CN108170029B - Parameter self-tuning method of MIMO full-format model-free controller based on partial derivative information - Google Patents

Parameter self-tuning method of MIMO full-format model-free controller based on partial derivative information Download PDF

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CN108170029B
CN108170029B CN201711323630.2A CN201711323630A CN108170029B CN 108170029 B CN108170029 B CN 108170029B CN 201711323630 A CN201711323630 A CN 201711323630A CN 108170029 B CN108170029 B CN 108170029B
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卢建刚
李雪园
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Zhejiang University ZJU
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Abstract

The invention discloses a parameter self-setting method of an MIMO full-format model-free controller based on partial derivative information, which utilizes a partial derivative information set as the input of a BP neural network, the BP neural network carries out forward calculation and outputs parameters to be set of the MIMO full-format model-free controller such as penalty factors, step factors and the like through an output layer, a control algorithm of the MIMO full-format model-free controller is adopted for calculation to obtain a control input vector aiming at a controlled object, the aim of minimizing the value of a system error function is taken as, a gradient descent method is adopted, the gradient information sets of the parameters to be set are respectively aimed at by combining control input, the system error back propagation calculation is carried out, the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network are updated in real time on line, and the parameter self-setting of the controller based on the partial derivative information is realized. The parameter self-setting method of the MIMO full-format model-free controller based on the partial derivative information can effectively overcome the difficulty of on-line setting of the controller parameters and has good control effect on an MIMO system.

Description

Parameter self-tuning method of MIMO full-format model-free controller based on partial derivative information
Technical Field
The invention belongs to the field of automatic control, and particularly relates to a parameter self-tuning method of an MIMO full-format model-free controller based on partial derivative information.
Background
The control problem of MIMO (Multiple Input and Multiple Output) system has been one of the major challenges faced in the field of automation control.
Existing implementations of MIMO controllers include MIMO full-format modeless controllers. The MIMO full-format modeless controller is a novel data driving control method, does not depend on any mathematical model information of a controlled object, only depends on input and output data measured by the MIMO controlled object in real time to analyze and design the controller, is simple and clear in realization, small in calculation burden and strong in robustness, can well control an unknown nonlinear time-varying MIMO system, and has a good application prospect. The theoretical basis of the MIMO full-format model-free controller is proposed by Hou faith and Jinshangtai in the 'model-free adaptive control-theory and application' (scientific publishing house, 2013, page 116), and the control algorithm is as follows:
Figure GDA0001608855250000011
where u (k) is a control input vector at time k, and u (k) is [ u (k) ]1(k),…,umu(k)]TMu is the number of control inputs, Δ u (k) ═ u (k) — u (k-1); e (k) is an error vector at time k, e (k) is [ e1(k),…,emy(k)]TMy is the output number; Δ y (k) ═ y (k) — y (k-1), y (k) is the MIMO system output actual value vector at time k, and y (k) ═ y[y1(k),…,ymy(k)]T；
Figure GDA0001608855250000012
For the MIMO system pseudo block jacobian matrix estimate at time k,
Figure GDA0001608855250000013
is composed of
Figure GDA0001608855250000014
The ith block (i ═ 1, …, Ly + Lu),
Figure GDA0001608855250000021
is a matrix
Figure GDA0001608855250000022
Figure GDA0001608855250000022
2 norm of (d); λ is a penalty factor, ρ1,…,ρLy+LuFor the step size factor, Ly is the control output linearization length constant, and Lu is the control input linearization length constant.
However, the MIMO full-format modeless controller needs to rely on empirical knowledge to set the penalty factor λ and the step-size factor ρ in advance before it is actually put into service1,…,ρLy+LuThe values of the isoparametric parameters have not realized a penalty factor lambda and a step factor rho in the actual application process1,…,ρLy+LuAnd (4) performing online self-tuning on the equal parameters. The lack of effective parameter setting means not only makes the use and debugging process of the MIMO full-format model-free controller time-consuming and labor-consuming, but also can seriously affect the control effect of the MIMO full-format model-free controller sometimes, and restricts the popularization and application of the MIMO full-format model-free controller. That is to say: the MIMO full-format modeless controller also needs to solve the problem of online self-tuning parameters in the actual application process.
Therefore, in order to break the bottleneck of restricting the popularization and application of the MIMO full-format modeless controller, the invention provides a parameter self-tuning method of the MIMO full-format modeless controller based on partial derivative information.
Disclosure of Invention
In order to solve the problems in the background art, an object of the present invention is to provide a parameter self-tuning method for a MIMO full-format modeless controller based on partial derivative information.
To this end, the above object of the present invention is achieved by the following technical solution, comprising the steps of:
step (1): for a MIMO (Multiple Input and Multiple Output) system with mu inputs (mu is an integer greater than or equal to 2) and my outputs (my is an integer greater than or equal to 2), adopting a MIMO full-format modeless controller for control; determining a control output linearization length constant Ly of the MIMO full-format model-free controller, wherein the Ly is an integer greater than or equal to 1; determining a control input linearization length constant Lu of the MIMO full-format model-free controller, wherein the Lu is an integer greater than or equal to 1; the MIMO full-format modeless controller parameters include a penalty factor λ and a step factor ρ1,…,ρLy+Lu(ii) a Determining parameters to be set of the MIMO full-format model-free controller, wherein the parameters to be set of the MIMO full-format model-free controller are part or all of the parameters of the MIMO full-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLy+LuAny one or any combination of the above; determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the MIMO full-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network; initializing partial derivative information in a set { partial derivative information set };
step (2): recording the current time as k time;
and (3): based on the jy output expected value and the jy output actual value (jy is more than or equal to 1 and less than or equal to my) of the MIMO system, adopting the jy error calculation function to calculate the jy error at the k moment, and marking the jy error as ejy(k) (ii) a The step is repeatedly executed for other my-1 outputs of the MIMO system until an error vector e (k) formed by my errors is obtained [ e ]1(k),…,emy(k)]TThen entering the step (4);
and (4): taking the partial derivative information in the set { partial derivative information set } as the input of a BP neural network, carrying out forward calculation by the BP neural network, and outputting a calculation result through an output layer of the BP neural network to obtain a value of a parameter to be set of the MIMO full-format model-free controller;
and (5): calculating a control input vector u (k) [ u ], [ u ]) of the MIMO full-format modeless controller at the time k for the controlled object by adopting a control algorithm of the MIMO full-format modeless controller based on the error vector e (k) obtained in the step (3) and the value of the parameter to be set of the MIMO full-format modeless controller obtained in the step (4)1(k),…,umu(k)]T；
And (6): aiming at the ju control input u in the control input vector u (k) obtained in the step (5)ju(k) (ju is more than or equal to 1 and less than or equal to mu), calculating the ju control input uju(k) Respectively aiming at the gradient information of the parameters to be set of each MIMO full-format model-free controller at the moment k, the specific calculation formula is as follows:
when the parameters to be set of the MIMO full-format model-free controller comprise penalty factor lambda and Lu is 1, the ju control input uju(k) The gradient information at the k moment for the penalty factor λ is:
Figure GDA0001608855250000031
when the parameters to be set of the MIMO full-format model-free controller contain penalty factors of lambda and Lu>1, the jth control input uju(k) The gradient information at the k moment for the penalty factor λ is:
Figure GDA0001608855250000041
when the parameters to be set of the MIMO full-format model-free controller contain the step factor rhoiAnd when i is more than or equal to 1 and less than or equal to Ly, the jth control input uju(k) For the step size factor piThe gradient information at time k is:
Figure GDA0001608855250000042
when the parameters to be set of the MIMO full-format model-free controller contain the step factor rhoLy+1Then, the said ju control input uju(k) For the step size factor pLy+1The gradient information at time k is:
Figure GDA0001608855250000043
when the parameters to be set of the MIMO full-format model-free controller contain the step factor rhoiAnd i is more than or equal to Ly +2 and less than or equal to Ly + Lu and Lu>1, the jth control input uju(k) For the step size factor piThe gradient information at time k is:
Figure GDA0001608855250000044
wherein, Δ uj(k)＝uj(k)-uj(k-1)，Δyj(k)＝yj(k)-yj(k-1)，
Figure GDA0001608855250000051
For the MIMO system pseudo block jacobian matrix estimate at time k,
Figure GDA0001608855250000052
is composed of
Figure GDA0001608855250000053
The ith block (i ═ 1, …, Ly + Lu),
Figure GDA0001608855250000054
is a matrix
Figure GDA0001608855250000055
The jy th row and the ju th column element,
Figure GDA0001608855250000056
is a matrix
Figure GDA0001608855250000057
Figure GDA0001608855250000057
2 norm of (d);
the set of all the gradient information is marked as { gradient information ju }, and a set { gradient information set } is put in;
recording the gradient information in the { gradient information ju } set as partial derivative information of the previous time in sequence, that is: when the parameters to be set of the MIMO full-format model-free controller contain penalty factor lambda, the gradient information in the set of gradient information ju
Figure GDA0001608855250000058
Recording as partial derivative information of previous time
Figure GDA0001608855250000059
When the parameters to be set of the MIMO full-format model-free controller contain the step factor rhoiAnd when i is more than or equal to 1 and less than or equal to Ly + Lu, gradient information in the set (gradient information ju)
Figure GDA00016088552500000510
Recording as partial derivative information of previous time
Figure GDA00016088552500000511
The set of all the partial derivative information is marked as { partial derivative information ju }, and the set { partial derivative information set } is put into;
repeating the step for the other mu-1 control inputs in the control input vector u (k) obtained in step (5) until the set { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information mu } } and the set { partial derivation information set } contains the set of all { { partial derivation information 1}, …, { partial derivation information mu } }, and then proceeding to step (7);
and (7): the value minimization of a system error function is taken as a target, a gradient descent method is adopted, the set { gradient information set } obtained in the step (6) is combined, the backward propagation calculation of the system error is carried out, and the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are updated and used as the weight coefficient of the hidden layer and the weight coefficient of the output layer when the BP neural network carries out forward calculation at the later moment;
and (8): and (4) after the control input vector u (k) acts on the controlled object, obtaining my output actual values of the controlled object at the later moment, returning to the step (2), and repeating the step (2) to the step (8).
While adopting the above technical scheme, the present invention can also adopt or combine the following further technical schemes:
the arguments of the jy-th error calculation function in the step (3) include a jy-th expected output value and a jy-th actual output value.
The jy th error calculation function in the step (3) adopts
Figure GDA0001608855250000061
Wherein
Figure GDA0001608855250000062
The jy th expected output value, y, set for time kjy(k) Sampling the jy output actual value at the k moment; or by using
Figure GDA0001608855250000063
Wherein
Figure GDA0001608855250000064
The jy th output expectation value at the time k +1, yjy(k) And outputting the actual value for the jy th output value sampled at the time k.
The independent variable of the system error function in the step (7) comprises any one or any combination of my errors, my output expected values and my output actual values.
Said systematic error function in said step (7) is
Figure GDA0001608855250000065
Wherein e isjy(k) For the jy error, Δ uju(k)＝uju(k)-uju(k-1)，ajyAnd bjuIs a constant greater than or equal to 0, jy is greater than or equal to 1 and less than or equal to my, and ju is greater than or equal to 1 and less than or equal to mu.
The parameter self-tuning method of the MIMO full-format model-free controller based on the partial derivative information can realize good control effect and effectively overcome penalty factor lambda and step factor rho1,…,ρLy+LuThe difficult problem of setting needs time and labor waste.
Drawings
FIG. 1 is a functional block diagram of the present invention;
FIG. 2 is a schematic diagram of a BP neural network structure employed in the present invention;
FIG. 3 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3,ρ4Meanwhile, a 1 st output control effect graph is obtained during self-tuning;
FIG. 4 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3,ρ4Meanwhile, a control effect graph of the 2 nd output in self-tuning;
FIG. 5 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3,ρ4Simultaneously self-timing control input diagram;
FIG. 6 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3,ρ4Meanwhile, self-adjusting a punishment factor lambda change curve;
FIG. 7 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3,ρ4Step size factor p while self-aligning1,ρ2,ρ3,ρ4A change curve;
FIG. 8 is a diagram of a two-input two-output MIMO system with a fixed penalty factor λ and a step size factor ρ1,ρ2,ρ3,ρ4The 1 st output control effect graph during self-tuning;
FIG. 9 shows a two-input two-output MIMO system with a fixed penalty factor λ and a step size factor ρ1,ρ2,ρ3,ρ4The control effect diagram of the 2 nd output during self-tuning;
FIG. 10 is a diagram of a two-input two-output MIMO system with a fixed penalty factor λ and a step size factor ρ1,ρ2,ρ3,ρ4A self-timed control input map;
FIG. 11 is a diagram of a two-input two-output MIMO system with a fixed penalty factor λ and a step size factor ρ1,ρ2,ρ3,ρ4Step factor p at self-alignment1,ρ2,ρ3,ρ4A curve of variation.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
Fig. 1 shows a schematic block diagram of the present invention. For a MIMO (Multiple Input and Multiple Output) system with mu inputs (mu is an integer greater than or equal to 2) and my outputs (my is an integer greater than or equal to 2), adopting a MIMO full-format modeless controller for control; determining a control output linearization length constant Ly of the MIMO full-format model-free controller, wherein the Ly is an integer greater than or equal to 1; determining a control input linearization length constant Lu of the MIMO full-format model-free controller, wherein the Lu is an integer greater than or equal to 1; the MIMO full-format model-free controller parameters comprise a penalty factor lambda and a step factor rho1,…,ρLy+Lu(ii) a Determining parameters to be set of the MIMO full-format model-free controller, wherein the parameters are part or all of the parameters of the MIMO full-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLy+LuAny one or any combination of the above; in fig. 1, the parameters to be set by the MIMO full-format modeless controller are penalty factor λ and step factor ρ1,…,ρLy+Lu(ii) a Determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the MIMO full-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network; the partial derivatives in the set { partial derivatives set } are initialized.
Record the current time asTime k; output the jy th expected value
Figure GDA0001608855250000081
And the jy th output actual value yjy(k) The difference is used as the jy error e at the k timejy(k) (ii) a The method is repeatedly executed for other my-1 outputs of the MIMO system until an error vector e (k) formed by my errors is obtained1(k),…,emy(k)]T(ii) a Then, the partial derivative information in the set { partial derivative information set } is used as the input of a BP neural network, the BP neural network carries out forward calculation, and a calculation result is output through an output layer of the BP neural network to obtain the value of a parameter to be set of the MIMO full-format model-free controller; based on the error vector e (k), the value of the parameter to be set of the MIMO full-format model-free controller, and the control algorithm of the MIMO full-format model-free controller, calculating to obtain the control input vector u (k) ═ u of the MIMO full-format model-free controller at the time k for the controlled object1(k),…,umu(k)]T(ii) a For the jth control input u in the control input vector u (k)ju(k) Calculating said ju-th control input uju(k) Respectively aiming at gradient information of parameters to be set of each MIMO full-format model-free controller at the time k, marking a set of all the gradient information as { gradient information ju }, putting the set { gradient information set }, sequentially marking the gradient information in the set of { gradient information ju } as partial derivative information of the previous time, marking the set of the partial derivative information as { partial derivative information ju }, and putting the set { partial derivative information set }; for the other mu-1 control inputs in the control input vector u (k), repeating until the set { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information mu } }, while the set { partial derivative information set } contains the set of all { { partial derivative information 1}, …, { partial derivative information mu } }; subsequently, in combination with the set { gradient information set }, the systematic error function whose contribution of all my errors is considered comprehensively is shown in fig. 1 with the goal of minimizing the value of the systematic error function
Figure GDA0001608855250000082
Is minimized to the target value, under gradientA step-down method, which is to perform system error back propagation calculation, update the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network, and use the updated hidden layer weight coefficient and the output layer weight coefficient as the hidden layer weight coefficient and the output layer weight coefficient when the BP neural network performs forward calculation at the later moment; and after the control input vector u (k) acts on the controlled object, my output actual values of the controlled object at the later moment are obtained, then the work in the paragraph is repeatedly executed, and the parameter self-tuning process of the MIMO full-format model-free controller at the later moment based on the partial derivative information is carried out.
FIG. 2 is a schematic diagram of a BP neural network structure adopted by the present invention, wherein the BP neural network may adopt a structure in which an implied layer is a single layer or a structure in which the implied layer is a multilayer, for simplicity, the BP neural network adopts a structure in which the implied layer is a single layer, that is, a three-layer network structure composed of an input layer, a single-layer implied layer and an output layer is adopted, the number of nodes of the input layer is set as my × (the number of parameters to be set is Ly + Lu +1 in FIG. 2), the number of nodes of the implied layer is 10, the number of nodes of the output layer is set as my + Lu +1 in FIG. 2. the number of nodes of the input layer is divided into my groups, the number of nodes of each group is the number of parameters to be set, wherein the nodes of the ju group and the partial derivative information in the { partial derivative information ju } set
Figure GDA0001608855250000091
Respectively correspond to each other. Node of output layer, penalty factor lambda and step factor rho1,…,ρLy+LuRespectively correspond to each other. The update process of the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network specifically comprises the following steps: the value of the systematic error function is minimized, and the systematic error function comprehensively considering all the my error contributions is shown in FIG. 2
Figure GDA0001608855250000092
The value of (4) is minimized to be a target, and a gradient descent method is adopted to combine the set { gradient information set }, so that the system error back propagation calculation is carried out, and the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are updated.
The following is a specific embodiment of the present invention.
The controlled object is a typical nonlinear two-input and two-output MIMO system:
Figure GDA0001608855250000093
Figure GDA0001608855250000094
Figure GDA0001608855250000095
Figure GDA0001608855250000101
y1(k)＝x11(k)
y2(k)＝x21(k)
where α (k) ═ 1+0.1sin (2k pi/1500) and β (k) ═ 1+0.1cos (2k pi/1500).
Desired value y of system output*(k) The following were used:
Figure GDA0001608855250000102
Figure GDA0001608855250000103
in this particular embodiment, mu-my-2.
The value of the control output linearization length constant Ly of the MIMO full-format modeless controller is usually set according to the complexity of the controlled object and the actual control effect, and is generally between 1 and 5, and an excessively large value will result in a large calculation amount, so that 1 or 3 is usually adopted, and Ly is taken as 1 in the specific embodiment; the value of the control input linearization length constant Lu of the MIMO full-format modeless controller is also usually set according to the complexity of the controlled object and the actual control effect, generally between 1 and 10, and too small will affect the control effect, and too large will result in large calculation amount, so 3 or 5 is usually adopted, and Lu is taken as 3 in this specific embodiment.
The BP neural network adopts a three-layer network structure consisting of an input layer, a single-layer hidden layer and an output layer, the number of nodes of the input layer is set to be 2 multiplied by the number of parameters to be set, the number of nodes of the hidden layer is set to be 10, and the number of nodes of the output layer is set to be the number of the parameters to be set.
For the above specific examples, two sets of experimental verification were performed.
During the first group of test verification, the number of input layer nodes of the BP neural network in FIG. 2 is preset to 10, the number of output layer nodes is preset to 5, and a penalty factor lambda and a step factor rho are calculated1,ρ2,ρ3,ρ4Performing the simultaneous self-tuning, wherein FIG. 3 is a control effect graph of the 1 st output, FIG. 4 is a control effect graph of the 2 nd output, FIG. 5 is a control input graph, FIG. 6 is a penalty factor lambda variation curve, and FIG. 7 is a step factor rho1,ρ2,ρ3,ρ4A curve of variation. The result shows that the method of the invention carries out the punishment factor lambda and the step factor rho1,ρ2,ρ3,ρ4The method has the advantages of realizing good control effect by carrying out self-tuning at the same time, and effectively overcoming the penalty factor lambda and the step factor rho1,ρ2,ρ3,ρ4The difficult problem of setting needs time and labor waste.
During the second group of test verification, the number of nodes of the input layer and the number of nodes of the output layer of the BP neural network in the graph 2 are preset to 8 and 4 respectively, firstly, the penalty factor lambda is fixedly set as the average value of the penalty factor lambda during the first group of test verification, and then, the step factor rho is subjected to1,ρ2,ρ3,ρ4Performing self-tuning, wherein FIG. 8 is a control effect graph of the 1 st output, FIG. 9 is a control effect graph of the 2 nd output, FIG. 10 is a control input graph, and FIG. 11 is a step factor ρ1,ρ2,ρ3,ρ4A curve of variation. The results also show that the method of the invention is implemented by applying the step factor rho when the penalty factor lambda is fixed1,ρ2,ρ3,ρ4Self-tuning is carried out, good control effect can be realized, and the method can haveEffectively overcoming the step factor rho1,ρ2,ρ3,ρ4The difficult problem of setting needs time and labor waste.
It should be noted that, in the above-described embodiment, the jy-th output expectation value is set
Figure GDA0001608855250000111
And the jy th output actual value yjy(k) The difference is used as the jy error e at the k timejy(k) That is to say
Figure GDA0001608855250000112
One method of calculating a function for only said jy-th error; the jy th output expectation value at the time k +1
Figure GDA0001608855250000113
And the jy output y at time kjy(k) The difference is used as the jy error ejy(k) That is to say
Figure GDA0001608855250000114
The jy-th error calculation function may also use other calculation methods in which the arguments include the jy-th expected output value and the jy-th actual output value, for example,
Figure GDA0001608855250000115
for the controlled object of the above embodiment, good control effects can be achieved by using the different system error calculation functions.
It should be more particularly noted that, in the above specific embodiment, when the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network are updated with the goal of minimizing the value of the systematic error function, the systematic error function employs the systematic error function comprehensively considering all the my error contributions
Figure GDA0001608855250000116
Only one of the systematic error functions; the system error function can also adopt independent variables containing my errors and my errorsOther functions of any one or any combination of the desired value of the output, the actual values of my outputs, e.g. the systematic error function
Figure GDA0001608855250000117
Or
Figure GDA0001608855250000121
That is to say by using
Figure GDA0001608855250000122
Another functional form of (1); as another example, the systematic error function employs
Figure GDA0001608855250000123
Wherein e isjy(k) For the jy error, Δ uju(k)＝uju(k)-uju(k-1)，ajyAnd bjuIs a constant greater than or equal to 0, jy is greater than or equal to 1 and less than or equal to my, and ju is greater than or equal to 1 and less than or equal to mu; obviously, when bjuEqual to 0, the systematic error function only takes into account
Figure GDA0001608855250000124
The contribution of (1) shows that the aim of minimization is to minimize the system error, namely pursuing high precision; when b isjuWhen the error is larger than 0, the system error function is simultaneously considered
Figure GDA0001608855250000125
Are made a contribution to
Figure GDA0001608855250000126
The contribution of (1) indicates that the goal of minimization is to pursue small system errors and small control input variation, namely to pursue both high precision and stable steering. For the controlled object of the above embodiment, good control effect can be achieved by adopting the different system error functions; considering only the systematic error function
Figure GDA0001608855250000127
Control of contribution timeCompared with the effect, the system error function is considered at the same time
Figure GDA0001608855250000128
Are made a contribution to
Figure GDA0001608855250000129
The contribution of (1) is that the control precision is slightly reduced and the operation stability is improved.
