摘要:

The Volterra series is used to investigate aperiodic solutions of certain second-order differential equations with non-linear damping and non-linear restoring force. Solutions are obtained in the phase plane for trajectories with zero initial conditions. These are obtained by approximating the Volterra series, and it is shown that the approximation involved is small over a wide range of values of linear damping.

ISSN:0020-7179    

DOI:10.1080/00207176608921361

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A method of simplification of switching functions involving a very large number of ‘ don't care’ states is suggested in the present paper. First a tabular technique is suggested which generates all the prime implicants starting from the maxterm type expressions of switching functions, avoiding generation of the prime implicants formed of ‘don't care’ states only. The technique presented is simple and iterative. Next it is suggested how the knowledge of the sets of prime implicants thus obtained can be utilized for finding minimal or other irredundant sums of switching functions.

ISSN:0020-7179    

DOI:10.1080/00207176608921362

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A relation is derived among the input autocorrelation function and the output autocorrelation functions for a half-wave and full-wave linear rectifier with non-stationary random inputs. The result generalizes the work of Rubin and Stacey on stationary Gaussian inputs and of Brown on stationary separable inputs.

ISSN:0020-7179    

DOI:10.1080/00207176608921363

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A relation is domed between the two-dimensional correlation time and spectral bandwidth previously introduced by the author and the corresponding one-dimensional quantities of Lampnrd. In the course of the derivation new times and widths are introduced which relate to the areas under the curves defined by the product of the autocorrelation function and one-dimensional correlation time, and the product of the generalized spectral density function and one-dimensional bandwidth.

ISSN:0020-7179    

DOI:10.1080/00207176608921364

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A linear optimal controller which is effective in a suitable neighbourhood of a reference optimal trajectoiy is derived. This is accomplished by parameterizing the canonical equations for this field. It is shown that depending on the parameters chosen, different feedback matrices can be calculated and an example comparing the performance of a process subject to a control function based on two possible matrices is presented.

ISSN:0020-7179    

DOI:10.1080/00207176608921365

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

This paper describes the practical problem of determining errors in the State vector resulting from the representation of a finite pulse width sampler by an impulse sampler in a sampled-data control system. It is shown that the response of the impulse sampling system is the limit of the response of the corresponding finite pulse width system with on associated gain factor, as the pulse width tends to zero. Conditions for the convergence of the errors in the state vector and the asymptotic equivalence of the two systems are; considered.

ISSN:0020-7179    

DOI:10.1080/00207176608921366

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

The uniqueness of the solution of the differential equations derived from Pontryagin's Maximum Principle is considered for a general control problem with a freo right end of the trajectory and fixed terminal time. Under several restrictive conditions on the controlled system and performance criterion, it is proved that those equations have a unique solution. This is done by embedding the problem into a class of similar problems by means of the introduction of a positive parameter • multiplying the performance criterion, and then making use of the uniqueness properties of an associated autonomous system together with the continuity of the solutions of the differential equations with respect to the parameter ∈ 

ISSN:0020-7179    

DOI:10.1080/00207176608921367

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

Variation of electrical conductance and capacity of chemically pure MnO2in pressed powder form under a stress 6·0 × 1011dynes/sq. cm has been studied within the temperature range 26°c to 110°c at 1 MC/s, Electrical conductance of samples in tablet, form (3 mm thick and 15 mm in diameter) was measured between 26°C and 110°before and after heat treatment at 300°c for 36 hours. Capacitance values were also measured simultaneously within the above temperature range. Electrical conductance was found to attain a maximum at about 78°c. There is a marked hysteresis in ‘;lnconductance’ − 1 /Tgraph when measurements are made while temperature is rising and while falling.

ISSN:0020-7179    

DOI:10.1080/00207176608921368

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A second-order method of successively improving a control sequence for a non-linear discrete-time system is derived. One step convergence is obtained for linear systems with quadratic performance functions. Although the results are of interest in their own right, a second-order method for continuous-time systems is obtained by formally allowing the sampling interval to approach zero. The equations so obtained differ slightly, because of the method of derivation, from results already obtained using the calculus of variations approach. The difference, which is an advantage of the method described in this paper, is that one vector differential equation less has to be integrated. The approach used in the derivation is motivated by dynamic programming and facilitates the application of gradient methods to stochastic problems which will be the subject of a future paper.

ISSN:0020-7179    

DOI:10.1080/00207176608921369

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

ISSN:0020-7179    

DOI:10.1080/00207176608921370

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor