There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA...There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA) estimation system based on self-organizing map (SOM) and designed for arbitrarily distributed sensor array is proposed. The essential principle of this method is that the map from distance difference of arrival (DDOA) to DOA is Lipschitz continuity, it indicates the similar topology between them, and thus Kohonen SOM is a suitable network to classify DOA through DDOA. The simulation results show that the DOA estimation errors are less than 1° for most signals between 0° to 180°. Compared to MUSIC, Root-MUSIC, ESPRIT, and RBF, the errors of signals under signal-to-noise ratios (SNR) declines from 20 dB to 2 dB are robust, SOM is better than RBF and almost close to MUSIC. Further, the network can be trained in advance, which makes it possible to be implemented in real-time.展开更多
在这份报纸,我们学习下列非线性的 BSDE:y (t) +1t f ( s , y , z ) ds+1t [ z +g1 ( s , y ) +g2 ( s , y , z )] dWs =, t [ 0,1 ],吗小 parameter.The 系数 f 在哪儿,是局部地在 y 和 z 的 Lipschitz ,系数 g1 是局部地...在这份报纸,我们学习下列非线性的 BSDE:y (t) +1t f ( s , y , z ) ds+1t [ z +g1 ( s , y ) +g2 ( s , y , z )] dWs =, t [ 0,1 ],吗小 parameter.The 系数 f 在哪儿,是局部地在 y 和 z 的 Lipschitz ,系数 g1 是局部地在 y 的 Lipschitz ,和系数 g2 是一致地在 y 的 Lipschitz 和 z.Let 行是局部地球 B 上的系数的 Lipschitz 常数( O ,吗 N ) Ra 栠浡汩潴楮湡??????????€ ???€ ??瘠?????????栠浡汩潴楮湡?????匠???????牯敤?湉?????????????????栠浡汩潴楮湡??展开更多
The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to p...The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis.The obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.展开更多
In this paper, we establish the weighted <span style="white-space:nowrap;"><em>L</em><sup><em>p</em></sup></span> <span style="white-space:nowrap;"...In this paper, we establish the weighted <span style="white-space:nowrap;"><em>L</em><sup><em>p</em></sup></span> <span style="white-space:nowrap;">(1 < <em>p</em> < ∞)</span> boundedness of variation operator for the commutators generated by one-sided Calderón-Zygmund singular integrals with Lipschitz functions.展开更多
Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and un...Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to展开更多
This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditi...This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditions,the authors derive less conservative criterion for the controller design and observer design.A new criterion is proposed to ensure the closed-loop system is finite-time bounded(FTB).The sufficient conditions are established to ensure the closed-loop system is H_(∞)finite-time bounded(H_(∞)FTB)in terms of matrix inequalities.The controller gains and observer gains are given.A numerical example is provided to demonstrate the effectiveness of the proposed results.展开更多
In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coef...In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.展开更多
In the theoretical study of numerical solution of stiff ODEs, it usually assumes that the righthand function f(y) satisfy one-side Lipschitz condition < f(y) - f(z),y - z >less than or equal to v(1)parallel to y...In the theoretical study of numerical solution of stiff ODEs, it usually assumes that the righthand function f(y) satisfy one-side Lipschitz condition < f(y) - f(z),y - z >less than or equal to v(1)parallel to y - z parallel to(2),f : Omega subset of or equal to C-m --> C-m, or another related one-side Lipschitz condition [F(Y) - F(Z), Y - Z](D) less than or equal to v'parallel to Y - Z parallel to(D)(2), F : Omega(s) subset of or equal to C-ms --> C-ms, this paper demonstrates that the difference of the two sets of all functions satisfying the above two conditions respectively is at most that v' - v' only is constant independent of stiffness of function f.展开更多
文摘There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA) estimation system based on self-organizing map (SOM) and designed for arbitrarily distributed sensor array is proposed. The essential principle of this method is that the map from distance difference of arrival (DDOA) to DOA is Lipschitz continuity, it indicates the similar topology between them, and thus Kohonen SOM is a suitable network to classify DOA through DDOA. The simulation results show that the DOA estimation errors are less than 1° for most signals between 0° to 180°. Compared to MUSIC, Root-MUSIC, ESPRIT, and RBF, the errors of signals under signal-to-noise ratios (SNR) declines from 20 dB to 2 dB are robust, SOM is better than RBF and almost close to MUSIC. Further, the network can be trained in advance, which makes it possible to be implemented in real-time.
文摘在这份报纸,我们学习下列非线性的 BSDE:y (t) +1t f ( s , y , z ) ds+1t [ z +g1 ( s , y ) +g2 ( s , y , z )] dWs =, t [ 0,1 ],吗小 parameter.The 系数 f 在哪儿,是局部地在 y 和 z 的 Lipschitz ,系数 g1 是局部地在 y 的 Lipschitz ,和系数 g2 是一致地在 y 的 Lipschitz 和 z.Let 行是局部地球 B 上的系数的 Lipschitz 常数( O ,吗 N ) Ra 栠浡汩潴楮湡??????????€ ???€ ??瘠?????????栠浡汩潴楮湡?????匠???????牯敤?湉?????????????????栠浡汩潴楮湡??
文摘The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis.The obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.
文摘In this paper, we establish the weighted <span style="white-space:nowrap;"><em>L</em><sup><em>p</em></sup></span> <span style="white-space:nowrap;">(1 < <em>p</em> < ∞)</span> boundedness of variation operator for the commutators generated by one-sided Calderón-Zygmund singular integrals with Lipschitz functions.
文摘Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to
基金supported by the Natural Science Foundation of Tianjin under Grant No.18JCYBJC88000.
文摘This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditions,the authors derive less conservative criterion for the controller design and observer design.A new criterion is proposed to ensure the closed-loop system is finite-time bounded(FTB).The sufficient conditions are established to ensure the closed-loop system is H_(∞)finite-time bounded(H_(∞)FTB)in terms of matrix inequalities.The controller gains and observer gains are given.A numerical example is provided to demonstrate the effectiveness of the proposed results.
基金supported by the National Natural Science Foundation of China(Nos.11671113,12071101).
文摘In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.
文摘In the theoretical study of numerical solution of stiff ODEs, it usually assumes that the righthand function f(y) satisfy one-side Lipschitz condition < f(y) - f(z),y - z >less than or equal to v(1)parallel to y - z parallel to(2),f : Omega subset of or equal to C-m --> C-m, or another related one-side Lipschitz condition [F(Y) - F(Z), Y - Z](D) less than or equal to v'parallel to Y - Z parallel to(D)(2), F : Omega(s) subset of or equal to C-ms --> C-ms, this paper demonstrates that the difference of the two sets of all functions satisfying the above two conditions respectively is at most that v' - v' only is constant independent of stiffness of function f.
基金Supported by the National Nature Science Foundation of China(61174065)the Jiangsu Provincial Department of Education(10KJB20002)+1 种基金Nature Science Foundation at Nantong University(11Z05511Z056)
基金Supported by National Basic Research Program of China(973 Program2007CB814901)+1 种基金National Natural Science Foundation of China(10826098)Anhui Natural Science Foundation (090416225)