CN104765929B - A kind of nonlinear state decoupling observation procedure based on Multiple Time Scales recurrent neural network - Google Patents
A kind of nonlinear state decoupling observation procedure based on Multiple Time Scales recurrent neural network Download PDFInfo
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Abstract
A kind of nonlinear state decoupling observation procedure based on Multiple Time Scales recurrent neural network, the described method comprises the following steps：Step (1)：Multiple Time Scales recurrent neural networks model is set up to approach actual nonlinear system；Step (2)：Set up Multiple Time Scales recurrent neural network observer model；Step (3)：Restrained by selecting appropriate Lyapunov function combinations singular perturbation theory to design right value update；Step (4)：By in measured relevant state variables input Multiple Time Scales recurrent neural network observation model, state observation is carried out by on-line study.The present invention realizes the decoupling observation to system mode and uncertain extraneous input, simplifies structure, improves pace of learning, lifting accuracy of observation.
Description
Technical field
The invention belongs to automatically control, information technology and advanced manufacture field, and in particular to for Unknown worm
A kind of state observation method based on Multiple Time Scales recurrent neural network of uncertain nonlinear system state observation problem.
Background technology
Towards in actual industrial process state observation, control process, some actual physics systems Chang Yinwei exists smaller
Inertia, electric capacity, conductance or time constant etc. so that there are multiple different time scales in system model, add extraneous input
Uncertainty to become very difficult to the state observation of such system.For example for the suspension system of vehicle, because spring is carried
The vibration frequency amount of quality and tire in itself is differential, causes in system containing the state change that dynamics time scale is different
Amount.In addition unknown road surface inputs to the state observation of system and brings difficulty.It is usually the thought using complex controll at present, i.e.,
By ignoring fast variable to reduce systematic education, the system for obtaining depression of order is used for the dynamic behavior of approximate original system, and respectively
System for depression of order is independently studied in the range of two or more time scales.But this ignore fast variable to reduce
The processing method of exponent number can cause original system high frequency dynamically missing, and can bring after depression of order system relative to original system performance
Singularity, the actual effect designed based on such simplified model is often far apart with design requirement.
The content of the invention
In order to solve the problems, such as the state observation of the above-mentioned uncertain nonlinear system that there are multiple time scales, the present invention is carried
Gone out a kind of state observation method based on Multiple Time Scales recurrent neural network, in the present invention using Lyapunov functions and
Singular perturbation theory devises a kind of right value update for being easy to practical engineering application and restrained, and by introducing dead in right value update rate
Area's characterization factor, realizes the decoupling observation to system mode and uncertain extraneous input.
The technical solution adopted for the present invention to solve the technical problems is：
It is a kind of based on Multiple Time Scales recurrent neural network nonlinear state decoupling observation procedure, methods described include with
Lower step：
Step (1)：Set up Multiple Time Scales recurrent neural networks model
Uncertain Multiple Time Scales nonlinear system is expressed as follows：
Wherein, x (t) ∈ Rn、y(t)∈RmThe state vector of the speed different time scales of expression system, fx,fyTo be unknown
Nonlinear function, u ∈ RpInputted for system,Exported for system, C1∈Rn×n、C2∈Rm×mTo be known
Output matrix, ξx,ξyFor Unknown worm, ε=(ε1…εm) represent different time scale coefficients；
Multiple Time Scales recurrent neural networks model is constructed to approach above-mentioned actual nonlinear system, it is as follows：
Wherein, X=[xT,yT]∈R1×(n+m),A∈Rn×n、B∈Rm×mFor stable matrix, For preferable weights and satisfaction(i=1,2,3,4), ξ1,ξ2For modeling error, σ1,2(·)、
φ1,2() is Sigmoid type excitation functions, can be obtained according to the property of Sigmoid type functions：
Step (2)：Multiple Time Scales recurrent neural network observer model is set up, it is as follows：
Wherein,Systematic observation quantity of state is represented,For weights
Matrix, K1,K2For observer gain matrix；
Step (3)：Online design right value update is restrained
Following right value update is designed by the Lyapunov function combinations singular perturbation theory being designed correctly to restrain：
Wherein,
Px,PyFor Lyapunov EquationSolution, L1,2,3,4For positive constant
Matrix, λ1,2,3,4For positive constant.d1、d2For the decoupling observation factor
Step (4)：Measured state variable is inputted into Multiple Time Scales recurrent neural network observer model, by
Line study is observed.
Further, in the step (4), for nonlinear system, the state variable needed for acquisition system observation, and carry out
The filtering process of early stage sensor nonlinear signal.
Beneficial effects of the present invention are mainly manifested in：Realize the decoupling observation to system mode and uncertain extraneous input,
Simplify structure, improve pace of learning, lifting accuracy of observation.
Brief description of the drawings
Fig. 1 is Multiple Time Scales Recursive Neural Network Structure figure.
Fig. 2 is sprung mass vertical displacement deformation quantity observed result.
Fig. 3 is the absolute velocity observed result figure of spring carried mass.
Fig. 4 is tire vertical displacement deformation quantity observed result figure.
Fig. 5 is the absolute velocity observed result figure of nonspring carried mass.
Fig. 6 is the observation error figure of each state.
Fig. 7 is the observed result figure of unknown road surface input.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.
1~Fig. 7 of reference picture, a kind of nonlinear state decoupling observation procedure based on Multiple Time Scales recurrent neural network,
It the described method comprises the following steps：
Step (1)：Set up Multiple Time Scales recurrent neural networks model
Uncertain Multiple Time Scales nonlinear system is expressed as follows：
Wherein, x (t) ∈ Rn、y(t)∈RmThe state vector of the speed different time scales of expression system, fx,fyTo be unknown
Nonlinear function, u ∈ RpInputted for system,Exported for system, C1∈Rn×n、C2∈Rm×mTo be known
Output matrix, ξx,ξyFor Unknown worm, ε=(ε1…εm) represent different time scale coefficients；
Multiple Time Scales recurrent neural networks model is constructed to approach above-mentioned actual nonlinear system, it is as follows：
Wherein, X=[xT,yT]∈R1×(n+m),A∈Rn×n、B∈Rm×mFor stable matrix, For preferable weights and satisfaction(i=1,2,3,4), ξ1,ξ2For modeling error, σ1,2(·)、
φ1,2() is Sigmoid type excitation functions, can be obtained according to the property of Sigmoid type functions：
Step (2)：Multiple Time Scales recurrent neural network observer model is set up, it is as follows：
Wherein,Systematic observation quantity of state is represented,For weights
Matrix, K1,K2For observer gain matrix；
The linear system that the recurrent neural networks model of each time scale is made up of a regression matrix respectively adds two
It is individual to be multiplied by two non-linear Sigmoid types excitation functions by different weights
Constitute.Wherein a1,b1,c1；a2,b2,c2Value is carried out according to different systematic parameters,For the observer state of system.Same
Two different neurons realize the solution to system mode and extraneous uncertain input by decoupling coefficient in individual time scale
Coupling is observed.The time scale dimension existed according to real system, constructs the recurrent neural network of different time scales respectively so that
The time state observation of system can be carried out in different time scales, substantially increase the speed and accuracy of observation.
Step (3)：Online design right value update is restrained
Following right value update is designed by the Lyapunov function combinations singular perturbation theory being designed correctly to restrain：
Wherein,
Px,PyFor Lyapunov EquationSolution, L1,2,3,4For positive constant
Matrix, λ1,2,3,4For positive constant.d1、d2The factor is observed for decoupling,Step (4)：
Measured state variable is inputted into Multiple Time Scales recurrent neural network observer model, is observed by on-line study.
Pass through formulaCalculating observation error mean square value.Wherein n is simulation step length number altogether, and e (i) is the
ithThe phantom error of step.If RMS≤E (system mean error tolerance limit), study terminates, and otherwise continues to adjust adaptive learning rule
Regulation parameter, improves system convergence speed and the degree of accuracy.
The initial parameter values of all Multiple Time Scales recurrent neural networks model observation models need not give in advance, whole shape
State estimation procedure is all online carries out, it is not necessary to off-line learning.Substantially increase accuracy of observation.Online design adaptive learning
Rule.The decoupling observation of non-linear system status and uncertain extraneous input is realized, can be obtained by adjusting different adaptive rates
To the different convergence rate of speed.Put forward Multiple Time Scales recurrent neural networks model is proved by designing Lyapunov functions
Observation model is input bounded stability system, with to unknown-model and extraneous uncertain very strong robustness.The present embodiment
In, set up Multiple Time Scales recurrent neural networks model observation model, it is only necessary to monolayer neural networks, and each state only needs
Single neuron, structure is greatly simplified, and improves pace of learning, is easy to practical engineering application.
Example：Test checking is carried out to certain car vehicle suspension system with the observation algorithm carried.
The absolute velocity that suspension deformation quantity and spring carried mass can be selected is observable quantity, and tyre type variable and road surface are unknown
Input as unknown quantity, the correlation behavior signal for then gathering sensor is filtered by step low-pass Butterworth filter
Afterwards in the nonlinear state decoupling observer of feeding Multiple Time Scales recurrent neural networks model model.
