摘要:

Nonlinear systems disturbed by Gaussian white noises (or by signals obtained from Gaussian white noises) can sometimes be analysed by setting up and solving the Fokker–Planck equation for the probability density in state space. In the present paper a simplified derivation of the Fokker–Planck equation is given. The uniqueness of the steady-state solution is discussed. Steady-state solutions are obtained for certain classes of system. These solutions correspond to or slightly generalize the Maxwell–Boltzmann distribution which is well known in classical statistical mechanics

ISSN:0020-7179    

DOI:10.1080/00207176908905786

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A combined analytic and graphic procedure is described for obtaining the dual-input describing functions for a class of non-linear elements subjected to a periodic input. The procedure is illustrated by considering the non-linearity to be a simple contactor involving hysteresis and the describing functions obtained for the element are presented.

ISSN:0020-7179    

DOI:10.1080/00207176908905787

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The optimal control problem for a furnace heating a one-dimensional slab with a quadratic performance index is analysed. This system is a typical distributed parameter system. The Hamiltonian is defined and the canonical equations are obtained. A Riccati type matrix partial differential equation is obtained from the canonical equations. An approximate method to solve these equations is derived and an example is presented to illustrate this method.

ISSN:0020-7179    

DOI:10.1080/00207176908905788

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

In many cases of practical interest there is concern with the behaviour of dynamic systems only over a finite time interval. This concern may arise in one of two ways: In one case the system under consideration is defined over a fixed and finite interval of time, while in the second case the system in question is defined for all time; however, the behaviour of the system is of interest only over a finite time interval.

ISSN:0020-7179    

DOI:10.1080/00207176908905789

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Analogue or hybrid computer methods for solving trajectory optimization problems usually require the solution of a two-point boundary value problem. A method of solving this problem is presented which does not require a good initial approximation to ensure convergence of the iteration. Analogue computer results are given with the method applied to a double integrator plant. Two different forms of performance index are considered.

ISSN:0020-7179    

DOI:10.1080/00207176908905790

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The origin, basic assumptions and some characteristics of two types of differential equations that arise in the study of control systems and processes which involve random variables are discussed in this paper. The first group are derived equations that follow from specified probabilistic considerations. These include retrospective and forward Kolmogorov differential equations and a transition rate differential equation. The second group are descriptive equations in the sense that they are taken as defining typical stochastic processes and systems. These include differential equations with an additive random variable, and differential equations describing systems with elements subject to random variation.

ISSN:0020-7179    

DOI:10.1080/00207176908905791

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor