CN109345809A - The distributed optimization method of solar energy radio acquisition system - Google Patents
The distributed optimization method of solar energy radio acquisition system Download PDFInfo
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Abstract
The present invention provides a kind of distributed optimization method of solar energy radio acquisition system, by considering the operating current of solar battery, is converted into objective function, finds out the minimum value of objective function sum；Design Lagrangian；Find out the dual function of objective function；It will not guidable objective function smoothing；It calculates and exempts from gradient prediction value at random；The estimated value of sensor supply current size in line interation；The estimation Distribution value for obtaining optimal sensor supply current size instructs the rated current of sensor in n solar energy acquisition system to be arranged with it.This method is directed to each rough situation of sensor cost function of multi-agent system under fixed topology, utilize Lagrangian and random derivative-free algorithm, it designs based on the primal dual algorithm for exempting from gradient at random, it can guarantee near cost and function convergence to optimal value, power supply efficiency when solar energy acquisition system powers to wireless sensor network is significantly improved, and improves the stability of solar powered micro-capacitance sensor.
Description
Technical field
The present invention relates to a kind of distributed optimization methods of solar energy radio acquisition system.
Background technique
In recent years, flourishing with science and technology, the especially appearance of the emerging fields such as cloud computing and big data, distribution
Formula optimum theory and application have obtained more and more attention, and it is raw gradually to penetrate into scientific research, engineer application and society
Various aspects living.So-called distributed optimization, which just refers to, has certain perception, communication, calculating and executive capability by a group
Intelligent body solves the optimization algorithm for the large-scale complex that many centralized algorithms can not be handled by modes such as communications.It is distributed excellent
Change one of the important development direction that theoretical and application has become contemporary systems and control science, is led in Control Science and Engineering
Domain, with the development of sensor network, digital communications network, the basic structure and the method for operation of control system are also had occurred at all
Change.One control system is no longer made of single controll plant, sensor or controller, but by multiple intelligent body collection
At a complicated control network, these intelligent bodies complete given task according to certain communication protocol by being connected with each other.
The process of entire control and decision is exactly co-operating process between each intelligent body.Therefore, compared with traditional control system,
One multi-agent system it control system and communication system are melted into a whole completely.
Currently, the development of solar energy acquisition technology is increasingly mature, it is widely used.By solar energy acquisition technology and wireless sensing
Network integration gets up, and not only can solve the energy supply problem of wireless sensor network, additionally it is possible to expand solar energy acquisition technology
Application field.And many important achievements are had been achieved for for the design of the distributed optimization algorithm of multisensor, but just
At present for popular research achievement, there are still following problems:
Consider in solar energy radio acquisition system, utilizes the sensor real-time monitoring and acquisition solar battery in network
A variety of data informations, and collected data information and adjacent sensor are interacted into calculating, power consumption interpretation of result.This
In wireless sensor network be substantially exactly a multi-agent system, each sensor is exactly an intelligent body.For one
A multi-agent system being made of sensor, each sensor often have a cost function, and the cost of whole network
By these individuals cost functions and indicate, such issues that purpose be need to design distributed algorithm to minimize this function
With.
For problems, existing method requires that greatly the function of optimization is convex function, but many times needs in practice
The problem of handling male-female function；On the other hand, for finding out function using the gradient or subgradient that calculate cost function
Optimal solution, there are a prominent disadvantages: for not guidable function, it is extremely difficult for calculating its subgradient or gradient
, even not possible with.This causes under some cases, multiple sensors be in communication with each other and coordination is affected, and then not
The optimal value for meeting system condition can be accurately calculated, so that existing use solar energy acquisition system to wireless sensor network
Inefficiency when power supply causes serious energy waste；And since the issued electric power of solar energy acquisition system cannot disappear in time
It receives and the unstable of micro-capacitance sensor can be caused.
The above problem should be paid attention to and be solved during the distributed optimization of solar energy radio acquisition system
Problem.
Summary of the invention
The object of the present invention is to provide a kind of distributed optimization methods of solar energy radio acquisition system to solve the prior art
Present in solar energy radio acquisition system, multiple sensors can directly exchange mutually communication；But due to data with
Machine, the cost function of each sensor may be male-female function, even not differentiable functions and lead to the phases of multiple sensors
Mutual communication and coordination are affected, and the optimal value for meeting system condition cannot be accurately calculated so that existing use the sun
When energy acquisition system powers to wireless sensor network the problem of inefficiency.
The technical solution of the invention is as follows:
A kind of distributed optimization method of solar energy radio acquisition system, comprising the following steps:
S1, the solar panel data for monitoring wireless sensor carry out interpretation of result, consider solar battery
Operating current is converted into output power objective function, then optimizes data, is integrated into solar powered power optimization and asks
Topic, finds out the minimum value of output power objective function sum；
S2, the solar powered power optimization problem in step S1 is considered as primal problem, finds out the antithesis of primal problem
Problem, and the dual function of design object function；
S3, Lagrangian is designed according to the dual problem of the obtained primal problem of step S2, and designs its power mesh
Scalar functions；
It S4, is smoothing formula to be designed, by power not guidable in step S3 the case where can not leading for Lagrangian
Objective function smoothing processing；
S5, the smoothing parameter for setting smoothing formula, calculate smooth function exempts from gradient prediction value at random；
S6, using gradient prediction value is exempted from step S5 at random, design iteration formula finally calculates biography by k iteration
Sensor supply current size；
S7, the estimation Distribution value for obtaining optimal sensor supply current size, instruct n solar energy acquisition system with it
The rated current of middle sensor is arranged.
Further, in step S1, the minimum value of objective function sum is found out, specifically:
subject to h(x)≤0
x∈X
Wherein, n is the number of sensor in solar energy acquisition system, and what x was indicated is estimating for sensor supply current size
Evaluation；What X was indicated is the constraint set of sensor supply current size；fi(x) the cost letter of i-th of sensor power supply is indicated
Number, h (x) indicate the physical condition constraint in solar energy acquisition system,Indicate the objective function for needing to optimize.
Further, in step S2, the dual function of objective function is found out, specifically:
max i mize q(λ)
subject to λ≥0
λ∈N
Wherein, what N was indicated is the constraint set of dual function, and N is nonempty closed set；Definition:
That is dual function q (λ) is the infimum of Lagrangian in step S3.
Further, in step S3, Lagrangian is designed, specifically:
Here, f (x) is original function, and h (x) is the derivative of f (x), and λ is Lagrange's multiplier, and λ ' is Lagrange's multiplier
The transposition of λ.
Further, in step S4, guidable objective function is smoothed, smooth function is designed:
Wherein, n remains the number of sensor in solar energy acquisition system,ξ is to meet solely
The vertical random sequence with distribution, μiFor smoothed out LagrangianSmoothing factor, and μi≥0。
Further, in step S5, calculating exempts from gradient prediction value at random, specifically:
Here xi(k) cost function that i-th of sensor is powered in the k time is indicated；λiIt (k) is xi(k) dual function；
μiIndicate the smoothing parameter of i-th of sensor power supply cost function, it is a constant greater than 0；It is to be sensed according to i-th
Lagrangian designed by device power supply cost function；The smooth function that be i-th of sensor design in the k time it is random
Sequence, and meet independent same distribution；
Wherein, i=1 ..., n indicate i-th of acquisition sensor；The number of k expression iteration；WithIt respectively indicates in primal problem and its dual problem iterative process and exempts from gradient prediction value.
Further, in step S6, the estimated value of sensor supply current size in line interation, specifically,
Here W indicates that sensor carries out the weight matrix of information exchange, it is a doubly stochastic matrix；WijIt indicates i-th
Communication cost weight between node and j-th of node has communication then W between the twoij> 0, otherwise Wij=0.
Then, what iterative formula here indicated is+1 iteration of kth；xi(k+1) indicate i-th of sensor in the k time
The cost function of power supply, λiIt (k+1) is still xi(k+1) dual function；WhereinIt indicates * project to constraint
Collect in X, similarlyIt indicates * project into constraint set N；αkIndicate the step-size in search in k iteration；It is original to ask
The projection set of topic and its dual problem is all that non-empty is closed.
The beneficial effects of the present invention are: the distributed optimization method of this kind of solar energy radio acquisition system, with the prior art
It compares, has the advantage that
One, the distributed optimization method of this kind of solar energy radio acquisition system, for the multiple agent system under fixed topology
Each rough situation of sensor cost function of uniting is designed and is based on using Lagrangian and random derivative-free algorithm
The primal dual algorithm for exempting from gradient at random, can guarantee to significantly improve solar energy near cost and function convergence to optimal value and adopt
Power supply efficiency when collecting system powers to wireless sensor network, while improving the stability of solar powered micro-capacitance sensor.
Two, the present invention considers the male-female problem in the distributed optimization process of solar energy radio acquisition system, by asking
The dual problem of primal problem designs Lagrangian out, eventually by proposing that a kind of Saddle Point Algorithm finds out its optimal solution.
Three, general distributed optimization algorithm is designed, wherein being mostly to go to solve to optimize using the method for subgradient
Problem；It can bring about two problems in this way: first, the subgradient of an objective function is calculated, the solution more than one often acquired,
As for which is selected thus bring difficulty to the design of algorithm as gradient estimator；Second, general distributed optimization
What problem considered be cost function is smooth situation, if cost function be it is rough, the subgradient for calculating it is just very tired
Difficulty can not even acquire.The method of the present invention is to exempt from the method for gradient at random, goes to substitute time ladder using gradient prediction value is exempted from random
Degree, can relax the requirement to objective function in this way.
Four, the distributed optimization method of this kind of solar energy radio acquisition system is successfully realized the limited lower solar energy of information
The design and analysis of the distributed optimization algorithm of wireless acquisition system.Here information is limited mainly to influence following two aspects,
First, the case where leading to objective function since information is limited in practical problem there are male-females, need to find out its dual function, and
It is solved the problems, such as using supergradient；Also cost function can be made to show as rough situation second, information is limited.It is above-mentioned two
The unfavorable factor of aspect causes the prior art to hardly result in the estimation Distribution value of optimal sensor supply current size, and this hair
It is bright to can be very good to solve above-mentioned technical problem.
Detailed description of the invention
Fig. 1 is the flow diagram of the distributed optimization method of solar energy radio acquisition system of the embodiment of the present invention.
Fig. 2 is the error function of the distributed optimization method acquisition of the solar energy radio acquisition system based on embodiment with repeatedly
The increased situation of change schematic diagram of generation number.
Specific embodiment
The preferred embodiment that the invention will now be described in detail with reference to the accompanying drawings.
Embodiment
A kind of distributed optimization method based on solar energy radio acquisition system, such as Fig. 1 include the following steps,
S1, the solar panel data for monitoring wireless sensor carry out interpretation of result, consider solar battery
Operating current is converted into objective function.Then data are optimized, is integrated into solar powered power optimization problem, finds out
The minimum value of output power objective function sum, specific as follows:
subject to h(x)≤0
x∈X
Wherein, n is the number of sensor in solar energy acquisition system, and what x was indicated is estimating for sensor supply current size
Evaluation, that X is indicated is the constraint set of sensor supply current size, fi(x) the cost letter of i-th of sensor power supply is indicated
Number, h (x) indicate the physical condition constraint in solar energy acquisition system,Indicate the objective function for needing to optimize.
S2, the solar powered power optimization problem in step S1 is considered as primal problem, finds out the antithesis of primal problem
Problem, and the dual function of design object function, specifically:
max i mize q(λ)
subject to λ≥0
λ∈N
Wherein, what N was indicated is the constraint set of dual function, and N is nonempty closed set；Definition:
That is dual function q (λ) is the infimum of Lagrangian in step S3.
S3, Lagrangian is designed according to the dual problem of the obtained primal problem of step S2, and designs its power mesh
Scalar functions.In step S3, Lagrangian is designed, specifically:
Here, f (x) is original function, and h (x) is the derivative of f (x), and λ is Lagrange's multiplier, and λ ' is Lagrange's multiplier
The transposition of λ.
It S4, is smoothing formula to be designed, by power not guidable in step S3 the case where can not leading for Lagrangian
Objective function smoothing processing；
Wherein, guidable objective function is smoothed, designs smooth function:
Wherein, n remains the number of sensor in solar energy acquisition system,ξ is to meet solely
The vertical random sequence with distribution, μiFor smoothed out LagrangianSmoothing factor, and μi≥0。
S5, the smoothing parameter for setting smoothing formula, calculate smooth function exempts from gradient prediction value at random；
In step S5, calculating exempts from gradient prediction value at random, specifically:
Here xi(k) cost function that i-th of sensor is powered in the k time is indicated；λiIt (k) is xi(k) dual function；
μiIndicate the smoothing parameter of i-th of sensor power supply cost function, it is a constant greater than 0；It is us according to i-th
Lagrangian designed by sensor power supply cost function；It is i-th of sensor smooth letter that we design in the k time
Several random sequences, and meet independent same distribution.
Wherein, i=1 ..., n indicate i-th of acquisition sensor；The number of k expression iteration；WithIt respectively indicates in primal problem and its dual problem iterative process and exempts from gradient prediction value.
S6, using gradient prediction value is exempted from step S5 at random, design iteration formula finally calculates biography by k iteration
Sensor supply current size.
In step S6, the estimated value of sensor supply current size in line interation, specifically,
Here W indicates that sensor carries out the weight matrix of information exchange, it is a doubly stochastic matrix；WijIt indicates i-th
Communication cost weight between node and j-th of node has communication then W between the twoij> 0, otherwise Wij=0.
Then, what iterative formula here indicated is+1 iteration of kth；xi(k+1) indicate i-th of sensor in the k time
The cost function of power supply, λiIt (k+1) is still xi(k+1) dual function；WhereinIt indicates * project to constraint
Collect in X, similarlyIt indicates * project into constraint set N；αkIndicate the step-size in search in k iteration；It is original to ask
The projection set of topic and its dual problem is all that non-empty is closed.
S7, the estimation Distribution value for obtaining optimal sensor supply current size, instruct n solar energy acquisition system with it
The rated current of middle sensor is arranged.
The theoretical validation of the distributed optimization method based on solar energy radio acquisition system of embodiment is as follows:
For wireless sensor network, it is set to meet following condition since its physical topology configures:
Condition 1: according to LagrangianL designed by each sensoriIt is continuous that (x, λ) all meets Lipschit, and
And have We take
Condition 2: the constraint set X of sensor states is bounded, is had for arbitrary x, y ∈ X | | x-y | |2≤ R, and
0∈X。
Condition 3: the weight matrix of connection sensor information exchange is double random.For scalar ω >=0, weight square
Element on the diagonal line of battle array meets Wii≥ω；In addition, if Wij>=0, there is W >=ω.
Condition 4: for all k >=0, there are a positive integer T, so that communication matrix non-directed graph: (V, E (W (kT)))
∪ ... ∪ E (W ((k+1) T-1)) meets strong continune.
Here, an innovative conclusion is proposed to prove the derivation and proof of step S6:
Innovative conclusion 1: according in step S6, about the iterative algorithm of sensor network optimization, sensor is at the k moment
Current value will converge near average value.Here make weight matrix W=I- ε L, L here is sensing system topological diagram
Laplacian Matrix, andHere αmaxIt refers to the maximum degree of sensor network, hasThen it to the demarcation of gradient prediction value, and the characteristic of utilization weight matrix is exempted from, obtains
Sensor is in the state value at k+1 moment and the relationship of sensor current average value:
Herelimk→∞ατ> 0；B is relevant to communication matrix connection cycle T
Constant, and For the maximum value of objective function lipschitz constant.It is attached that objective function also converges to optimal value
It is close:
Wherein γk=maxI, j ∈ VE[||xi(k)-xj(k) | |], i, j=1 ..., n；x*For the optimal solution of optimization problem, f (x*) be optimization problem optimal value.
Embodiment analyzes the convergence state of intelligent body to the demarcation of gradient prediction value is exempted from random；And ideal function is close
Seemingly converge to optimal value, smoothing factor μ of the convergence error with objective functioni, Lipschitz constantIt is related.Finally obtain knot
By: the optimal value that the algorithm obtains converges on actual optimum value.
Conventional solar energy radio acquisition system framework is arranged, Fig. 2 gives the mistake obtained based on embodiment method
Difference function is with the increased situation of change of the number of iterations.From figure 2 it can be seen that after taking around iteration 10000 times, error function
Curve it is smooth-out, approximate convergence to 0.It can be seen that the distributed optimization side of the solar energy radio acquisition system of embodiment
Method, can overcome the cost function due to each sensor may be male-female function even not differentiable functions and cause multiple
The technology for being in communication with each other and coordinating to be affected and the optimal value for meeting system condition cannot be accurately calculated of sensor is asked
Topic, and can be improved efficiency when existing use solar energy acquisition system powers to wireless sensor network.
Unspecified part of the present invention belongs to field technical staff's common knowledge, and the foregoing is merely of the invention one
A specific embodiment, is not intended to limit the invention, all within the spirits and principles of the present invention, made any modification, etc.
With replacement, improvement etc., should all be included in the protection scope of the present invention.
