CN116861792B - CAID power learning model construction method based on incremental network - Google Patents
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Abstract
The invention discloses a CAID power learning model construction method based on an incremental network, which comprises the steps of firstly, establishing a CAID dynamics model, determining a profit matrix and a fitness function, secondly, establishing a student power model with an incremental network generation algorithm, thirdly, establishing a power learning model considering that students are affected by multiple unknown nonlinear environments, fourthly, introducing an incremental network with dynamic weight and teacher guidance to deal with the environmental influence, and fifthly, using a Lyapunov function to analyze and verify the convergence of the CAID dynamics model; the algorithm of the CAID power learning model constructed by the invention generates an effective communication network based on information convergence among students so as to improve classroom efficiency, and the model has multiple layers of nonlinearities, simulates the environmental influence of students, and effectively reflects various unknown nonlinear environmental influences.
Description
Technical Field
The invention relates to the technical field of machine learning, in particular to a CAID power learning model construction method based on an incremental network.
Background
The learning mode emphasizes the cooperation, interaction and communication among students, rather than relying on the traditional one-way teacher-student relationship to conduct classroom teaching; in the learning mode, each student can play own advantages, benefit from experience and knowledge of other people, deepen own understanding of learning contents by teaching other people, and the peer learning is widely applied in the education field, especially the higher education field; the student learning system can promote communication and interaction among students, strengthen autonomous learning and criticizing thinking capability of the students, improve learning efficiency and achievement of the students, and can be applied to various fields such as workplaces, community organizations and the like besides school application of the students to promote collective learning and knowledge sharing.
In the existing and previous research, a method for improving student performance based on survey data analysis is provided by a learner, and a method for modeling student behavior under noise conditions is also provided by the learner, so that all student models are consistent in the mathematical modeling process at present, which is not in accordance with the actual situation, because each student in reality is very unique, meanwhile, the learning effect in a classroom is influenced by not only a teacher, but also various aspects of environment, and how to simulate the environment by using a mathematical method is also a problem to be considered, and therefore, the invention provides a CAID dynamic learning model construction method based on an incremental network to solve the problem in the prior art.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a CAID power learning model construction method based on an incremental network, wherein an algorithm of the CAID power learning model constructed by the CAID power learning model construction method based on the incremental network generates an effective communication network based on information convergence among students so as to improve classroom efficiency, and the model has multiple layers of nonlinearities, simulates environmental influences suffered by students and effectively reflects various unknown nonlinear environmental influences.
In order to achieve the purpose of the invention, the invention is realized by the following technical scheme: a CAID power learning model construction method based on an incremental network comprises the following steps:
step one, establishing CAID dynamics models based on different environments, and determining a profit matrix and an adaptability function of the models;
step two, establishing a student power model with an incremental network generation algorithm;
step three, establishing a dynamic learning model considering that students are affected by multiple unknown nonlinear environments;
introducing an incremental network with dynamic weight and teacher guidance to the model in the step three to cope with environmental influence;
and fifthly, analyzing and verifying the convergence of the CAID dynamic model by using a Lyapunov function based on an incremental network generation algorithm and a plurality of unknown nonlinear environmental influences.
The further improvement is that: the profit matrix in the first step is expressed as follows:
wherein mu 0 、μ 1 、μ 2 、μ 3 Representing the benefit of each student in a traditional evolutionary dynamics model, the fitness function for the strategy selected by student i is represented by
Wherein x is i Representing the strategy corresponding to student i, x i ∈[0，1]I e {1,2,., N) represents students, x i When=0, traitor is represented, x i When=1, this means complete cooperation.
The further improvement is that: in the incremental network generation algorithm of the second step, the network which is disconnected from the connection and the weak connection is converted into the network which is strongly connected, specifically, the undirected graph G is split into a plurality of strongly connected components by using a strong component algorithm TarjanSCC, and for each pair of strongly connected components [ (S) i ，S j )]If S i Cannot reach, then from S j At least one node and S i And adds a directed edge between them, repeating this step until all strongly connected components are connected to each other.
The further improvement is that: the power learning model in the third step is represented by the following formula:
wherein p is ij To switch to the probability of a proximity policy, f i Unknown nonlinear environmental influence, f, experienced by unmanned aerial vehicle i i ＝[sinxi，cos x i ，...]Is composed of multiple nonlinear functions, a ij Is an element in the undirected graph G adjacency matrix, deg (v i ) The degree of the undirected graph.
The further improvement is that: in the fourth step, the dynamic learning model after the incremental network is introduced to influence the environment is represented by the following formula:
wherein eta i The influence caused by the optimal instruction of the teacher is represented, the optimal level of the instruction of the teacher is obtained by utilizing a radial basis function neural network fitting method,beta represents a constant greater than 0.
The further improvement is that: the radial basis function neural network is fitted specifically by the following formula:
the input vector is x= [ X ] 1 ，…，x n ]Weight vector w= [ W ] 1 ，…，W N ]From this, a suitable approximation is represented by the formula W (T) Transpose of W
Wherein the method comprises the steps ofRepresenting the estimated value for the weight matrix, the estimated error is represented by the following formula
The estimation error of the above-mentioned obtained function is represented by the following formula
Wherein the method comprises the steps ofRepresenting a gaussian function, ζ represents the fitting error of a nonlinear function.
The further improvement is that: in the fifth step, the following two sets of quotients are introduced when the CAID dynamic model convergence analysis of the incremental network generation algorithm is performed:
if graph G k For strong connectivity, there is one spanning tree and the rank of Lk is N-1;
if the rank of L is N-1, then 1 alpha is the unique vector in the null space of L, and there is a steady state x for a particular constant alpha s ＝1α；
Wherein L is k ＝L(G k ) Representation of diagram G k And x (t) represents the state of the system, and can be calculated by the following formula.
The further improvement is that: in the fifth step, an assumption is introduced when performing a CAID kinetic model convergence analysis under a plurality of unknown nonlinear environmental influences:
assume 1 the unknown ideal neural network weight matrix W is represented by W F ≤W M Is the boundary;
suppose 2, neural network activation functionBounded, there is +.>
Theorem is introduced in analysis: assuming the system given in 1, making the communication map strongly connected; the optimal level of instruction for selecting the teacher is represented by
While the weight matrix update rate is represented by
The systemConvergence, where e i And e j Representing the errors, w, of student i and student j, respectively ij Is an element in the unknown weight matrix NN.
The beneficial effects of the invention are as follows: the algorithm of the CAID power learning model constructed by the invention generates an effective communication network based on information convergence among students so as to improve classroom efficiency, and the model has multiple layers of nonlinearities, simulates the environmental influence of students, and effectively reflects various unknown nonlinear environmental influences;
meanwhile, the Lyapunov function is designed to analyze and verify the convergence of the model, and mathematics prove that the CAID power learning model is stable, so that the model can be ensured to be converged to a balance state under any condition, and phenomena such as chaos or oscillation and the like of the model can be avoided, and the model is not influenced by parameters, so that the model is more applicable.
Drawings
FIG. 1 is a flow chart of a method according to embodiment 1 of the present invention.
Fig. 2 is a graph showing the iterative result of the caid model in the unconnected network in embodiment 2 of the present invention.
Fig. 3 is a graph showing the iterative result of the caid model in the strong communication network according to embodiment 2 of the present invention.
Fig. 4 is a graph showing the iterative result of the CAISD model in the unconnected network in embodiment 2 of the present invention.
Fig. 5 is a graph showing the iterative result of the CAISD model in the strong communication network in embodiment 2 of the present invention.
Fig. 6 is a graph of the iteration of the caid in the incremental network without teacher guidance for n=20 in example 2 of the present invention.
Fig. 7 is a graph of the iteration of the caid under a teacher-guided incremental network for n=20 in example 2 of the present invention.
Fig. 8 is a graph of the iteration of CAISD in the incremental network without teacher guidance at n=20 in example 2 of the present invention.
Fig. 9 is a graph of the iteration of CAISD under a teacher-guided incremental network for n=20 in example 2 of the present invention.
Detailed Description
The present invention will be further described in detail with reference to the following examples, which are only for the purpose of illustrating the invention and are not to be construed as limiting the scope of the invention.
Example 1
According to the embodiment shown in fig. 1, a CAID power learning model construction method based on an incremental network is provided, which includes the following steps:
step one, establishing CAID dynamics models based on different environments, and determining a profit matrix and an adaptability function of the models;
the communication relationship between students is represented by an undirected graph g= (V, a), where v= { V 1 ，v 2 …，v N The letter "is a set of students, A.epsilon.R is an adjacency matrix if student v j With student v i If a communication relationship exists, a can be obtained ij =1 or a ij In this way, the information transfer between the classmates is abstracted into a game model, and in the traditional model, only two strategies of sharing information or not sharing information can be selected between the classmates, in the invention, x i Representing the strategy corresponding to student i, x i ∈[0，1]，i∈{1，2,., N } represents students, x i When=0, traitor is represented, x i When=1, the complete cooperation is represented, the important factor affecting the evolution dynamics is the profit matrix, which is the basis of the student selection strategy, and different choices bring different rewards.
The benefit matrix is represented as follows:
wherein mu 0 、μ 1 、μ 2 、μ 3 Representing the benefit of each student in a traditional evolutionary dynamics model, the fitness function for the strategy selected by student i is represented by
The difference in fitness function between student i and student j is expressed as Δf=f (x i )-F(x j ) According to the imitation dynamics, each student switches to an adjacent strategy with a certain probability, and the following strategy evolution rule is introduced:
where k represents the number of iterations
p ij ＝sig(β|ΔF ji |)
Students in the iteration use probability p ij Switching to an adjacent strategy;
the policy adaptation law for student i can be expressed by the following formula
Order theThe above can be simplified to->
Regarding stability, the solution is achieved by using Lyapunov function, and the dynamic model in the system is regarded asx (t) represents the state of the system, f (t, x) represents the continuous state function of the system, and there are two arguments:
1. if the balance point Lyapunov function is stable, there is one delta > 0 for all epsilon > 0, if ||x 0 Alpha < delta, there will be
2. For functionsThe energy function satisfies V (x, t) not less than 0,/and> balance pointAnd (3) stability.
Step two, establishing a student power model with an incremental network generation algorithm;
in the incremental network generation algorithm, a network which is disconnected from communication and is weakly communicated is converted into a network which is strongly communicated, specifically, an undirected graph G is split into a plurality of strongly communicated components by using a strong component algorithm TarjanSCC, and for each pair of strongly communicated components [ (S) i ，S j )]If S i Cannot reach, then from S j At least one node and S i And adds a directed edge between them, repeating this step until all strongly connected components are connected to each other.
The network generated by the above is a strong connectivity graph, and the pseudo code of the algorithm is as follows:
step three, establishing a dynamic learning model considering that students are affected by multiple unknown nonlinear environments;
the power learning model is represented by the following formula:
f i for students i to be subjected to unknown nonlinear environmental influences, while students' classroom behaviors are subjected to many factors including personal characteristics, subject factors, teaching methods, course content, classroom environments, home and social environments, etc., due to the complexity of these factors, it is difficult to give an accurate mathematical description, thus f in the CAID dynamics model i ＝[sin x i ，cos x i ，...]Is composed of a plurality of nonlinear functions, and each student randomly selects a different nonlinear function for simulation in each step in the simulation process.
Introducing an incremental network with dynamic weight and teacher guidance to the model in the step three to cope with environmental influence;
if there is a teacher-directed relationship between two students, there is a ij > 0, otherwise a ij And < 0, thereby introducing a teacher-guided incremental network with dynamic weights to cope with environmental impact, and introducing a dynamic learning model after the incremental network has the environmental impact to be represented by the following formula:
wherein eta i Representing the influence caused by the optimal instruction of the teacher, and obtaining the optimal level of the instruction of the teacher by using a radial basis function neural network (RBF-NN) fitting method;
radial basis function neural networks are a typical nonlinear modeling tool because modeling of highly uncertain and complex systems can approximate any ongoing function, fitting the optimal level of teacher guidance is represented specifically by the following equation:
the input vector is x= [ X ] 1 ，…，x n ]Weight vector w= [ W ] 1 ，…，W N ]Whereby a suitable approximation is represented by
Wherein the method comprises the steps ofRepresenting the estimated value for the weight matrix, the estimated error is represented by the following formula
The estimation error of the above-mentioned obtained function is represented by the following formula
Wherein the method comprises the steps ofRepresents a Gaussian function, ζ represents a nonlinear functionIs a fitting error of (a).
Step five, analyzing and verifying the convergence of the CAID dynamic model by using a Lyapunov function based on an incremental network generation algorithm and a plurality of unknown nonlinear environmental influences;
the system is described as if it were performing CAID dynamics model convergence analysis for incremental network generation algorithmsWherein L is k ＝L(G k ) Is a graph G k The Laplacian of (2) can be calculated from the following formula
Let α be the balance point of the power system, e be the error between the state x and the balance point α, then x (t) =α+e, then there are the following two sets of quotients:
1. if graph G k For strong communication, there is a spanning tree and L k Is N-1;
2. if the rank of L is N-1, then 1 alpha is the unique vector in the null space of L, and there is a steady state x for a particular constant alpha s ＝1α。
From 2 quotientsThus can get +.>And because e j -e i ＝x j (t)-x i (t) then there are
Wherein the method comprises the steps of
To demonstrate that this evolutionary dynamic model of N classmates is convergent, the lyapunov function is set as:
the derivative is represented by
From the following componentsCan be rewritten as follows
Thus proving that the CAID dynamics model for limited learning capacity is convergent.
In performing CAID dynamics model convergence analysis under multiple unknown nonlinear environmental influences, it is involved inWill not meet-> The error cannot be calculated using x (t) =α+e, so the error of student i is set to +.> Policy value representing maximum fitness in student i's neighborhood, with +/for each time t>If the relationship between students is completely connected, there is +.> Thereby obtaining the following formula
The following introduction assumes:
assume 1 the unknown ideal neural network weight matrix W is represented by W F ≤W M Is the boundary;
suppose 2, neural network activation functionBounded, there is +.>
Theorem is introduced in analysis: assuming the system given in 1, making the communication map strongly connected; the optimal level of instruction for selecting the teacher is represented by
While the weight matrix update rate is represented by
The systemAnd (5) convergence.
In order to prove the convergence of CAID dynamic models under the influence of a plurality of unknown nonlinear environments, the Lyapunov function is set as
The derivative of the function is represented by
Replacement is performed according to the following
Substituting the derivative of the function results in the following
When meeting the requirements
Can obtainThus (2)
Substitution into
If it meetsThen there is
In a corresponding manner,definitions-> The following can be obtained
Based on hypothesis 1, letThe following formula can be obtained
Thereby proving that the CAID dynamics model in the teacher-guided incremental network is convergent.
Example 2
According to the embodiment, as shown in fig. 2-9, a CAID power learning model construction method based on an incremental network is provided, a network between students is established by aiming at prisoner dilemma and snowpile dilemma respectively, and convergence verification is performed on a dynamic model of the students.
The method comprises the following steps:
step 1: randomly generating a graph G with 20 students (n=20);
step 2: the incremental network generation algorithm is used to output a strong connectivity network G', specifically as follows:
first, for the current undirected graph G, it is split into several strongly connected components using the strong component algorithm TarjanSCC. If there is no direct path between any two of these strongly communicating components, at least one directed edge is added between them, causing them to communicate with each other. Next, for each pair of strongly connected components [ (S) i ，S j )]If S i Cannot reach, then from S j At least one node and S i One node at random and add a directed edge between them. This step is repeated until all strongly connected components are connected to each other.
The pseudo code is as follows:
step 3: aiming at two specific examples of prisoner dilemma and snowpile dilemma, a student dynamics model is established, and CAID model parameters are set
Dilemma of prisoner:
caid: caid corresponds to a classical example in game theory: prisoner is dilemma. It represents a non-zero and game. This game reflects that it may be the best choice for an individual but not for a community. In the prisoner dilemma game, the best personal strategy is traitor escape. However, if all students choose to escape, then everyone's circumstances are worse, resulting in a conflict between personal interests and group interests.
The profit matrix is:
where b is the benefit the person obtains and c is the effort of the partner, satisfying b < c.
The fitness function of student i is:
the difference in fitness function between student i and student j is:
wherein: p is p ij ＝sig(β|ΔF ij )
Snow heap dilemma:
CAISD: CAISD corresponds to snow heap dilemma: the two drivers are blocked by wind and snow, the cost required for removing the snow pile to enable the road to be unobstructed is c, and the benefit brought to each person if the road is unobstructed is quantized to b. If two people shovel snow together, their benefit is r=b-c/2; if only one person shovels snow, while both persons can go home, traitors escape labor, with a yield of t=b, and a partner with a yield of s=b-c; if both people choose not to cooperate, both people are blocked by the snow heap and cannot go home, and their benefits are p=0.
The benefit matrix may be expressed as:
the fitness function of student i is:
the difference in fitness function between student i and student j is:
wherein: p is p ij ＝sig(β|ΔF ji )
CAID parameter is set to b=5, c=1, β=1
Step 4: CAID model convergence was verified on graph G and graph G', respectively:
as shown in fig. 2 of the specification, the caid model does not converge in the unconnected graph, and when the incremental network algorithm is used, a strong connected network is obtained, and the model also converges, as shown in fig. 3 of the specification.
As shown in fig. 4 of the specification, the caisd model does not converge in the unconnected graph, and when the incremental network algorithm is used, a strong connected network is obtained, and the model also converges, as shown in fig. 5 of the specification.
Step 5: verifying the role of an incremental network guided by a teacher under the influence of multiple nonlinear environments:
select f i For the unknown nonlinear environmental influence suffered by student i, f i ＝[sinx i ，cosx i ，…]Consists of a plurality of nonlinear functions, and a teacher-guided incremental network with dynamic weights is introduced to deal with environmental impact. If there is teacher-directed communication between two students, a ij <0, anti-regular a ij =0. A teacher-guided incremental network is therefore introduced to combat environmental effects.
Can be expressed as:
η i is the effect caused by the teacher's best instruction. And obtaining the optimal level of teacher guidance by using a neural network fitting method.
As shown in fig. 7 of the specification, the teacher-guided incremental network can avoid the negative impact of environmental impact in the caid that would make it difficult for the model in fig. 6 of the specification to achieve global convergence. Comparing figure 8 of the specification with figure 9 of the specification, the teacher directed incremental network may also accelerate global convergence of CAISD, further indicating the effectiveness of the teacher directed incremental network.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (5)
1. The CAID power learning model construction method based on the incremental network is characterized by comprising the following steps of:
step one, establishing CAID dynamics models based on different environments, and determining a profit matrix and an adaptability function of the models;
step two, establishing a student power model with an incremental network generation algorithm;
in the incremental network generation algorithm, the network which is disconnected from the connection and the weak connection is converted into the network with strong connection, specifically, the non-connection graph G is split into a plurality of strong connection components by using a strong component algorithm TarjanSCC, and for each pair of strong connection components [ (S) i ，S j )]If S i Cannot reach, then from S j At least one node and S i Randomly selecting a node, adding a directed edge between the nodes, and repeating the step until all the strongly connected components are mutually connected;
step three, establishing a dynamic learning model considering that students are affected by multiple unknown nonlinear environments;
the power learning model is represented by the following formula:
wherein p is ij To switch to the probability of a proximity policy, f i For the unknown nonlinear environmental influence suffered by student i, f i ＝[sinx i ，cosx i ，…]Is composed of multiple nonlinear functions, a ij Is an element in the undirected graph G adjacency matrix, deg (v i ) Degree of undirected graph;
introducing an incremental network with dynamic weight and teacher guidance to the model in the step three to cope with environmental influence;
the dynamic learning model after the incremental network is introduced to influence the environment is represented by the following formula:
wherein eta i The influence caused by the optimal instruction of the teacher is represented, the optimal level of the instruction of the teacher is obtained by utilizing a radial basis function neural network fitting method,beta represents a constant greater than 0;
and fifthly, analyzing and verifying the convergence of the CAID dynamic model by using a Lyapunov function based on an incremental network generation algorithm and a plurality of unknown nonlinear environmental influences.
2. The incremental network-based CAID power learning model building method of claim 1, wherein the profit matrix in step one is expressed as follows:
wherein mu 0 、μ 1 、μ 2 、μ 3 Representing the benefit of each student in a traditional evolutionary dynamics model, the fitness function for the strategy selected by student i is represented by
Wherein a is ij Representing elements in the undirected graph G adjacency matrix, x i And x j Representing policies corresponding to student i and student j, x i And x j All e [0,1 ]]Each of i and j is E {1,2, …, N } represents students, x i Or x j When=0, traitor is represented, x i Or x j When=1, this means complete cooperation.
3. The incremental network-based CAID power learning model building method of claim 1, wherein the fitting of the radial basis function neural network is specifically represented by the following formula:
the input vector is x= [ X ] 1 ，…，x n ]Weight vector w= [ W ] 1 ，…，W N ]From this, a suitable approximation is represented by the formula W (T) Transpose of W
Wherein the method comprises the steps ofRepresenting the estimated value for the weight matrix, the estimated error is represented by the following formula
The estimation error of the above-mentioned obtained function is represented by the following formula
Wherein the method comprises the steps ofRepresenting a gaussian function, ζ represents the fitting error of a nonlinear function.
4. The incremental network-based CAID dynamic learning model construction method according to claim 1, wherein the following two sets of quotients are introduced when the CAID dynamic model convergence analysis of the incremental network generation algorithm is performed in the fifth step:
if graph G k For strong communication, there is a spanning tree and L k Is N-1;
if the rank of L is N-1, then 1 alpha is the unique vector in the null space of L, and there is a steady state x for a particular constant alpha s ＝1α；
Wherein L is k ＝L(G k ) Representation of diagram G k And x (t) represents the state of the system, and can be calculated by the following formula.
5. The incremental network-based CAID dynamic learning model construction method according to claim 1, wherein in the fifth step, the assumption is introduced when the CAID dynamic model convergence analysis under the influence of a plurality of unknown nonlinear environments is performed:
assume 1 the unknown ideal neural network weight matrix W is represented by W F ≤W M Is the boundary;
suppose 2, neural network activation functionBounded, there is +.>
Theorem is introduced in analysis: assuming the system given in 1, making the communication map strongly connected; the optimal level of instruction for selecting the teacher is represented by
While the weight matrix update rate is represented by
The systemConvergence, where e i And e j Representing the errors, w, of student i and student j, respectively ij Eta is an element in an unknown weight matrix NN i (t) represents the influence of the teacher's best guidance at time t, and the fitting of the radial basis function neural network is approximately expressed as +.>
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6064997A (en) * | 1997-03-19 | 2000-05-16 | University Of Texas System, The Board Of Regents | Discrete-time tuning of neural network controllers for nonlinear dynamical systems |
| CN113346552A (en) * | 2021-04-19 | 2021-09-03 | 国网重庆市电力公司 | Self-adaptive optimal AGC control method based on integral reinforcement learning |
| CN114660942A (en) * | 2022-03-30 | 2022-06-24 | 南京航空航天大学 | Combined type helicopter full-mode self-adaptive control method |
| CN114675536A (en) * | 2022-03-09 | 2022-06-28 | 广州大学 | Self-adaptive width learning unknown direction control method of 2-DOF helicopter |
| CN115390445A (en) * | 2022-08-01 | 2022-11-25 | 中山大学 | Safety self-adaptive control method of multi-unmanned aerial vehicle system based on learning |
-
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- 2023-07-14 CN CN202310867062.1A patent/CN116861792B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6064997A (en) * | 1997-03-19 | 2000-05-16 | University Of Texas System, The Board Of Regents | Discrete-time tuning of neural network controllers for nonlinear dynamical systems |
| CN113346552A (en) * | 2021-04-19 | 2021-09-03 | 国网重庆市电力公司 | Self-adaptive optimal AGC control method based on integral reinforcement learning |
| CN114675536A (en) * | 2022-03-09 | 2022-06-28 | 广州大学 | Self-adaptive width learning unknown direction control method of 2-DOF helicopter |
| CN114660942A (en) * | 2022-03-30 | 2022-06-24 | 南京航空航天大学 | Combined type helicopter full-mode self-adaptive control method |
| CN115390445A (en) * | 2022-08-01 | 2022-11-25 | 中山大学 | Safety self-adaptive control method of multi-unmanned aerial vehicle system based on learning |
Non-Patent Citations (1)
| Title |
|---|
| 无人直升机的姿态增强学习控制设计与验证;安航;鲜斌;;控制理论与应用(04);全文 * |
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