The Suspension Model of Multiple Time Scales 1/4 used is as follows：
Wherein：ksFor suspension rate, bsFor suspension damping, u=FaInputted for main dynamic Control, msFor body quality, muFor
Nonspring carried mass, ktFor tire vertical stiffness, x1For sprung mass vertical displacement deformation quantity, x2For the absolute velocity of spring carried mass,
x3For tire vertical displacement deformation quantity, x4For the absolute velocity of nonspring carried mass, zrFor road surface vertical drive.For
In the different time scale coefficient of speed, this example state observation is carried out by two time scales.The extracting method in order to verify
Decoupling observation effect, road surface input preceding 10 seconds is that smooth road surface Unknown worm is that road surface inputs and is behind zero, 10 seconds
0.01sin(πt)。
Suspension parameter used is as follows：
As a result such as Fig. 2-Fig. 7, by observed result as can be seen that method proposed by the invention can be realized to uncertain
The online observation while state of nonlinear system and extraneous input.
Claims (3)
1. a kind of nonlinear state decoupling observation procedure based on Multiple Time Scales recurrent neural network, it is characterised in that
It the described method comprises the following steps：
Step (1)：Set up Multiple Time Scales recurrent neural networks model
Uncertain Multiple Time Scales nonlinear system is expressed as follows：
Wherein, x (t) ∈ Rn、y(t)∈RmThe state vector of the speed different time scales of expression system, fx,fyTo be unknown non-
Linear function, u ∈ RpInputted for system,Exported for system, C1∈Rn×n、C2∈Rm×mFor known output
Matrix, ξx,ξyFor Unknown worm, ε=(ε1…εm) represent different time scale coefficients；
Multiple Time Scales recurrent neural networks model is constructed to approach above-mentioned uncertain Multiple Time Scales nonlinear system, it is as follows：
Wherein, X=[xT,yT]∈R1×(n+m)For excitation function input matrix, A ∈ Rn×n、B∈Rm×mFor stable matrix,For preferable weight matrix andξ1,ξ2For modeling error,
σ1,2(·)、φ1,2() is Sigmoid type excitation functions, is obtained by the property of Sigmoid type functions：
Step (2)：Set up Multiple Time Scales recurrent neural network observer model
Wherein,Systematic observation quantity of state is represented,For weight matrix,
K1,K2For observer gain matrix；
Step (3)：Online design right value update is restrained
Following right value update is designed by the Lyapunov function combinations singular perturbation theory being designed correctly to restrain：
Wherein,
Px,PyFor Lyapunov EquationSolution, L1,2,3,4For positive constant matrices,
λ1,2,3,4For positive constant, d1、d2The factor is observed for decoupling,Step (4)：It will be surveyed
The state variable input Multiple Time Scales recurrent neural network observer model obtained, is observed by on-line study.
2. a kind of nonlinear state decoupling observation side based on Multiple Time Scales recurrent neural network as claimed in claim 1
Method, it is characterised in that in the step (4), for nonlinear system, the state variable needed for acquisition system observation, and carry out
The filtering process of early stage sensor nonlinear signal.
3. a kind of nonlinear state decoupling observation side based on Multiple Time Scales recurrent neural network as claimed in claim 2
Method, it is characterised in that in the step (4), pass through formulaCalculating observation error mean square value, wherein n
For simulation step length number altogether, e (i) is i-ththThe phantom error of step, if RMS≤E, E are system mean error tolerance limit, then learns
Terminate, otherwise continue to adjust adaptive learning rule parameter.
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| CN1431769A (en) * | 2003-02-20 | 2003-07-23 | 东南大学 | Neural network reversal control frequency converter of induction motor and structure method |
| KR101022785B1 (en) * | 2008-09-17 | 2011-03-17 | 포항공과대학교 산학협력단 | mapping method for circumstances of robot using a nerve network and evolutionary computation |
| CN104158456A (en) * | 2014-05-28 | 2014-11-19 | 东南大学 | Non-position sensing control method for electric vehicle drive motor |
| CN104407514A (en) * | 2014-10-21 | 2015-03-11 | 河海大学常州校区 | Micro-gyroscope backstepping control method based on neural network state observer |
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| CN1431769A (en) * | 2003-02-20 | 2003-07-23 | 东南大学 | Neural network reversal control frequency converter of induction motor and structure method |
| KR101022785B1 (en) * | 2008-09-17 | 2011-03-17 | 포항공과대학교 산학협력단 | mapping method for circumstances of robot using a nerve network and evolutionary computation |
| CN104158456A (en) * | 2014-05-28 | 2014-11-19 | 东南大学 | Non-position sensing control method for electric vehicle drive motor |
| CN104407514A (en) * | 2014-10-21 | 2015-03-11 | 河海大学常州校区 | Micro-gyroscope backstepping control method based on neural network state observer |
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