Claims (7)
1. a kind of distributed optimization method of solar energy radio acquisition system, which comprises the following steps:
S1, the solar panel data for monitoring wireless sensor carry out interpretation of result, consider the work of solar battery
Electric current is converted into output power objective function, then optimizes data, is integrated into solar powered power optimization problem,
Find out the minimum value of output power objective function sum；
S2, the solar powered power optimization problem in step S1 is considered as primal problem, finds out the dual problem of primal problem,
And the dual function of design object function；
S3, Lagrangian is designed according to the dual problem of the obtained primal problem of step S2, and designs its power target letter
Number；
It S4, is smoothing formula to be designed, by power target not guidable in step S3 the case where can not leading for Lagrangian
Function smoothing processing；
S5, the smoothing parameter for setting smoothing formula, calculate smooth function exempts from gradient prediction value at random；
S6, using gradient prediction value is exempted from step S5 at random, design iteration formula finally calculates sensor by k iteration
Supply current size；
S7, the estimation Distribution value for obtaining optimal sensor supply current size, instruct to pass in n solar energy acquisition system with it
The rated current of sensor is arranged.
2. the distributed optimization method of the solar energy radio acquisition system as described in patent requirements 1, it is characterised in that: step S1
In, the minimum value of objective function sum is found out, specifically:
subject to h(x)≤0
x∈X
Wherein, n is the number of sensor in solar energy acquisition system, and what x was indicated is the estimated value of sensor supply current size；
What X was indicated is the constraint set of sensor supply current size；fi(x) cost function of i-th of sensor power supply, h (x) are indicated
Indicate the physical condition constraint in solar energy acquisition system,Indicate the objective function for needing to optimize.
3. the distributed optimization method of the solar energy radio acquisition system as described in patent requirements 2, it is characterised in that: step S2
In, the dual function of objective function is found out, specifically:
maximize q(λ)
subject to λ≥0
λ∈N
Wherein, what N was indicated is the constraint set of dual function, and N is nonempty closed set；Definition:I.e. pair
Even function q (λ) is the infimum of Lagrangian in step S3.
4. the distributed optimization method of the solar energy radio acquisition system as described in patent requirements 3, it is characterised in that: step S3
In, Lagrangian is designed, specifically:
Here, f (x) is original function, and h (x) is the derivative of f (x), and λ is Lagrange's multiplier, and λ ' is lagrangian multiplier
Transposition.
5. the distributed optimization method of the solar energy radio acquisition system as described in patent requirements 4, it is characterised in that: step S4
In, guidable objective function is smoothed, smooth function is designed:
Wherein, n remains the number of sensor in solar energy acquisition system,ξ is that satisfaction is independent same
The random sequence of distribution, μiFor smoothed out LagrangianSmoothing factor, and μi≥0。
6. the distributed optimization method of the solar energy radio acquisition system as described in patent requirements 1-5, it is characterised in that: step S5
In, calculating exempts from gradient prediction value at random, specifically:
Here xi(k) cost function that i-th of sensor is powered in the k time is indicated；λiIt (k) is xi(k) dual function；μiIt indicates
The smoothing parameter of i-th of sensor power supply cost function, it is a constant greater than 0；It is to be powered according to i-th of sensor
Lagrangian designed by cost function；The random sequence for the smooth function that be i-th of sensor design in the k time,
And meet independent same distribution；
Wherein, i=1 ..., n indicate i-th of acquisition sensor；The number of k expression iteration；gX, μ i(xi(k), λiAnd g (k))λ, μ i
(xi(k), λi(k)) it respectively indicates in primal problem and its dual problem iterative process and exempts from gradient prediction value.
7. the distributed optimization method of solar energy radio acquisition system as described in any one in claim 1-5, it is characterised in that:
In step S6, the estimated value of sensor supply current size in line interation, specifically,
Here W indicates that sensor carries out the weight matrix of information exchange, it is a doubly stochastic matrix；WijIndicate i-th of node
Communication cost weight between j-th of node has communication then W between the twoij> 0, otherwise Wij=0.
Then, what iterative formula here indicated is+1 iteration of kth；xi(k+1) indicate what i-th of sensor was powered in the k time
Cost function, λiIt (k+1) is still xi(k+1) dual function；WhereinIt indicates by * project into constraint set X,
SimilarlyIt indicates * project into constraint set N；αkIndicate the step-size in search in k iteration；Primal problem and its
The projection set of dual problem is all that non-empty is closed.
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