp;omega;</mi> <mo>~</mo> </mover> <mi>d</mi> </msub> <mo>+</mo> <msubsup> <mi>f</mi> <mi>d</mi> <mi>T</mi> </msubsup> <msub> <mover> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>+</mo> <msub> <mover> <mover> <mi>c</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> 1
2) transformed error v=η (t) z is defined1Controlled with the default capabilities for realizing system, wherein, η (t)=1/ ((1-bf)κ-1(t)+ bf) it is error transfer function, κ (t) is taken from the rate function in rate function pond, bfIt is the constant parameter freely designed；
The function in wherein rate function pond meets condition：1) function is positive definite and changes to infinite and monotonic increase from 0 over time； 2) value at t=0 is 1；3) when t ∈ [0, ∞) when, function differentiable；
3) Liapunov Krasovskii functions are introduced, with compensation system time delay；
Liapunov Krasovskii functions are：
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>V</mi> <msub> <mi>Q</mi> <mn>1</mn> </msub> </msub> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mi>t</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> <mi>t</mi> </msubsup> <msup> <mi>v</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <msubsup> <mi>Q</mi> <mn>11</mn> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> <mo>)</mo> </mrow> <msub> <mi>d</mi> <mi>&amp;tau;</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>V</mi> <msub> <mi>Q</mi> <mi>i</mi> </msub> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>i</mi> </munderover> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mi>t</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> <mi>t</mi> </msubsup> <msubsup> <mi>z</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <msubsup> <mi>Q</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mover> <mi>z</mi> <mo>&amp;OverBar;</mo> </mover> <mi>j</mi> </msub> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> <mo>)</mo> </mrow> <msub> <mi>d</mi> <mi>&amp;tau;</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
4) a smooth preferable input is obtained according to implicit function theoremFor i=1 .., n-1 orObtain
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;chi;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mo>&amp;CenterDot;</mo> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>..</mn> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;chi;</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mo>&amp;CenterDot;</mo> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, χi(), i=1 .., n-1 is independently of xi+1Function, χn() is independently of u function；And according to intermediate value The pure-feedback systems that step one is set up are converted into Affine Systems by theorem, and specific reformulationses are as follows：
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>g</mi> <msub> <mi>o</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>,</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>g</mi> <msub> <mi>o</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msub> <mi>&amp;beta;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, The smooth unknown function β of close approximation is carried out using neutral netn, it is shown below：
βi=Wi *TSi(Zi)+εi(Zi), i=1 ..., n
Wherein, Wi *It is the preferable weight vector of neutral net, εi(Zi) it is neural network approximate error, Si(Zi) it is gaussian basis letter Number vector,Had according to the characteristic of neutral net | εi (·)|≤εMi<∞ is set up, εMiIt is normal number；
Be re-introduced into a virtual parameter θ=g -1max{||Wi *||2, i=1 ..., n }, so as to need the adaptive ginseng of on-line tuning Number only one of which；
5) limiting bed error y is introducedi
<mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msubsup> <mi>&amp;alpha;</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> </mrow>
Introduce firstorder filterWherein ζiIt is time constant；
Obtaining control strategy based on dynamic surface technology is：
<mrow> <msubsup> <mi>&amp;alpha;</mi> <mn>1</mn> <mo>*</mo> </msubsup> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mi>v</mi> <mi>&amp;eta;</mi> <mo>-</mo> <mfrac> <mrow> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>|</mo> <mo>|</mo> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mi>v</mi> <mi>&amp;eta;</mi> </mrow> <mrow> <mn>2</mn> <msubsup> <mi>&amp;gamma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;chi;</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mn>7</mn> <mn>4</mn> </mfrac> <mi>v</mi> <mi>&amp;eta;</mi> <mo>-</mo> <mover> <mover> <mi>y</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mfrac> <mover> <mi>&amp;eta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>&amp;eta;</mi> </mfrac> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mi>&amp;eta;</mi> </mfrac> <msubsup> <mi>Q</mi> <mn>11</mn> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> </mrow> 2
<mrow> <msubsup> <mi>&amp;alpha;</mi> <mn>2</mn> <mo>*</mo> </msubsup> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <mfrac> <mrow> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>|</mo> <mo>|</mo> <msub> <mi>S</mi> <mn>2</mn> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <msub> <mi>z</mi> <mn>2</mn> </msub> </mrow> <mrow> <mn>2</mn> <msubsup> <mi>&amp;gamma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;chi;</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>g</mi> <mn>1</mn> </msub> <mi>v</mi> <mi>&amp;eta;</mi> <mo>+</mo> <mn>2</mn> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mover> <mi>&amp;alpha;</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>2</mn> </munderover> <msub> <mi>z</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mi>Q</mi> <mrow> <mn>2</mn> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>z</mi> <mo>&amp;OverBar;</mo> </mover> <mi>j</mi> <mn>2</mn> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msubsup> <mi>&amp;alpha;</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>|</mo> <mo>|</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <msub> <mi>z</mi> <mi>i</mi> </msub> </mrow> <mrow> <mn>2</mn> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;chi;</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>g</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>z</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mi>i</mi> <mo>+</mo> <mn>6</mn> </mrow> <mn>4</mn> </mfrac> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>&amp;alpha;</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>i</mi> </munderover> <msub> <mi>z</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mi>Q</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>z</mi> <mo>&amp;OverBar;</mo> </mover> <mi>j</mi> <mn>2</mn> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> </mrow>
<mrow> <mi>u</mi> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mi>n</mi> </msub> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>|</mo> <mo>|</mo> <msub> <mi>S</mi> <mi>n</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <msub> <mi>z</mi> <mi>n</mi> </msub> </mrow> <mrow> <mn>2</mn> <msubsup> <mi>&amp;gamma;</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;chi;</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>g</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>z</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mi>n</mi> <mo>+</mo> <mn>6</mn> </mrow> <mn>4</mn> </mfrac> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mover> <mi>&amp;alpha;</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>z</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mi>Q</mi> <mrow> <mi>n</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>z</mi> <mo>&amp;OverBar;</mo> </mover> <mi>j</mi> <mn>2</mn> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein Λ1It is positive definite matrix, σ1,σ2,λ1,λ2It is positive constant,It is known bounded function, ki,γi, i= 1 ..., n is positive constant；
6) virtual parameter adaptive rate is
<mrow> <mover> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <msub> <mi>&amp;sigma;</mi> <mn>3</mn> </msub> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>+</mo> <mfrac> <msub> <mi>&amp;sigma;</mi> <mn>4</mn> </msub> <mrow> <mn>2</mn> <msubsup> <mi>&amp;gamma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>|</mo> <mo>|</mo> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <msup> <mi>v</mi> <mn>2</mn> </msup> <msup> <mi>&amp;eta;</mi> <mn>2</mn> </msup> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>2</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <msub> <mi>&amp;sigma;</mi> <mn>4</mn> </msub> <mrow> <mn>2</mn> <msubsup> <mi>&amp;gamma;</mi> <mi>j</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>|</mo> <mo>|</mo> <msub> <mi>S</mi> <mi>j</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <msubsup> <mi>z</mi> <mi>j</mi> <mn>2</mn> </msubsup> </mrow>
Wherein, σ3,σ4It is normal number；
Step 4: realizing system output to unknown reason as the control input of the actuator of controlled nonlinear system controlled quentity controlled variable u Think the default capabilities tracking of track.
CN201710500697.2A 2017-06-27 2017-06-27 Tracking and controlling method independent of the non-linear pure time delay system of ideal trajectory Pending CN107092193A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710500697.2A CN107092193A (en) 2017-06-27 2017-06-27 Tracking and controlling method independent of the non-linear pure time delay system of ideal trajectory

