Lagrange Formula

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Jui-lin E. Lu - One of the best experts on this subject based on the ideXlab platform.

  • A practical (t, n) threshold proxy signature scheme based on the RSA cryptosystem
    IEEE Transactions on Knowledge and Data Engineering, 2003
    Co-Authors: Min-shiang Hwang, Jui-lin E. Lu
    Abstract:

    In a (t, n) threshold proxy signature scheme, the original signer delegates the power of signing messages to a designated proxy group of n members. Any t or more proxy signers of the group can cooperatively issue a proxy signature on behalf of the original signer, but (t - 1) or less proxy signers cannot. Previously, all of the proposed threshold proxy signature schemes have been based on the discrete logarithm problem and do not satisfy all proxy requirements. In this paper, we propose a practical, efficient, and secure (t, n) threshold proxy signature scheme based on the RSA cryptosystem. Our scheme satisfies all proxy requirements and uses only a simple Lagrange Formula to share the proxy signature key. Furthermore, our scheme requires only 5 percent of the computational overhead and 8 percent of the communicational overhead required in Kim's scheme.

Min-shiang Hwang - One of the best experts on this subject based on the ideXlab platform.

  • A practical (t, n) threshold proxy signature scheme based on the RSA cryptosystem
    IEEE Transactions on Knowledge and Data Engineering, 2003
    Co-Authors: Min-shiang Hwang, Jui-lin E. Lu
    Abstract:

    In a (t, n) threshold proxy signature scheme, the original signer delegates the power of signing messages to a designated proxy group of n members. Any t or more proxy signers of the group can cooperatively issue a proxy signature on behalf of the original signer, but (t - 1) or less proxy signers cannot. Previously, all of the proposed threshold proxy signature schemes have been based on the discrete logarithm problem and do not satisfy all proxy requirements. In this paper, we propose a practical, efficient, and secure (t, n) threshold proxy signature scheme based on the RSA cryptosystem. Our scheme satisfies all proxy requirements and uses only a simple Lagrange Formula to share the proxy signature key. Furthermore, our scheme requires only 5 percent of the computational overhead and 8 percent of the communicational overhead required in Kim's scheme.

Gan Chen - One of the best experts on this subject based on the ideXlab platform.

  • AuCC - Robust LQ control for parallel wheeled inverted pendulum
    2013 Australian Control Conference, 2013
    Co-Authors: Shuma Nagaya, Takamitsu Morikawa, Isao Takami, Gan Chen
    Abstract:

    In this study, we consider a controller of the parallel wheeled inverted pendulum named Beauto Balancer Duo. The mathematical model of the inverted pendulum is derived by using the Euler Lagrange Formula. Kinetic coefficients of the motor are derived from a specification sheet. The inverted pendulum has an uncertain viscous friction coefficient around the wheel, that causes perturbation of the dynamics. Therefore, an upper bound and a lower bound of the viscous friction coefficient are estimated by several experiments. Two controllers are synthesized in order to compare by simulations and experiments. One controller provides optimal performance only for a nominal model, and other controller has a robustness for the range of the viscous friction coefficient. From comparing two controllers, an accuracy of the derived mathematical model and an accuracy of the estimated viscous friction coefficient are verified.

  • Robust LQ control for parallel wheeled inverted pendulum
    2013 Australian Control Conference, 2013
    Co-Authors: Shuma Nagaya, Takamitsu Morikawa, Isao Takami, Gan Chen
    Abstract:

    In this study, we consider a controller of the parallel wheeled inverted pendulum named Beauto Balancer Duo. The mathematical model of the inverted pendulum is derived by using the Euler Lagrange Formula. Kinetic coefficients of the motor are derived from a specification sheet. The inverted pendulum has an uncertain viscous friction coefficient around the wheel, that causes perturbation of the dynamics. Therefore, an upper bound and a lower bound of the viscous friction coefficient are estimated by several experiments. Two controllers are synthesized in order to compare by simulations and experiments. One controller provides optimal performance only for a nominal model, and other controller has a robustness for the range of the viscous friction coefficient. From comparing two controllers, an accuracy of the derived mathematical model and an accuracy of the estimated viscous friction coefficient are verified.

O V Viskov - One of the best experts on this subject based on the ideXlab platform.

Shuma Nagaya - One of the best experts on this subject based on the ideXlab platform.

  • AuCC - Robust LQ control for parallel wheeled inverted pendulum
    2013 Australian Control Conference, 2013
    Co-Authors: Shuma Nagaya, Takamitsu Morikawa, Isao Takami, Gan Chen
    Abstract:

    In this study, we consider a controller of the parallel wheeled inverted pendulum named Beauto Balancer Duo. The mathematical model of the inverted pendulum is derived by using the Euler Lagrange Formula. Kinetic coefficients of the motor are derived from a specification sheet. The inverted pendulum has an uncertain viscous friction coefficient around the wheel, that causes perturbation of the dynamics. Therefore, an upper bound and a lower bound of the viscous friction coefficient are estimated by several experiments. Two controllers are synthesized in order to compare by simulations and experiments. One controller provides optimal performance only for a nominal model, and other controller has a robustness for the range of the viscous friction coefficient. From comparing two controllers, an accuracy of the derived mathematical model and an accuracy of the estimated viscous friction coefficient are verified.

  • Robust LQ control for parallel wheeled inverted pendulum
    2013 Australian Control Conference, 2013
    Co-Authors: Shuma Nagaya, Takamitsu Morikawa, Isao Takami, Gan Chen
    Abstract:

    In this study, we consider a controller of the parallel wheeled inverted pendulum named Beauto Balancer Duo. The mathematical model of the inverted pendulum is derived by using the Euler Lagrange Formula. Kinetic coefficients of the motor are derived from a specification sheet. The inverted pendulum has an uncertain viscous friction coefficient around the wheel, that causes perturbation of the dynamics. Therefore, an upper bound and a lower bound of the viscous friction coefficient are estimated by several experiments. Two controllers are synthesized in order to compare by simulations and experiments. One controller provides optimal performance only for a nominal model, and other controller has a robustness for the range of the viscous friction coefficient. From comparing two controllers, an accuracy of the derived mathematical model and an accuracy of the estimated viscous friction coefficient are verified.