摘要:

A condition for the existence of a limit cycle for a class of second-order non-linear control systems with a type zero linear plant is derived. The limit cycle stability is assured whenF(a,b, α, β)/Ecurve has a positive slope at the point of intersection ofF(a,b, α, β) andKloci. A typical second-order non-linear system is analysed for the purpose of illustrating the method of finding the amplitude and frequency of sustained oscillation. The method of studying the effects of variation ofK, α and β on the amplitude and frequency of oscillation of the system is indicated. With regard to this, the proposed method has certain advantages over the usual method of analysis.

ISSN:0020-7179    

DOI:10.1080/00207177008905946

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

This paper presents the approximate solution of the non-linear two-point boundary value problem for maximum aposterioriestimation. Filtering, fixed point smoothing, fixed interval smoothing, and fixed lag smoothing algorithms are obtained by the discrete invariant embedding procedure. These are tabulated as well as the associated approximate error variances.

ISSN:0020-7179    

DOI:10.1080/00207177008905947

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

When a plant consists of several pure delays and lumped-parameter systems arranged in cascade the optimization problem may be solved by considering an equivalent optimization problem for a delay free system. The method of applying this transformation is discussed in this paper and a number of examples are given.

ISSN:0020-7179    

DOI:10.1080/00207177008905948

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The object of this paper is to present an approximate technique for state estimation of non-linear dynamical systems under noisy observations. The conditional cumulant is introduced, by which the conditional probability density can be characterized. A set of dynamical equations satisfied by conditional cumulants is derived, and an approximate method is proposed for computing the cumulants. The relation of the cumulant method to the stochastic linearization technique is also discussed. Finally the state estimation problem for linear stochaatic system with state-dependent disturbance is solved to illustrate the use of the Gaussian approximation.

ISSN:0020-7179    

DOI:10.1080/00207177008905949

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The formulas for different methods of state space version of statistical linearization are given and applied to sub-optimal stochastic control of non-linear systems, as recently suggested by Wonham and Cashman (1968). Comparison with their optimal results shows that there is no immediate reason to prefer one linearization method to another. Especially the conjecture of Kazakov does not hold in general, i.e. the mean coefficients of two different linearization methods must provide best results.

ISSN:0020-7179    

DOI:10.1080/00207177008905950

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

In practice, many systems are complex and of high dimension. Many such systems may be viewed as being composed of several simpler sub-systems which when connected in an appropriate fashion yield the original composite system. The stability, the transient behaviour and estimates for the trajectory bounds of certain composite systems are analysed in terms of their sub-systems. This is accomplished by defining the stability of sub-systems and of composite systems in terms of certain time-varying sub-sets of the state space which are pre-specified in a given problem.

ISSN:0020-7179    

DOI:10.1080/00207177008905951

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor