CN108107718A - The emulation mode of the adaptive sliding-mode observer of nonlinear system - Google Patents
The emulation mode of the adaptive sliding-mode observer of nonlinear system Download PDFInfo
- Publication number
- CN108107718A CN108107718A CN201711103810.XA CN201711103810A CN108107718A CN 108107718 A CN108107718 A CN 108107718A CN 201711103810 A CN201711103810 A CN 201711103810A CN 108107718 A CN108107718 A CN 108107718A
- Authority
- CN
- China
- Prior art keywords
- nonlinear
- svm
- formula
- parameter
- vector
- 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
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)
- Feedback Control In General (AREA)
Abstract
The emulation mode of the adaptive sliding-mode observer of nonlinear system belongs to artificial intelligence and control field, and for solving the problems, such as closed-loop control system Asymptotic Stability, technical essential is：Adaptive sliding-mode observer method is imposed to nonlinear system, the input for taking LS SVM structural regressions is x=[x1 x2]T, export as u*100 pairs are selected from the data of u and x as training sample, simultaneously, 40 pairs of data therein is taken, using the mean square error of output system output error as evaluation index, the hyper parameter of LS SVM structural regressions to be acquired using cross validation optimization as test sample, the hyper parameter obtained using optimization, study and training are re-started, the initial parameter values of the nonlinear feedback controller based on the fitting of LS SVM structural regressions is obtained, selects system reference signal as ym(t)=sin (t), original state x=[0 1]T, applying equation (9) is to system progress in-circuit emulation experiment.
Description
Technical field
The invention belongs to artificial intelligence and control field, it is related to a kind of adaptive sliding-mode observer method of nonlinear system.
Background technology
The Sliding mode variable structure control of Nonlinear Uncertain Systems is always to control the hot spot of boundary's concern, and many scholars are herein
Field achieves achievement in research.The rough mathematical model of system, increases known to the sliding formwork control of nonlinear system needs
Dependence of the sliding formwork control to system model is added.With the development of artificial intelligence theory, fuzzy logic and neutral net are introduced into
Sliding formwork control designs, and efficiently reduces dependence of the sliding formwork control to system model.Document [3] is had studied based on high-gain
The nonlinear system Adaptive Fuzzy Sliding Mode Control of observer, document [4] have studied the nonlinear system based on neutral net certainly
Sliding formwork control is adapted to, they mainly utilize the ability of fuzzy logic or neutral net to arbitrary None-linear approximation.But mould
There are the problems such as algorithm is complicated, pace of learning is slow in fuzzy logic and Application of Neural Network, and least square method supporting vector machine (LS-
SVM) solves the above problem.LS-SVM maintains powerful extensive and global optimum's ability of standard SVM, drastically increases
Training effectiveness, while the Control of Nonlinear Systems research based on LS-SVM achieves abundant achievement].But by LS-SVM and
The Nonlinear Uncertain Systems analysis and the method for design that Sliding mode variable structure control is combined are then relatively fewer.
The content of the invention
In order to solve the problems, such as closed-loop control system Asymptotic Stability, and to verify adaptive sliding-mode observer method to closed loop
The asymptotically stable influence of control system, the present invention propose following scheme：
For Nonlinear Uncertain Systems
In formula,B=1.5+0.5sin (5t), d=12cos (t)
Adaptive sliding-mode observer method is imposed to nonlinear system, the input for taking LS-SVM structural regressions is x=[x1 x2
]T, export as u*, choose KT=(k1,k2)=(2,1), controller parameter Γθ, η, D and bLRespectively 2,0.5,12 and 1, control
Amount u takes white noise signal, obtains state x=[x1 x2]TMeasurement data, selected from the data of u and x 100 pairs as training
Sample, meanwhile, 40 pairs of data therein is taken to refer to as test sample by evaluation of the mean square error of output system output error
Mark, the hyper parameter of LS-SVM structural regressions is acquired using cross validation optimization, and the hyper parameter obtained using optimization is re-started
Study and training obtain the initial parameter values of the nonlinear feedback controller based on the fitting of LS-SVM structural regressions, select system ginseng
Signal is examined as ym(t)=sin (t), original state x=[0 1]T, applying equation (9) is to system progress in-circuit emulation experiment.
Advantageous effect：The present invention includes the nonlinear system of uncertain and unknown bounded external disturbance for one kind, carries
A kind of self-adaptive controlled sliding method of moulding is gone out.This method makes full use of the nonlinear function approximation capability design that LS-SVM is returned
Feedback linearization controller, the approximate error and uncertain external disturbance that introducing sliding formwork control compensation LS-SVM is returned are to system
The influence of output carries out the adjustment of LS-SVM weighting parameters, designing scheme is tested finally by a simulation example
Card, illustrates that the present invention can solve the problems, such as closed-loop control system Asymptotic Stability.
Description of the drawings
Fig. 1 is state and desired output schematic diagram；
Fig. 2 is state x2And desired output schematic diagram；
Fig. 3 is control input schematic diagram；
Fig. 4 is state x1And desired output schematic diagram；
Fig. 5 is state x2And desired output schematic diagram；
Fig. 6 is control input schematic diagram；
Fig. 7 is tracking error schematic diagram；
Fig. 8 is LS-SVM structural formulas.
Specific embodiment
Embodiment 1：The present embodiment includes the nonlinear system of uncertain and unknown bounded external disturbance for one kind,
A kind of self-adaptive controlled sliding method of moulding or system based on liapunov function are proposed, this method execution makes full use of LS-
The nonlinear function approximation capability design of feedback Linearizing controller that SVM is returned introduces what sliding formwork control compensation LS-SVM was returned
The influence that approximate error and uncertain external disturbance export system carries out LS-SVM weighting parameters using Lyapunov functions
Adjustment, designing scheme is verified finally by a simulation example.
1 problem describes
Consider Nonlinear Uncertain Systems
WhereinIt is unknown nonlinear function, b is unknown control gain, and d is bounded
Interference, u ∈ R and y ∈ R are outputting and inputting for system respectively, and n is the exponent number of system mode.If
It is the state vector of system, acquisition can be measured.
Control targe be namely based on LS-SVM return realize STATE FEEDBACK CONTROL, so as to ensure closed-loop system uniform bound,
Tracking error is small.In order to realize target, hypothesis below is provided：
Assuming that 1.1 reference signal ymAndContinuous bounded, subscript m represent reference signal.DefinitionYm∈Ωm∈Rn(ΩmCompacted to be known), then output error is
That is e=ym- x,AndDefine K=(k1,k2,…,kn)TFor
Hurwitz vectors.
Assuming that 1.2 control gain b meet b >=bL＞ 0, bLFor the lower bound of b.Disturb d boundeds, it is assumed that its upper bound is D, i.e., | d
|≤D gives D ＞ 0.
If function f (x) is known and interference d=0, state feedback controller are
It is calculated by formula (2) and formula (1)
e(n)+kne(n-1)+…+k1E=0 (3)
Formula (3) shows by proper choice of ki(i=1,2 ..., n), it is ensured that sn+knsn-1+…+k1=0 it is all
Root is all in complex plane Left half-plane, i.e. limt→∞e1(t)=0.
The 2 adaptive law designs returned based on LS-SVM
Least square line sexual system is introduced SVM by LS-SVM, is asked instead of traditional supporting vector using QUADRATIC PROGRAMMING METHOD FOR
Solution classification and Function Estimation problem, the derivation of algorithm is referring to document [5].
For u in approximant (2)*LS-SVM structures[10]As shown in Figure 8
Wherein：X=[x1 x2 … xn-1 xn]TFor input vector, the number of nodes of hidden layer is N+1, and N is input vector
Sample number.Wherein the 1st node definition is the deviation of hidden layer, wj(1 ..., N, N+1) it is power of the hidden layer to output layer
Value, Xj(j=1 ..., N, N+1) be supporting vector, K (Xj, x) (j=1 ..., N, N+1) it is kernel function.
The input/output relation that LS-SVM is returned is u (x, θ)=θTβ (4)
In formula：θ=[w1 w2 … wN+1]T, β=[1, K (X1,x),…,K(XN,x)]T。
It returns to obtain u using LS-SVM*Be approximately For weighting parameter estimate vector.
If preferable weighting parameter vector is
In formulaAnd Ωx=x | | | x | |≤D2Be respectively weighting parameter and state vector bounded aggregate
It closes, D1And D2It is the parameter designed by user.Then have
Wherein ε (x) is the approximate error of LS-SVM, to arbitrary constant Δ ε ＞ 0, is met | ε (x) |≤Δ ε.
OrderIt can obtain
Defining sliding-mode surface is
S=KTe (7)
Wherein kn=1, then
In formula,WithIt represents to differentiate to variable s and vector e, e(i)(i=1 ..., n) represents the i-th order derivative of e, and u is
Control input in system (1).
According to (6), based on sliding formwork control technology, the control input u of design system is
Wherein
It takes
D is the upper bound (see hypothesis 1.2) of d in formula, and η ＞ 0 are design parameter.
The adaptive law of weighting value parameter vector is
In formula, Γθ＞ 0 is design parameter.
The Nonlinear Uncertain Systems that theorem is described for formula (1), it is approximant (2) using the LS-SVM regressive structures of Fig. 1
In u*, control input is taken as formula (9), and weighting parameter vector adaptive law is (11), then in closed-loop system there is all signals
Boundary.
It proves：Select following Lyapunov functions
V is made, which to differentiate the time, to be had
It can be obtained by formula (11)
η ＞ Δ ε ＞ 0 are taken, can be obtained using formula (10)
Understand that closed-loop system is asymptotically stable.
3 simulation studies
Consider Nonlinear Uncertain Systems
In formula,B=1.5+0.5sin (5t), d=12cos (t)
The adaptive sliding-mode observer returned based on LS-SVM is realized first.It is x=[x to take the input that LS-SVM is returned1 x2
]T, export as u*.Choose KT=(k1,k2)=(2,1), controller parameter Γθ, η, D and bLRespectively 2,0.5,12 and 1.Control
Amount u takes white noise signal (average 0, variance 0.01), obtains state x=[x1 x2]TMeasurement data.It is selected from the data of u and x
100 pairs are selected as training sample, meanwhile, 40 pairs of data therein are taken as test sample.With the mean square error of system output errors
Difference is evaluation index, and the hyper parameter of LS-SVM recurrence is acquired using cross validation optimization.The hyper parameter obtained using optimization, weight
Newly learnt and trained, obtain the initial parameter values of the nonlinear feedback controller based on LS-SVM regression fits.Selection system
Reference signal is ym(t)=sin (t), original state x=[0 1]T, applying equation (9) is to system progress in-circuit emulation experiment.System
The state x of system1(t)、x2(t) and the simulation curve of controlled quentity controlled variable u as shown in Figure 1, Figure 2 and Figure 3.From simulation result it can be seen that originally
Design method achieves more satisfactory control effect.
Then the adaptive sliding-mode observer based on neutral net is realized.Nerve network controller structure and parameter chooses ginseng
Examine document [11].The simulation result of adaptive sliding-mode observer based on neutral net such as Fig. 4, Fig. 5 and Fig. 7.Wherein, Fig. 7 two
The tracking error curve of kind control method.Compare tracking error curve understand, the average error based on LS-SVM methods for-
0.0093, the average error based on neural network method is -0.0207, shows the present embodiment control method control accuracy more
It is high.
4 conclusions
The present embodiment is had studied based on the adaptive of the LS-SVM a kind of single-input single-output Nonlinear Uncertain Systems returned
Answer sliding formwork control problem.In the design of control system, returned using the feedback linearization technology and LS-SVM of nonlinear system
Any Nonlinear Function approximation capability construction feedback controller, the robust of control system is improved by sliding formwork control technology
Property, and demonstrate proposed control program and can ensure closed-loop control system Asymptotic Stability.Simulation results show this method
Validity.
Bibliography (References)
[1]Cong S,Liang Y Y.Adaptive Sliding Mode Tracking Control of
Nonlinear System with Time-varying Uncertainty[J].Control Engineering
ofChina,2009, 16(4):383-387.
[2]Koshkouei A J,Burnham K J.Adaptive Backstepping Sliding Mode
Control for Feedforward Uncertain Systems[J].International Journal of Systems
Sciece,2011,42(12):1935-1946.
[3] Liu Yunfeng, Peng Yunhui, Yang little Gang, nonlinear systems of the flat of Miao Dong, Yuan Run based on High-gain observer are adaptive
Fuzzy sliding mode tracking control [J] system engineerings and electronic technology, 2009,31 (7):1723-1727.
[4]Park B S,Yoo S J,Park J B,et al.Adaptive Neural Sliding Mode
Control of Nonholonomic Wheeled Mobile Robots with Model Uncertainty[J].IEEE
Transactions on Control Systems Technology,2009,17(1):207-214.
[5]Suykens J A K.Nonlinear Modeling and Support Vector Machines[A],
Proc of the 18th IEEE Conf on Instrumentation and Measurement Technolog[C].
Budapest,2001:287-294.
[6]Yuan X F,Wang Y N,Wu L H.Adaptive Inverse Control of Excitation
System with Actuator Uncertainty[J].WSEAS Transactions on Systems and
Control,2007,8(2):419-427.
[7] long range predictive identifications of Guo Zhenkai, Song Zhaoqing, the Mao Jianqin based on least square method supporting vector machine
[J] is controlled and decision-making, 2009,24 (4):520-525.
[8] Mu Chaoxu, Zhang Ruimin, grandson grow nonlinear system least square method supporting vector machines of the silver based on particle group optimizing
Forecast Control Algorithm [J] control theories and application, 2010,27 (2):164-168.
[9] research [D] of nonlinear system self-adaptation control methods of the Xie Chunli based on least square method supporting vector machine
Dalian：Dalian University of Technology, 2011.
[10] mono- nonlinear systems of Xie Chunli, Shao Cheng, Zhao Dan pellet based on least square method supporting vector machine directly from
Suitable solution [J] is controlled and decision-making, 2010,25 (8):1261-1264.
[11]Yang Y S,Wang X F.Adaptive HBB∞BBtracking control for a class of
uncertain nonlinear systems using radial basis function neural networks[J].
Neurocomputing,2007,70(4-6):932-941.
Embodiment 2, as the system that method in embodiment 1 performs, the present embodiment includes following scheme：
A kind of adaptive sliding-mode observer system of nonlinear system, is stored with a plurality of instruction, and described instruction is suitable for processor
It loads and performs：
Perfect condition feedback controller is approached to construct new feedback control using LS-SVM structures to the nonlinear system
Device processed；
It is compensated by the approximate error for imposing sliding formwork control to be returned to LS-SVM and/or uncertain external disturbance；
Weighting parameter vector is determined with adaptive rate.
The nonlinear system approaches perfect condition feedback controller to construct based on following manner using LS-SVM structures
New feedback controller
The nonlinear system
Wherein：It is unknown nonlinear function, b is unknown control gain, and d is bounded
Interference, u ∈ R and y ∈ R are outputting and inputting for system respectively, and n is the exponent number of system mode, if
It is the state vector of system；
Assuming that reference signal ymAndContinuous bounded, subscript m represent reference signal, definition
Ym∈Ωm∈Rn, ΩmIt is compacted to be known, output error is
AndDefine K=(k1,k2,…,kn)TFor Hurwitz vectors；
Assuming that control gain b meets b >=bL＞ 0, bLFor the lower bound of b.Disturb d boundeds, it is assumed that its upper bound is D, i.e., | d |≤
D gives D ＞ 0；
If function f (x) is known and interference d=0, state feedback controller are
It is calculated by formula (2) and formula (1)
e(n)+kne(n-1)+…+k1E=0 (3)
Formula (3) shows by proper choice of ki(i=1,2 ..., n), can guarantee sn+knsn-1+…+k1All of=0
All in complex plane Left half-plane, make limt→∞e1(t)=0；
The LS-SVM structures are as shown in Figure 8.
Wherein：X=[x1 x2 … xn-1 xn]TFor input vector, the number of nodes of hidden layer is N+1, and N is input vector
Sample number.Wherein the 1st node definition is the deviation of hidden layer, wj(1 ..., N, N+1) it is power of the hidden layer to output layer
Value, Xj(j=1 ..., N, N+1) be supporting vector, K (Xj, x) (j=1 ..., N, N+1) it is kernel function；
The input/output relation of LS-SVM structural regressions is u (x, θ)=θTβ (4)
In formula：θ=[w1 w2 … wN+1]T, β=[1, K (X1,x),…,K(XN,x)]T；
It is approximately using what LS-SVM structural regressions obtained u* For weighting parameter estimate vector.
If preferable weighting parameter vector is
In formulaAnd Ωx=x | | | x | |≤D2Be respectively weighting parameter and state vector bounded aggregate
It closes, D1And D2It is the parameter designed by user, then has
Wherein ε (x) is the approximate error of LS-SVM structures, to arbitrary constant Δ ε ＞ 0, is met | ε (x) |≤Δ ε.
To nonlinear system by the approximate error that imposes sliding formwork control to be returned to LS-SVM and/or uncertain external dry
Compensation is disturbed to be realized by following manner：Define sliding-mode surface s
S=KTe (7)
The control input u of nonlinear system is
Wherein
It takes
D is the upper bound of d in formula, and η ＞ 0 are design parameter.
Determine that weighting parameter vector is realized by following manner with adaptive rate：The adaptive law of weighting value parameter vector is
In formula, Γθ＞ 0 is design parameter.
The above is only the preferable specific embodiment of the invention, but the protection domain of the invention is not
This is confined to, in the technical scope that any one skilled in the art discloses in the invention, according to the present invention
The technical solution of creation and its inventive concept are subject to equivalent substitution or change, should all cover the protection domain in the invention
Within.
Claims (1)
1. a kind of emulation mode of the adaptive sliding-mode observer of nonlinear system, it is characterised in that：
For Nonlinear Uncertain Systems
In formula,B=1.5+0.5sin (5t), d=12cos (t)
Adaptive sliding-mode observer method is imposed to nonlinear system, the input for taking LS-SVM structural regressions is x=[x1 x2]T, it is defeated
Go out for u*, choose KT=(k1,k2)=(2,1), controller parameter Γθ, η, D and bLRespectively 2,0.5,12 and 1, controlled quentity controlled variable u takes
White noise signal obtains state x=[x1 x2]TMeasurement data, 100 pairs are selected from the data of u and x as training sample,
Meanwhile 40 pairs of data therein is taken, using the mean square error of output system output error as evaluation index, to be utilized as test sample
Cross validation optimizes the hyper parameter for acquiring LS-SVM structural regressions, and the hyper parameter obtained using optimization re-starts study and instruction
Practice, obtain based on LS-SVM structural regressions fitting nonlinear feedback controller initial parameter values, select system reference signal for
ym(t)=sin (t), original state x=[0 1]T, applying equation (9) is to system progress in-circuit emulation experiment；The nonlinear system
The adaptive sliding-mode observer method of system：
Above-mentioned Nonlinear Uncertain Systems are determined by formula (1)
Wherein：It is unknown nonlinear function, b is unknown control gain, and d is BOUNDED DISTURBANCES, u
∈ R and y ∈ R are outputting and inputting for system respectively, and n is the exponent number of system mode, ifIt is to be
The state vector of system；
Assuming that reference signal ymAndContinuous bounded, subscript m represent reference signal, definitionYm
∈Ωm∈Rn, ΩmIt is compacted to be known, output error isAndDefine K=(k1,k2,…,kn)TFor Hurwitz vectors；
Assuming that control gain b meets b >=bL＞ 0, bLFor the lower bound of b.Disturb d boundeds, it is assumed that its upper bound is D, i.e., | d |≤D gives
Determine D ＞ 0；
If function f (x) is known and interference d=0, state feedback controller are
It is calculated by formula (2) and formula (1)
e(n)+kne(n-1)+…+k1E=0 (3)
Formula (3) shows by proper choice of ki(i=1,2 ..., n), can guarantee sn+knsn-1+…+k1All of=0 are multiple
Plane Left half-plane, makes limt→∞e1(t)=0；
The LS-SVM structures are as shown in Figure 8；
X=[x1 x2 … xn-1 xn]TFor input vector, the number of nodes of hidden layer is N+1, and N is the sample number of input vector.Its
In the 1st node definition be hidden layer deviation, wj(1 ..., N, N+1) is hidden layer to the weights of output layer, Xj(j=1 ...,
N, N+1) for supporting vector, K (Xj, x) (j=1 ..., N, N+1) it is kernel function；
The input/output relation of LS-SVM structural regressions is u (x, θ)=θTβ (4)
In formula：θ=[w1 w2 … wN+1]T, β=[1, K (X1,x),…,K(XN,x)]T；
U is obtained using LS-SVM structural regressions*Be approximately For weighting parameter estimate vector.
If preferable weighting parameter vector is
In formulaAnd Ωx=x | | | x | |≤D2It is respectively weighting parameter and the bounded set of state vector, D1
And D2It is the parameter designed by user, then has
Wherein ε (x) is the approximate error of LS-SVM structures, to arbitrary constant Δ ε ＞ 0, is met | ε (x) |≤Δ ε.
Define sliding-mode surface s
S=KTe (7)
The control input u of nonlinear system is
Wherein
It takes
D is the upper bound of d in formula, and η ＞ 0 are design parameter.
The adaptive law of weighting value parameter vector is
In formula, Γθ＞ 0 is design parameter.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711103810.XA CN108107718A (en) | 2017-11-10 | 2017-11-10 | The emulation mode of the adaptive sliding-mode observer of nonlinear system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711103810.XA CN108107718A (en) | 2017-11-10 | 2017-11-10 | The emulation mode of the adaptive sliding-mode observer of nonlinear system |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN108107718A true CN108107718A (en) | 2018-06-01 |
Family
ID=62206655
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201711103810.XA Pending CN108107718A (en) | 2017-11-10 | 2017-11-10 | The emulation mode of the adaptive sliding-mode observer of nonlinear system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108107718A (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105035079A (en) * | 2015-07-29 | 2015-11-11 | 江苏大学 | Power switching coordination control method of coaxial parallel hybrid electric vehicle with engine torque observer |
| CN105116934A (en) * | 2015-08-14 | 2015-12-02 | 北京航空航天大学 | A dual-frame MSCMG frame system high-precision control method based on self-adaptive sliding mode compensation |
| CN106773691A (en) * | 2016-12-19 | 2017-05-31 | 西北工业大学 | Hypersonic aircraft self adaptation time-varying default capabilities control method based on LS SVM |
-
2017
- 2017-11-10 CN CN201711103810.XA patent/CN108107718A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105035079A (en) * | 2015-07-29 | 2015-11-11 | 江苏大学 | Power switching coordination control method of coaxial parallel hybrid electric vehicle with engine torque observer |
| CN105116934A (en) * | 2015-08-14 | 2015-12-02 | 北京航空航天大学 | A dual-frame MSCMG frame system high-precision control method based on self-adaptive sliding mode compensation |
| CN106773691A (en) * | 2016-12-19 | 2017-05-31 | 西北工业大学 | Hypersonic aircraft self adaptation time-varying default capabilities control method based on LS SVM |
Non-Patent Citations (1)
| Title |
|---|
| 谢春利: "《基于最小二乘支持向量机的非线性系统自适应控制方法的研究》", 《中国博士学位论文全文数据库 基础科学辑》 * |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Cao et al. | Data-driven multi-agent deep reinforcement learning for distribution system decentralized voltage control with high penetration of PVs | |
| Wei et al. | Adaptive dynamic programming for optimal tracking control of unknown nonlinear systems with application to coal gasification | |
| Song et al. | Adaptive dynamic programming for a class of complex-valued nonlinear systems | |
| Ni et al. | GrDHP: A general utility function representation for dual heuristic dynamic programming | |
| Zhang et al. | Data-driven optimal consensus control for discrete-time multi-agent systems with unknown dynamics using reinforcement learning method | |
| Vrdoljak et al. | Sliding mode based load-frequency control in power systems | |
| Zhu et al. | Policy iteration for $ H_\infty $ optimal control of polynomial nonlinear systems via sum of squares programming | |
| Jin et al. | Multiple model LPV approach to nonlinear process identification with EM algorithm | |
| Zhang et al. | Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method | |
| Shakibjoo et al. | Load frequency control for multi-area power systems: A new type-2 fuzzy approach based on Levenberg–Marquardt algorithm | |
| Song et al. | Optimal fixed-point tracking control for discrete-time nonlinear systems via ADP | |
| Menon et al. | Collaborative extremum seeking for welfare optimization | |
| Ye et al. | Design of model predictive controllers for adaptive damping of inter-area oscillations | |
| CN108155648A (en) | Method for estimating state based on the infinite Extended Kalman filter of adaptive H | |
| Guo et al. | Policy approximation in policy iteration approximate dynamic programming for discrete-time nonlinear systems | |
| Zhao et al. | Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming | |
| CN105974795B (en) | Inhibit the model predictive control method of low-frequency oscillation of electric power system based on controlled reactor | |
| CN113489015B (en) | Multi-time-scale reactive voltage control method for power distribution network based on reinforcement learning | |
| CN106532691A (en) | Adaptive dynamic programming-based frequency compound control method of single-region power system | |
| CN108153259A (en) | A kind of multi-controller optimal State Estimation control strategy design method based on Kalman filtering | |
| CN108107719A (en) | The adaptive sliding-mode observer system of nonlinear system | |
| Zhang et al. | Nonlinear decoupling control with ANFIS-based unmodeled dynamics compensation for a class of complex industrial processes | |
| Liu et al. | Online H∞ control for continuous-time nonlinear large-scale systems via single echo state network | |
| CN108448594B (en) | Frequency self-adaptive learning control method for micro-grid | |
| Menhas et al. | Real/binary co-operative and co-evolving swarms based multivariable PID controller design of ball mill pulverizing system |
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 | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20180601 |
|
| RJ01 | Rejection of invention patent application after publication |