CN110703787A - Aircraft redundancy control method based on mixed multi-target PSO algorithm of preference matrix - Google Patents
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Abstract
The invention discloses an aircraft redundancy control method based on a mixed multi-target PSO algorithm of a preference matrix, and belongs to the field of aircraft control simulation. Firstly, the control redundancy problem of an aircraft with a multi-target flight task is analyzed and converted into a mixed multi-target optimization problem, an optimization objective function is designed according to the multi-target flight task of the aircraft, the mixed multi-target optimization problem is converted into a single-target optimization problem through a linear weighting method, the value range of a preference matrix constraint weight coefficient based on a judgment matrix is utilized, a dynamically updated evaluation function is utilized to optimize a particle swarm position and speed evolution formula, the optimization result is guaranteed to be optimal simultaneously on the basis of meeting the preference requirement, and the problems that the control surface of the aircraft is redundant and difficult to control are solved.
Description
Technical Field
The invention belongs to the field of aircraft control simulation, and particularly relates to an aircraft redundancy control method based on a mixed multi-target PSO algorithm of a preference matrix.
Background
In recent years, aircrafts are developed rapidly, particularly, rotary-wing aircrafts, composite helicopters, small unmanned planes and the like become research hotspots in the field of domestic and foreign aviation, but the aircrafts need to be provided with aircrafts with complex control mechanisms to complete control of tracks and postures of the aircrafts due to the severe flying environment, the complex control mechanisms enable the control plane dimension of the aircrafts to be larger than the virtual control instruction dimension output by a controller, and control redundancy exists.
At present, scholars at home and abroad have proposed various control allocation schemes to solve the problem of the control redundancy of the aircraft, such as a direct allocation method, a pseudo-inverse method, a chain type incremental method and the like, but such schemes can only solve the problem of simple linear control allocation generally, but cannot solve the problem of complex aircraft redundancy systems with control surface constraints directly; in addition, for the flight mission comprising multiple targets of minimum deflection of the control surface, maximum control efficiency, minimum energy consumption and the like, a simple control allocation scheme cannot be solved.
In addition, in the solution of the multi-objective optimization problem, the research of the multi-objective optimization algorithm has made some progress, but most of the research results are concentrated on obtaining the optimal distribution of Pareto frontier of the multi-objective optimization problem, and the research of a constraint condition processing method of the multi-objective optimization problem is lacked, so that the solution of the constraint optimization problem is more complicated compared with the unconstrained optimization problem. Therefore, the multi-objective optimization algorithm for solving the constrained multi-objective optimization problem simply and efficiently is increasingly emphasized. For the constrained multi-objective optimization problem, some scholars determine the weight coefficient of the optimization target by using a judgment matrix method and convert the multi-objective optimization problem into a single-objective optimization problem by using a linear weighted sum method, but the weight coefficient designed by the method is a fixed value in the multi-objective optimization problem, so that the solution result cannot be guaranteed to be a global optimal solution. In addition, some scholars propose a method for converting the constrained multi-objective optimization problem into an unconstrained problem by using a penalty function, which can simplify the complexity of the multi-objective optimization problem to a certain extent, but the design of penalty factors of the penalty function is not a fixed method, and unreasonable values can cause the multi-objective optimization problem to fall into a local optimal solution.
Disclosure of Invention
The invention aims to provide an aircraft redundancy control method based on a mixed multi-target PSO algorithm of a preference matrix, which aims at overcoming the defects of the background technology, converts the control distribution problem into a multi-target optimization problem with constraint conditions, designs a self-adaptive particle swarm algorithm, solves the aircraft control surface yaw rate through online optimization, and solves the problem of multi-target flight mission aircraft redundancy control distribution with constraint.
The invention adopts the following technical scheme for realizing the aim of the invention:
a mixed multi-objective optimization problem comprising a mixed multi-objective optimization function, control rudder surface boundary constraint, virtual control instruction and control rudder surface numerical value constraint is constructed, linear weighted summation is carried out on the mixed multi-objective optimization function to convert the mixed multi-objective optimization problem into a single-objective optimization problem, a judgment matrix is established according to the importance of each objective function relative to other objective functions, a preference matrix is established according to the judgment matrix to construct constraint of objective function weight coefficients, the constraint of the objective function weight coefficients is brought into the single-objective optimization problem, and an optimal solution is obtained by carrying out online optimization on the weight coefficients and the control rudder surface. The method specifically comprises the following six steps.
Analyzing the control surface characteristics of an aircraft redundancy system, and determining the numerical relationship between an aircraft control surface and a virtual control instruction;
the general aircraft control surface is complex and has dimension larger than that of a virtual control instruction, the control redundancy exists, and a relation formula of the virtual control instruction v and the control surface delta is obtained by performing dynamic balancing and linearization analysis through aircraft balance points:
v＝Bδ (1)，
in the formula (1), δ ═ δ [ δ ]1,δ2,…,δd]Representing aircraftD-dimension control surface, B is control distribution efficiency matrix.
Step two, analyzing the flight environment and the flight mission of the aircraft, determining the mission objective of the aircraft and designing an objective function f1(δ),f2(δ),...,fn(δ)。
Analyzing the dynamic characteristics of the aircraft control surface, determining control surface boundary constraint conditions, equality constraint conditions and inequality constraint conditions, and establishing a mixed multi-objective optimization function:
in the formula (2), min gamma indicates that a plurality of objective functions reach the optimum simultaneously; gl(δ) p inequality constraints representing the steering surface; h isk(δ) q equality constraints representing δ; deltamin、δmaxThe boundary values of the steering control surface are indicated.
Step four, converting the mixed multi-objective function into a single-objective optimization function by using a linear weighted sum method, solving the problem that the mixed multi-objective optimization problem cannot solve the global optimum value:
in the formula (3), wiRepresenting the weight coefficient of the ith objective function and converting the manipulated boundary constraints into inequality constraints, namely:
the optimization function can be expressed as:
step five, designing a preference matrix PoConstraint wiAnd using an optimization algorithm to compare wiAnd delta are simultaneously optimized on line by motionChange of state wiAnd solving the multi-objective optimization problem to enable each objective function to obtain an optimal solution at the same time, so that the design requirement of the flight task preference of the aircraft is met.
And sixthly, designing a self-adaptive particle swarm algorithm and performing online optimization, solving the control plane delta, and completing control plane distribution of the aircraft redundancy system.
Further, the preference matrix P in step fiveoThe specific design method is as follows:
step 5.1, according to the importance degree of the flight mission, performing pairwise judgment on the n target functions respectively, and designing a judgment matrix according to the importance degree;
suppose fiRelative to fjThe degree of importance of isijThe parameters were designed according to table 1.
TABLE 1 significance index of decision matrix
Further, a decision matrix can be obtained as:
and 5.2, carrying out consistency analysis on the judgment matrix A to ensure the harmony of the importance degree of each optimized objective function.
Step 5.3, designing a preference matrix P according to the judgment matrix AoWith a constraint weight coefficient wiThe value range of (A):
a is known from the judgment matrix Aii＝1，aij＝1/aji，fiAnd fjThe importance relationship of can be represented by aij′＝aij(j > i) so that wiAnd wjCan be expressed as wi/a′ij-wj≧ 0, its matrix representational shapeThe formula is as follows:
further, the specific method for analyzing the consistency of the judgment matrix in the step 5.2 is as follows:
let M be [ M ]ij]n×n，D＝[d1,d2,…,dn]，
The derivation matrix of the design judgment matrix is as follows:
if all elements of the H matrix are 1, A meets the requirement of consistency, but when the method is applied to a practical system for numerical simulation analysis, all elements of H cannot be guaranteed to be 1. Therefore, the present invention applies the variance s2Judging the degree of deviation of each element of the H matrix from 1, and when the design requirement is met, namely s2If the sum of.
Where tol represents the minimum error of each element from 1, the variance s2Can be expressed as:
further, the specific design steps of the adaptive particle swarm algorithm in the sixth step include:
step 6.1, determining an adaptive function minf (X), a decision variable X ═ W, δ and constraint conditions of the particle swarm algorithm;
the optimization objective function can be expressed as:
further, the method can be obtained as follows:
step 6.2, initializing a particle swarm algorithm, comprising the following steps: the particle swarm size N is N + d and the maximum inertia weight wmaxMinimum inertial weight wminMaximum number of iterations TmaxLearning factor c1And c2Minimum global error gradient tau, maximum convergence speed v of particle swarmmaxAnd an initial particle position x (t) ([ x ])1,x2… xm… xN]And initial particle velocity v (t) ([ v)1v2… vm… vN]. Where t represents the number of iterations.
And 6.3, substituting the initial state X (t) into an adaptive function minf (X), calculating an adaptive value corresponding to each group of particles, and further obtaining an individual optimal value pmb (t) of the particles and a global optimal value pb (t).
Step 6.4, designing a self-adaptive learning evaluation function rv (X), and correcting the convergence rate of the particles to enable the particles near the constraint condition to be close to a feasible domain, thereby fully utilizing the boundary information of the particles;
6.5, updating the speed vm (t +1) and the position xm (t +1) according to the particle group speed and position evolution formula;
the updating formula of the self-adaptive particle swarm algorithm is as follows:
in the formula (12), vm(t)、vm(t +1) is the speed of the mth individual in the tth iteration and the t +1 th iteration, respectively, c1Learning factors for individuals, c2Is a global learning factor, c1＝c2∈[0,4]，r1、r2Respectively an individual learning evaluation scale factor and a global learning evaluation scale factor, pmb(t) is the local optimum position of the mth individual in the tth iteration, Rv(X) is an adaptive evaluation function, pb(t) global maximum in the t-th iteration for all individualsPreferred position, xm(t)、xm(t +1) is the position of the mth individual in the tth iteration and the t +1 th iteration, respectively.
Step 6.6, bringing the particle swarm X (t +1) updated by the t iteration into a fitness function, calculating an adaptive value, and updating an individual optimal value pmb(t +1), global optimum pb(t+1)。
Step 6.7, repeating the steps 6.4 to 6.6 until the global optimal value pb(T) satisfies a minimum global error gradient τ or a number of iterations Tmax。
Further, the evaluation function R is adaptively learned in step 6.4vThe method for designing (X) and correcting the convergence rate comprises the following steps:
designing a particle swarm violation performance index function R (X) according to the constraint condition of the hybrid multi-objective optimization problem;
if R (x (t)) is 0, it indicates that the particle satisfies the constraint condition, and is defined as a feasible particle, and if R (x (t)) is not 0, the particle does not satisfy the constraint condition, and is defined as an infeasible particle.
According to the violation degree of the particle swarm, standardizing the violation performance index function R (X) of the particle swarm to obtain the self-adaptive learning evaluation function Rv(X)；
By adopting the technical scheme, the invention has the following beneficial effects:
(1) the aircraft redundancy multi-objective control method based on the mixed multi-objective PSO algorithm of the preference matrix analyzes the problem of aircraft control redundancy with multi-objective flight tasks, converts the problem of control redundancy into the problem of mixed multi-objective optimization, solves the problem of aircraft multi-objective flight control redundancy with control surface constraint by on-line optimizing, completes on-line control distribution of control surface deflection, reduces the difficulty of aircraft controller design, and can be applied to control systems with control redundancy such as control reconstruction and the like.
(2) The invention provides a mixed multi-target self-adaptive particle swarm optimization strategy based on a preference matrix, can convert a complex multi-objective optimization problem into a single-objective optimization problem, solves the problems that the multi-objective optimization problem is complex and the global optimal solution is difficult to solve directly, designs a preference matrix for constraining objective function weight coefficients based on a judgment matrix, determines the importance degree of each optimization objective by utilizing a consistency judgment matrix, constrains the value range of the weight coefficients by utilizing the preference matrix, and the optimization algorithm is utilized to obtain the optimal weight coefficient, thereby avoiding the error caused by personal experience design weight coefficient, ensuring that a plurality of optimized performance indexes reach the optimal simultaneously on the basis of meeting the preference requirement of the optimization result, the method can simultaneously meet the task preference requirement, and is suitable for the hybrid multi-objective optimization problem with higher solution precision requirement and complex optimization performance index importance degree.
(3) The invention provides a particle swarm algorithm based on an evaluation function of adaptive learning, which can be used for solving a target optimization problem with constraint. The self-adaptive learning evaluation function of the algorithm does not need to design penalty factors according to personal experience, the problem that the penalty factors of the penalty functions are difficult to design is solved, the value of the function can be dynamically adjusted according to the iteration result of the particle swarm algorithm, the evaluation function is used for optimizing the position and speed evolution formula of the particle swarm, particle information near the particle swarm constraint boundary can be fully utilized, the precision and the optimizing speed of the algorithm are improved, and the good real-time performance of an aircraft control system is guaranteed.
Drawings
FIG. 1 is a flow chart of a hybrid multi-objective adaptive particle swarm optimization strategy based on a preference matrix according to the present invention.
FIG. 2 is a flow chart of a particle swarm algorithm of the present invention.
Fig. 3(a), 3(b), and 3(c) are graphs illustrating the relationship between the longitudinal velocity, the lateral velocity, and the vertical velocity of the hybrid rotorcraft in the simulated transition flight mode and the time when the hybrid rotorcraft performs the velocity command tracking according to the embodiment of the present invention.
Fig. 4(a), 4(b), and 4(c) are graphs of the relationship between the pitch angle, yaw angle, and roll angle of the compound rotorcraft in the simulated transitional flight mode and the time when the compound rotorcraft performs speed command tracking according to the embodiment of the present invention.
The labels in the figure are: rad-radians (units of angle); time-time; s-seconds (units of time); m-meters (length units); u-longitudinal speed; v-transverse velocity; w-vertical velocity;
-a pitch angle; theta-yaw angle; psi-roll angle.
Detailed Description
The technical scheme of the invention is explained in detail in the following with reference to the attached drawings.
The invention discloses a preference matrix-based aircraft redundancy system multi-objective control allocation strategy, which is shown in FIG. 1 and comprises the following six steps.
Analyzing the control surface characteristics of an aircraft redundancy system, and determining the numerical relationship between an aircraft control surface and a virtual control instruction;
the general aircraft control plane is complex and has dimension larger than that of a virtual control instruction, control redundancy exists, dynamic balancing and linearization analysis can be carried out through aircraft balance points, and the relation between the virtual control instruction v and the control plane delta is obtained as follows:
v＝Bδ (1)，
in the formula (1), δ ═ δ [ δ ]1,δ2,…,δd]Representing the d-dimension control surface of the aircraft, and B is a control distribution efficiency matrix.
Step two, analyzing the flight environment and the flight task of the aircraft, determining the task target of the aircraft and designing a target function f1(δ),f2(δ),...,fn(δ)。
Analyzing the dynamic characteristics of the control surface of the aircraft, determining boundary constraint conditions, equality constraint conditions and inequality constraint conditions of the control surface, and establishing a mixed multi-objective optimization function;
in the formula (2), min gamma indicates that a plurality of objective functions reach the optimum simultaneously; gl(δ) p inequality constraints representing the steering surface; h isk(δ) q equality constraint constraints δ representing δmin，δmaxThe boundary values of the steering control surface are indicated.
Converting the mixed multi-objective function into a single-objective optimization function by using a linear weighted sum method, and solving the problem that the mixed multi-objective optimization problem cannot solve the global optimum value;
wherein, wiRepresenting the weight coefficients of the ith objective function. And converting the manipulated boundary constraints into inequality constraints, namely:
the optimization function can be expressed as:
step five, designing a preference matrix PoConstraint wiAnd using an optimization algorithm to compare wiAnd delta are simultaneously optimized on line by dynamically changing wiAnd solving the multi-objective optimization problem to enable each objective function to obtain an optimal solution at the same time, so that the design requirement of the flight task preference of the aircraft is met.
Step 5.1, according to the importance degree of the flight mission target, judging every two of the n target functions respectively, and designing a judgment matrix according to the importance degree;
suppose fiRelative to fjThe degree of importance of isijThe parameters were designed according to table 1.
TABLE 1 significance index of decision matrix
| fi/fj | aij | fi/fj | aij |
| Of |
1 | Of some importance | 7 |
| Of |
3 | Of great importance | 9 |
| Is a little bit important | 5 | Of utmost importance | 11 |
The decision matrix can be found to be:
step 5.2, carrying out consistency analysis on the judgment matrix A to ensure the harmony of the importance degree of each optimized objective function;
let M be [ M ]ij]n×n，D＝[d1,d2,…,dn]，
The derivation matrix of the design judgment matrix is as follows:
if all elements of the H matrix are 1, A meets the requirement of consistency, but when the method is applied to a practical system for numerical simulation analysis, all elements of H cannot be guaranteed to be 1. Therefore, the present invention applies the variance s2Judging the degree of deviation of each element of the H matrix from 1, and when the design requirement is met, namely s2If the sum of.
Where tol represents the minimum error of each element from 1, the variance s2Can be expressed as:
step 5.3, designing a preference matrix P according to the judgment matrix AoWith a constraint weight coefficient wiThe value range of (a);
a is known from the judgment matrix Aii＝1，aij＝1/aji，fiAnd fjThe importance relationship of can be represented by aij′＝aij(j > i) so that wiAnd wjCan be expressed as wi/a′ij-wjAnd the matrix expression is that the matrix expression is greater than or equal to 0:
and sixthly, designing a self-adaptive particle swarm algorithm and performing online optimization as shown in FIG. 2, solving the control plane delta, and completing control plane allocation of the aircraft redundancy system.
Step 6.1, determining an adaptive function min f (X) of the particle swarm algorithm, wherein a decision variable X is [ W, delta ] and a constraint condition;
the optimization objective function can be expressed as:
further, the method can be obtained as follows:
step 6.2, initializing a particle swarm algorithm, wherein the particle swarm size N is N + d, and the maximum inertia weight wmaxMinimum inertial weight wminMaximum number of iterations TmaxLearning factor c1，c2Minimum global error gradient τ, maximum convergence velocity v of the particle swarmmaxInitial particle initial position x (t) ([ x ])1,x2… xm… xN]And initial particle velocity v (t) ([ v)1v2… vm… vN]. Where t represents the number of iterations.
Step 6.3, substituting the initial state X (t) into an adaptive function minf (X), calculating an adaptive value corresponding to each group of particles, and further obtaining an individual optimal value p of the particlesmb(t), global optimum pb(t)
Step 6.4, designing an adaptive learning evaluation function Rv(X) correcting the convergence rate of the particles so that the particles near the constraint condition can approach the feasible region, thereby making full use of the particle boundary information.
Designing a particle swarm violation performance index function R (X) according to the constraint condition of the hybrid multi-objective optimization problem;
if r (x) ≠ 0, it means that the particle satisfies the constraint condition and is defined as a feasible particle, and if r (x) ≠ 0, it does not satisfy the constraint condition and is defined as an unfeasible particle.
According to the particlesStandardizing the particle swarm violation performance index function R (X) to obtain the self-adaptive learning evaluation function Rv(X)；
Step 6.5, updating the velocity v according to the particle group velocity and the position evolution formulam(t +1) and position Xid(t +1), the updating formula of the adaptive particle swarm algorithm is as follows:
in the formula (14), vm(t)、vm(t +1) is the speed of the mth individual in the tth iteration and the t +1 th iteration, respectively, c1Learning factors for individuals, c2Is a global learning factor, c1＝c2∈[0,4]，r1、r2Respectively an individual learning evaluation scale factor and a global learning evaluation scale factor, pmb(t) is the local optimum position of the mth individual in the tth iteration, Rv(X) is an adaptive evaluation function, pb(t) is the global optimum position, x, of all individuals in the t-th iterationm(t)、xm(t +1) is the position of the mth individual in the tth iteration and the t +1 th iteration, respectively.
Step 6.6, substituting X (t +1) into the fitness function, calculating an adaptive value, and updating the individual optimal value pmb(t +1), global optimum pb(t+1)；
Step 6.7, repeating the steps 6.4 to 6.6 until the global optimal value pb(T) satisfies a minimum global error gradient τ or a number of iterations TmaxAnd the deflection of each control plane can be obtained, and control and distribution of the control planes of the aircraft are completed.
According to the method, the minimum manipulated variable deflection, the minimum instruction tracking error and the maximum control distribution efficiency are used as optimization performance indexes, speed instruction tracking simulation is carried out on a transition mode of the composite rotary wing aircraft under a mixed multi-target optimization control distribution strategy based on a classical particle swarm optimization and a mixed multi-target optimization control distribution strategy based on an improved particle swarm optimization, a forward flight instruction with the initial speed of 40m/s and the tracking speed of 70m/s is selected, and the simulation result is shown in fig. 3 and 4.
Wherein, fig. 3 is a change curve of the flight speed of the composite rotary wing aircraft along with time, as can be seen from fig. 3(a), the control distribution strategy based on the improved particle swarm algorithm needs about 6s to complete the speed instruction tracking, while the control distribution strategy based on the classical particle swarm algorithm needs about 14s to complete, which is about 2 times of the former; as can be seen from fig. 3(a), 3(b), and 3(c), under the improved particle swarm optimization, the fluctuation of the speed variation curve of the compound rotorcraft is small, which indicates that the improved particle swarm optimization has higher search speed and higher solution accuracy.
Fig. 4 is a time-dependent change curve of the attitude angle of the composite rotary wing aircraft, and as can be seen from fig. 4(a), 4(b), and 4(c), under the control allocation strategy based on the improved particle swarm algorithm, the jitter of the attitude angle is small, which indicates that the stability of the composite rotary wing aircraft is high. The mixed multi-objective self-adaptive particle swarm optimization strategy based on the preference matrix can be applied to a complex system with a multi-objective optimization problem and high requirements on time and precision.
Claims (8)
1. The aircraft redundancy control method of the mixed multi-objective PSO algorithm based on the preference matrix is characterized by comprising the steps of constructing a mixed multi-objective optimization problem comprising a mixed multi-objective optimization function, an operating control surface boundary constraint, a virtual control instruction and an operating control surface numerical value constraint, carrying out linear weighted summation on the mixed multi-objective optimization function to convert the mixed multi-objective optimization problem into a single-objective optimization problem, establishing a judgment matrix according to the importance of each objective function relative to other objective functions, establishing the preference matrix according to the judgment matrix to construct the constraint of an objective function weight coefficient, bringing the constraint of the objective function weight coefficient into the single-objective optimization problem, and obtaining an optimal solution by carrying out online optimization on the weight coefficient and the operating control surface.
2. The aircraft redundancy control method of the preference matrix-based hybrid multi-objective PSO algorithm according to claim 1, wherein the method for establishing the decision matrix according to the importance of each objective function relative to other objective functions comprises: establishing an importance index table, searching the importance index table according to the importance of each target function relative to other target functions, determining the value of each element in the judgment matrix, then performing consistency judgment on the judgment matrix, and reconstructing the judgment matrix when the judgment matrix does not meet the consistency requirement.
3. The aircraft redundancy control method of the preference matrix-based hybrid multi-objective PSO algorithm according to claim 1, wherein the objective function weight coefficient constraint constructed by establishing the preference matrix according to the judgment matrix is as follows:
wi/a'ij-wj≥0，aij'＝aij(j＞i)，
4. The aircraft redundancy control method of the preference matrix-based hybrid multi-objective PSO algorithm according to claim 1, wherein a particle swarm algorithm is adopted to optimize a weight coefficient and a control surface on line, the weight coefficient and the control surface are taken as decision variables, an adaptive function is constructed according to a linear weighted sum hybrid multi-objective optimization function, iteration is started after a population is initialized, the particle swarm updated in each iteration is taken into the adaptive function to calculate an adaptive value and update an individual optimal value and a global optimal value, the convergence speed of the particle swarm is corrected according to adaptive learning evaluation after updating the individual optimal value and the global optimal value, and optimization is finished when the global optimal value meets a global error gradient or reaches the maximum iteration number.
5. The aircraft redundancy control method of the preference matrix-based hybrid multi-target PSO algorithm according to claim 2, characterized in that the method for performing consistency judgment on the judgment matrix is as follows: constructing a derived matrix H of the judgment matrix A by using the variance s2Judging the deviation degree tol of each element of the derived matrix from 1, and judging the matrix at s2When the total mass is less than tol, the consistency is satisfied,
a11is the importance index of the 1 st objective function relative to the 1 st objective function, a1nIs the importance index of the 1 st objective function relative to the n-th objective function, an1Is the importance index of the nth objective function relative to the 1 st objective function, annIs an importance index of the nth objective function relative to the nth objective function, aijIs the importance index of the ith objective function relative to the jth objective function.
6. The aircraft redundancy control method of the preference matrix-based hybrid multi-objective PSO algorithm according to claim 4, characterized in that the optimization problem of online optimization of the weight coefficients and the control surface by the particle swarm optimization is as follows:
x is a decision variable, f (X) is an adaptive function, gl(X) p +2d inequality constraints, h, for the decision variablesk(X) q +1 equality constraints for decision variables, wiIs the weight coefficient of the ith objective function, W is the weight coefficient matrix, PoIs a preference matrix.
7. The aircraft redundancy control method of the preference matrix-based hybrid multi-objective PSO algorithm according to claim 4, characterized in that the adaptive learning evaluation function Rv(X) is:
8. the aircraft redundancy control method of the preference matrix-based hybrid multi-objective PSO algorithm according to claim 7, wherein the expressions for updating the individual optimal values and the global optimal values are:
vm(t)、vm(t +1) is the speed of the mth individual in the tth iteration and the t +1 th iteration, respectively, c1Learning factors for individuals, c2Is a global learning factor, c1＝c2∈[0,4]，r1、r2Respectively an individual learning evaluation scale factor and a global learning evaluation scale factor, pmb(t) is the local optimum position of the mth individual in the tth iteration, pb(t) is the global optimum position, x, of all individuals in the t-th iterationm(t)、xm(t +1) is the position of the mth individual in the tth iteration and the t +1 th iteration, respectively.
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| CN112985412A (en) * | 2021-03-11 | 2021-06-18 | 北京理工大学 | Formation optimization method for co-location of multiple unmanned aerial vehicles |
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