摘要:

The method or generalized orthogonal polynomials (GOP) is applied to the analysis and optimal control of time-varying systems. The proposed GOP can represent all kinds of individual orthogonal-polynomial and non-orthogonal Taylor series. The operational matrix for the forward and backward integration of the generalized orthogonal polynomials, and the operational matrix of the product of r' and the generalized orthogonal-polynomial vector are derived and applied to time-varying systems. By using these three kinds of operational matrices, the computational algorithm for calculating the expansion coefficients is very simple and effective. Three satisfactory examples illustrate the usefulness of the method.

ISSN:0020-7179    

DOI:10.1080/00207178608933640

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

A recursive identification of a discrete dynamical system is presented in this paper. Two methods of recursive identification, namely the recursive extended least-squares method and the recursive maximum likelihood method, are described and analysed. The techniques are illustrated numerically with simulations.

ISSN:0020-7179    

DOI:10.1080/00207178608933641

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In a recent series of papers, Drager and Martin have shown global observability for a variety of particular classes of systems (including both discrete and continuous time systems). The underlying philosophy behind their methods is apparently that if a flow is ergodic and the system observation has a sufficiently special value, the system is completely observable. In this paper we prove observability for observed systems whose underlying flow is minimal and distal. While our results hold also in discrete time, we illustrate this result for invariant ergodic systems on nilmanifolds, i.e. those invariant flows with an infinitesimal generator that is ‘irrational modulo the commutator’. One well-known example of such a flow is the irrational flow on a torus studied by Drager and Martin.

ISSN:0020-7179    

DOI:10.1080/00207178608933642

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Given a polynomial P(s) = ansn+ an−11Sn−1+ … -+ a1s + a0which satisfies the Routh-Hurwitz criterion, a procedure is given for finding non-conservative upper bounds on the allowable variations of the coefficients such that the perturbed polynomial maintains the stability property.

ISSN:0020-7179    

DOI:10.1080/00207178608933643

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The shifted Jacobi delay operational matrix is introduced, and applied to the approximation of the solutions of linear systems with arbitrary time delay. The parameter-identification problem for time-delay systems is also dealt with. The new method is algebraic and computer-oriented. Two examples are given, and the results are very accurate and satisfactory.

ISSN:0020-7179    

DOI:10.1080/00207178608933644

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Linear-time temporal logic is applied to the verification of control systems. A formal language and proof system are adapted from those used in the verification of concurrent programs by Manna and Pnueli. Properties of some simple control systems are then verified by formally deducing temporal logic specifications of desired behaviour from descriptions of system dynamics. Finally, the usefulness of temporal logic in control theory is discussed and topics for future research are suggested.

ISSN:0020-7179    

DOI:10.1080/00207178608933645

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

During the 1920s the German engineer Karl Küpfmüller made substantial advances in the development of a theory of linear systems, notably by adopting a ‘systems approach’ to modelling electrical networks and control systems. Küpfmüller's achievements included an appreciation of the significance of the ‘time × bandwidth product’ for information transmission, and the establishment of an approximate stability criterion for a certain type of control system. This early work is outlined in the context of contemporary developments outside Germany, and a brief indication is given of the scope of Küpfmüller's later career.

ISSN:0020-7179    

DOI:10.1080/00207178608933646

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The classical Segré, Weyr characteristic theory of the standard eigenvalue-eigenvector problem defined on A ϵ ℝn×nis extended to the case of right (left) regular pencils sF — G, F, G ϵ ℝm×n. The notions of α-Toeplitz matrices and of the right (left) α. — (F, G) sequences Jαr(F,G) (Jα1(F,G)) respectively are introduced. For right (left) regular pairs it is shown that Jαr(F,G) (Jα1(F,G)) are piecewise arithmetic progression sequences (PAPS); the singular points of those PAPS define the possible degrees of the elementary divisors (e.d.) at α, whereas the deviations, or gaps from the arithmetic progression sequence, define the multiplicity of the corresponding degree e.d.s. The links between the algebraic notion of the Segré characteristic and the geometric notion of the Weyr characteristic are established for such families of pencils. Two different procedures for the computation of the Segré characteristic are given; the first is based on the analysis of singular points of PAPS and the second is based on the conjugate partitioning property of the algebraic multiplicity of a zero of sF - G at α by the Weyr and Segré characteristics at a. In the latter case a Ferrers-type diagram is suggested as the tool for the computation of the Segré characteristic from the Weyr characteristic. The results provide a procedure for the computation of the Weierstrass part of the Kronecker form of right (left) regular pencils by rank tests on α-Toeplitz matrices.

ISSN:0020-7179    

DOI:10.1080/00207178608933647

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Based on the concept of the interaction factor, a method for obtaining rapid graphical estimates of equivalent single-loop gain functions and interaction ratios is used in the design of 2 x 2 systems with severe interaction by classical techniques.

ISSN:0020-7179    

DOI:10.1080/00207178608933648

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

By applying differential form theory, we consider the singular control problem for non-linear systems with control variables appearing linearly in both the system dynamics and the performance index. First, we derive necessary conditions of singular optimality for a single-input system, including the relation to the Euler-Poisson equation and to the generalized Legendre-Clebsch condition. Defining thedegree of singularity,we develop necessary conditions satisfied by the singular trajectory embedded in a reduced space. For a time-invariant system, we clarify the relation between the dynamic and the related static optimality. Second, we derive necessary conditions for singular optimality for a multi-input system where the dimension of the control vector is equal to that of the state space. We show that the Shima-Sawaragi condition for the optimality of boundary controls and the generalized Legendre-Clebsch condition are obtained from these conditions. The results are also applied to the analysis of a time-invariant system.

ISSN:0020-7179    

DOI:10.1080/00207178608933649

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor