摘要:

The linear-quadratic optimal control problem is considered for time-varying descriptor systems of the formE(t+1)x(t+1)=A(t)x(t)+B(t)u(t)+C(t)f(t),whereEis a square matrix with constant rankr(which may be singular) andf(t) is a known vector. By using variational techniques, necessary conditions are derived for the existence of optimal control. By transforming to a coordinate system which can be computed by performing a non-singular linear transformation, necessary con- ditions for the existence of optimal control can be changed to a two-point boundary value problem which looks like the usual two-point boundary problem of linear- quadratic optimal control. By applying the sweep method, such a two-point boundary value problem results in a matrix Riccati equation and a linear difference equation. At the same time, the optimal control is uniquely determined in terms of the ‘state’ x1(t), which is the dynamic part of the descriptor vector x(t). The optimal cost is also given in terms of x1(t).

ISSN:0020-7179    

DOI:10.1080/00207178908559717

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Invariance is a primary characteristic of a control system. It is strongly interrelated with the system structure where the latter provides a necessary condition for the invariance. The relationship is established by using various formal languages among which the graph-theoretic model seems most adequate when it comes to analysing the causal relations between components of the system. The present work aims to reflect the close interdependence between a number of invariance types and graph structures. Some typical algorithms for solving the problems of structure selection are demonstrated.

ISSN:0020-7179    

DOI:10.1080/00207178908559718

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Traditionally, PID controllers are designed either as regulating or as tracking controllers because, usually, it is not possible to fulfil both functions simultaneously. Designing rules complementary to Ziegler and Nichols ones are introduced. They allow, using a special connection of the classical PID, the tracking behaviour to be improved without modifying the regulating characteristics.

ISSN:0020-7179    

DOI:10.1080/00207178908559719

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The derivation of necessary conditions for the optimality of singular controls (in the sense of Pontryagin's maximum principle) in optimal control problems is inves- tigated. A new class of the necessary conditions is developed. This class of necessary conditions is composed of two parts, the first-order and second-order necessary conditions. As an application of these necessary conditions, an illustrative example is given, which shows that the necessary conditions developed are stronger than the generalized Legendre-Clebsch condition. That is, the singular control in the example satisfies the generalized Legendre-Clebsch condition, but does not satisfy the necessary conditions developed in this paper.

ISSN:0020-7179    

DOI:10.1080/00207178908559720

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Controllability and observability are studied for linear retarded systems in a Banach spaceX.Both theX-exact and theX-approximate controllability are considered and a number of necessary and sufficient conditions in terms of the coefficient operators and/or the fundamental solution are presented. Various corresponding concepts for observability are introduced and the duality between controllability and observability is clarified. An applicable condition for theX-approximate controllability and theX*-observability is established under the assumptions that the control is a finite dimensional one and the system of generalized eigenspaces is projectively complete. The condition is stated in terms of eigenvectors and controllers.

ISSN:0020-7179    

DOI:10.1080/00207178908559721

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The cell-mapping method previously used to study the global behaviour of strongly non-linear systems is extended to optimal control problems. Approximate optimal control results are extracted from the family of controlled mappings by a systematic search. Provisions are made to account for rigid barriers to flow in the continuum state space. A method of implementation is also proposed, which involves linear interpolation of the discrete optimal controls.

ISSN:0020-7179    

DOI:10.1080/00207178908559722

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A model-reduction problem is considered which involves bothL2(quadratic) andH∞(worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize anL2model-reduction criterion subject to a prespecifiedH∞constraint on the model-reduction error. The principal result is a sufficient condition for characterizing reduced-order models with boundedL2andH∞approximation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e. idempotent matrix. When theH∞constraint is absent, the sufficient condition specializes to theL2model-reduction result given by Hyland and Bernstein (1985).

ISSN:0020-7179    

DOI:10.1080/00207178908559723

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A new failure isolation scheme is proposed using an extended robust observation approach. A systematic procedure is developed for designing fault detection observers. This new failure isolation scheme can isolate a much larger class of failure modes than previous failure isolation schemes in the relevant literature, so that failure diagnosing precision may be greatly improved.

ISSN:0020-7179    

DOI:10.1080/00207178908559724

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A new method is presented for designing load frequency self-tuning regulators for interconnected power systems having unknown deterministic load disturbances. A discrete-type optimal control law is obtained by defining a cost function with a term for presenting the constraints on the control effort and then by minimizing it with respect to the control variable. An attractive feature of the proposed control scheme is that the effect of the load disturbances is decoupled from the plant output and the large value of control is discouraged indirectly by penalizing the rate of change of control. Another feature is that it considers the time delay due to the identification and control computations and the transmission time of the system data over the telemeter links to the controlling plant. The control effects of the proposed regulator are examined using digital simulations of a two-area power system provided with reheat steam turbines.

ISSN:0020-7179    

DOI:10.1080/00207178908559725

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The problem of modelling critically linear systems with product non-linearity is considered. A new linearization technique is proposed using mathematical perturbation methods. The class of systems considered is represented by an extended linear state space model. An upper bound on the order of the developed model is obtained. Conditions of asymptotic stability are derived and it is shown that the model, under the appropriate conditions, is observable provided the unperturbed part of the nonlinear system is observable.

ISSN:0020-7179    

DOI:10.1080/00207178908559726

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor