A formulation by minimization of differential entropy for optimal control system

Masayuki Goto, Nobuhiko Tawara

    Research output: Contribution to journalArticle

    Abstract

    This paper proposes a new formulation which minimizes the differential entropy for an optimal control problem. The conventional criterion of the optimal regulator control is a standard quadratic cost function E[M{x(t)}2 + N{u(t)}2], where x(t) is a state variable, u(t) is an input value, and M and N are positive weights. However, increasing the number of the variables of the system it is complex to find the solution of the optimal regulator control. Therefore, the simplicity of the solution is required. In contrast to the optimal regulator control, we propose the minimum entropy control which minimizes a differential entropy of the weighted sum of x(t) and u(t). This solution is derived on the assumptions that the linear control and x(t)u(t) ≦ 0 are satisfied. As the result, the formula of the minimum entropy control is very simple and clear. This result will be useful for the further work with multi variables of simple control formulation.

    Original languageEnglish
    Pages (from-to)569-575
    Number of pages7
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    VolumeE79-A
    Issue number4
    Publication statusPublished - 1996

    Fingerprint

    Optimal control systems
    Optimal System
    Optimal Control
    Entropy
    Control System
    Formulation
    Regulator
    Minimise
    Linear Control
    Weighted Sums
    Quadratic Function
    Cost Function
    Optimal Control Problem
    Simplicity
    Cost functions

    Keywords

    • Control theory
    • Differential entropy
    • Minimum entropy control
    • Optimal regulator control

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Hardware and Architecture
    • Information Systems

    Cite this

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    abstract = "This paper proposes a new formulation which minimizes the differential entropy for an optimal control problem. The conventional criterion of the optimal regulator control is a standard quadratic cost function E[M{x(t)}2 + N{u(t)}2], where x(t) is a state variable, u(t) is an input value, and M and N are positive weights. However, increasing the number of the variables of the system it is complex to find the solution of the optimal regulator control. Therefore, the simplicity of the solution is required. In contrast to the optimal regulator control, we propose the minimum entropy control which minimizes a differential entropy of the weighted sum of x(t) and u(t). This solution is derived on the assumptions that the linear control and x(t)u(t) ≦ 0 are satisfied. As the result, the formula of the minimum entropy control is very simple and clear. This result will be useful for the further work with multi variables of simple control formulation.",
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    T1 - A formulation by minimization of differential entropy for optimal control system

    AU - Goto, Masayuki

    AU - Tawara, Nobuhiko

    PY - 1996

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    N2 - This paper proposes a new formulation which minimizes the differential entropy for an optimal control problem. The conventional criterion of the optimal regulator control is a standard quadratic cost function E[M{x(t)}2 + N{u(t)}2], where x(t) is a state variable, u(t) is an input value, and M and N are positive weights. However, increasing the number of the variables of the system it is complex to find the solution of the optimal regulator control. Therefore, the simplicity of the solution is required. In contrast to the optimal regulator control, we propose the minimum entropy control which minimizes a differential entropy of the weighted sum of x(t) and u(t). This solution is derived on the assumptions that the linear control and x(t)u(t) ≦ 0 are satisfied. As the result, the formula of the minimum entropy control is very simple and clear. This result will be useful for the further work with multi variables of simple control formulation.

    AB - This paper proposes a new formulation which minimizes the differential entropy for an optimal control problem. The conventional criterion of the optimal regulator control is a standard quadratic cost function E[M{x(t)}2 + N{u(t)}2], where x(t) is a state variable, u(t) is an input value, and M and N are positive weights. However, increasing the number of the variables of the system it is complex to find the solution of the optimal regulator control. Therefore, the simplicity of the solution is required. In contrast to the optimal regulator control, we propose the minimum entropy control which minimizes a differential entropy of the weighted sum of x(t) and u(t). This solution is derived on the assumptions that the linear control and x(t)u(t) ≦ 0 are satisfied. As the result, the formula of the minimum entropy control is very simple and clear. This result will be useful for the further work with multi variables of simple control formulation.

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    KW - Differential entropy

    KW - Minimum entropy control

    KW - Optimal regulator control

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