Using K-T optimality condition of nonsmooth optimization, we establish two equivalent systems of the nonsmooth equations for the constrained minimax problem directly. Then generalized Newton methods are applied to so...Using K-T optimality condition of nonsmooth optimization, we establish two equivalent systems of the nonsmooth equations for the constrained minimax problem directly. Then generalized Newton methods are applied to solve these systems of the nonsmooth equations. Thus a new approach to solving the constrained minimax problem is developed.展开更多
A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct t...A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged Ito stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs （HJI） equation. Numerical results for a controlled and stochastically excited DulTlng oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.展开更多
Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, ...Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, opti-mal estimation leads to a simple solution. LQL control scheme, is further discussed to make it rational in the actual application.展开更多
Due to the problems of few fault samples and large data fluctuations in the blast furnace(BF)ironmaking process,some transfer learning-based fault diagnosis methods are proposed.The vast majority of such methods perfo...Due to the problems of few fault samples and large data fluctuations in the blast furnace(BF)ironmaking process,some transfer learning-based fault diagnosis methods are proposed.The vast majority of such methods perform distribution adaptation by reducing the distance between data distributions and applying a classifier to generate pseudo-labels for self-training.However,since the training data is dominated by labeled source domain data,such classifiers tend to be weak classifiers in the target domain.In addition,the features generated after domain adaptation are likely to be at the decision boundary,resulting in a loss of classification performance.Hence,we propose a novel method called minimax entropy-based co-training(MMEC)that adversarially optimizes a transferable fault diagnosis model for the BF.The structure of MMEC includes a dual-view feature extractor,followed by two classifiers that compute the feature's cosine similarity to representative vector of each class.Knowledge transfer is achieved by alternately increasing and decreasing the entropy of unlabeled target samples with the classifier and the feature extractor,respectively.Transfer BF fault diagnosis experiments show that our method improves accuracy by about 5%over state-of-the-art methods.展开更多
As computers have become faster at performing computations over the decades, algorithms to play games have also become more efficient. This research paper seeks to see how the performance of the Minimax search evolves...As computers have become faster at performing computations over the decades, algorithms to play games have also become more efficient. This research paper seeks to see how the performance of the Minimax search evolves on increasing Connect-4 grid sizes. The objective of this study is to evaluate the effectiveness of the Minimax search algorithm in making optimal moves under different circumstances and to understand how well the algorithm scales. To answer this question we tested and analyzed the algorithm several times on different grid sizes with a time limit to see its performance as the complexity increases, we also looked for the average search depth for each grid size. The obtained results show that despite larger grid sizes, the Minimax search algorithm stays relatively consistent in terms of performance.展开更多
The article is devoted to the discussion of the possibilities of approbation of one of the probabilistic methods of verification of evaluation works-the minimax method or the method of establishing the minimum risk of...The article is devoted to the discussion of the possibilities of approbation of one of the probabilistic methods of verification of evaluation works-the minimax method or the method of establishing the minimum risk of making erroneous diagnoses of the instability of the planetary boundary layer of air.Within the framework of this study,the task of probabilistic forecasting of diagnostic parameters and their combinations,leading in their totality to the formation of an unstable state of the planetary boundary layer of the atmosphere,was carried out.It is this state that,as shown by previous studies,a priori contribution to the development of a number of weather phenomena dangerous for society(squalls,hail,heavy rains,etc.).The results of applying the minimax method made it possible to identify a number of parameters,such as the intensity of circulation,the activity of the Earth’s magnetosphere,and the components of the geostrophic wind velocity,the combination of which led to the development of instability.In the future,it is possible to further expand the number of diagnosed parameters to identify more sensitive elements.In this sense,the minimax method,the usefulness of which is shown in this study,can be considered as one of the preparatory steps for the subsequent more detailed method for forecasting individual hazardous weather phenomena.展开更多
文摘Using K-T optimality condition of nonsmooth optimization, we establish two equivalent systems of the nonsmooth equations for the constrained minimax problem directly. Then generalized Newton methods are applied to solve these systems of the nonsmooth equations. Thus a new approach to solving the constrained minimax problem is developed.
基金the National Natural Science Foundation of China (No. 10772159)the Specialized Research Fund for DoctorProgram of Higher Education of China (No. 20060335125) theNatural Science Foundation of Zhejiang Province (No. Y607087),China
文摘A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged Ito stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs （HJI） equation. Numerical results for a controlled and stochastically excited DulTlng oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.
文摘Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, opti-mal estimation leads to a simple solution. LQL control scheme, is further discussed to make it rational in the actual application.
基金supported in part by the National Natural Science Foundation of China(61933015)in part by the Central University Basic Research Fund of China under Grant K20200002(for NGICS Platform,Zhejiang University)。
文摘Due to the problems of few fault samples and large data fluctuations in the blast furnace(BF)ironmaking process,some transfer learning-based fault diagnosis methods are proposed.The vast majority of such methods perform distribution adaptation by reducing the distance between data distributions and applying a classifier to generate pseudo-labels for self-training.However,since the training data is dominated by labeled source domain data,such classifiers tend to be weak classifiers in the target domain.In addition,the features generated after domain adaptation are likely to be at the decision boundary,resulting in a loss of classification performance.Hence,we propose a novel method called minimax entropy-based co-training(MMEC)that adversarially optimizes a transferable fault diagnosis model for the BF.The structure of MMEC includes a dual-view feature extractor,followed by two classifiers that compute the feature's cosine similarity to representative vector of each class.Knowledge transfer is achieved by alternately increasing and decreasing the entropy of unlabeled target samples with the classifier and the feature extractor,respectively.Transfer BF fault diagnosis experiments show that our method improves accuracy by about 5%over state-of-the-art methods.
文摘As computers have become faster at performing computations over the decades, algorithms to play games have also become more efficient. This research paper seeks to see how the performance of the Minimax search evolves on increasing Connect-4 grid sizes. The objective of this study is to evaluate the effectiveness of the Minimax search algorithm in making optimal moves under different circumstances and to understand how well the algorithm scales. To answer this question we tested and analyzed the algorithm several times on different grid sizes with a time limit to see its performance as the complexity increases, we also looked for the average search depth for each grid size. The obtained results show that despite larger grid sizes, the Minimax search algorithm stays relatively consistent in terms of performance.
文摘The article is devoted to the discussion of the possibilities of approbation of one of the probabilistic methods of verification of evaluation works-the minimax method or the method of establishing the minimum risk of making erroneous diagnoses of the instability of the planetary boundary layer of air.Within the framework of this study,the task of probabilistic forecasting of diagnostic parameters and their combinations,leading in their totality to the formation of an unstable state of the planetary boundary layer of the atmosphere,was carried out.It is this state that,as shown by previous studies,a priori contribution to the development of a number of weather phenomena dangerous for society(squalls,hail,heavy rains,etc.).The results of applying the minimax method made it possible to identify a number of parameters,such as the intensity of circulation,the activity of the Earth’s magnetosphere,and the components of the geostrophic wind velocity,the combination of which led to the development of instability.In the future,it is possible to further expand the number of diagnosed parameters to identify more sensitive elements.In this sense,the minimax method,the usefulness of which is shown in this study,can be considered as one of the preparatory steps for the subsequent more detailed method for forecasting individual hazardous weather phenomena.
