Granted Patent B2

US 12,271,663 · App. 18/603,317 · Granted Apr 8, 2025

Inventors: Xiaomin Zhao (Hefei, CN); Zhengrong Cui (Hefei, CN); Fangfang Dong (Hefei, CN); Chang Pan (Hefei, CN); Binhe Li (Hefei, CN)

Assignee: HEFEI UNIVERSITY OF TECHNOLOGY

G06F30/18G05D1/69

Abstract

Claims (2685)

1. An unmanned cluster system comprising a plurality of unmanned systems and a computer terminal, wherein the computer terminal comprises a processor and storage storing computer programs to be executed by the processor, and the computer programs are for:

step S 1 , collecting both targets for tracking and spatial status information of each unmanned system in the unmanned cluster system;

step S 2 , establishing a kinematic model of the unmanned cluster system in order to get a constraint following error of each unmanned system according to the target and the spatial status information correspondingly;

step S 3 , constructing a dynamic model of each unmanned system, the dynamic models being affected by an uncertainty of system parameters and an influence of network attack inputs of the unmanned cluster system;

step S 4 , constructing an uncertainty boundary function of each unmanned system based on the dynamic model correspondingly, and the uncertainty boundary function being relative to the uncertainty and the influence; and

step S 5 , constructing an adaptive robust controller of each unmanned system according to the constraint following error and the uncertainty boundary function correspondingly;

wherein the step for constructing the uncertainty boundary function comprises:

step S 41 , decomposing the dynamic model of an i'th unmanned system as follows according to an effect on the uncertainty of system parameters:

{

ℳ

i

(

p

i

,

t

)

:=

ℳ

¯

i

(

p

i

,

t

)

+

Δℳ

i

(

p

i

,

t

)

H

i

(

p

i

,

t

)

:=

ℳ

¯

i

-

1

(

p

i

,

t

)

Δ

⁢

H

i

(

p

i

,

ϱ

i

,

t

)

:=

M

i

-

1

(

p

i

,

ϱ

i

,

t

)

-

ℳ

¯

i

-

1

⁢

(

p

i

,

t

)

E

i

(

p

i

,

ϱ

i

,

t

)

:=

ℳ

¯

i

(

p

i

,

t

)

⁢

M

i

-

1

(

p

i

,

ϱ

i

,

t

)

-

I

Δ

⁢

H

i

(

p

i

,

ϱ

i

,

t

)

:=

H

i

(

p

i

,

t

)

⁢

E

i

(

p

i

,

ϱ

i

,

t

)

in these formulas, i being defined as a nominal part and the Δ i (p i ,t) being defined as an uncertain part; i (p i , i ,t) meaning an inertia matrix of the i'th unmanned system; each of H i , ΔH i , and E i being defined as an alegbraic quantity; i meaning a sequence number of the unmanned system on the unmanned cluster system, i∈N + , N + ={1, 2, . . . , n}; n meaning a total number of the unmanned systems; p i meaning a spatial position of the i'th unmanned system; t meaning time; i meaning the uncertainty of system parameters of the i'th unmanned system;

step S 42 , decomposing an input matrix D ai of the i'th unmanned system based on the network attack input as follows:

D

ai

=

D

ˆ

ai

+

D

~

ai

in this formula,

{

D

ˆ

ai

=

(

A

i

⁢

H

i

)

T

[

(

A

i

⁢

H

i

)

⁢

(

A

i

⁢

H

i

)

T

]

-

1

⁢

A

i

⁢

H

i

⁢

D

ai

D

~

ai

=

D

ai

-

(

A

i

⁢

H

i

)

T

[

(

A

i

⁢

H

i

)

⁢

(

A

i

⁢

H

i

)

T

]

-

1

⁢

A

i

⁢

H

i

⁢

D

ai

;

A i meaning a constrain matrix; and

step S 43 , getting a boundary function Θ i (γ i ,p i ,{dot over (p)} i ,t) for describing uncertainty boundary information of the uncertainty and the influence, the step of getting the boundary function Θ i (γ i ,p i ,{dot over (p)} i ,t) comprising:

(a) constructing a formula with a constant vector γ i and the boundary function Θ i (γ i ,p i ,{dot over (p)} i ,t) as follows:

max

ϱ

i

∈

Γ

i

,

v

ai

∈

∑

i

⁢



K

i

⁢

A

i

(

p

i

,

t

)

[

⁠

ℳ

i

-

1

(

p

i

,

ϱ

i

,

t

)

⁢

(

-

C

i

(

p

i

,

p

˙

i

,

ϱ

i

,

t

)

⁢

p

˙

i

-

G

i

(

p

i

,

ϱ

i

,

t

)

-



F

i

(

p

i

,

p

˙

i

,

ϱ

i

,

t

)

)

-

H

i

(

p

i

,

t

)

⁢

D

ˆ

ai

(

p

i

,

p

˙

i

,

t

)

⁢

v

ai

-

Δ

⁢

H

i

(

p

i

,

t

)

⁢

D

ai

(

p

i

,

p

˙

i

,

t

)

⁢

v

ai

]

-

K

i

⁢

b

i



≤

(

1

+

δ

E

i

)

⁢

Θ

i

(

γ

i

,

p

i

,

p

˙

i

,

t

)

in this formula, γ i meaning uncertain variables of the i'th unmanned system, K i meaning a positive definite matrix of the i'th unmanned system, b i meaning a second-order constrained vector of the i'th unmanned system; ν ai meaning the network attack input of the i'th unmanned system, ν ai ∈Σ i ⊂R l , Σ i ⊂R l meaning a compact set of the unmanned cluster system, R l meaning l dimensional vector space in a field of real numbers, Σ i meaning a possible boundary of ν ai ; i (t) meaning the uncertainty of system parameters of the i'th unmanned system, i (t)⊂Γ i ⊂R p , R p meaning p dimensional vector space in the field of real numbers, Γ i meaning a possible boundary of i (t); C i (p i ,{dot over (p)} i , i ,t){dot over (p)} i meaning a Coriolis/Centrifugal force; G i (p i , i ,t) meaning a gravitational force; F i (p i ,{dot over (p)} i , i ,t) meaning the other force; δ E i meaning a constant satisfying the following condition:

-

2

<

2

⁢

δ

E

i

≤

min

ϱ

i

∈

Γ

i

λ

min

[

ϕ

i

(

p

i

,

ϱ

i

,

t

)

+

ϕ

i

T

(

p

i

,

ϱ

i

,

t

)

]

,

in this formula,

Φ

i

(

p

i

,

ϱ

i

,

t

)

=

K

i

⁢

A

i

(

p

i

,

t

)

⁢

H

i

(

p

i

,

t

)

⁢

E

i

(

p

i

,

ϱ

i

,

t

)

⁢

ℳ

_

i

(

p

i

,

t

)

×

A

i

T

(

p

i

,

t

)

⁢

(

A

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

)

-

1

⁢

K

i

-

1

,

λ min (⋅) meaning a minimum value of a matrix eigenvalue; and

(b) the boundary function Θ i (γ i ,p i ,{dot over (p)} i ,t) being a continuous concave function as for the constant vector γ i , and to any vector in the field of real numbers, γ i1 and γ i2 meeting the following condition:

Θ

i

(

γ

i

⁢

1

)

-

Θ

⁡

(

γ

i

⁢

2

)

≤

∂

Θ

i

∂

γ

i

⁢

(

γ

i

⁢

2

)

⁢

(

γ

i

⁢

1

-

γ

i

⁢

2

)

;

wherein the step of constructing the adaptive robust controller comprises:

step S 51 , constructing an adaptive law {circumflex over ({dot over (γ)})} i for estimating the constant vector γ i based on the constraint following error ϵ i and the boundary function Θ i ({circumflex over (γ)} i ,p i ,{dot over (p)} i ,t),

γ

^

˙

i

=

Y

i

⁢

1

⁢

∂

Θ

i

T

∂

γ

i

⁢

(

γ

^

i

,

p

i

,

p

˙

i

,

t

)

⁢



ϵ

i



-

Y

i

⁢

2

⁢

γ

^

i

in this formula, {circumflex over (γ)} i being an estimated value of γ i , {circumflex over (γ)} i (t 0 )>0, t 0 meaning an initial time; Y i1 and Y i2 both meaning a parameter matrix with adjustable adaptive law, Y i1 >0, Y i2 >0, {dot over (p)} i meaning a speed of the i'th unmanned system;

step S 52 , constructing an adaptive robust controller as following formulas based on the adaptive law {acute over ({dot over (γ)})} i and the constraint following error ϵ i :

τ

i

(

t

)

=

s

i

⁢

1

(

p

i

,

p

.

i

,

t

)

+

s

i

⁢

2

(

γ

^

i

,

p

i

,

p

.

i

,

t

)

s

i

⁢

1

(

p

i

,

p

.

i

,

t

)

=

-

κ

i

⁢

ℳ

_

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

[

A

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

]

-

1

⁢

K

i

-

1

⁢

ϵ

i

(

p

i

,

p

.

i

,

t

)

s

i

⁢

2

(

γ

^

i

,

p

i

,

p

.

i

,

t

)

=

-

ℳ

_

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

⁢

(

A

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

)

-

1

⁢

K

i

-

1

⁢

ϵ

i

(

p

i

,

p

.

i

,

t

)

×

Θ

i

2

(

γ

^

i

,

p

i

,

p

.

i

,

t

)

in this formula, κ i meaning a controlling and adjusting parameter which is greater than 0; s i1 (p i ,{dot over (p)} i ,t) used to handle initial incompatibility problems; s i2 ({circumflex over (γ)} i ,p i ,{dot over (p)} i ,t) used to handle the uncertainty and the influence; A i (p i ,t) meaning the constrain matrix of the i'th unmanned system; and

step S 6 , controlling the plurality of unmanned systems using the constructed adaptive robust controller.

2. The unmanned cluster system according to claim 1 , wherein in step S 1 , the spatial status information of each target comprises p* and {dot over (p)}*(t) also named {dot over (p)}*, p* meaning a spatial position of the corresponding target, {dot over (p)}* meaning a speed of the corresponding target; the spatial status information of each unmanned system comprises p i and {dot over (p)} i (t) also named {dot over (p)} i , p i ∈R k , k meaning a coordinate dimension of each unmanned system, R k meaning k dimensional vector space in the field of real numbers.

3. The unmanned cluster system according to claim 2 , wherein the step for getting the constraint following error comprises:

step S 21 , ensuring a potential function U ij (⋅) with regard to the i'th unmanned system and a j'th unmanned system, and solving a partial derivative of the potential function U ij (⋅) according to p i and p j , p j meaning a spatial position of the j'th unmanned system, j∈N + ;

step S 22 , ensuring a potential function U i* (⋅) with regard to the i'th unmanned system and the corresponding target; and solving a partial derivative of the potential function U i* (⋅) according to p i and p*;

step S 23 , establishing the kinematic model of the unmanned cluster system:

p

˙

i

=

-

∑

j

=

1

,

j

≠

i

n

∂

U

ij

∂

p

i

⁢

(

p

i

,

p

j

)

-

∂

U

i

*

∂

p

i

⁢

(

p

i

,

p

*

)

+

p

˙

*

step S 24 , transforming the kinematic model to a first-order constrained-differential equation with performance constraint:

A

i

(

p

i

,

t

)

⁢

p

˙

i

=

c

i

(

p

i

,

t

)

,

solving a partial derivative of the first-order constrained-differential equation to a second-order standard constraint form by transposing:

A

i

(

p

i

,

t

)

⁢

p

¨

i

=

b

i

(

p

i

,

p

˙

i

,

t

)

;

then, getting the constraint following error ϵ i :

ϵ

i

=

A

i

(

p

i

,

t

)

⁢

p

˙

i

-

c

i

(

p

i

,

t

)

in these formulas, c i (p i ,t) meaning a first-order constrained vector of the i'th unmanned system, b i (p i ,{dot over (p)} i ,t) meaning a second-order constrained vector of the i'th unmanned system.

4. The unmanned cluster system according to claim 3 , wherein the step for constructing the dynamic model comprises:

step S 31 , constructing the dynamic model as follows:

ℳ

i

(

p

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

⁢

p

¨

i

(

t

)

+

C

i

(

p

i

(

t

)

,

p

˙

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

⁢

p

˙

i

(

t

)

+

G

i

(

p

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

+

F

i

(

p

i

(

t

)

,

p

˙

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

=

τ

i

(

t

)

{umlaut over (p)} i (t) meaning an accelerated speed of the i'th unmanned system also named {umlaut over (p)} i ; τ i (t) meaning an input of control force; i (p i , i ,t), C i (p i ,{dot over (p)} i , i ,t){dot over (p)} i , F i (p i ,{dot over (p)} i , i ,t), G i (p i , i ,t), all being exact dimensions; M i (⋅), C i (⋅), G i (⋅), F i (⋅) all being continuous function;

step S 32 , reconstructing the dynamic model as follows:

ℳ

i

(

p

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

⁢

p

¨

i

(

t

)

+

C

i

(

p

i

(

t

)

,

p

.

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

⁢

p

.

i

(

t

)

+

G

i

(

p

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

+

F

i

(

p

i

(

t

)

,

p

.

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

+

D

ai

(

p

i

(

t

)

,

p

.

i

(

t

)

,

t

)

⁢

v

ai

=

ϕ

i

(

t

)

⁢

τ

i

(

t

)

D ai (p i (t), {dot over (p)} i (t),t) meaning input matrix of the network attack input of the i'th unmanned system, ϕ i (t) meaning an influence coefficient for controlling the network attack input; D ai (p i (t),{dot over (p)} i (t),t) being an exact dimension; D ai (⋅) being a continuous function;

step S 33 , setting constraint conditions to the dynamic model:

if any (p i ,t) being (p o ,t)∈R k ×R, i ∈Γ i , the inertia matrix M i (p i , i ,t) meaning a positive definite matrix;

if any (p i ,t) being (p i , )∈R k ×R and A i (p i ,t) being full rank, the inertia matrix A i (p i ,t) A i T (p i ,t) being reversible;

if any t being t∈R, ϕ i (t) having a lower limiting value ϕ i , ϕ i ≤ϕ i (t)≤1.

5. The unmanned cluster system according to claim 1 , further comprising:

Step S 53 , analyzing a stability of the adaptive robust controller by a Lyapunov function as follows:

V

=

∑

i

=

1

n

V

i

V

i

=

1

2

⁢

ϵ

i

T

⁢

K

i

⁢

ϵ

i

+

1

2

⁢

(

1

+

δ

E

i

)

⁢

(

γ

^

i

-

γ

i

)

T

⁢

Y

i

⁢

1

-

1

(

γ

^

i

-

γ

i

)

.

6. The unmanned cluster system according to claim 1 , wherein the step of constructing the adaptive robust controller further comprises:

step S 54 , adjusting parameters of the adaptive robust controller, the parameters comprising κ i , Y i1 , Y i2 .

7. The unmanned cluster system according to claim 1 , wherein each unmanned system is selected from a group consisting of an unmanned vehicle, an unmanned ship, and an unmanned aerial vehicle.

8. A non-transitory readable computer storage media, storing computer programs, wherein the computer programs, when executed by a processor, achieve collaborative controlling networks resilience of an unmanned cluster system, the computer programs comprises instructions for:

step S 1 , collecting both targets for tracking and spatial status information of each unmanned system in the unmanned cluster system;

step S 2 , establishing a kinematic model of the unmanned cluster system in order to get a constraint following error of each unmanned system according to the target and the spatial status information correspondingly;

step S 3 , constructing a dynamic model of each unmanned system, the dynamic models being affected by an uncertainty of system parameters and an influence of network attack inputs of the unmanned cluster system;

step S 4 , constructing an uncertainty boundary function of each unmanned system based on the dynamic model correspondingly, and the uncertainty boundary function being relative to the uncertainty and the influence; and

step S 5 , constructing an adaptive robust controller of each unmanned system according to the constraint following error and the uncertainty boundary function correspondingly;

wherein the step for constructing the uncertainty boundary function comprises:

step S 41 , decomposing the dynamic model of an i'th unmanned system as follows according to an effect on the uncertainty of system parameters:

{

ℳ

i

(

p

i

,

t

)

:=

ℳ

_

i

(

p

i

,

t

)

+

Δℳ

i

(

p

i

,

t

)

H

i

(

p

i

,

t

)

:=

ℳ

_

i

-

1

(

p

i

,

t

)

△

⁢

H

i

(

p

i

,

ϱ

i

,

t

)

:=

ℳ

i

-

1

(

p

i

,

ϱ

i

,

t

)

-

ℳ

_

i

-

1

(

p

i

,

t

)

E

i

(

p

i

,

ϱ

i

,

t

)

:=

ℳ

_

i

(

p

i

,

t

)

⁢

ℳ

i

-

1

(

p

i

,

ϱ

i

,

t

)

-

I

△

⁢

H

i

(

p

i

,

ϱ

i

,

t

)

:=

H

i

(

p

i

,

t

)

⁢

E

i

(

p

i

,

ϱ

i

,

t

)

in these formulas, i being defined as a nominal part and the Δ i (p i ,t) being defined as an uncertain part; i (p i , i ,t) meaning an inertia matrix of the i'th unmanned system; each of H i , ΔH i , and E i being defined as an algebraic quantity; i meaning a sequence number of the unmanned system on the unmanned cluster system, i∈N + , N + ={1, 2, . . . , n}; n meaning a total number of the unmanned systems; p i meaning a spatial position of the i'th unmanned system; t meaning time; i meaning the uncertainty of system parameters of the i'th unmanned system;

step S 42 , decomposing an input matrix D ai of the i'th unmanned system based on the network attack input as follows:

D

ai

=

D

^

ai

+

D

~

ai

in this formula,

{

D

^

ai

=

(

A

i

⁢

H

i

)

T

[

(

A

i

⁢

H

i

)

⁢

(

A

i

⁢

H

i

)

T

]

-

1

⁢

A

i

⁢

H

i

⁢

D

ai

D

~

ai

=

D

ai

-

(

A

i

⁢

H

i

)

T

[

(

A

i

⁢

H

i

)

⁢

(

A

i

⁢

H

i

)

T

]

-

1

⁢

A

i

⁢

H

i

⁢

D

ai

;

A i meaning a constrain matrix; and

step S 43 , getting a boundary function Θ i (γ i ,p i ,{dot over (p)} i ,t) for describing uncertainty boundary information of the uncertainty and the influence, the step of getting the boundary function Θ i (γ i ,p i ,{dot over (p)} i ,t) comprising:

(a) constructing a formula with a constant vector yi and the boundary function Θ i (γ i ,p i ,{dot over (p)} i ,t) as follows:

max

ϱ

i

∈

Γ

i

,

v

ai

∈

∑

i



K

i

⁢

A

i

(

p

i

,

t

)

[

ℳ

i

-

1

⁢





⁢

(

p

i

,

ϱ

i

,

t

)

⁢

(

-

C

i

(

p

i

,

p

˙

i

,

ϱ

i

,

t

)

⁢

p

˙

i

⁢





-

G

i

(

p

i

,

ϱ

i

,

t

)

-

F

i

(

p

i

,

p

˙

i

,

ϱ

i

,

t

)

)

-

H

i

(

p

i

,

t

)

⁢

D

^

ai

(

p

i

,

p

˙

i

,

t

)

⁢

v

ai

-

Δ

⁢

H

i

(

p

i

,

t

)

⁢

D

ai

(

p

i

,

p

˙

i

,

t

)

⁢

v

ai

]

-

K

i

⁢

b

i



≤

(

1

+

δ

E

i

)

⁢

Θ

i

(

γ

i

,

p

i

,

p

.

i

,

t

)

in this formula, γ i meaning uncertain variables of the i'th unmanned system, K i meaning a positive definite matrix of the i'th unmanned system, b i meaning a second-order constrained vector of the i'th unmanned system; ν ai meaning the network attack input of the i'th unmanned system, ν ai ∈Σ i ⊂R l , Σ i ⊂R l meaning a compact set of the unmanned cluster system, R l meaning l dimensional vector space in a field of real numbers, Σ i meaning a possible boundary of ν ai ; i (t) meaning the uncertainty of system parameters of the i'th unmanned system, i (t)⊂γ i ⊂R p , R p meaning p dimensional vector space in the field of real numbers, γ i meaning a possible boundary of i (t); C i (p i ,{dot over (p)} i , i ,t){dot over (p)} i meaning a Coriolis/Centrifugal force, G i (p i , i ,t) meaning a gravitational force, F i (p i ,{dot over (p)} i , i ,t) meaning the other force; δ E i meaning a constant satisfying the following condition:

-

2

<

2

⁢

δ

E

t

≤

min

ϱ

i

∈

Γ

i

λ

min

[

ϕ

i

(

p

i

,

ϱ

i

,

t

)

+

ϕ

i

T

(

p

i

,

ϱ

i

,

t

)

]

,

in this formula,

Φ

i

(

p

i

,

ϱ

i

,

t

)

=



K

i

⁢

A

i

(

p

i

,

t

)

⁢

H

i

(

p

i

,

t

)

⁢

⁠

E

i

(

p

i

,

ϱ

i

,

t

)

⁢

ℳ

_

i

(

p

i

,

t

)

×

A

i

T

(

p

i

,

t

)

⁢

(

A

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

)

-

1

⁢

K

i

-

1

λ min (⋅) meaning a minimum value of a matrix eigenvalue; and

(b) the boundary function Θ i (γ i ,p i ,{dot over (p)} i ,t) being a continuous concave function as for the constant vector γ i , and to any vector in the field of real numbers, γ i1 and γ i2 meeting the following condition:

Θ

i

(

γ

i

⁢

1

)

-

Θ

⁡

(

γ

i

⁢

2

)

≤

∂

Θ

i

∂

γ

i

⁢

(

γ

i

⁢

2

)

⁢

(

γ

i

⁢

1

-

γ

i

⁢

2

)

;

wherein the step of constructing the adaptive robust controller comprises:

step S 51 , constructing an adaptive law {circumflex over ({dot over (γ)})} i for estimating the constant vector γ i based on the constraint following error ϵ i and the boundary function Θ i ({circumflex over (γ)} i ,p i ,{dot over (p)} i ,t),

γ

ˆ

˙

i

=

Y

i

⁢

1

⁢

∂

Θ

i

T

∂

γ

i

⁢

(

γ

ˆ

i

,

p

i

,

p

˙

i

,

t

)

⁢



ϵ

i



-

Y

i

⁢

2

⁢

γ

ˆ

i

in this formula, {circumflex over (γ)} i being an estimated value of γ i , {circumflex over (γ)} i (t 0 )>0, t 0 meaning an initial time; Y i1 and Y i2 both meaning a parameter matrix with adjustable adaptive law, Y i1 0, Y i2 0, {dot over (p)} i meaning a speed of the i'th unmanned system;

step S 52 , constructing an adaptive robust controller as following formulas based on the adaptive law {circumflex over ({dot over (γ)})} i and the constraint following error ϵ i :

τ

i

(

t

)

=

s

i

⁢

1

(

p

i

,

p

.

i

,

t

)

+

s

i

⁢

2

(

γ

^

i

,

p

i

,

p

.

i

,

t

)

s

i

⁢

1

(

p

i

,

p

.

i

,

t

)

=

-

κ

i

⁢

ℳ

_

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

[

A

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

]

-

1

⁢

K

i

-

1

⁢

ϵ

i

(

p

i

,

p

.

i

,

t

)

s

i

⁢

2

(

γ

^

i

,

p

i

,

p

.

i

,

t

)

=

-

ℳ

_

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

⁢

(

A

i

(

p

i

,

t

)

⁢

A

i

T

(

p

i

,

t

)

)

-

1

⁢

K

i

-

1

⁢

ϵ

i

(

p

i

,

p

.

i

,

t

)

×

Θ

i

2

(

γ

^

i

,

p

i

,

p

.

i

,

t

)

in this formula, κ i meaning a controlling and adjusting parameter which is greater than 0; s i1 (p i ,{dot over (p)} i t) used to handle initial incompatibility problems; s i2 ({circumflex over (γ)} i ,p i ,{dot over (p)} i ,t) used to handle the uncertainty and the influence; A i (p i ,t) meaning the constrain matrix of the i'th unmanned system; and

step S 6 , controlling the unmanned cluster system using the constructed adaptive robust controller.

9. The non-transitory readable computer storage media according to claim 8 , wherein in step S 1 , the spatial status information of each target comprises p* and {dot over (p)}*(t) also named {dot over (p)}*, p* meaning the spatial position of the corresponding target, {dot over (p)}* meaning the speed of the corresponding target; the spatial status information of each unmanned system comprises p i and {dot over (p)} i (t) also named {dot over (p)} i , p i ∈R k , k meaning the coordinate dimension of each unmanned system, R k meaning k dimensional vector space in the field of real numbers.

10. The non-transitory readable computer storage media according to claim 9 , wherein the step for getting the constraint following error comprises:

step S 21 , ensuring a potential function U ij (⋅) with regard to the i'th unmanned system and a j'th unmanned system, and solving a partial derivative of the potential function U ij (⋅) according to p i and p j , p j meaning a spatial position of the j'th unmanned system, j∈N + ;

step S 22 , ensuring a potential function U i* (⋅) with regard to the i'th unmanned system and the corresponding target; and solving a partial derivative of the potential function U i* (⋅) according to p i and p*;

step S 23 , establishing the kinematic model of the unmanned cluster system:

p

˙

i

=

-

∑

j

=

1

,

j

≠

i

n

∂

U

ij

∂

p

i

⁢

(

p

i

,

p

j

)

-

∂

U

i

*

∂

p

i

⁢

(

p

i

,

p

*

)

+

p

˙

*

step S 24 , transforming the kinematic model to a first-order constrained-differential equation with performance constraint:

A

i

(

p

i

,

t

)

⁢

p

˙

i

=

c

i

(

p

i

,

t

)

,

solving a partial derivative of the first-order constrained-differential equation to a second-order standard constraint form by transposing:

A

i

(

p

i

,

t

)

⁢

p

¨

i

=

b

i

(

p

i

,

p

˙

i

,

t

)

;

then, getting the constraint following error ϵ i :

ϵ

i

=

A

i

(

p

i

,

t

)

⁢

p

˙

i

-

c

i

(

p

i

,

t

)

in these formulas, c i (p i ,t) meaning a first-order constrained vector of the i'th unmanned system, b i (p i ,{dot over (p)} i ,t) meaning a second-order constrained vector of the i'th unmanned system.

11. The non-transitory readable computer storage media according to claim 10 , wherein the step for constructing the dynamic model comprises:

step S 31 , constructing the dynamic model as follows:

ℳ

i

(

p

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

⁢

p

¨

i

(

t

)

+

C

i

(

p

i

(

t

)

,

p

.

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

⁢

p

.

i

(

t

)

+

G

i

(

p

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

+

F

i

(

p

i

(

t

)

,

p

.

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

=

τ

i

(

t

)

{umlaut over (p)} u (t) meaning an accelerated speed of the i'th unmanned system also named {umlaut over (p)} i ; τ i (t) meaning an input of control force; i (p i , i ,t), C i (p i ,{dot over (p)} i , i ,t){dot over (p)} i , F i (p i ,{dot over (p)} i , i ,t), G i (p i , i ,t), all being exact dimensions; M i (⋅), C i (⋅), G i (⋅), F i (⋅) all being continuous function;

step S 32 , reconstructing the dynamic model as follows:

ℳ

i

(

p

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

⁢

p

¨

i

(

t

)

+

C

i

(

p

i

(

t

)

,

p

.

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

⁢

p

.

i

(

t

)

+

G

i

(

p

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

+

F

i

(

p

i

(

t

)

,

p

.

i

(

t

)

,

ϱ

i

(

t

)

,

t

)

+

D

ai

(

p

i

(

t

)

,

p

.

i

(

t

)

,

t

)

⁢

v

ai

=

ϕ

i

(

t

)

⁢

τ

i

(

t

)

D ai (p i (t),{dot over (p)} i (t),t) meaning input matrix of the network attack input of the i'th unmanned system, ϕ i (t) meaning an influence coefficient for controlling the network attack input; D ai (p i (t),{dot over (p)} i (t),t) being an exact dimension; D ai (⋅) being a continuous function;

step S 33 , setting constraint conditions to the dynamic model:

if any (p i ,t) being (p i ,t)∈R k ×R, i ∈Γ i , the inertia matrix M i (p i , i ,t) meaning a positive definite matrix;

if any (p i ,t) being (p i , t)∈R k ×R and A i (p i ,t) being full rank, the inertia matrix A i (p i ,t) A i T (p i ,t) being reversible;

if any t being t∈R, ϕ i (t) having a lower limiting value ϕ i , ϕ i ≤ϕ i (t)≤1.

12. The non-transitory readable computer storage media according to claim 8 , wherein the step for collaborative controlling networks resilience comprises:

Step S 53 , analyzing a stability of the adaptive robust controller by a Lyapunov function as follows:

V

=

∑

i

=

1

n

V

i

V

i

=

1

2

⁢

ϵ

i

T

⁢

K

i

⁢

ϵ

i

+

1

2

⁢

(

1

+

δ

E

i

)

⁢

(

γ

^

i

-

γ

i

)

T

⁢

Y

i

⁢

1

-

1

(

γ

^

i

-

γ

i

)

.

13. The non-transitory readable computer storage media according to claim 8 , wherein the step of constructing the adaptive robust controller further comprises:

step S 54 , adjusting parameters of the adaptive robust controller, the parameters comprising κ i , Y i1 , Y i2 .

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Priority Claims (1)

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References Cited (14)