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710500697.2A CN107092193A (en) 2017-06-27 2017-06-27 Tracking and controlling method independent of the non-linear pure time delay system of ideal trajectory

Publications (1)

Publication Number Publication Date
CN107092193A true CN107092193A (en) 2017-08-25

Family

ID=59641549

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710500697.2A Pending CN107092193A (en) 2017-06-27 2017-06-27 Tracking and controlling method independent of the non-linear pure time delay system of ideal trajectory

Country Status (1)

Country Link
CN (1) CN107092193A (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108303880A (en) * 2018-01-18 2018-07-20 西北工业大学 A kind of teleoperation of robot forecast Control Algorithm based on delay compensation
CN108326857A (en) * 2018-03-20 2018-07-27 迪比（重庆）智能科技研究院有限公司 Calligraphy based on Robust Adaptive Control algorithm and Sculpture robot control method
CN114063458A (en) * 2021-11-19 2022-02-18 中国矿业大学 Preset performance control method of non-triangular structure system independent of initial conditions

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
WANG W等: ""Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots"", 《AUTOMATICA》 *
YONGDUAN SONG等: ""Neuro-Adaptive Fault-Tolerant Tracking Control of Lagrange Systems Pursuing Targets With Unknown Trajectory"", 《IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS》 *
余修端等: ""基于控制性能的MIMO非线性系统动态面控制"", 《信息与控制》 *
赵凯: ""两类MIMO非线性系统的自适应神经网络控制算法研究"", 《信息科技辑》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108303880A (en) * 2018-01-18 2018-07-20 西北工业大学 A kind of teleoperation of robot forecast Control Algorithm based on delay compensation
CN108303880B (en) * 2018-01-18 2020-11-06 西北工业大学 Robot teleoperation prediction control method based on time delay compensation
CN108326857A (en) * 2018-03-20 2018-07-27 迪比（重庆）智能科技研究院有限公司 Calligraphy based on Robust Adaptive Control algorithm and Sculpture robot control method
CN108326857B (en) * 2018-03-20 2023-04-07 迪比（重庆）智能科技研究院有限公司 Calligraphy and carving robot control method based on robust adaptive control algorithm
CN114063458A (en) * 2021-11-19 2022-02-18 中国矿业大学 Preset performance control method of non-triangular structure system independent of initial conditions

Similar Documents

Publication Publication Date Title
Fang et al. Adaptive fuzzy control for nontriangular stochastic high-order nonlinear systems subject to asymmetric output constraints
Liu et al. Adaptive tracking control for a class of nonlinear systems with a fuzzy dead-zone input
CN104950898B (en) A kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle
Liu et al. Adaptive predefined performance control for MIMO systems with unknown direction via generalized fuzzy hyperbolic model
CN108828949A (en) A kind of optimally in distributed mode collaboration fault tolerant control method based on adaptive Dynamic Programming
CN105137999A (en) Aircraft tracking control direct method with input saturation
Bao et al. Fuzzy finite-time tracking control for a class of nonaffine nonlinear systems with unknown dead zones
CN107092193A (en) Tracking and controlling method independent of the non-linear pure time delay system of ideal trajectory
CN107102634A (en) A kind of parameter Estimation and tracking and controlling method based on table servo system
CN105068420A (en) Non-affine uncertain system self-adaptive control method with range restraint
CN106774379A (en) A kind of strong robust attitude control method of intelligent supercoil
CN107203138A (en) A kind of aircraft robust control method of input and output saturation
CN103399488B (en) Multiple Model Control Method based on self study
Yin et al. ZG control for ship course tracking with singularity considered and solved
CN114509949A (en) Control method for presetting performance of robot
Zhang et al. Singularity-conquering ZG controller for output tracking of a class of nonlinear systems
Ma et al. Finite-time filtering of TS fuzzy semi-Markov jump systems with asynchronous mode-dependent delays
CN107450311A (en) Inversion model modeling method and device and adaptive inverse control and device
Li et al. A new event-triggered adaptive tracking controller for nonlinear systems with unknown virtual control coefficients
CN110095989B (en) Distributed multi-Lagrange system tracking control strategy based on back stepping method
Ji et al. Tunnel Prescribed Control of Nonlinear Systems With Unknown Control Directions
Hedman et al. FFTSMC with optimal reference trajectory generated by MPC in robust robotino motion planning with saturating inputs
CN110888323A (en) Control method for intelligent optimization of switching system
CN107272418A (en) A kind of bionic intelligence control method for the neutral net that is self-regulated based on many intensions
Zhang et al. Controller design of nonlinear system for fully trackable and partially trackable paths by combining ZD and GD

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
CB03 Change of inventor or designer information
CB03 Change of inventor or designer information

Inventor after: Song Yongduan

Inventor after: Liu Xiulan

Inventor after: Zhang Beibei

Inventor after: Lai Junfeng

Inventor after: Gao Hui

Inventor before: Song Yongduan

Inventor before: Zhang Beibei

Inventor before: Lai Junfeng

Inventor before: Gao Hui

RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20170825