摘要:

The problem of determining whether or not a dynamical system ℒ controllable has been an active research topic in recent years. However, the complementary problem of determining just why a system ℒ uncontrollable has received relatively little attention. In this paper the physical acid mathematical mechanism of uncontrollability is studied with particular emphasis on how uncontrollability of a general class of non-linear dynamical systems can originate with the inadvertent selection of a non-minimal dimension ‘ state vector ’. The state-apace geometry corresponding to this particular mode of uncontrollability, which we call ‘state over-description’, is examined in detail. A fundamental necessary condition for the existence of state over-description in non-linear dynamical systems is derived and its application is illustrated by five examples.

ISSN:0020-7179    

DOI:10.1080/00207177408932625

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

A method is developed for solving optimal-control problems having cost functional or system functions that are continuous but have discontinuous partial derivatives with respect to the state variables. The method is based on splitting the total time interval on which the problem is defined into segments where the trajectory either totally avoids the points of discontinuity or stays fixed at such a point. Examples are given which motivate consideration of such problems and illustrate the proposed method of solution.

ISSN:0020-7179    

DOI:10.1080/00207177408932626

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

An established technique for computing optimal bang-bang controls is to minimize the coat of the bang-bang control with respect to the switching times and final time using a direct search method. In this paper, explicit expressions are obtained for the gradient of the cost of a bang-bang control with respect to these parameters. This enables the minimization to be performed more accurately, and also more rapidly, using a gradient search method such as that of Davidon. The use of this approach to compute time-optimal controls for a fifth-order system, and to minimize integral-square-error for a third-order system is described.

ISSN:0020-7179    

DOI:10.1080/00207177408932627

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

The problem of estimation of the state of a linear dynamic system driven by white Gaussian noise with unknown covarianceQand observed by a linear function of the state contaminated by white Gaussian noise with unknown covarianceRis considered. Bayesian recursion relations for the probability densities of the unknown random variables conditioned on all available data are developed. Initially a relation giving thea posterioridensities ofQandRconditioned on all available data is developed. However since the possible range ofQandRis generally unbounded and also becauseQandRmay have quite large dimension, a mechanization of the aforesaid algorithm by representingQandRwith a grid of possible values is considered unfeasible for any realistic problems. Therefore, the random variablesQandRare transformed to random variables representing the optimal gain and the covariance of the innovations process by use of the steady state Kalman filter relations. The resulting probability density is reduced to theposterioridensity of the optimal gain by the law of total probability. Based on the recursion relations for this density a practical, new, recursive algorithm for optimal state estimation in the presence of noise with unknown noise covariance is developed. Two examples are presented showing the results of the new algorithm.

ISSN:0020-7179    

DOI:10.1080/00207177408932628

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

Integrated excitation and/or governor control systems are the result of using novel approaches for the selection of stabilizing signals in electric power systems. Such controllers have usually been derived on the basis of a linearized system model, an attractive practical feature of these being that a linear, time-invariant optimal controller may be derived. The power system is non-linear, however, and it is for this non-linear system that an optimal controller is ideally required. Previous work in the area is shown to be deficient in the light of this requirement and subsequently time-invariant integrated controllers suitable for use with the non-linear system are developed. These controllers incorporate model following with integral action and are shown to effect improved control of the nonlinear system over a wide range of operating conditions. The manner in which the proposed control system design procedure may permit the integrated control of large power systems is also of considerable practical importance.

ISSN:0020-7179    

DOI:10.1080/00207177408932629

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

Several definitions of stability for a set relative to a difference equation are considered, and stability theorems are established. These theorems provide sufficient conditions for stability and are obtained by employing the idea of a positive semi-definite Lyapunov function which has a strongly negative definite difference. These results represent the discrete-time analogues of the recent work of Grimmer and Haddock (1973).

ISSN:0020-7179    

DOI:10.1080/00207177408932630

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

This paper discusses the canonical state equations of linear time-varying large-scale systems in vector block diagram form. It is shown, with the aid of the adjacency matrix of the signal flow graph, that a canonical state equation is derived under a natural condition. Some sufficient conditions for the system to be described by a canonical state equation are presented. As the main result, a property of linear systems is obtained by considering the converse system, which means a system represented in vector block diagram form with reversed directions and dual subsystems. The result states that, the converse system is described by n dual form of the original state equation. This result can be used for the design of multivariate systems.

ISSN:0020-7179    

DOI:10.1080/00207177408932631

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

The order of a system not in state-space form has been defined elsewhere. Degree has been defined for rational transfer function matrices, and by extension to systems of least order : this definition is generalized for systems not having least order. A new concept of ‘ complexity ’ is introduced, and these ideas are used to resolve a confusion which exists in the literature.

ISSN:0020-7179    

DOI:10.1080/00207177408932632

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

The inclusion in a, digital adaptive control scheme of control laws based on the minimum of a discrete set of quadratic cost functional evaluations is considered ; controlling inputs being constrained to take elements of a predefined set of levels. Initially single input controllers are developed on a ‘ demand following ’ and model reference basis. A direct projection of the basic theory to multivariable processes is proposed and an alternative systematic approach developed to overcome the mounting computational problems associated with the direct scheme. Identified state transition and state driving matrices, with sampled states, provide the data necessary for the implementation, on line, of the proposed adaptive schemes. The applicability of the controllers in the case of second, third and fourth-order plants, and for single and multiple inputs, is demonstrated

ISSN:0020-7179    

DOI:10.1080/00207177408932633

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

This paper presents a method for stabilizing a linear discrete-time system with unknown constant parameters. Simultaneous identification and control of the system are considered. The optimal control strategy is obtained by using the Bayes approach. Some numerical results are also included.

ISSN:0020-7179    

DOI:10.1080/00207177408932634

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor