The Sphere-packing bound, Singleton bound, Wang-Xing-Safavi-Naini bound, Johnson bound, and Gilbert-Varshamov bound on the subspace codesn+l,M,d,(m,1)qbased on subspaces of type(m,1)in singular linear spaceFq(n+l)over finite fieldsFqare presented. Then, we prove that codes based on subspaces of type(m,1)in singular linear space attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures inFq(n+l).
{"title":"Bounds on Subspace Codes Based on Subspaces of Type(m,1)in Singular Linear Space","authors":"You Gao, G. Wang","doi":"10.1155/2014/497958","DOIUrl":"https://doi.org/10.1155/2014/497958","url":null,"abstract":"<jats:p>The Sphere-packing bound, Singleton bound, Wang-Xing-Safavi-Naini bound, Johnson bound, and Gilbert-Varshamov bound on the subspace codes<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>based on subspaces of type<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math>in singular linear space<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant=\"double-struck\">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>over finite fields<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>are presented. Then, we prove that codes based on subspaces of type<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\"><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math>in singular linear space attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures in<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant=\"double-struck\">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>.</jats:p>","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2014/497958","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64520366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is a very difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms, neural networks, and particle swarm algorithm, it is hard to say which one is more appropriate and more feasible. Each method has its advantages. Most of the existed works can only deal with the data consisting of classic numbers which may arise limitations in practical applications. It is not reasonable to assume that all data are real data before we elicit them from practical data. Sometimes, fuzzy data may exist, such as in pharmacological, financial and sociological applications. Thus, we make an attempt to determine a more generalized type of general fuzzy measures from fuzzy data by means of genetic algorithms and Choquet integrals. In this paper, we make the first effort to define the rules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on rules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.
{"title":"Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data","authors":"Chen Li, Gong Zeng-tai, Duan Gang","doi":"10.1155/2013/542153","DOIUrl":"https://doi.org/10.1155/2013/542153","url":null,"abstract":"Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is a very difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms, neural networks, and particle swarm algorithm, it is hard to say which one is more appropriate and more feasible. Each method has its advantages. Most of the existed works can only deal with the data consisting of classic numbers which may arise limitations in practical applications. It is not reasonable to assume that all data are real data before we elicit them from practical data. Sometimes, fuzzy data may exist, such as in pharmacological, financial and sociological applications. Thus, we make an attempt to determine a more generalized type of general fuzzy measures from fuzzy data by means of genetic algorithms and Choquet integrals. In this paper, we make the first effort to define the <path id=\"x1D70E\" d=\"M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109\u0000q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z\" /> <path id=\"x1D706\" d=\"M529 97q-70 -109 -136 -109q-41 0 -56 94q-23 144 -37 284q-38 -88 -99 -202.5t-93 -156.5q-26 -8 -76 -19l-9 21q71 78 145.5 193t124.5 232q-5 84 -15 128q-12 55 -29.5 75.5t-42.5 20.5q-21 0 -45 -13l-8 24q16 17 46 30t55 13q43 0 70 -46.5t40 -169.5\u0000q27 -249 51 -392q7 -46 23 -46q24 0 70 60z\" /> rules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on rules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/542153","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64147388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bandwidth is defined as the maximum amount of green time for a designated movement as it passes through an arterial. In most previous studies, bandwidth has been referred to arterial bandwidth. In practice, a balance between link bandwidth and arterial bandwidth has proven to be important in optimizing coordinated signal timing plans, because not all drivers need to pass through all the intersections on an arterial. This study proposes an algorithm on how to obtain an optimal coordinated signal timing plan with both optimal link bandwidth and optimal arterial bandwidth considering practical vehicles’ speed. The weighted link bandwidth attainability is introduced as an additional measure of effectiveness for assessing the optimization results. The link bandwidth optimization is built based on the improvement of Messer’s algorithm about bandwidth optimization. The arterial bandwidth optimization algorithm takes into consideration the weighted link bandwidth attainability while selecting phase sequences. The proposed algorithm is demonstrated in a case study, and many improvements are archived when a balanced consideration is given to both link bandwidth and arterial bandwidth. Fine-tuning of initial signal timing plan is done using practical travel speed. The evaluation results show a rather significant improvement which is achieved.
{"title":"Link-Based Signalized Arterial Progression Optimization with Practical Travel Speed","authors":"Wu Xianyu, Hu Peifeng, Yuan Zhen-zhou","doi":"10.1155/2013/197313","DOIUrl":"https://doi.org/10.1155/2013/197313","url":null,"abstract":"Bandwidth is defined as the maximum amount of green time for a designated movement as it passes through an arterial. In most previous studies, bandwidth has been referred to arterial bandwidth. In practice, a balance between link bandwidth and arterial bandwidth has proven to be important in optimizing coordinated signal timing plans, because not all drivers need to pass through all the intersections on an arterial. This study proposes an algorithm on how to obtain an optimal coordinated signal timing plan with both optimal link bandwidth and optimal arterial bandwidth considering practical vehicles’ speed. The weighted link bandwidth attainability is introduced as an additional measure of effectiveness for assessing the optimization results. The link bandwidth optimization is built based on the improvement of Messer’s algorithm about bandwidth optimization. The arterial bandwidth optimization algorithm takes into consideration the weighted link bandwidth attainability while selecting phase sequences. The proposed algorithm is demonstrated in a case study, and many improvements are archived when a balanced consideration is given to both link bandwidth and arterial bandwidth. Fine-tuning of initial signal timing plan is done using practical travel speed. The evaluation results show a rather significant improvement which is achieved.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/197313","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64389869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The behaviour of the soil-structure interface is crucial to the design of a pile foundation. Radial unloading occurs during the process of hole boring and concrete curing, which will affect the load transfer rule of the pile-soil interface. Through large shear tests on the interface between clay and concrete, it can be concluded that the normal stress history significantly influences the shear behaviour of the interface. The numerical simulation of the bored shaft-soil interaction problem requires proper modelling of the interface. By taking the energy accumulated on the interface as a hardening parameter and viewing the shearing process of the interface as the process of the energy dissipated to do work, considering the influence of the normal stress history on the shearing rigidity, a mechanical model of the interface between clay and concrete is proposed. The methods to define the model parameters are also introduced. The model is based on a legible mathematical theory, and all its parameters have definite physical meaning. The model was validated using data from a direct shear test; the validation results indicated that the model can reproduce and predict the mechanical behaviour of the interface between clay and concrete under an arbitrary stress history.
{"title":"Elastoplastical Analysis of the Interface between Clay and Concrete Incorporating the Effect of the Normal Stress History","authors":"Zhao Cheng, Zhao Chunfeng, Gongling Hui","doi":"10.1155/2013/673057","DOIUrl":"https://doi.org/10.1155/2013/673057","url":null,"abstract":"The behaviour of the soil-structure interface is crucial to the design of a pile foundation. Radial unloading occurs during the process of hole boring and concrete curing, which will affect the load transfer rule of the pile-soil interface. Through large shear tests on the interface between clay and concrete, it can be concluded that the normal stress history significantly influences the shear behaviour of the interface. The numerical simulation of the bored shaft-soil interaction problem requires proper modelling of the interface. By taking the energy accumulated on the interface as a hardening parameter and viewing the shearing process of the interface as the process of the energy dissipated to do work, considering the influence of the normal stress history on the shearing rigidity, a mechanical model of the interface between clay and concrete is proposed. The methods to define the model parameters are also introduced. The model is based on a legible mathematical theory, and all its parameters have definite physical meaning. The model was validated using data from a direct shear test; the validation results indicated that the model can reproduce and predict the mechanical behaviour of the interface between clay and concrete under an arbitrary stress history.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/673057","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64199639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Distributed adaptive synchronization control for complex dynamical networks with nonlinear derivative coupling is proposed. The distributed adaptive strategies are constituted by directed connections among nodes. By means of the parameters separation, the nonlinear functions can be transformed into the linearly form. Then effective distributed adaptive techniques are designed to eliminate the effect of time-varying parameters and made the considered network synchronize a given trajectory in the sense of square error norm. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible. An example shows the applicability and feasibility of the approach.
{"title":"Distributed Adaptive Synchronization for Complex Dynamical Networks with Uncertain Nonlinear Neutral-Type Coupling","authors":"Shirui Miao, Li Junmin","doi":"10.1155/2013/548375","DOIUrl":"https://doi.org/10.1155/2013/548375","url":null,"abstract":"Distributed adaptive synchronization control for complex dynamical networks with nonlinear derivative coupling is proposed. The distributed adaptive strategies are constituted by directed connections among nodes. By means of the parameters separation, the nonlinear functions can be transformed into the linearly form. Then effective distributed adaptive techniques are designed to eliminate the effect of time-varying parameters and made the considered network synchronize a given trajectory in the sense of square error norm. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible. An example shows the applicability and feasibility of the approach.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/548375","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64150608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consensus algorithm for networked dynamic systems is an important research problem for data fusion in sensor networks. In this paper, the distributed filter with consensus strategies known as Kalman consensus filter and information consensus filter is investigated for state estimation of distributed sensor networks. Firstly, an in-depth comparison analysis between Kalman consensus filter and information consensus filter is given, and the result shows that the information consensus filter performs better than the Kalman consensus filter. Secondly, a novel optimization process to update the consensus weights is proposed based on the information consensus filter. Finally, some numerical simulations are given, and the experiment results show that the proposed method achieves better performance than the existing consensus filter strategies.
{"title":"Distributed Filter with Consensus Strategies for Sensor Networks","authors":"Xie Li, Huang Caimou, Hu Haoji","doi":"10.1155/2013/683249","DOIUrl":"https://doi.org/10.1155/2013/683249","url":null,"abstract":"Consensus algorithm for networked dynamic systems is an important research problem for data fusion in sensor networks. In this paper, the distributed filter with consensus strategies known as Kalman consensus filter and information consensus filter is investigated for state estimation of distributed sensor networks. Firstly, an in-depth comparison analysis between Kalman consensus filter and information consensus filter is given, and the result shows that the information consensus filter performs better than the Kalman consensus filter. Secondly, a novel optimization process to update the consensus weights is proposed based on the information consensus filter. Finally, some numerical simulations are given, and the experiment results show that the proposed method achieves better performance than the existing consensus filter strategies.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/683249","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64205177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the indefinite stochastic LQ control problem with quadratic and mixed terminal state equality constraints, which can be transformed into a mathematical programming problem. By means of the Lagrangian multiplier theorem and Riesz representation theorem, the main result given in this paper is the necessary condition for indefinite stochastic LQ control with quadratic and mixed terminal equality constraints. The result shows that the different terminal state constraints will cause the endpoint condition of the differential Riccati equation to be changed. It coincides with the indefinite stochastic LQ problem with linear terminal state constraint, so the result given in this paper can be viewed as the extension of the indefinite stochastic LQ problem with the linear terminal state equality constraint. In order to guarantee the existence and the uniqueness of the linear feedback control, a sufficient condition is also presented in the paper. A numerical example is presented at the end of the paper.
{"title":"Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints","authors":"Yang Hongli","doi":"10.1155/2013/674327","DOIUrl":"https://doi.org/10.1155/2013/674327","url":null,"abstract":"This paper studies the indefinite stochastic LQ control problem \u0000with quadratic and mixed terminal state equality constraints, which can \u0000be transformed into a mathematical programming problem. By means \u0000of the Lagrangian multiplier theorem and Riesz representation theorem, the \u0000main result given in this paper is the necessary condition for indefinite \u0000stochastic LQ control with quadratic and mixed terminal equality \u0000constraints. The result shows that the different terminal state constraints \u0000will cause the endpoint condition of the differential Riccati equation \u0000to be changed. It coincides with the indefinite stochastic LQ problem \u0000with linear terminal state constraint, so the result given in this paper can \u0000be viewed as the extension of the indefinite stochastic LQ problem \u0000with the linear terminal state equality constraint. In order to guarantee \u0000the existence and the uniqueness of the linear feedback control, a \u0000sufficient condition is also presented in the paper. A numerical example \u0000is presented at the end of the paper.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/674327","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64200299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the bifurcation and stability of trivial stationary solution of coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type equations (KS-GL) on a bounded domain with Neumann's boundary conditions. The asymptotic behavior of the trivial solution of the equations is considered. With the length of the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches is studied, and the stability of the bifurcated solutions is analyzed as well.
{"title":"Bifurcation Analysis of a Coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-Type Model","authors":"Lei Shi","doi":"10.1155/2013/926512","DOIUrl":"https://doi.org/10.1155/2013/926512","url":null,"abstract":"We study the bifurcation and stability of trivial stationary solution of coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type equations (KS-GL) on a bounded domain with Neumann's boundary conditions. The asymptotic behavior of the trivial solution of the equations is considered. With the length of the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches is studied, and the stability of the bifurcated solutions is analyzed as well.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/926512","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64314876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the problem of output-feedback stabilization for a class of stochastic nonlinear systems in which the nonlinear terms depend on unmeasurable states besides measurable output. We extend linear growth conditions to power growth conditions and reduce the control effort. By using backstepping technique, choosing a high-gain parameter, an output-feedback controller is designed to ensure the closed-loop system to be globally asymptotically stable in probability, and the inverse optimal stabilization in probability is achieved. The efficiency of the output-feedback controller is demonstrated by a simulation example.
{"title":"Output-Feedback and Inverse Optimal Control of a Class of Stochastic Nonlinear Systems with More General Growth Conditions","authors":"Jianwei Liu, Longchuan Guo, Zuo Xin, Huaqing Liang","doi":"10.1155/2013/251340","DOIUrl":"https://doi.org/10.1155/2013/251340","url":null,"abstract":"This paper investigates the problem of output-feedback stabilization for a class of stochastic nonlinear systems in which the nonlinear terms depend on unmeasurable states besides measurable output. We extend linear growth conditions to power growth conditions and reduce the control effort. By using backstepping technique, choosing a high-gain parameter, an output-feedback controller is designed to ensure the closed-loop system to be globally asymptotically stable in probability, and the inverse optimal stabilization in probability is achieved. The efficiency of the output-feedback controller is demonstrated by a simulation example.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/251340","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64395875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cognitive radar is an intelligent system, and it can adaptively transmit waveforms to the complex environment. The intelligent radar system should be able to provide different trade-offs among a variety of performance objectives. In this paper, we investigate the mutual information (MI) in signal-dependent interference and channel noise. We propose a waveform design method which can efficiently synthesize waveforms and provide a trade-off between estimation performance and detection performance. After obtaining a local optimal waveform, we apply the technique of generating a constant modulus signal with the given Fourier transform magnitude to the waveform. Finally we obtain a waveform that has constant modulus property.
{"title":"Adaptive Waveform Design for Multiple Radar Tasks Based on Constant Modulus Constraint","authors":"Wang Bin, Yang Wenfang, Wang Jinkuan","doi":"10.1155/2013/295493","DOIUrl":"https://doi.org/10.1155/2013/295493","url":null,"abstract":"Cognitive radar is an intelligent system, and it can adaptively transmit waveforms to the complex environment. The intelligent radar system should be able to provide different trade-offs among a variety of performance objectives. In this paper, we investigate the mutual information (MI) in signal-dependent interference and channel noise. We propose a waveform design method which can efficiently synthesize waveforms and provide a trade-off between estimation performance and detection performance. After obtaining a local optimal waveform, we apply the technique of generating a constant modulus signal with the given Fourier transform magnitude to the waveform. Finally we obtain a waveform that has constant modulus property.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/295493","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64401978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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