Finally, it should be noted that the parameters to be set of the MIMO full-format model-less controller include a penalty factor λ and a step factor ρ1,…,ρLy+LuAny one or any combination of the above; in the above specific embodiment, the first set of trial validations is performed with a penalty factor λ and a step-size factor ρ1,ρ2,ρ3,ρ4Realizes the simultaneous self-tuning, the punishment factor lambda is fixed and the step factor rho is adopted during the verification of the second group of tests1,ρ2,ρ3,ρ4Self-tuning is realized; in practical application, any combination of parameters to be set can be selected according to specific conditions, for example, the step factor ρ1,ρ2Fixed penalty factor lambda, step factor rho3,ρ4Self-tuning is realized; in addition, the MIMO full-format modeless controller has to set parameters including, but not limited to, penalty factor λ and step factor ρ1,…,ρLy+LuFor example, according to specific situations, the method can also comprise the estimated value of the pseudo block Jacobian matrix of the MIMO system
Figure GDA00016088552500001210
And the like.
The above-described embodiments are intended to illustrate the present invention, but not to limit the present invention, and any modifications, equivalents, improvements, etc. made within the spirit of the present invention and the scope of the claims fall within the scope of the present invention.

Claims (3)

  1. The parameter self-tuning method of the MIMO full-format model-free controller based on the partial derivative information is characterized by comprising the following steps of:
    step (1): for a MIMO (Multiple Input and Multiple output) system with mu inputs and my outputs, wherein mu is an integer greater than or equal to 2, and my is an integer greater than or equal to 2, the MIMO system is controlled by adopting a MIMO full-format modeless controller; determining a control output linearization length constant Ly of the MIMO full-format model-free controller, wherein the Ly is an integer greater than or equal to 1; determining a control input linearization length constant Lu of the MIMO full-format model-free controller, wherein the Lu is an integer greater than or equal to 1; the MIMO full-format modeless controller parameters include a penalty factor λ and a step factor ρ1,…,ρLy+Lu(ii) a Determining parameters to be set of the MIMO full-format model-free controller, wherein the parameters to be set of the MIMO full-format model-free controller are part or all of the parameters of the MIMO full-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLy+LuAny one or any combination of the above; determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the MIMO full-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network; initializing partial derivative information in a set { partial derivative information set };
    step (2): recording the current time as k time;
    and (3): based on the jy output expected value and the jy output actual value of the MIMO system, wherein jy is more than or equal to 1 and less than or equal to my, calculating by adopting the jy error calculation function to obtain the jy error at the k moment, and marking as ejy(k) (ii) a The independent variables of the jy error calculation function comprise the jy output expected value and the jy output actual value; the step is repeatedly executed for other my-1 outputs of the MIMO system until an error vector e (k) formed by my errors is obtained [ e ]1(k),…,emy(k)]TThen entering the step (4);
    and (4): taking the partial derivative information in the set { partial derivative information set } as the input of a BP neural network, carrying out forward calculation by the BP neural network, and outputting a calculation result through an output layer of the BP neural network to obtain a value of a parameter to be set of the MIMO full-format model-free controller;
    and (5): calculating a control input vector u (k) [ u ], [ u ]) of the MIMO full-format modeless controller at the time k for the controlled object by adopting a control algorithm of the MIMO full-format modeless controller based on the error vector e (k) obtained in the step (3) and the value of the parameter to be set of the MIMO full-format modeless controller obtained in the step (4)1(k),…,umu(k)]T；
    And (6): aiming at the ju control input u in the control input vector u (k) obtained in the step (5)ju(k) Wherein ju is not less than 1 and not more than mu, calculating the ju control input uju(k) Respectively aiming at the gradient information of the parameters to be set of each MIMO full-format model-free controller at the moment k, the specific calculation formula is as follows:
    when the parameters to be set of the MIMO full-format model-free controller comprise penalty factor lambda and Lu is 1, the ju control input uju(k) The gradient information at the k moment for the penalty factor λ is:
    Figure FDA0002552730920000021
    when the parameters to be set of the MIMO full-format model-free controller contain penalty factors of lambda and Lu>1, the jth control input uju(k) The gradient information at the k moment for the penalty factor λ is:
    Figure FDA0002552730920000022
    when the parameters to be set of the MIMO full-format model-free controller contain the step factor rhoiAnd when i is more than or equal to 1 and less than or equal to Ly, the jth control input uju(k) For the step size factor piThe gradient information at time k is:
    Figure FDA0002552730920000031
    when the parameters to be set of the MIMO full-format model-free controller contain the step factor rhoLy+1Then, the said ju control input uju(k) For the step size factor pLy+1The gradient information at time k is:
    Figure FDA0002552730920000032
    when the parameters to be set of the MIMO full-format model-free controller contain the step factor rhoiAnd i is more than or equal to Ly +2 and less than or equal to Ly + Lu and Lu>1, the jth control input uju(k) For the step size factor piThe gradient information at time k is:
    Figure FDA0002552730920000033
    wherein, Δ uj(k)＝uj(k)-uj(k-1)，Δyj(k)＝yj(k)-yj(k-1)，
    Figure FDA0002552730920000034
    For the MIMO system pseudo block jacobian matrix estimate at time k,
    Figure FDA0002552730920000035
    is composed of
    Figure FDA0002552730920000036
    Wherein i ═ 1, …, Ly + Lu,
    Figure FDA0002552730920000037
    is a matrix
    Figure FDA0002552730920000038
    The jy th row and the ju th column element,
    Figure FDA0002552730920000039
    is a matrix
    Figure FDA00025527309200000310
    2 norm of (d);
    the set of all the gradient information is marked as { gradient information ju }, and a set { gradient information set } is put in;
    recording the gradient information in the { gradient information ju } set as partial derivative information of the previous time in sequence, that is: when the parameters to be set of the MIMO full-format model-free controller contain penalty factor lambda, the gradient information in the set of gradient information ju
    Figure FDA00025527309200000311
    Recording as partial derivative information of previous time
    Figure FDA00025527309200000312
    When the parameters to be set of the MIMO full-format model-free controller contain the step factor rhoiAnd when i is more than or equal to 1 and less than or equal to Ly + Lu, gradient information in the set (gradient information ju)
    Figure FDA00025527309200000313
    Recording as partial derivative information of previous time
    Figure FDA00025527309200000314
    The set of all the partial derivative information is marked as { partial derivative information ju }, and the set { partial derivative information set } is put into;
    repeating the step for the other mu-1 control inputs in the control input vector u (k) obtained in step (5) until the set { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information mu } } and the set { partial derivation information set } contains the set of all { { partial derivation information 1}, …, { partial derivation information mu } }, and then proceeding to step (7);
    and (7): the value minimization of a system error function is taken as a target, a gradient descent method is adopted, the set { gradient information set } obtained in the step (6) is combined, the backward propagation calculation of the system error is carried out, and the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are updated and used as the weight coefficient of the hidden layer and the weight coefficient of the output layer when the BP neural network carries out forward calculation at the later moment; the independent variable of the system error function comprises any one or any combination of my errors, my output expected values and my output actual values;
    and (8): and (4) after the control input vector u (k) acts on the controlled object, obtaining my output actual values of the controlled object at the later moment, returning to the step (2), and repeating the step (2) to the step (8).
  2. 2. The MIMO full-format model-less controller parameter self-tuning method of claim 1, wherein the jy-th error calculation function in the step (3) adopts a partial derivative information-based parameter self-tuning method
    Figure FDA0002552730920000041
    Wherein
    Figure FDA0002552730920000042
    The jy th expected output value, y, set for time kjy(k) Sampling the jy output actual value at the k moment; or by using
    Figure FDA0002552730920000043
    Wherein
    Figure FDA0002552730920000044
    The jy th output expectation value at the time k +1, yjy(k) And outputting the actual value for the jy th output value sampled at the time k.
  3. 3. The MIMO full-format model-less controller parameter self-tuning method of claim 1, wherein the systematic error function in step (7) is
    Figure FDA0002552730920000045
    Wherein e isjy(k) For the jy error, Δ uju(k)＝uju(k)-uju(k-1)，ajyAnd bjuIs a constant greater than or equal to 0, jy is greater than or equal to 1 and less than or equal to my, and ju is greater than or equal to 1 and less than or equal to mu.
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