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Ito, K.

Publications and source records attributed to Ito, K..

36 records · Page 2
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NASA NTRS1986

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

Banks, H. T.↗
NASA NTRS1986

Legendre-tau approximations for functional differential equations

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Ito, K.↗
NASA NTRS1985

Observations of ultraheavy cosmic ray particles at 10 GV cutoff rigidity

Ultraheavy cosmic ray particles with Z 45 and Fe were observed in two balloon flights at a mean geomagnetic cutoff rigidity of 10 GV. Fluxes of these particles at the top of the atmosphere are presented. A ratio of (Z 45)/(Fe) is compared with other experimental results. The ratio decreases with increasing energy in the energy range from 1 to 10 GeV/amu. A possibility is presented to explain the variation of the ratio with energy.

Yanagimachi, T.↗
NASA NTRS1985

Observations of solar energetic particles at a synchronous orbit

The Space Environment Monitors (SEM) on board the Japanese geostationary meteorological satellites (GMS-1 and GMS-2) observed energetic protons, alpha particles and electrons continuously for February 1978 to September 1984. The satellites were at 6.6 Earth radii above 140 deg E equator.

Takenaka, T.↗
NASA NTRS1985

Chandrasekhar equations for infinite dimensional systems

Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

Ito, K.↗
NASA NTRS1985

Chandrasekhar equations for infinite dimensional systems

The existence of Chandrasekhar equations for linear time-invariant systems defined on Hilbert spaces is investigated. An important consequence is that the solution to the evolutional Riccati equation is strongly differentiable in time, and that a strong solution of the Riccati differential equation can be defined. A discussion of the linear-quadratic optimal-control problem for hereditary differential systems is also included.

Ito, K.↗
NASA NTRS1985

Legendre-tau approximation for functional differential equations. III - Eigenvalue approximations and uniform stability

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Ito, K.↗
NASA NTRS1984

Chandrasekhar equations and computational algorithms for distributed parameter systems

The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas.

Burns, J. A.↗
NASA NTRS1984

Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Ito, K.↗
NASA NTRS1984

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, K.↗
NASA NTRS1983

Computational methods for estimation of parameters in hyperbolic systems

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

Banks, H. T.↗
NASA NTRS1983

Legendre-Tau approximations for functional differential equations

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

Ito, K.↗
NASA NTRS1983

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

Ito, K.↗
NASA NTRS1982

Feedback stabilization and control of linear neutral systems

The first problem treated here is the realization and stabilization of linear neutral systems with discrete delays. It is shown that any autonomous linear neutral system with discrete delays is zero-state equivalent to an abstract linear system over a local ring of operators. Using the abstract model, the basic existence question for neutral realization is then settled. For general infinite dimensional linear systems, there is no precise analog of the finite dimensional state space isomorphism theorem. Because of this, the notion of spectral minimality must be introduced. For the case of single input-single output systems, realizations are obtained that are both minimal and spectrally minimal. Using the Cruz-Hale theory of stable D-operators, conditions are given that ensure that any poles introduced into the realization are strictly contained in the left half plane and indeed are characterized as characteristic values of the D-operator. The problem of the feedback stabilization of neutral systems is then considered using the abstract model. It is shown that, for neutral systems with commensurable delays and a stable D-operator in the sense of Cruz and Hale, Morses theorem (1976) on pole assignment over a PID implies stabilizability in the reachable case.

Tarn, T. J.↗
NASA NTRS1973

Detection of S02 and N02 in Stack Plume by Raman Scattering and Fluorescence

We have been studying laser-Raman radar which can be used as the remote detector of sulfur dioxide concentration in the stack plume of boiler exhaust gas, and some results have been published. In this paper, we report the interference of nitrogen dioxide fluorescence against sulfur dioxide Raman scattering and the measuring method of sulfur dioxide and nitrogen dioxide concentration. In a stack plume, high density dust and high concentration carbon dioxide are included, therefore very strong Mie back-scattering and carbon dioxide Raman scattering are observed. The separation of these scattering signals from sulfur dioxide Raman signal was the first problem for the laser-Raman radar. But, this problem was solved by using the filter which have high resolving power. It is well known that nitrogen dioxide can be excited to emit fluorescence of broad spectrum by blue-green light. The light source of the laser-Raman radar is SH of Nd:YAG laser, and boiler exhaust gas includes several tens ppm of nitrogen dioxide, then the interference of nitrogen dioxide fluorescence brings the error to sulfur dioxide measurement. 'rhe rejection of the interference can be achieved by the subtraction of the nitrogen dioxide fluorescence contribution from detected signal at sulfur dioxide Raman scattering wavelength. The nitrogen dioxide fluorescence contribution can be measured by two methods. The first is to convert the nitrogen dioxide fluorescence intensity which is measured at a different wavelength from sulfur dioxide Raman line into the one at sulfur dioxide Raman line. The second is to convert the detected signal intensity, which is obtained when the range gate is set just behind the plume, into the one obtained at the range of the plume using the difference of the time dependence between sulfur dioxide Raman scattering and nitrogen dioxide fluorescence. Nitrogen dioxide fluorescence has lifetime of about 300nS, while Raman scattering has none. By either of the two methods, the contribution of nitrogen dioxide fluorescence is determined. Then, we can measure the nitrogen dioxide and sulfur dioxide concentration.The minimum detectable concentration and the experimental results of the remote sensing of sulfur dioxide and nitrogen dioxide in stack plume will be discussed in detail.

Nakahara, S.↗