CN108132600B - Parameter self-tuning method of MIMO (multiple input multiple output) compact-format model-free controller based on partial derivative information - Google Patents

Parameter self-tuning method of MIMO (multiple input multiple output) compact-format model-free controller based on partial derivative information Download PDF

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CN108132600B
CN108132600B CN201711263375.7A CN201711263375A CN108132600B CN 108132600 B CN108132600 B CN 108132600B CN 201711263375 A CN201711263375 A CN 201711263375A CN 108132600 B CN108132600 B CN 108132600B
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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 (multiple input multiple output) compact form model-free controller based on partial derivative information, which is characterized in that a partial derivative information set is used as the input of a BP (back propagation) neural network, the BP neural network carries out forward calculation and outputs parameters to be set of the MIMO compact form model-free controller such as penalty factors, step factors and the like through an output layer, a control input vector aiming at a controlled object is obtained by adopting the control algorithm calculation of the MIMO compact form model-free controller, the value minimization of a system error function is taken as a target, a gradient descent method is adopted, and 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. The parameter self-setting method of the MIMO compact-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 (multiple input multiple output) compact-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 a MIMO (multiple input multiple output) compact-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 compact-format modeless controllers. The MIMO compact-format model-free controller is a novel data-driven 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 compact-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 93) of the union of Hou faith and Jinshangtai, and the control algorithm is as follows:
Figure GDA0001608841470000011
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; e (k) is an error vector at time k, e (k) is [ e1(k),…,emy(k)]TMy is the output number;
Figure GDA0001608841470000012
for the estimated pseudo-jacobian matrix of the MIMO system at time k,
Figure GDA0001608841470000013
is a matrix
Figure GDA0001608841470000014
2 norm of (d); λ is a penalty factor and ρ is a step factor.
However, before actual application, the MIMO compact-format modeless controller needs to rely on empirical knowledge to set values of parameters such as the penalty factor λ and the step factor ρ in advance, and online self-tuning of parameters such as the penalty factor λ and the step factor ρ has not been realized in the actual application process. Due to the lack of effective parameter setting means, the use and debugging process of the MIMO compact-format model-free controller is time-consuming and labor-consuming, the control effect of the MIMO compact-format model-free controller is also seriously influenced sometimes, and the popularization and application of the MIMO compact-format model-free controller are restricted. That is to say: the MIMO compact-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 compact-format model-free controller, the invention provides a parameter self-tuning method of the MIMO compact-format model-free 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 compact-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 Multiple Input and Multiple Output (MIMO) 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 compact format model-free controller for control; the parameters of the MIMO compact-format model-free controller comprise a penalty factor lambda and a step factor rho; determining parameters to be set by the MIMO compact-format model-free controller, wherein the parameters to be set by the MIMO compact-format model-free controller are part or all of the parameters of the MIMO compact-format model-free controller and comprise any one or any combination of a penalty factor lambda and a step factor rho; 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 compact-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 compact-format model-free controller;
and (5): calculating to obtain the control of the MIMO compact format model-free controller at the time k aiming at the controlled object by adopting the control algorithm of the MIMO compact format model-free 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 compact format model-free controller obtained in the step (4)Producing an input vector u (k) ═ u1(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 compact-format model-free controller at the moment k, the specific calculation formula is as follows:
when the parameters to be set of the MIMO compact-format model-free controller contain a penalty factor lambda, the ju control input uju(k) The gradient information at the k moment for the penalty factor λ is:
Figure GDA0001608841470000031
when the parameters to be set of the MIMO compact-format model-free controller contain step factors rho, the ju control input uju(k) The gradient information at the k moment for the step factor ρ is:
Figure GDA0001608841470000032
wherein the content of the first and second substances,
Figure GDA0001608841470000041
for the estimated pseudo-jacobian matrix of the MIMO system at time k,
Figure GDA0001608841470000042
is a matrix
Figure GDA0001608841470000043
The jy th row and the ju th column element,
Figure GDA0001608841470000044
is a matrix
Figure GDA0001608841470000045
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 compact-format model-free controller contain penalty factor lambda, the gradient information in the set of gradient information ju
Figure GDA0001608841470000046
Recording as partial derivative information of previous time
Figure GDA0001608841470000047
When the parameters to be set of the MIMO compact-format model-free controller contain the step factor rho, the gradient information in the set of the gradient information ju
Figure GDA0001608841470000048
Recording as partial derivative information of previous time
Figure GDA0001608841470000049
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 GDA0001608841470000051
Wherein
Figure GDA0001608841470000052
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 GDA0001608841470000053
Wherein
Figure GDA0001608841470000054
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 GDA0001608841470000055
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-setting method of the MIMO compact-format model-free controller based on the partial derivative information can achieve good control effect and effectively overcome the problem that the penalty factor lambda and the step factor rho need to be time-consuming and labor-consuming to set.
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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 is a diagram illustrating the control effect of the 1 st output of a two-input and two-output MIMO system during the simultaneous self-tuning of a penalty factor λ and a step factor ρ;
FIG. 4 is a diagram illustrating the control effect of the 2 nd output of a two-input and two-output MIMO system during the simultaneous self-tuning of a penalty factor λ and a step factor ρ;
FIG. 5 is a control input diagram for a two-input two-output MIMO system with penalty factor λ and step-size factor ρ self-timed simultaneously;
FIG. 6 is a plot of the variation of penalty factor λ for a two-input two-output MIMO system with simultaneous self-alignment of penalty factor λ and step size factor ρ;
FIG. 7 is a plot of the change in the step size factor ρ for a two-input two-output MIMO system when the penalty factor λ and the step size factor ρ are self-aligned simultaneously;
FIG. 8 is a diagram illustrating the control effect of the 1 st output of a two-input and two-output MIMO system when the penalty factor λ is fixed and the step factor ρ is self-tuning;
FIG. 9 is a diagram of the control effect of the 2 nd output of a two-input two-output MIMO system when the penalty factor λ is fixed and the step factor ρ is self-tuning;
FIG. 10 is a control input diagram for a two-input two-output MIMO system with a fixed penalty factor λ and a self-setting step size factor ρ;
fig. 11 is a plot of the change in the step size factor ρ for a two-input, two-output MIMO system with a fixed penalty factor λ and a self-setting step size factor ρ.
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 Multiple Input and Multiple Output (MIMO) 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 compact format model-free controller for control; the parameters of the MIMO compact format model-free controller comprise a penalty factor lambda and a step factor rho; determining parameters to be set of the MIMO compact-format model-free controller, wherein the parameters are part or all of the parameters of the MIMO compact-format model-free controller and comprise any one or any combination of a penalty factor lambda and a step factor rho; in fig. 1, the parameters to be set by the MIMO compact-format modeless controller are penalty factor λ and step factor ρ; 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 compact-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.
Recording the current time as k time; output the jy th expected value
Figure GDA0001608841470000061
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 compact-format model-free controller; based on the error vector e (k) and the value of the parameter to be set of the MIMO tight format model-free controller, the control algorithm of the MIMO tight format model-free controller is adopted to calculate and obtain a control input vector u (k) ═ u of the MIMO tight 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 the gradient information of the parameters to be set of each MIMO compact-format model-free controller at the moment k, and collecting all the gradient informationRecording the set as { gradient information ju }, putting a set { gradient information set }, recording the gradient information in the { gradient information ju } set as partial derivative information of a previous moment in sequence, recording the set of 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 GDA0001608841470000071
The value of (1) is minimized as a target, a gradient descent method is adopted to carry out system error back propagation calculation, and the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are updated to be 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 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 compact-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 with a single hidden layer or a structure with multiple hidden layers, for simplicity, the BP neural network adopts a structure with a single hidden layer, that is, a three-layer network structure composed of an input layer, a single hidden layer and an output layer, the number of nodes of the input layer is set as my × (the number of parameters to be set is 2 in FIG. 2), the number of nodes of the hidden layer is 6, the number of nodes of the output layer is set as the number of parameters to be set (the number of parameters to be set is 2 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 set of { partial derivative information ju }, and the number of the nodes of the ju group is set
Figure GDA0001608841470000081
Respectively correspond to each other. And the nodes of the output layer correspond to the penalty factor lambda and the step factor rho respectively. 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 GDA0001608841470000082
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 GDA0001608841470000083
Figure GDA0001608841470000084
Figure GDA0001608841470000085
Figure GDA0001608841470000086
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 GDA0001608841470000087
Figure GDA0001608841470000088
in this particular embodiment, mu-my-2.
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 6, 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 experimental verification, the number of input layer nodes of the BP neural network in fig. 2 is preset to 4, the number of output layer nodes is preset to 2, and penalty factor λ and step factor ρ are self-tuned simultaneously, fig. 3 is a control effect diagram of the 1 st output, fig. 4 is a control effect diagram of the 2 nd output, fig. 5 is a control input diagram, fig. 6 is a change curve of penalty factor λ, and fig. 7 is a change curve of step factor ρ. The result shows that the method can realize good control effect by self-setting the penalty factor lambda and the step factor rho at the same time, and can effectively overcome the problem that the penalty factor lambda and the step factor rho need to be time-consuming and labor-consuming to set.
During the second group of test verification, the number of input layer nodes of the BP neural network in fig. 2 is preset to 2, the number of output layer nodes is preset to 1, the penalty factor λ is first fixed to be an average value of the penalty factor λ during the first group of test verification, then the step factor ρ is self-tuned, fig. 8 is a control effect diagram of the 1 st output, fig. 9 is a control effect diagram of the 2 nd output, fig. 10 is a control input diagram, and fig. 11 is a change curve of the step factor ρ. The result also shows that the method can realize good control effect by self-tuning the step factor rho when the penalty factor lambda is fixed, and can effectively overcome the problem that the step factor rho needs to be time-consuming and labor-consuming to be tuned.
It should be noted that, in the above-described embodiment, the jy-th output expectation value is set
Figure GDA0001608841470000091
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 GDA0001608841470000092
One method of calculating a function for only said jy-th error; the jy th output expectation value at the time k +1
Figure GDA0001608841470000093
And the jy output y at time kjy(k) The difference is used as the jy error ejy(k) That is to say
Figure GDA0001608841470000094
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 GDA0001608841470000101
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 GDA0001608841470000102
Only one of the systematic error functions; the system error function may also adopt other functions of which the independent variables comprise any one or any combination of my errors, my expected output values and my actual output values, for example, the system error function adopts
Figure GDA0001608841470000103
Or
Figure GDA0001608841470000104
That is to say by using
Figure GDA0001608841470000105
Another functional form of (1); as another example, the systematic error function employs
Figure GDA0001608841470000106
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 GDA0001608841470000107
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 GDA0001608841470000108
Are made a contribution to
Figure GDA0001608841470000109
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 GDA00016088414700001010
Compared with the control effect during contribution, the system error function is considered simultaneously
Figure GDA00016088414700001011
Are made a contribution to
Figure GDA00016088414700001012
The contribution of (1) is that the control precision is slightly reduced and the operation stability is improved.
Finally, it should be particularly pointed out that the parameters to be set by the MIMO compact-format modeless controller include any one or any combination of a penalty factor λ and a step factor ρ; in the above specific embodiment, the penalty factor λ and the step factor ρ realize simultaneous self-tuning during the first set of test verification, and the penalty factor λ is fixed and the step factor ρ realizes self-tuning during the second set of test verification; in practical application, any combination of parameters to be set can be selected according to specific conditions, for example, the step factor rho is fixed, and the penalty factor lambda realizes self-setting; in addition, the parameters to be set by the MIMO compact-format modeless controller include, but are not limited to, a penalty factor λ and a step factor ρ, for example, according to the specific situation, the parameters may further include a pseudo-jacobian matrix estimated value of the MIMO system
Figure GDA0001608841470000111
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 compact-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 compact format model-free controller; the parameters of the MIMO compact-format model-free controller comprise a penalty factor lambda and a step factor rho; determining parameters to be set by the MIMO compact-format model-free controller, wherein the parameters to be set by the MIMO compact-format model-free controller are part or all of the parameters of the MIMO compact-format model-free controller and comprise any one or any combination of a penalty factor lambda and a step factor rho; 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 compact-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 compact-format model-free controller;
    and (5): calculating a control input vector u (k) [ u ], [ u ]) of the MIMO tight format model-less controller at the time k for the controlled object by adopting a control algorithm of the MIMO tight format model-less 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 tight format model-less 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 compact-format model-free controller at the moment k, a specific calculation formulaThe following were used:
    when the parameters to be set of the MIMO compact-format model-free controller contain a penalty factor lambda, the ju control input uju(k) The gradient information at the k moment for the penalty factor λ is:
    Figure FDA0002534547970000021
    when the parameters to be set of the MIMO compact-format model-free controller contain step factors rho, the ju control input uju(k) The gradient information at the k moment for the step factor ρ is:
    Figure FDA0002534547970000022
    wherein the content of the first and second substances,
    Figure FDA0002534547970000023
    for the estimated pseudo-jacobian matrix of the MIMO system at time k,
    Figure FDA0002534547970000024
    is a matrix
    Figure FDA0002534547970000025
    The jy th row and the ju th column element,
    Figure FDA0002534547970000026
    is a matrix
    Figure FDA0002534547970000027
    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 compact-format model-free controller contain penalty factor lambda, the { gradient information ju } setIntegrated gradient information
    Figure FDA0002534547970000028
    Recording as partial derivative information of previous time
    Figure FDA0002534547970000029
    When the parameters to be set of the MIMO compact-format model-free controller contain the step factor rho, the gradient information in the set of the gradient information ju
    Figure FDA0002534547970000031
    Recording as partial derivative information of previous time
    Figure FDA0002534547970000032
    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 compact format model-less controller parameter self-tuning method of claim 1, wherein the jy-th error calculation function in step (3) adopts a partial derivative information-based parameter self-tuning method
    Figure FDA0002534547970000033
    Wherein
    Figure FDA0002534547970000034
    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 FDA0002534547970000035
    Wherein
    Figure FDA0002534547970000036
    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 compact format model-less controller partial derivative information-based parameter self-tuning method of claim 1, wherein the systematic error function in step (7) is
    Figure FDA0002534547970000037
    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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