摘要:

The second-order expressions of Boolean functions can have either sum-of-product or product-of-sum forms. For a Boolean function specified in the irredundant sum-of-product form as the disjunction of a number of prime implicants orpterms, groups of thesepterms can sometimes be more economically realized in the minimal product-of-sum forms than in the sum-of-product forms. To know whether a group ofpterms in the irredundant sum-of-product form of the function has a more economic realization in the product-of-sum form, the concept of coincidence between thepterms of the function is introduced in the paper and a number of interesting properties of the function in relation to coincidence are established. The coincidence between a pair ofpterms in a function is defined as the number of literals occurring as mutually common in their algebraic representations. It is next shown that the study of the properties of Boolean functions in relation to coincidence also aids in readily obtaining the economic third-order expressions of general Boolean functions.

ISSN:0020-7179    

DOI:10.1080/00207176908905761

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A system is described for which Loeb's criterion for the determination of stability of limit cycles fails. Details of an investigation into the reasons for this failure are given. The Hamel locus is extended to include time-delay in a general way and the results applied to the above system along with associated sampled-data techniques for the accurate determination of stability. The cause of failure is discussed in detail.

ISSN:0020-7179    

DOI:10.1080/00207176908905762

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A new approach to error evaluation is suggested for the determination of optimization indices of feedback control systems. Comparison of actual output with that from single-time-constant ideal designed to meet settlement requirements is envisaged, instead of comparison with the impractical ideal of a step output. It is shown that the optimum systems obtained for integral of squared error (I.S.E.) minimization with the modified definition of error are found to be better damped compared to what would be obtained under the conventional approach.

ISSN:0020-7179    

DOI:10.1080/00207176908905763

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

An iterative method is presented for the training of a two-layered machine used for pattern dichotomization. It is assumed that there is only one TLU in the second layer and a number of TLU's in the first layer. The central idea of the method is getting the desired responses of the first-layer TLU's, knowing the desired response of the output TLU. Using these desired responses the TLU's are adjusted. A method is given for testing the non-linear separability ofRcategory case.

ISSN:0020-7179    

DOI:10.1080/00207176908905764

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The realization of network transfer functions by commutating the input signal to a number of low-pass filters is well established. This paper shows that such an arrangement produces more than one transfer function, depending on the phase of the output brush with respect to the input brush. It is shown that when the output is picked up from the contact undergoing commutation the output is not only of different phase but also of different magnitude from that obtained from any of the other contacts.

ISSN:0020-7179    

DOI:10.1080/00207176908905765

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A previous paper treating the problem of optimal control of systems whoso control signals belong to a pre-specified class of functions is discussed. The problem is re-examined for a broader class of systems and the results are formulated in a maximum principle of the Pontryagin type. The maximum principle states that a necessary condition for the optimal control is that the first variation of the time integral of the Hamiltonian is zero if the control function can vary in two opposite directions, is non-positive if the control function can vary in only one direction. The free end-point and the fixed end-point problems as well as the variable end-point problems are considered. The admissible controls are assumed to be piecewise continuous and bounded. The requirement of operative convexity as imposed in the related paper is lifted.

ISSN:0020-7179    

DOI:10.1080/00207176908905766

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Impulse response of a linear time invariant system is partitioned by dividing the time axis into equal intervals of time. Then the impulse response is expressed as a sum of these partitioned portions. Each individual portion is approximated by a finite sum of orthogonalized sinusoids satisfying integral squared error criteria. Four different sets are given for this purpose. If the time reversed functions from these sets are applied to the system then the sampled values of the system response at the partitioning instants directly yield the system coefficients as required for the least integral squared error. Knowing these coefficients the best approximation to the impulse response can be constructed as illustrated by the examples considered. Sampled values of the Fourier transform of system impulse response are obtained as a by-product.

ISSN:0020-7179    

DOI:10.1080/00207176908905767

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Some methods of handling command inputs via the linear optimal control theory are compared, and the convergence of the associated Riccati matrix differential equation is investigated.

ISSN:0020-7179    

DOI:10.1080/00207176908905768

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

This paper investigates the problem of designing a multiple-input, single-output linear compensator for a single-input, multiple-output linear plant in such a manner that a quadratic performance index is minimized. It is shown howoptimalcontrol may be achieved without measuring or estimating the state variables of the plant. A design procedure is suggested which depends for its success on the controllability and observability properties of the plant. It is pointed out how these observability properties are related to Luenberger's observer theory.

ISSN:0020-7179    

DOI:10.1080/00207176908905769

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor