CN104880945A - Self-adaptive inverse control method for unmanned rotorcraft based on neural networks - Google Patents

Abstract

The invention discloses a self-adaptive inverse control method for an unmanned rotorcraft based on neural networks. The self-adaptive inverse control method is characterized by controlling in accordance with the following formula as shown in the description, where <Eta> is the learning rate, two items as shown in the description represent values of the p-th nerve cell in a hidden layer and the t-th nerve cell in an output layer after training for the n+1-th time and the n-th time respectively, another two items as shown in the description represent values of the m-th nerve cell in an input layer and the p-th nerve cell in the hidden layer after training for the n+1-th time and the n-th time respectively, and the last two items as shown in the description represent negative gradient directions of a capability function EC with variables Wtp and Vpm. Two neural networks are used for respectively establishing forward and reverse models of an unmanned rotorcraft system model respectively so as to achieve the fully control and identification of the unmanned rotorcraft.

Description

Based on the adaptive inverse control of the rotor wing unmanned aerial vehicle of neural network

Technical field

The invention belongs to unmanned air vehicle technique field, relate to a kind of adaptive inverse control of the rotor wing unmanned aerial vehicle based on neural network.

Background technology

Rotor wing unmanned aerial vehicle be a kind of can vertical takeoff and landing, using several rotors as propulsion system, do not carry a kind of aircraft of operating personnel.It is with can vertical takeoff and landing, and hovering waits control mode and the feature such as the simple noise of structure is little flexibly arbitrarily, progressively becomes a study hotspot in recent years.Have the features such as strong coupling, drive lacking and strong nonlinearity due to rotor wing unmanned aerial vehicle kinetic model, designing an effective rotor wing unmanned aerial vehicle controller is very not easily, especially under object model Parameters variation and extraneous noisy situation.In existing technology, general way is simplified by rotor wing unmanned aerial vehicle kinetic model, to reduce the complexity of its Controller gain variations, and then utilizes tradition or modern control method to carry out Controller gain variations to this simplified model.

In prior art in rotor wing unmanned aerial vehicle controller design method, general way is that rotor wing unmanned aerial vehicle kinetic model is carried out simplify processes, lowers its Controller gain variations difficulty.But reduced mechanism carries out Controller gain variations also will cause the unmatched problem of system model, and then makes in working control, and designed controller does not reach desirable control effects.

Summary of the invention

The object of this invention is to provide a kind of adaptive inverse control of the rotor wing unmanned aerial vehicle based on neural network, solve problems of the prior art, two neural networks are utilized to set up the forward model of rotor wing unmanned aerial vehicle system model and reverse model respectively, thus the control realized complete rotor wing unmanned aerial vehicle and identification.

The technical solution adopted in the present invention is, a kind of adaptive inverse control of the rotor wing unmanned aerial vehicle based on neural network, controls according to the following formula:

$W_{\mathrm{tp}}^{n+1}=W_{\mathrm{tp}}^n+\mathrm{\&eta;}(-\frac{\&PartialD;E_C}{\&PartialD;W_{\mathrm{tp}}}),$

$V_{\mathrm{pm}}^{n+1}=V_{\mathrm{pm}}^n+\mathrm{\&eta;}(-\frac{\&PartialD;E_C}{\&PartialD;W_{\mathrm{pm}}}),$

Wherein: η is learning rate, with be respectively in hidden layer in p neuron and output layer t neuron train for (n+1)th time and n-th time after value, with be respectively in input layer in m neuron and hidden layer p neuron train for (n+1)th time and n-th time after value, with representing respectively can force function E _cto variable W _tpand V _pmnegative gradient direction.

The invention has the beneficial effects as follows, utilize neural network to have stronger non-linear mapping capability, Controller gain variations is carried out to rotor wing unmanned aerial vehicle complete model.Two neural networks are utilized to set up the forward model of rotor wing unmanned aerial vehicle system model and reverse model respectively, thus the control realized complete rotor wing unmanned aerial vehicle and identification.The effect of System Discrimination device (forward model) is for system inverse controller provides learning signal, so realize inverse controller disturb to external world with rotor wing unmanned aerial vehicle inherent parameters change there is good robustness.Any simplify processes is not carried out to rotor wing unmanned aerial vehicle system model, and directly Controller gain variations is carried out to complete rotor wing unmanned aerial vehicle model.Because complete rotor wing unmanned aerial vehicle system model and true rotor wing unmanned aerial vehicle system have better consistance, the controller of therefore the present invention's design at actual rotor wing unmanned aerial vehicle in-flight, has better control effects.

Accompanying drawing explanation

Fig. 1 is control system frame diagram in the present invention.

Fig. 2 be process after sample set to the training method figure of System Discrimination device.

Fig. 3 be process after sample set to the training method figure of inverse system controller.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

Set up the System Discrimination device under rotor wing unmanned aerial vehicle idealized system model case and inverse system controller, to reach the input/output relation of System Discrimination device reflection idealized system model, the input/output relation of inverse system controller reflection ideal inverse system model.When echo signal value is input to control system as shown in Figure 1, exports because the reasons such as external interference, load-carrying change make system model export produce error with target, by adaptive algorithm, feedback compensation is done to System Discrimination device and inverse system controller and made control system disturb to external world and load-carrying changes and has good robustness.In the present invention, the effect of System Discrimination device sets up the mapping relations be equivalent between system object input and output, for inverse system controller provides learning information.

The adaptive inverse control of a kind of rotor wing unmanned aerial vehicle based on neural network of the present invention, specifically carry out according to following steps:

1. training sample set collection

White noise signal can motivate whole features of system.Therefore with the certain white noise signal of amplitude as system incentive signal during sample collection, and with this excitation signal energizes rotor wing unmanned aerial vehicle object, obtain the correspondence of object under this excitation and export.Circulate this operation, obtains the training sample set of a suitable size.

2. sample process

Screening Treatment is carried out to sample set.Because rotor wing unmanned aerial vehicle attitude angle change in normal flight operations is little, therefore always limit attitude angle size in the present invention at-10 ° ~ 10 °, and carry out Screening Treatment as standard to exporting the sample exceeding this scope.Although treated sample weakens mapped nonlinear strength, this process enormously simplify neural network structure and training time, and meets the real flight conditions of rotor wing unmanned aerial vehicle.

3. the neural network structure of certainty annuity identifier and inverse system controller

The input layer of neural network and the neuron number of output layer are determined by the nonlinear function of required matching, and the neuron number of hidden layer is obtained by experience.The training method based on BP principle according to Fig. 2 and Fig. 3 can the input layer of certainty annuity controller network and System Discrimination device network and output layer neuron number be all 9 and 3.Experimental formula according to determining hidden layer: wherein, m represents hidden layer neuron number, and n represents input layer number, and l represents output layer neuron number, and a is the constant between 1-10.Therefore, the number of hidden layer neuron can be defined as 10.In this programme, mutually isostructural BP neural network can be adopted with System Discrimination device by certainty annuity controller: each layer neuron number of neural network adopts the structure of 9 × 10 × 3 and hidden layer activation function adopts S type logarithmic function, namely (wherein, x represents each neuronic input in hidden layer, and f (x) represents each neuronic output in hidden layer).

4. System Discrimination device and inverse system controller training

According to fixed neural network structure, utilize the sample set after process to train System Discrimination device and inverse system controller, training method as shown in Figure 2 and Figure 3.System Discrimination device to utilize in sample set white noise signal as input signal, and corresponding objects output signal is trained as the training objective signal of System Discrimination device.Inverse system controller utilizes object in sample set to output signal as input signal, and corresponding white noise signal is trained as the training objective signal of system controller.

5. adaptive algorithm design

According to BP algorithm principle, the adaptive algorithm of design system identifier and inverse system controller.The specific design process of adaptive algorithm is hereafter providing.

6. on-line tuning

When the actual output of object exports error with target, using this error as feedback signal, the network weight of adaptive algorithm to System Discrimination device and inverse system controller is utilized to do feedback adjusting.

Wherein, the adaptive algorithm design of control system is the core content in the present invention.Below provide based on BP principle adaptive algorithm design process.The conveniently elaboration of follow-up work, provides to give a definition and illustrate:

The network structure of System Discrimination device and inverse system controller is all M × P × T, and namely input layer number is M, and hidden layer neuron number is P, and output layer neuron number is T.

For inverse system controller, V=(V _pm) _{p × M}, W=(W _tp) _{t × P}represent the connection weight value matrix (V between input layer and hidden layer, between hidden layer and output layer respectively _pmand W _tprespectively tabular form input layer m neuron is to the individual neuronic connection weights of hidden layer p and hidden layer p neuron to the individual neuronic connection weights of output layer t).Further, for convenience of describing, definition V _p:=(V _p1, V _p2..., V _pM), p=1,2 ... P; W _t:=(W _t1, V _t2..., V _tP), t=1,2 ... T, represent respectively be associated with hidden layer p neuron in ground floor weight matrix weight vector and second layer weight matrix in be associated with output layer t neuron weight vector.

Corresponding with above-mentioned inverse controller, in System Discrimination device, Q=(Q _pm) _{p × M}, U=(U _tp) _{t × P}represent the connection weight value matrix (Q between input layer and hidden layer, between hidden layer and output layer respectively _pmand U _tprespectively tabular form input layer m neuron is to the individual neuronic connection weights of hidden layer p and hidden layer p neuron to the individual neuronic connection weights of output layer t).With HI=(HI _p) _{p × 1}, HO=(HO _p) _{p × 1}represent input, the output vector (HI of hidden layer in system controller respectively _pand HO _prepresent the individual neuronic input of p, output in hidden layer respectively), X _i, X _crepresent the input vector of System Discrimination device and inverse system controller respectively.

Y _d=(φ _d, θ _d, ψ _d), y=(φ, θ, ψ), be respectively aims of systems to export, the actual output of system object and the actual output of System Discrimination device.Wherein, φ _d, θ _d, ψ _drepresent target Eulerian angle, φ, θ, ψ represent actual output Eulerian angle, represent the actual Eulerian angle angular velocity exported.System Discrimination device error vector and inverse system controller error vector are respectively e _c=y-y _d.

Set up the error energy function of System Discrimination device and inverse system controller respectively:

$E_I=\frac{1}{2}{(y\left(k\right)-\stackrel{\&CenterDot;}{y}\left(k\right))}^2---\left(1\right)$

$E_C=\frac{1}{2}{(y\left(k\right)-y_d\left(k\right))}^2---\left(2\right)$

In whole system control system, notice that the error of System Discrimination device is at its output terminal, therefore the adaptive algorithm of its on-line tuning is conventional BP algorithm or improved back-propagation, directly provides the BP algorithm based on Gradient Descent here.

According to E _iwith the mapping relations between U, Q, E _irespectively to U _tp, Q _pmask local derviation, can obtain:

$\frac{\&PartialD;E_I}{\&PartialD;U_{\mathrm{tp}}}=e_{\mathrm{It}}\frac{1}{1+e^{-Q_p{X}_I}}---\left(3\right)$

$\frac{\&PartialD;E_I}{\&PartialD;Q_{\mathrm{pm}}}={\mathrm{\&gamma;}}_p{X}_{\mathrm{Im}}^T{U}_p^T{e}_I---\left(4\right)$

Wherein, ${\mathrm{\&gamma;}}_p=\frac{1}{{1+e}^{-Q_p{X}_I}}(1-\frac{1}{{1+e}^{-Q_p{X}_I}}).$

R _pbe the variable conveniently writing definition, there is no physical meaning.

Therefore, the adaptive algorithm of the on-line tuning of System Discrimination device is just obtained:

$U_{\mathrm{tp}}^{n+1}=U_{\mathrm{tp}}^n+\mathrm{\&eta;}(-\frac{\&PartialD;E_I}{\&PartialD;U_{\mathrm{tp}}})---\left(5\right)$

$Q_{\mathrm{pm}}^{n+1}=Q_{\mathrm{pm}}^n+\mathrm{\&eta;}(-\frac{\&PartialD;E_I}{\&PartialD;Q_{\mathrm{pm}}})---\left(6\right)$

Design the online adaptive algorithm of inverse system controller below.In order to obtain error energy function E _cright W _tplocal derviation first we calculate with according to the neural network structure of System Discrimination device, obtain:

$y_t=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{U}_{\mathrm{tp}}f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{pm}}{X}_{\mathrm{Im}}\right)---\left(7\right)$

Therefore,

$\frac{\&PartialD;y_t}{\&PartialD;u_k}=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{U}_{\mathrm{tp}}f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{pm}}{X}_{\mathrm{Im}}\right)(1-f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{pm}}{X}_{\mathrm{Im}}\right))Q_{\mathrm{pk}}---\left(8\right)$

According to the neural network structure of inverse system controller, can obtain:

$u_k=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{W}_{\mathrm{tp}}f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{V}_{\mathrm{pm}}{X}_{\mathrm{Cm}}\right)---\left(9\right)$

Therefore,

$\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}=f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{V}_{\mathrm{pm}}{X}_{\mathrm{Cm}}\right)---\left(10\right)$

Because before on-line tuning, System Discrimination device does off-line training, and before inverse system controller adjustment, has first done the on-line tuning of System Discrimination device, therefore can think now so,

$\begin{array}{c}\frac{\&PartialD;E_C}{\&PartialD;W_{\mathrm{tp}}}=\frac{\&PartialD;E_C}{\&PartialD;y_1}\frac{\&PartialD;y_1}{\&PartialD;u_k}\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}+\frac{\&PartialD;E_C}{\&PartialD;y_2}\frac{\&PartialD;y_2}{\&PartialD;u_k}\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}+\frac{\&PartialD;E_C}{\&PartialD;y_3}\frac{\&PartialD;y_3}{\&PartialD;u_k}\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}\\ =e_{c1}\frac{\&PartialD;y_1}{\&PartialD;u_k}\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}+e_{c2}\frac{\&PartialD;y_2}{\&PartialD;u_k}\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}+e_{c3}\frac{\&PartialD;y_3}{\&PartialD;u_k}\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}\\ \&ap;e_{c1}\frac{\&PartialD;{\stackrel{\&CenterDot;}{y}}_1}{\&PartialD;u_k}\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}+e_{c2}\frac{\&PartialD;{\stackrel{\&CenterDot;}{y}}_2}{\&PartialD;u_k}\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}+e_{c3}\frac{\&PartialD;{\stackrel{\&CenterDot;}{y}}_3}{\&PartialD;u_k}\frac{\&PartialD;u_k}{\&PartialD;W_{\mathrm{tp}}}\end{array}---\left(11\right)$

Can obtain in conjunction with above-mentioned (8) (10) (11) result:

$\begin{array}{c}\frac{\&PartialD;E_C}{\&PartialD;W_{\mathrm{tp}}}\&ap;e_{c1}\underset{j=1}{\overset{P}{\mathrm{\&Sigma;}}}\left[U_{1j}f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{jm}}{X}_{\mathrm{Im}}\right)(1-f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{jm}}{X}_{\mathrm{Im}}\right))Q_{\mathrm{jk}}\right]f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{V}_{\mathrm{pm}}{X}_{\mathrm{Cm}}\right)\\ +e_{c2}\underset{j=1}{\overset{P}{\mathrm{\&Sigma;}}}\left[U_{2j}f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{jm}}{X}_{\mathrm{Im}}\right)(1-f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{jm}}{X}_{\mathrm{Im}}\right))Q_{\mathrm{jk}}\right]f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{V}_{\mathrm{pm}}{X}_{\mathrm{Cm}}\right)\\ +e_{c3}\underset{j=1}{\overset{P}{\mathrm{\&Sigma;}}}\left[U_{3j}f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{jm}}{X}_{\mathrm{Im}}\right)(1-f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{jm}}{X}_{\mathrm{Im}}\right))Q_{\mathrm{jk}}\right]f\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{V}_{\mathrm{pm}}{X}_{\mathrm{Cm}}\right)\end{array}$

In like manner, in order to obtain error energy function E _cto V _pmlocal derviation first calculate according to inverse system controller neural network structure, obtain:

HO _p＝f(HI _p) (12)

${\mathrm{HI}}_p=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{V}_{\mathrm{pm}}{X}_{\mathrm{Cm}}---\left(13\right)$

So have,

$\frac{\&PartialD;{\mathrm{HO}}_p}{\&PartialD;{\mathrm{HI}}_p}=f\left({\mathrm{HI}}_p\right)(1-f\left({\mathrm{HI}}_p\right))---\left(14\right)$

$\frac{\&PartialD;{\mathrm{HI}}_p}{\&PartialD;V_{\mathrm{pm}}}=X_{\mathrm{Cm}}---\left(15\right)$

$\frac{\&PartialD;E_C}{\&PartialD;{\mathrm{HO}}_p}=\frac{\&PartialD;E_C}{\&PartialD;u_1}\frac{\&PartialD;u_1}{\&PartialD;{\mathrm{HO}}_p}+\frac{\&PartialD;E_C}{\&PartialD;u_2}\frac{\&PartialD;u_2}{\&PartialD;{\mathrm{HO}}_p}+\frac{\&PartialD;E_C}{\&PartialD;u_3}\frac{\&PartialD;u_3}{\&PartialD;{\mathrm{HO}}_p}---\left(16\right)$

Again because,

$\begin{array}{c}\frac{\&PartialD;E_C}{\&PartialD;u_k}=\frac{\&PartialD;E_C}{\&PartialD;y_1}\frac{\&PartialD;y_1}{\&PartialD;u_k}+\frac{\&PartialD;E_C}{\&PartialD;y_2}\frac{\&PartialD;y_2}{\&PartialD;u_k}+\frac{\&PartialD;E_C}{\&PartialD;y_3}\frac{\&PartialD;y_3}{\&PartialD;u_k}\\ =e_{c1}\frac{\&PartialD;y_1}{\&PartialD;u_k}+e_{c2}\frac{\&PartialD;y_2}{\&PartialD;u_k}+e_{c3}\frac{\&PartialD;y_3}{\&PartialD;u_k}\end{array}---\left(17\right)$

So, to sum up can obtain:

So just obtain the adaptive algorithm of the on-line tuning of the inverse system controller based on BP algorithm principle:

$W_{\mathrm{tp}}^{n+1}=W_{\mathrm{tp}}^n+\mathrm{\&eta;}(-\frac{\&PartialD;E_C}{\&PartialD;W_{\mathrm{tp}}}),$

$V_{\mathrm{pm}}^{n+1}=V_{\mathrm{pm}}^n+\mathrm{\&eta;}(-\frac{\&PartialD;E_C}{\&PartialD;W_{\mathrm{pm}}}).$

Wherein, η is learning rate.

Claims (3)

1. based on an adaptive inverse control for the rotor wing unmanned aerial vehicle of neural network, it is characterized in that, control according to the following formula:

Wherein: η is learning rate, with be respectively in hidden layer in p neuron and output layer t neuron train for (n+1)th time and n-th time after value, with be respectively in input layer in m neuron and hidden layer p neuron train for (n+1)th time and n-th time after value, with representing respectively can force function E _cto variable W _tpand V _pmnegative gradient direction.

2. the adaptive inverse control of a kind of rotor wing unmanned aerial vehicle based on neural network according to claim 1, is characterized in that, specifically carry out according to following steps:

The collection of step 1. training sample set;

With white noise signal as system incentive signal during sample collection, and with this excitation signal energizes rotor wing unmanned aerial vehicle object, obtain the correspondence of object under this excitation and export, circulate this operation, obtains a training sample set;

Step 2. sample process;

Screening Treatment is carried out to sample set, limits attitude angle size at-10 ° ~ 10 °, and carry out Screening Treatment as standard to exporting the sample exceeding this scope;

The neural network structure of step 3. certainty annuity identifier and inverse system controller;

The input layer of neural network and the neuron number of output layer are determined by the nonlinear function of required matching, and the neuron number of hidden layer is obtained by experience, based on the training method of BP principle, the input layer of certainty annuity controller network and System Discrimination device network and output layer neuron number are all 9 and 3, the experimental formula according to determining hidden layer: wherein, m represents hidden layer neuron number, and n represents input layer number, and l represents output layer neuron number, and a is the constant between 1-10, and the number of hidden layer neuron is defined as 10; Certainty annuity controller adopts mutually isostructural BP neural network with System Discrimination device: each layer neuron number of neural network adopts the structure of 9 × 10 × 3 and hidden layer activation function adopts S type logarithmic function, namely wherein, x represents each neuronic input in hidden layer, and f (x) represents each neuronic output in hidden layer;

Step 4. System Discrimination device and inverse system controller training;

According to fixed neural network structure, the sample set after process is utilized to train System Discrimination device and inverse system controller, System Discrimination device to utilize in sample set white noise signal as input signal, and corresponding objects output signal is trained as the training objective signal of System Discrimination device; Inverse system controller utilizes object in sample set to output signal as input signal, and corresponding white noise signal is trained as the training objective signal of system controller;

Step 5. adaptive algorithm designs;

According to BP algorithm principle, the adaptive algorithm of design system identifier and inverse system controller;

Step 6. on-line tuning;

When the actual output of object exports error with target, using this error as feedback signal, the network weight of adaptive algorithm to System Discrimination device and inverse system controller is utilized to do feedback adjusting.

3. the adaptive inverse control of a kind of rotor wing unmanned aerial vehicle based on neural network according to claim 2, is characterized in that, adaptive algorithm design is carried out according to following steps:

Provide to give a definition and illustrate:

The network structure of System Discrimination device and inverse system controller is all M × P × T, and namely input layer number is M, and hidden layer neuron number is P, and output layer neuron number is T;

For inverse system controller, V=(V _pm) _{p × M}, W=(W _tp) _{t × P}represent the connection weight value matrix between input layer and hidden layer, between hidden layer and output layer respectively, V _pmand W _tprespectively tabular form input layer m neuron is to hidden layer p neuronic connection weights and hidden layer p neuron to the individual neuronic connection weights of output layer t, and, define V _p:=(V _p1, V _p2..., V _pM), p=1,2 ... P; W _t:=(W _t1, V _t2..., V _tP), t=1,2 ... T, represent respectively be associated with hidden layer p neuron in ground floor weight matrix weight vector and second layer weight matrix in be associated with output layer t neuron weight vector;

Corresponding with above-mentioned inverse controller, in System Discrimination device, Q=(Q _pm) _{p × M}, U=(U _tp) _{t × P}represent the connection weight value matrix between input layer and hidden layer, between hidden layer and output layer respectively, Q _pmand U _tprespectively tabular form input layer m neuron is to the individual neuronic connection weights of hidden layer p and hidden layer p neuron to the individual neuronic connection weights of output layer t; With HI=(HI _p) _{p × 1}, HO=(HO _p) _{p × 1}represent input, the output vector of hidden layer in system controller respectively, HI _pand HO _prepresent the individual neuronic input of p, output in hidden layer respectively, X _i, X _crepresent the input vector of System Discrimination device and inverse system controller respectively;

Y _d=(φ _d, θ _d, y _d), y=(φ, θ, y), be respectively aims of systems to export, the actual output of system object and the actual output of System Discrimination device; Wherein, φ _d, θ _d, y _drepresent target Eulerian angle, φ, θ, y represent actual output Eulerian angle, represent the actual Eulerian angle angular velocity exported; System Discrimination device error vector and inverse system controller error vector are respectively

Set up the error energy function of System Discrimination device and inverse system controller respectively:

According to E _iwith the mapping relations between U, Q, E _irespectively to U _tp, Q _pmask local derviation, can obtain:

Wherein,

R _pbe the variable of definition, therefore, just obtain the adaptive algorithm of the on-line tuning of System Discrimination device:

The online adaptive algorithm of design inverse system controller:

According to the neural network structure of System Discrimination device, obtain:

Therefore,

According to the neural network structure of inverse system controller, obtain:

Therefore,

Because before on-line tuning, System Discrimination device does off-line training, and before inverse system controller adjustment, has first done the on-line tuning of System Discrimination device, therefore thought now so,

Can obtain in conjunction with above-mentioned (8) (10) (11) result:

In like manner, in order to obtain error energy function E _cto V _pmlocal derviation first calculate according to inverse system controller neural network structure, obtain:

HO _p＝f(HI _p) (29)

Again because,

So, to sum up can obtain:

Obtain the adaptive algorithm of the on-line tuning of the inverse system controller based on BP algorithm principle:

Wherein, η is learning rate.