Infimum

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

  • non iterative computation of Infimum in discrete time h optimization and solvability conditions for the discrete time disturbance decoupling problem
    International Journal of Control, 1996
    Co-Authors: Ben M. Chen, Yi Guo, Zongli L N
    Abstract:

    A non-iterative method for the computation of the Infimum for a class of discrete-time H ∞ optimal control problems, and the solvability conditions for the general discrete-time disturbance decoupling problem are given in this paper. The method for the computation of the Infimum is applicable to systems where the transfer functions from the disturbance input to the measurement output and from the control input to the controlled output are free of unit circle invariant zeros and satisfy certain geometric conditions. The solvability conditions we obtained for the general discrete-time disturbance decoupling problem are also necessary and sufficient conditions.

  • Non-iterative computation of Infimum in discrete-time H∞-optimization and solvability conditions for the discrete-time disturbance decoupling problem
    International Journal of Control, 1996
    Co-Authors: Ben M. Chen, Yi Guo, Zongli L N
    Abstract:

    A non-iterative method for the computation of the Infimum for a class of discrete-time H ∞ optimal control problems, and the solvability conditions for the general discrete-time disturbance decoupling problem are given in this paper. The method for the computation of the Infimum is applicable to systems where the transfer functions from the disturbance input to the measurement output and from the control input to the controlled output are free of unit circle invariant zeros and satisfy certain geometric conditions. The solvability conditions we obtained for the general discrete-time disturbance decoupling problem are also necessary and sufficient conditions.

  • a non iterative method for computing the Infimum in h optimization
    International Journal of Control, 1992
    Co-Authors: Ben M. Chen, Ali Saberi, L Y Uyloi
    Abstract:

    This paper presents a simple and non-iterative procedure for the computation of the exact value of the Infimum in the singular H ",,-optimization problem, and is an extension of our earlier work. The problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H ",,-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions. The computation of the Infimum in our method involves solving two well-defined Riccati and two Lyapunov equations.

  • A non-iterative method for computing the Infimum in H∞ -optimization
    International Journal of Control, 1992
    Co-Authors: Ben M. Chen, Ali Saberi
    Abstract:

    This paper presents a simple and non-iterative procedure for the computation of the exact value of the Infimum in the singular H ",,-optimization problem, and is an extension of our earlier work. The problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H ",,-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions. The computation of the Infimum in our method involves solving two well-defined Riccati and two Lyapunov equations.

  • A non-iterative method for computing the Infimum in H(infinity)-optimization
    1991
    Co-Authors: Ben M. Chen, Ali Saberi
    Abstract:

    This paper presents a simple and non-iterative procedure for the computation of the exact value of the Infimum in the singular H(infinity)-optimization problem, and is an extension of our earlier work. The problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the j-omega axis and also satisfy certain geometric conditions. The computation of the Infimum in our method involves solving two well-defined Riccati and two Liapunov equations.

Pierre-paul Romagnoli - One of the best experts on this subject based on the ideXlab platform.

  • Shearer’s inequality and Infimum rule for Shannon entropy and topological entropy
    Dynamics and Numbers, 2016
    Co-Authors: Tomasz Downarowicz, Bartosz Frej, Pierre-paul Romagnoli
    Abstract:

    We review subbadditivity properties of Shannon entropy, in particular, from the Shearer's inequality we derive the "Infimum rule" for actions of amenable groups. We briefly discuss applicability of the "Infimum formula" to actions of other groups. Then we pass to topological entropy of a cover. We prove Shearer's inequality for disjoint covers and give counterexamples otherwise. We also prove that, for actions of amenable groups, the supremum over all open covers of the "Infimum fomula" gives correct value of topological entropy.

  • shearer s inequality and Infimum rule for shannon entropy and topological entropy
    arXiv: Dynamical Systems, 2015
    Co-Authors: Tomasz Downarowicz, Bartosz Frej, Pierre-paul Romagnoli
    Abstract:

    We review subbadditivity properties of Shannon entropy, in particular, from the Shearer's inequality we derive the "Infimum rule" for actions of amenable groups. We briefly discuss applicability of the "Infimum formula" to actions of other groups. Then we pass to topological entropy of a cover. We prove Shearer's inequality for disjoint covers and give counterexamples otherwise. We also prove that, for actions of amenable groups, the supremum over all open covers of the "Infimum fomula" gives correct value of topological entropy.

Ryo Nomura - One of the best experts on this subject based on the ideXlab platform.

  • overflow probability of variable length codes with codeword cost
    IEEE Transactions on Information Theory, 2019
    Co-Authors: Ryo Nomura
    Abstract:

    Lossless variable-length source coding with codeword cost is considered for general sources. The problem setting, where we impose on unequal costs on code symbols, is called the variable-length coding with codeword cost. In this problem, the Infimum of average codeword cost have already been determined for general sources. On the other hand, the overflow probability, which is defined as the probability of codeword cost being above a threshold, have not been considered yet. In this paper, we first determine the Infimum of achievable threshold in the first-order sense and the second-order sense for general sources with additive memoryless codeword cost. Then, we compute it for some special sources such as i.i.d. sources and mixed sources. A generalization of the codeword cost is also discussed.

  • overflow probability of variable length codes with codeword cost
    arXiv: Information Theory, 2013
    Co-Authors: Ryo Nomura
    Abstract:

    Lossless variable-length source coding with codeword cost is considered for general sources. The problem setting, where we impose on unequal costs on code symbols, is called the variable-length coding with codeword cost. In this problem, the Infimum of average codeword cost have been determined for general sources. On the other hand, overflow probability, which is defined as the probability of codeword cost being above a threshold, have not been considered yet. In this paper, we determine the Infimum of achievable threshold in the first-order sense and the second-order sense for general sources and compute it for some special sources such as i.i.d. sources and mixed sources. A relationship between the overflow probability of variable-length coding and the error probability of fixed-length coding is also revealed. Our analysis is based on the information-spectrum methods.

Zongli L N - One of the best experts on this subject based on the ideXlab platform.

Mostafa Fazly - One of the best experts on this subject based on the ideXlab platform.

  • Liouville Type Theorems for Stable Solutions of
    2012
    Co-Authors: Mostafa Fazly
    Abstract:

    We establish Liouville type theorems for elliptic systems with various classes of nonlinearities on R N . We show, among other things, that a system has no semi-stable solution in any dimension, whenever the Infimum of the derivati ves of the corresponding non-linearities is positive. We give some immediate applications to various standard systems, such as the Gelfand, and certain Hamiltonian systems. The case where the Infimum is zero is more interesting and quite challenging. We show that any C 2 (R N ) positive entire semi-stable solution of the following Lane-Emden system,

  • liouville type theorems for stable solutions of certain elliptic systems
    Advanced Nonlinear Studies, 2012
    Co-Authors: Mostafa Fazly
    Abstract:

    We establish Liouville type theorems for elliptic systems with various classes of nonlinearities on RN . We show, among other things, that a system has no semi-stable solution in any dimension, whenever the Infimum of the derivatives of the corresponding non-linearities is positive. We give some immediate applications to various standard systems, such as the Gelfand, and certain Hamiltonian systems. The case where the Infimum is zero is more interesting and quite challenging. We show that any C2(RN ) positive entire semi-stable solution of the following Lane-Emden system,

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