CN104375416A - Synonymy redundancy elimination grid method of point locating in control system - Google Patents

Abstract

A synonymy redundancy elimination grid method of point locating in a control system is divided into two main stages, namely an off-line computing stage and an on-line computing stage. A multi-parametric quadratic program theory is introduced into the off-line computing stage. A computer can divide a state space of the control system into protruding cells and compute the corresponding control rates of the cells. In the on-line computing stage, the cell where a current state point of the system is placed is determined, the corresponding control rate of the cell is obtained, and the control output amount of the system is obtained through simple linear operation.

Description

The synonym de-redundancy gridding method of control system mid point orientation problem

Technical field

The present invention be directed to the optimization of independent positioning method in explicit model PREDICTIVE CONTROL, this synonym de-redundancy gridding method can improve the online search efficiency of point location greatly, and reduces the demand of data space to a certain extent.

Background technology

The on-line optimization existed in traditional Model Predictive Control repeatedly calculates, and it causes controller overload and inefficiency.In order to address these problems, before and after 2002, the scholar such as Manfred Morari and Alberto Bemporad introduces multiparameter quadratic programming theory, establishes explicit model forecast Control Algorithm system.It mainly utilizes the piecewise affine rule of model predictive control system inherence, according to the information such as model, constraint, performance requirement of control object, by multiparameter quadratic programming (multi-parametric Quadratic Program, mp-QP) system state space be divided into subregion convex one by one and precompute optimum control rate corresponding on each subregion.This means to complete before complicated time-consuming on-line optimization process is advanceed to control system actual motion in traditional Model Predictive Control, and during On-line Control, only need subregion residing for certainty annuity current state point, corresponding optimum control rate can be obtained.This efficiency of searching computing calculates far above on-line optimization repeatedly, and the real-time performance of control system is greatly improved, and also reduces the requirement to control system software and hardware simultaneously.

Which subregion is certain judging in space be a bit in, and is called as point location problem in computational geometry.The main task of the actual On-line Control process of explicit model PREDICTIVE CONTROL solves point location problem exactly, and the performance of the independent positioning method that we adopt is directly connected to the performance of explicit model Predictive Control System.Here the performance of independent positioning method refer to storage space shared by data, the calculated off-line time and online computing time these three aspects.

Traditional independent positioning method has method of directly searching, can reach zone method, Hash table method etc., although they also reality can solve point location problem effectively, can not meet our demand for control at aspect of performance.Such as directly search method, although it does not need calculated off-line, its online search efficiency is very low, and does not also preponderate on storage space shared by data.The online search efficiency that can reach zone method is determined according to control system characteristic, although be improved in this, preprocessing process but seems particularly very long, and shared by data, storage space also increases greatly.With can to reach zone method similar, Hash table method needs extra storage Hash table data, and improve the demand stored space, its pretreatment time is shorter, but the lifting of online search efficiency is but very limited.

Summary of the invention

The present invention, in order to overcome the above-mentioned shortcoming of prior art, provides a kind of synonym de-redundancy gridding method, it can improve its online search efficiency further and reduce needed for storage space.

The essence of point location is exactly determining certain any residing subregion in space, then obtaining this zonal control rate and realize control effects.For the deficiency of Hash table method in existing conventional point localization method, the invention provides a kind of new point location thinking.Although traditional Hash table method has and shorter searches the time online, it sacrifices space performance and pretreatment time achieves the goal.When division parameter increases, the pretreatment time needed for method and memory space requirements can rise fast, and division parameter is increased to a certain degree, and the lifting of efficiency is just more and more not obvious.And synonym de-redundancy gridding method provided by the invention can improve its online search efficiency further and reduce needed for storage space.

Synonym de-redundancy gridding method is divided into two main stages---calculated off-line stage and online calculation stages.It is theoretical that the calculated off-line stage introduces multiparameter quadratic programming, calculates function and voluntarily the state space of control system be divided into subregion convex one by one and calculate control rate corresponding to each subregion.Online calculation stages is exactly subregion residing for the current state point of certainty annuity, and obtains control rate corresponding to this subregion, is obtained the control output quantity of system by simple linear computing.

The synonym de-redundancy gridding method of control system mid point orientation problem of the present invention, specifically comprises the following steps:

Step 1, synonym de-redundancy gridding method off-line process

1.1, calculate hash function according to division parameter, the data obtained be recorded in an array, we are array called after Fhash.Here hash function as shown in the formula:

$f\left(X\right)=\mathrm{floor}((X-a)\×\frac{N}{b-a})---\left(1\right)$

Here N representative divides parameter, a and b is the boundary coordinate in certain dimension, we need to be recorded in data in array for-a and

1.2, in space, the division of subregion is according to eigenwert---in same subregion, there is a little identical eigenwert.Subregion equal for eigenwert is called synonym subregion by us.In explicit model PREDICTIVE CONTROL, partition characteristics value (being here the control rate of explicit model PREDICTIVE CONTROL) is called as FG matrix.Such as certain explicit model PREDICTIVE CONTROL output dimension is the FG matrix of the two-dimensional state space partition zone P of 1:

FG ₁＝[f ₁₁f ₁₂g ₁] (2)

The FG matrix of adjacent another subregion Q is:

FG ₂＝[f ₂₁f ₂₂g ₂] (3)

If meet

(f ₁₁-f ₂₁) ²+(f ₁₂-f ₂₂) ²+(g ₁-g ₂) ²≤δ (4)

Wherein f and g is the element of composition characteristic value matrix, and it is calculated by eigenwert and state vector that the control that we need exports.When δ is a minimum positive number, then think that P and Q is synonym, they are synonym subregion each other.

By determining that the formula (4) of synonym subregion calculates synonym subregion and divides into groups, each group synonym subregion only retains a characteristic value data, is deposited in by characteristic value data in FG_temp matrix array successively.Calculate rear FG_temp matrix array and replaced the FG matrix array produced after mp-QP, retain synonym partition packet data for subsequent use.

1.3, according to division parametric configuration Hash table net region polytope, it being got friendship with each subregion successively, if handing over operation result is not empty (being the polytope of full dimension), being then stored in intersecting the child partition obtained successively in PinGrid polytope array.If the friendship of this net region and each subregion is empty, then record corresponding in Hash array is designated as 0.

1.4, the synonym partition packet data that query steps 2 is preserved, by the child partition in the PinGrid array in current grid region according to synonym partition packet.Can observe, the eigenwert distribution in different net region presents 5 kinds of different situations:

A. whole net region is in interior volume, and inside only has a kind of eigenwert.

B. whole net region is in interior volume, and is dispersed with two or more different eigenwert.

C. Partial Mesh region is at outside, and is dispersed with two or more different eigenwert.

D. Partial Mesh region is at outside, and inside only has a kind of eigenwert.

E. whole grid is all at outside.

If current grid region belongs to a class net region, suppose that its eigenwert is numbered nfg, record corresponding in Hash array is designated as-nfg; If current grid region belongs to b, c or d class, then each group synonym child partition is respectively asked for also (process also of getting contains the convexification subdivision to Non-convex region), then operation result be recorded in polytope array NewP_temp successively and number, the position corresponding in Hash array by the number record of wherein first new subregion.The numbering of the eigenwert of each new subregion generated in current grid is recorded successively in FGN_temp array.

1.5, step 3 and step 4 are performed, until calculated last block net region to next net region.

1.6, in NewP_temp array, extract the Description Matrix of each new subregion successively, be recorded in successively in HK array.The home record address of the Description Matrix of each new subregion in HK array is recorded in the NC array of one dimension successively.

1.7, the FGN_temp array of one dimension is incorporated in NC array as new row.For the ease of searching online, using the Hash array of one-dimensional as Hash table.

1.8, delete all intermediate data, finally only retain these five arrays of Fhash, Hash, NC, HK and FG.

Step 2, the online processing procedure of synonym de-redundancy gridding method

2.1, according to state point coordinate, calculated by Fhash array and determine net region subscript.

2.2, calculate this net region subscript in Hash array, determine the partition number in this net region.Wherein Hash element is that this net region of 0 expression is all positioned at outside space, for negative explanation directly can obtain eigenwert, also needs to determine a little to belong to the eigenwert which new subregion just can obtain it for canonical illustrates.

The first row of 2.3, NC array describes the home record address of HK Description Matrix in HK array of each new subregion successively, and secondary series then indicates the numbering of each new subregion characteristic of correspondence value successively.

Divisional description matrix H K can be obtained by NC array by partition number, judge this state point is in which subregion successively.

2.4, determine subregion residing for state point, from FG array, obtain partition characteristics value according to subscript.

Advantage of the present invention is: its online search efficiency can be improved and reduce needed for storage space.

Accompanying drawing explanation

Fig. 1 is that the present invention introduces state space schematic diagram after synonym subregion

Fig. 2 is Partial Mesh region of the present invention partial enlarged drawing

Fig. 3 is synonym de-redundancy gridding method data structure schematic diagram of the present invention

Fig. 4 is synonym de-redundancy gridding method of the present invention and Hash table method method performance comparison in storage space

Fig. 5 contrasts the average online computing time of synonym de-redundancy gridding method of the present invention and Hash table method

Fig. 6 is that the pretreatment time of synonym de-redundancy gridding method of the present invention and Hash table method contrasts

Embodiment

Below in conjunction with accompanying drawing, further illustrate the present invention.With reference to accompanying drawing 1-6:

The synonym de-redundancy gridding method of control system mid point orientation problem of the present invention, comprises the steps:

Step 1, the off-line process of synonym de-redundancy gridding method

1.1, calculate hash function data according to division parameter, be recorded in Fhash array.

1.2, calculate synonym subregion according to formula (4) and divide into groups, each group synonym divides block reservation a characteristic value data, deposits in successively in FG_temp matrix array, has calculated rear FG_temp matrix array and replaced original FG matrix array.Retain synonym partition packet data for subsequent use.

1.3, structure net region polytope, gets friendship with each subregion successively by it, if hand over operation result not to be empty, is then stored in intersecting the child partition obtained successively in PinGrid polytope array.If the friendship of this net region and each subregion is empty, then record corresponding in Hash array is designated as 0.

1.4) the synonym partition packet data of query steps 2 preservation, by the child partition in the PinGrid array in current grid region according to synonym partition packet.If current grid region belongs to a class net region as shown in Figure 2, suppose that its eigenwert is numbered nfg, record corresponding in Hash array is designated as-nfg; If current grid region belongs to b, c, d class, then each group synonym child partition is respectively asked for also (process also of getting contains the subdivision of convexification again to non-convex result), then operation result be recorded in polytope array NewP_temp successively and number, the position corresponding in Hash array by the number record of wherein first new subregion.The numbering of the eigenwert of each new subregion generated in current grid is recorded successively in FGN_temp array.

1.5) step 3 and step 4 are performed, until calculated last block net region to next net region.

1.6) in NewP_temp array, extract the HK Description Matrix of each new subregion successively, be recorded in successively in HK array.By each new subregion the home record address of HK Description Matrix in HK array be recorded in successively in the NC array of one dimension.

1.7) the FGN_temp array of one dimension is incorporated in NC array as new row.

1.8) for the ease of searching online, using the Hash array of one-dimensional as Hash table.

1.9) delete all intermediate data, finally only retain these five arrays of Fhash, Hash, NC, HK and FG.

Step 2, the online computation process of synonym de-redundancy gridding method

Conveniently and image illustrates the online calculation procedure of synonym de-redundancy gridding method understandablely, we introduce Fig. 3, and Fig. 3 shows the data structure schematic diagram that certain two-dimensional state space obtains after above-mentioned steps pre-service, and it divides parameter is 6.

It should be noted that, for the ease of in Hash table to the differentiation of different situations, to the numbering of new subregion from 1, the subscript of above-mentioned each array then according to the standard of C language by 0.What first element being designated as 0 under namely in NC array first row described is be numbered 1 first new subregion, the rest may be inferred.

2.1, such as certain any coordinate is (-4.000,1.000), then can calculate the subscript of its net region, place according to the data in Fhash array:

p ₁＝floor((-4.000+5.000)×0.600)＝0

p ₂＝floor((1.000+1.769)×1.696)＝4

Be designated as (0,4) under the net region at then this place.

2.2, calculate the subscript of this net region in the Hash table of of one-dimensional:

p _hash＝0×6+4＝4

The element value being designated as 4 under in Hash array is 2.The value of getting next element is-2, casts out; The value of getting next element is again 0, casts out; The value of getting next element is again 5, and in the net region that this place is described, total 5-2=3 subregion, numbers and be respectively 2,3,4.

2.3 the HK matrix that the element being designated as 1 under in NC array first row indicates the subregion being numbered 2 stores in HK array from the 5th row, and the HK matrix that next element then indicates the subregion being numbered 3 stores from eighth row.Illustrate that the 5th row of HK array is the Description Matrix of the subregion being numbered 2 to the 7th row.

2.4, the 5th row getting HK array, to the 7th row, judges that this point is whether in this subregion.If so, be then designated as in the element of 1 from NC array secondary series and obtain characteristic of correspondence value and be numbered 3, obtaining from FG array the element being designated as 3, is exactly the eigenwert of required point; Otherwise get next subregion to continue to judge, until find correct subregion.If 3 subregions traveled through in this net region also do not find correct subregion, then illustrate that this point is outside state space.

Case analysis

The present invention by a second order example compare Hash table method and its through optimizes obtain each comfortable memory space requirements of synonym de-redundancy gridding method, off-line pretreatment time, online computing time three aspects performance, the superiority of displaying synonym de-redundancy trellis algorithm.

Fig. 4, Fig. 5 and Fig. 6 compared for synonym de-redundancy gridding method and the performance of Hash table method in memory space requirements, average online computing time, pretreatment time three respectively.As can be seen from form, synonym de-redundancy gridding method is not preponderated on pretreatment time, but has all had very big raising in memory space requirements and online search efficiency.In most of the cases, pretreatment time does not affect the performance of algorithm in application realizes, memory space requirements, average online computing time these two aspects performance be then related to method and can be applicable to the practical application relatively high to the requirement of cost and efficiency.

Content described in this instructions embodiment is only enumerating the way of realization of inventive concept; protection scope of the present invention should not be regarded as being only limitted to the concrete form that embodiment is stated, protection scope of the present invention also and conceive the equivalent technologies means that can expect according to the present invention in those skilled in the art.

Claims (1)

1. the synonym de-redundancy gridding method of control system mid point orientation problem, comprises the steps:

Step 1, synonym de-redundancy gridding method off-line process

1.1, calculate hash function according to division parameter, the data obtained be recorded in an array, we are array called after Fhash.Here hash function as shown in the formula:

$f\left(X\right)=\mathrm{floor}((X-a)\×\frac{N}{b-a})---\left(1\right)$

Here N representative divides parameter, a and b is the boundary coordinate in certain dimension, we need to be recorded in data in array for-a and

1.2, in space, the division of subregion is according to eigenwert---in same subregion, there is a little identical eigenwert.Subregion equal for eigenwert is called synonym subregion by us.In explicit model PREDICTIVE CONTROL, partition characteristics value (being here the control rate of explicit model PREDICTIVE CONTROL) is called as FG matrix.Such as certain explicit model PREDICTIVE CONTROL output dimension is the FG matrix of the two-dimensional state space partition zone P of 1:

FG ₁＝[f ₁₁f ₁₂g ₁] (2)

The FG matrix of adjacent another subregion Q is:

FG ₂＝[f ₂₁f ₂₂g ₂] (3)

If meet

(f ₁₁-f ₂₁) ²+(f ₁₂-f ₂₂) ²+(g ₁-g ₂) ²≤δ (4)

Wherein f and g is the element of constitutive characteristic value matrix, controls to export to be calculated by eigenvalue matrix and state vector.When δ is a minimum positive number, then think that P and Q is synonym, they are synonym subregion each other.

By determining that the formula (4) of synonym subregion calculates synonym subregion and divides into groups, each group synonym subregion only retains a characteristic value data, is deposited in by characteristic value data in FG_temp matrix array successively.Calculate rear FG_temp matrix array and replaced the FG matrix array produced after mp-QP, retain synonym partition packet data for subsequent use.

1.3, according to division parametric configuration Hash table net region polytope, it being got friendship with each subregion successively, if handing over operation result is not empty (being the polytope of full dimension), being then stored in intersecting the child partition obtained successively in PinGrid polytope array.If the friendship of this net region and each subregion is empty, then record corresponding in Hash array is designated as 0.

1.4, the synonym partition packet data that query steps 2 is preserved, by the child partition in the PinGrid array in current grid region according to synonym partition packet.Can observe, the eigenwert distribution in different net region presents 5 kinds of different situations:

A. whole net region is in interior volume, and inside only has a kind of eigenwert.

B. whole net region is in interior volume, and is dispersed with two or more different eigenwert.

C. Partial Mesh region is at outside, and is dispersed with two or more different eigenwert.

D. Partial Mesh region is at outside, and inside only has a kind of eigenwert.

E. whole grid is all at outside.

If current grid region belongs to a class net region, suppose that its eigenwert is numbered nfg, record corresponding in Hash array is designated as-nfg; If current grid region belongs to b, c or d class, then each group synonym child partition is respectively asked for also (process also of getting contains the convexification subdivision to Non-convex region), then operation result be recorded in polytope array NewP_temp successively and number, the position corresponding in Hash array by the number record of wherein first new subregion.The numbering of the eigenwert of each new subregion generated in current grid is recorded successively in FGN_temp array.

1.5, step 3 and step 4 are performed, until calculated last block net region to next net region.

1.6, in NewP_temp array, extract the Description Matrix of each new subregion successively, be recorded in successively in HK array.The home record address of the Description Matrix of each new subregion in HK array is recorded in the NC array of one dimension successively.

1.7, the FGN_temp array of one dimension is incorporated in NC array as new row.For the ease of searching online, using the Hash array of one-dimensional as Hash table.

1.8, delete all intermediate data, finally only retain these five arrays of Fhash, Hash, NC, HK and FG.

Step 2, the online processing procedure of synonym de-redundancy gridding method

2.1, according to state point coordinate, calculated by Fhash array and determine net region subscript.

2.2, calculate this net region subscript in Hash array, determine the partition number in this net region.Wherein Hash element is that this net region of 0 expression is all positioned at outside space, for negative explanation directly can obtain eigenwert, also needs to determine a little to belong to the eigenwert which new subregion just can obtain it for canonical illustrates.

The first row of 2.3, NC array describes the home record address of HK Description Matrix in HK array of each new subregion successively, and secondary series then indicates the numbering of each new subregion characteristic of correspondence value successively.

Divisional description matrix H K can be obtained by NC array by partition number, judge this state point is in which subregion successively.

2.4, determine subregion residing for state point, from FG array, obtain partition characteristics value according to subscript.