摘要:

Extended gradient methods which enable, through adequate transformations, the solution of problems which are singular when using ordinary gradient techniques are considered. Using the extended gradient methods it is possible to solve control problems with unspecified initial conditions, minimum time, or problems in which the gradient with respect to one of the control functions vanishes in every step of the iteration.

ISSN:0020-7721    

DOI:10.1080/00207727608941922

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

A novel method for factorizing the transfer function matrix of a multivariable system described by the triple (A,B,C) is presented. The factorization consists of a product of two rational function matrices, one of which is the inverse of a rational function matrix. Various properties of the factorization are given and the factorization procedure is illustrated by an example.

ISSN:0020-7721    

DOI:10.1080/00207727608941923

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

Following developments in non-linear leastpth optimization by the authors it is possible to derive two new methods of non-linear minimax optimization. Unlike the Polya algorithm in which a sequence of leastpth optimizations asp→∞ is taken our methods do not require the value ofpto tend to infinity. Instead we construct a sequence of leastpth optimization problems with a finite value ofp. It is shown that this sequence will converge to a minimax solution. Two interesting minimax problems were constructed which illustrate some of the theoretical ideas. Further numerical evidence is presented on the modelling of a fourth-order system by a second-order model with values ofpvarying between 2 and 10 000.

ISSN:0020-7721    

DOI:10.1080/00207727608941924

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

This paper deals with the approach to general systems via information which has been initiated by the author, and tests the theory against the reality. After a brief background on the relativisticinternalandexternal entropyand their Lorentz transformation, it is shown that deterministic dynamic systems can be described by our thermodynamics information model. Thenrelativisticinformation is defined and some consequences arc examined. One shows that, as expected, these equations yield Shannon results when the organizability of the considered system is small. This relativistic information is applied to stochastic systems : we find again.Jaynes' principle and the Folker-Plank-Kolmogorov equation, but in addition we obtain an approach to random stochastic filtering based on the maximization of the relativistic information. Then we attempt to apply these ideas to biological systems and we exhibit the differences that exist between our approach and that of Rosen's in quantum genetics. To conclude, we examine the question of structural stability and morphogenesis.

ISSN:0020-7721    

DOI:10.1080/00207727608941925

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

The first time independent, parallel processes consisting of two alternating renewal functions, say function zero and one, will be in phase zero together under equilibrium and non-equilibrium starting conditions is found. With function one an exponential distribution and function zero a non-lattice type, the distribution of the aforementioned time is found by taking advantage of a point of renewal. Further results are derived when both functions are exponential with the same parameter value by likening the situation to an Ehrenfest model

ISSN:0020-7721    

DOI:10.1080/00207727608941926

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

In this paper a weak stability property of a random rotational motion of a ship with a two position automatic pilot, is dealt with. This is done by choosing two different sets of stochastic differential equations as mathematical models for the ships motion. For each model, a partial differential equation over a bounded domain in the state space is derived. The value of the solution to the PDE at a pointPin the domain provides the conditional expectation of the first time that the system's trajectory in the state space hits the boundary given that P is the starting point of the trajectory. The partial differential equations derived for the two models are of two and three independent variables, respectively. Numerical procedures for solving these equations are suggested, and their efficiency and applicability are demonstrated with examples. For each model, a functional is defined on the PDE solutions. The values of the functionals serve as a measure of the system's stochastic stability.

ISSN:0020-7721    

DOI:10.1080/00207727608941927

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

An optimal control problem, concerned with a stochastic distributed process related to chemical kinetics, is posed. Duo to the stochastic and complicated form of the process' representation, only a suboptimal version of the problem is treated. This is done in the following manner. First the process is modelled by using an adequate pair of stochastic partial differential equations. Then, a pair of partial differential equations, serving as an estimator for the process' state, is constructed. Based on this estimator, sufficient conditions are found on suboptimal controls in the form of a set of four non-linear partial differential equations. Two numerical procedures are suggested for solving the final set of PDE, and their efficiency and applicability are demonstrated with examples. Finally, steady-state values of the solutions are computed for a certain class of cases.

ISSN:0020-7721    

DOI:10.1080/00207727608941928

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

The design of a sampled-data system using output feedback and a digital controller in cascade with the system, is considered. The problems of exact model matching, decoupling, and of minimum settling time are discussed and constraints are derived using polynomial equations. The techniques are illustrated by numerical examples.

ISSN:0020-7721    

DOI:10.1080/00207727608941929

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

A recursive pseudo-inverse algorithm is presented for estimating the parameters of the transfer-function matrix of a multiple-input-multiple-output discrete-time system from the samples of the input-output data. The algorithm is suitable for on-line identification of linear multivariable systems.

ISSN:0020-7721    

DOI:10.1080/00207727608941930

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

In this paper three theorems for finite time stability and uniform finite time stability are presented. The inverse Liapunov problem is considered and solved for each of these theorems. This consists of determining the class of systems which can be proven stable using a given Liapunov function and a given stability theorem.

ISSN:0020-7721    

DOI:10.1080/00207727608941931

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor