In this paper, the extended affine Lie algebra sl2（Cq） is quantized from three different points of view, which produces three non-commutative and non-cocommutative Hopf algebra structures, and yields other three qua...In this paper, the extended affine Lie algebra sl2（Cq） is quantized from three different points of view, which produces three non-commutative and non-cocommutative Hopf algebra structures, and yields other three quantizations by an isomorphism of sl2 （Cq） correspondingly. Moreover, two of these quantizations can be restricted to the extended affine Lie algebra sl2（Cq）.展开更多
Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented and bounded in one o...Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented and bounded in one orientation, e.g., a strictly positive coordinate. We open discussion using canonical and affine quantizations for two simple problems so each procedure can be understood. That analysis opens a modest treatment of quantum gravity gleaned from some typical features that exhibit the profound differences between aspects of seeking the quantum treatment of Einstein’s gravity.展开更多
Quantized control systems design is motivated by the convergence of controls and communications to address modern engineering applications involving the use of information technology. This paper presents an overview o...Quantized control systems design is motivated by the convergence of controls and communications to address modern engineering applications involving the use of information technology. This paper presents an overview of recent developments on the control of linear and nonlinear systems when the control input is subject to quantization or the quantized states or outputs are used as feedback measurements. The co-existence of high-dimeasionality, quantization, nonlinearity and uncertainty poses great challenges to quantized control of nonlinear systems and thus calls for new ideas and techniques. The field of quantized nonlinear control is still at its infancy. Preliminary results in our recent work based on input-to-state stability and cyclic-small-gain theorems are reviewed. The open problems in quantized nonlinear control are also outlined.展开更多
Abstract--This paper conducts a survey on iterative learn- ing control （ILC） with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, includ...Abstract--This paper conducts a survey on iterative learn- ing control （ILC） with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, including passive and active types, can cause data loss or fragment due to various factors. Passive incomplete information refers to incomplete data and information caused by practical system limitations during data collection, storage, transmission, and processing, such as data dropouts, delays, disordering, and limited transmission bandwidth. Active incomplete information refers to incomplete data and information caused by man-made reduction of data quantity and quality on the premise that the given objective is satisfied, such as sampling and quantization. This survey emphasizes two aspects： the first one is how to guarantee good learning performance and tracking performance with passive incomplete data, and the second is how to balance the control performance index and data demand by active means. The promising research directions along this topic are also addressed, where data robustness is highly emphasized. This survey is expected to improve understanding of the restrictive relationship and trade-off between incomplete data and tracking performance, quantitatively, and promote further developments of ILC theory. Index Terms--Data dropout, data robustness, incomplete in- formation, iterative learning controi（ILC）, quantized control, sampled control, varying lengths.展开更多
针对常见雷达信号识别方法不能适应小脉宽信号识别的问题,本文提出了一种基于频谱复杂度的雷达信号调制方式识别方法。该方法通过提取信号频谱复杂度特征、信号平方频谱特征、谱峰特征以及最小二乘直线拟合方差特征,以4个特征参数为出发...针对常见雷达信号识别方法不能适应小脉宽信号识别的问题,本文提出了一种基于频谱复杂度的雷达信号调制方式识别方法。该方法通过提取信号频谱复杂度特征、信号平方频谱特征、谱峰特征以及最小二乘直线拟合方差特征,以4个特征参数为出发点,设计了一个基于频谱复杂度的树形结构流程。该流程首先对雷达信号的频谱序列进行量化,计算量化后的6种雷达信号的频谱复杂度,根据信号频谱复杂度的不同进行分类,然后根据所求特征参数对6种雷达信号进行分层次识别。仿真结果表明,基于频谱复杂度的雷达信号调制方式识别方法能够实现在窄脉冲的情况下的雷达信号调制方式识别,当信噪比大于6 d B时具有比较好的识别效果。展开更多
This paper concerns the stabilization of switched dynamical networks with logarithmic quantization couplings in a settling time.The switching sequence is constrained by hybrid dwell time. Controller is designed by usi...This paper concerns the stabilization of switched dynamical networks with logarithmic quantization couplings in a settling time.The switching sequence is constrained by hybrid dwell time. Controller is designed by using limited information. Due to the quantization and switching, traditional finite-time analysis methods cannot be utilized directly. By designing multiple Lyapunov functions and constructing comparison systems, a general criterion formulated by matrix inequalities is first given. Then specific conditions in terms of linear matrix inequalities are established by partitioning the dwell time and using convex combination technique. An optimal algorithm is proposed for the estimation of settling time. Numerical simulations are given to verify the effectiveness of the theoretical results.展开更多
In this paper, we present some modules over the rank-three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined.
This paper proposes a fault-tolerant strategy for hypersonic reentry vehicles with mixed aerodynamic surfaces and reaction control systems（RCS） under external disturbances and subject to actuator faults.Aerodynamic ...This paper proposes a fault-tolerant strategy for hypersonic reentry vehicles with mixed aerodynamic surfaces and reaction control systems（RCS） under external disturbances and subject to actuator faults.Aerodynamic surfaces are treated as the primary actuator in normal situations,and they are driven by a continuous quadratic programming（QP） allocator to generate torque commanded by a nonlinear adaptive feedback control law.When aerodynamic surfaces encounter faults,they may not be able to provide sufficient torque as commanded,and RCS jets are activated to augment the aerodynamic surfaces to compensate for insufficient torque.Partial loss of effectiveness and stuck faults are considered in this paper,and observers are designed to detect and identify the faults.Based on the fault identification results,an RCS control allocator using integer linear programming（ILP） techniques is designed to determine the optimal combination of activated RCS jets.By treating the RCS control allocator as a quantization element,closed-loop stability with both continuous and quantized inputs is analyzed.Simulation results verify the effectiveness of the proposed method.展开更多
This paper studies the identification of linear systems with quantized output observations.Recursive estimates for the linear system and the quantization thresholds are derived by the stochastic approximation algorith...This paper studies the identification of linear systems with quantized output observations.Recursive estimates for the linear system and the quantization thresholds are derived by the stochastic approximation algorithms with expanding truncations(SAAWET).Under suitable conditions,it is shown that the estimates converge to the true values almost surely.展开更多
In this paper we rewrite the gravitational constant based on its relationship with the Planck length and based on this, we rewrite the Planck mass in a slightly different form (that gives exactly the same value). In t...In this paper we rewrite the gravitational constant based on its relationship with the Planck length and based on this, we rewrite the Planck mass in a slightly different form (that gives exactly the same value). In this way we are able to quantize a series of end results in Newton and Einstein’s gravitation theories. The formulas will still give exactly the same values as before, but everything related to gravity will then come in quanta. This also gives some new insight;for example, the gravitational deflection of light can be written as only a function of the radius and the Planck length. Numerically this only has implications at the quantum scale;for macro objects the discrete steps are so tiny that they are close to impossible to notice. Hopefully this can give additional insight into how well or not so well (ad hoc) quantized Newton and Einstein’s gravitation is potentially linked with the quantum world.展开更多
In this tutorial paper, we explore the field of quantized feedback control, which has gained significant attention due to the growing prevalence of networked control systems. These systems require the transmission of ...In this tutorial paper, we explore the field of quantized feedback control, which has gained significant attention due to the growing prevalence of networked control systems. These systems require the transmission of feedback information, such as measurements and control signals, over digital networks, presenting novel challenges in estimation and control design. Our examination encompasses various topics, including the minimal information needed for effective feedback control, the design of quantizers, strategies for quantized control design and estimation,achieving consensus control with quantized data, and the pursuit of high-precision tracking using quantized measurements.展开更多
Quantized neural networks (QNNs), which use low bitwidth numbers for representing parameters and performing computations, have been proposed to reduce the computation complexity, storage size and memory usage. In QNNs...Quantized neural networks (QNNs), which use low bitwidth numbers for representing parameters and performing computations, have been proposed to reduce the computation complexity, storage size and memory usage. In QNNs, parameters and activations are uniformly quantized, such that the multiplications and additions can be accelerated by bitwise operations. However, distributions of parameters in neural networks are often imbalanced, such that the uniform quantization determined from extremal values may underutilize available bitwidth. In this paper, we propose a novel quantization method that can ensure the balance of distributions of quantized values. Our method first recursively partitions the parameters by percentiles into balanced bins, and then applies uniform quantization. We also introduce computationally cheaper approximations of percentiles to reduce the computation overhead introduced. Overall, our method improves the prediction accuracies of QNNs without introducing extra computation during inference, has negligible impact on training speed, and is applicable to both convolutional neural networks and recurrent neural networks. Experiments on standard datasets including ImageNet and Penn Treebank confirm the effectiveness of our method. On ImageNet, the top-5 error rate of our 4-bit quantized GoogLeNet model is 12.7%, which is superior to the state-of-the-arts of QNNs.展开更多
This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achi...This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.展开更多
文摘In this paper, the extended affine Lie algebra sl2（Cq） is quantized from three different points of view, which produces three non-commutative and non-cocommutative Hopf algebra structures, and yields other three quantizations by an isomorphism of sl2 （Cq） correspondingly. Moreover, two of these quantizations can be restricted to the extended affine Lie algebra sl2（Cq）.
文摘Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented and bounded in one orientation, e.g., a strictly positive coordinate. We open discussion using canonical and affine quantizations for two simple problems so each procedure can be understood. That analysis opens a modest treatment of quantum gravity gleaned from some typical features that exhibit the profound differences between aspects of seeking the quantum treatment of Einstein’s gravity.
基金Supported by National Science Foundation of USA （DMS-0906659. ECCS-1230040）
文摘Quantized control systems design is motivated by the convergence of controls and communications to address modern engineering applications involving the use of information technology. This paper presents an overview of recent developments on the control of linear and nonlinear systems when the control input is subject to quantization or the quantized states or outputs are used as feedback measurements. The co-existence of high-dimeasionality, quantization, nonlinearity and uncertainty poses great challenges to quantized control of nonlinear systems and thus calls for new ideas and techniques. The field of quantized nonlinear control is still at its infancy. Preliminary results in our recent work based on input-to-state stability and cyclic-small-gain theorems are reviewed. The open problems in quantized nonlinear control are also outlined.
基金supported by the National Natural Science Foundation of China(61673045)Beijing Natural Science Foundation(4152040)
文摘Abstract--This paper conducts a survey on iterative learn- ing control （ILC） with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, including passive and active types, can cause data loss or fragment due to various factors. Passive incomplete information refers to incomplete data and information caused by practical system limitations during data collection, storage, transmission, and processing, such as data dropouts, delays, disordering, and limited transmission bandwidth. Active incomplete information refers to incomplete data and information caused by man-made reduction of data quantity and quality on the premise that the given objective is satisfied, such as sampling and quantization. This survey emphasizes two aspects： the first one is how to guarantee good learning performance and tracking performance with passive incomplete data, and the second is how to balance the control performance index and data demand by active means. The promising research directions along this topic are also addressed, where data robustness is highly emphasized. This survey is expected to improve understanding of the restrictive relationship and trade-off between incomplete data and tracking performance, quantitatively, and promote further developments of ILC theory. Index Terms--Data dropout, data robustness, incomplete in- formation, iterative learning controi（ILC）, quantized control, sampled control, varying lengths.
文摘针对常见雷达信号识别方法不能适应小脉宽信号识别的问题,本文提出了一种基于频谱复杂度的雷达信号调制方式识别方法。该方法通过提取信号频谱复杂度特征、信号平方频谱特征、谱峰特征以及最小二乘直线拟合方差特征,以4个特征参数为出发点,设计了一个基于频谱复杂度的树形结构流程。该流程首先对雷达信号的频谱序列进行量化,计算量化后的6种雷达信号的频谱复杂度,根据信号频谱复杂度的不同进行分类,然后根据所求特征参数对6种雷达信号进行分层次识别。仿真结果表明,基于频谱复杂度的雷达信号调制方式识别方法能够实现在窄脉冲的情况下的雷达信号调制方式识别,当信噪比大于6 d B时具有比较好的识别效果。
基金supported by the National Natural Science Foundation of China(Grants Nos.61673078,61573096,61273220&61472257)
文摘This paper concerns the stabilization of switched dynamical networks with logarithmic quantization couplings in a settling time.The switching sequence is constrained by hybrid dwell time. Controller is designed by using limited information. Due to the quantization and switching, traditional finite-time analysis methods cannot be utilized directly. By designing multiple Lyapunov functions and constructing comparison systems, a general criterion formulated by matrix inequalities is first given. Then specific conditions in terms of linear matrix inequalities are established by partitioning the dwell time and using convex combination technique. An optimal algorithm is proposed for the estimation of settling time. Numerical simulations are given to verify the effectiveness of the theoretical results.
基金NSF Grant No.Z0511046 of Fujian and NSF Grant No.10471091 of China
文摘In this paper, we present some modules over the rank-three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined.
基金supported by the National Natural Science Foundation of China(Nos.61374116 and 61533009)the Six Talent Peaks Project in Jiangsu Province(No.HKHT010)
文摘This paper proposes a fault-tolerant strategy for hypersonic reentry vehicles with mixed aerodynamic surfaces and reaction control systems（RCS） under external disturbances and subject to actuator faults.Aerodynamic surfaces are treated as the primary actuator in normal situations,and they are driven by a continuous quadratic programming（QP） allocator to generate torque commanded by a nonlinear adaptive feedback control law.When aerodynamic surfaces encounter faults,they may not be able to provide sufficient torque as commanded,and RCS jets are activated to augment the aerodynamic surfaces to compensate for insufficient torque.Partial loss of effectiveness and stuck faults are considered in this paper,and observers are designed to detect and identify the faults.Based on the fault identification results,an RCS control allocator using integer linear programming（ILP） techniques is designed to determine the optimal combination of activated RCS jets.By treating the RCS control allocator as a quantization element,closed-loop stability with both continuous and quantized inputs is analyzed.Simulation results verify the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China under Grant No.11571186
文摘This paper studies the identification of linear systems with quantized output observations.Recursive estimates for the linear system and the quantization thresholds are derived by the stochastic approximation algorithms with expanding truncations(SAAWET).Under suitable conditions,it is shown that the estimates converge to the true values almost surely.
文摘In this paper we rewrite the gravitational constant based on its relationship with the Planck length and based on this, we rewrite the Planck mass in a slightly different form (that gives exactly the same value). In this way we are able to quantize a series of end results in Newton and Einstein’s gravitation theories. The formulas will still give exactly the same values as before, but everything related to gravity will then come in quanta. This also gives some new insight;for example, the gravitational deflection of light can be written as only a function of the radius and the Planck length. Numerically this only has implications at the quantum scale;for macro objects the discrete steps are so tiny that they are close to impossible to notice. Hopefully this can give additional insight into how well or not so well (ad hoc) quantized Newton and Einstein’s gravitation is potentially linked with the quantum world.
基金partially supported by National Natura Science Foundation of China (62350710214, U23A20325)Shenzhen Key Laboratory of Control Theory and Intelligent Systems (ZDSYS20220330161800001)。
文摘In this tutorial paper, we explore the field of quantized feedback control, which has gained significant attention due to the growing prevalence of networked control systems. These systems require the transmission of feedback information, such as measurements and control signals, over digital networks, presenting novel challenges in estimation and control design. Our examination encompasses various topics, including the minimal information needed for effective feedback control, the design of quantizers, strategies for quantized control design and estimation,achieving consensus control with quantized data, and the pursuit of high-precision tracking using quantized measurements.
文摘Quantized neural networks (QNNs), which use low bitwidth numbers for representing parameters and performing computations, have been proposed to reduce the computation complexity, storage size and memory usage. In QNNs, parameters and activations are uniformly quantized, such that the multiplications and additions can be accelerated by bitwise operations. However, distributions of parameters in neural networks are often imbalanced, such that the uniform quantization determined from extremal values may underutilize available bitwidth. In this paper, we propose a novel quantization method that can ensure the balance of distributions of quantized values. Our method first recursively partitions the parameters by percentiles into balanced bins, and then applies uniform quantization. We also introduce computationally cheaper approximations of percentiles to reduce the computation overhead introduced. Overall, our method improves the prediction accuracies of QNNs without introducing extra computation during inference, has negligible impact on training speed, and is applicable to both convolutional neural networks and recurrent neural networks. Experiments on standard datasets including ImageNet and Penn Treebank confirm the effectiveness of our method. On ImageNet, the top-5 error rate of our 4-bit quantized GoogLeNet model is 12.7%, which is superior to the state-of-the-arts of QNNs.
基金supported by the National Natural Science Foundation of China (NSFC)(62222308, 62173181, 62073171, 62221004)the Natural Science Foundation of Jiangsu Province (BK20200744, BK20220139)+3 种基金Jiangsu Specially-Appointed Professor (RK043STP19001)the Young Elite Scientists Sponsorship Program by CAST (2021QNRC001)1311 Talent Plan of Nanjing University of Posts and Telecommunicationsthe Fundamental Research Funds for the Central Universities (30920032203)。
文摘This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.
