摘要:

An equivalent stochastic feedback system can be found for many recursive identification and adaptive control schemes. This equivalent feedback system has a certain structure which is used here for constructing near supermartingales, allowing the establishment of a.s. convergence. Explicit convergence conditions are then obtained for recursive identification and adaptive control schemes which admit an equivalent stochastic feedback representation of the form considered. The usefulness of the results is illustrated by their application to the straightforward convergence analysis of several schemes which have not been considered previously, and to the re-derivation of the known convergence conditions for two other schemes.

ISSN:0020-7179    

DOI:10.1080/00207178208922615

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The definition and properties of sector conditions introduced by Zames for scalar systems can be extended to the multivariable case. The present paper makes use of appropriate forms of sector conditions in conjunction with the decomposition of a linear operator into two linear operators φ and G - φ, where φ has a normal transfer function matrix ; and proposes a useful stability criterion for a class of multivariable non-linear feedback systems. The relevant stability result is developed further by a suitable interpretation of sector conditions in the frequency domain. A particular choice for φ leads to a generalization of the circle criterion in which the Nyquist plot of the frequency response of scalar systems is replaced by bands swept by circles whose centres and radii are related in a direct manner to the numerical range ofG(jω). The result has a simple graphical interpretation and lends itself to a computer implementation which can be shown to be numerically stable. The approach is also suitable for the study of stability in the face of additive perturbations in the system model. Further choices of φ lead to stability tests which are based on the direct and inverse Nyquist plots of the diagonal elements ofG(jω).

ISSN:0020-7179    

DOI:10.1080/00207178208922616

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

Considering linear time-invariant distributed feedback systems, a necessary and sufficient condition for robust stability is derived with respect to plant perturbations belonging to a specified ball. The conclusion is shown to exhibit design limitations imposed by plant uncertainties.

ISSN:0020-7179    

DOI:10.1080/00207178208922617

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

Optimal motorway traffic control strategies are derived on the basis of a highly accurate, non-linear, discrete dynamical traffic flow model. By application of these strategies, traffic can be driven back to its nominal state condition in a prescribed optimal manner after occurrence of a severe disturbance. Because of the high order of the optimal traffic control problem, four known decomposition methods arc applied, in order to reduce the computational effort needed for its solution. Simulation results obtained for a realistic traffic situation on a 30 km long motorway are discussed both from an algorithmical and a traffic control engineering viewpoint.

ISSN:0020-7179    

DOI:10.1080/00207178208922618

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

A vertically aligned spiral spring of negligible mass, fixed at its lower end, and carrying a heavy load which is constrained to move in the vertical direction, the motion being resisted by viscous damping, is considered. For a real spring, a large compression causes the coils to close up and ultimately to form an impenetrable barrier to the load. Thus, the spring control force becomes infinite at a certain point, and the non-linear differential equation of motion has a singularity at this point, in contrast to the classical cases of mass-spring systems. Assuming plausible analytic expressions for the singular control force, we obtain several exact solutions of the differential equation. The effects of the magnitudes of the damping, the control and the constant terms of the differential equation on the character of the motion (over-damped or oscillatory) are exhibited for several concrete cases that may be useful in applications.

ISSN:0020-7179    

DOI:10.1080/00207178208922619

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

Certain physical systems are modelled by linear systems having a high degree of internal symmetry. In this paper it is shown that this internal symmetry can he exploited to yield new system-theoretic invariants and a better understanding of how the underlying structure affects overall system performance.

ISSN:0020-7179    

DOI:10.1080/00207178208922620

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The paper investigates controllability and stabilizability of sensitivity combined systems for distributed parameter systems of parabolic type. The sensitivity combined system consists of a model equation and its parameter sensitivity equation. The existence of a sensitivity function which is a unique solution of the sensitivity equation is shown. Conditions of controllability for the sensitivity combined systems are sought. Also investigated is the exponential stabilizability of the sensitivity combined systems in the case of constructing controllers (observations).

ISSN:0020-7179    

DOI:10.1080/00207178208922621

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The problem of stochastic stability of continuous dynamic systems is examined from the point of view of entropy. The concept of entropy, as it was defined by Shannon, represents a measure of average uncertainty in a random situation. In this research, the entropy of the state of a system is considered and conditions for keeping it within certain bounds or minimizing it are sought. For this purpose several tools and results of the theory of stochastic differential equations are used. Previous results of narrow scope concerned only systems with initial random conditions. Here, the problem is generalized to systems with noise inputs. The systems under consideration are with constant or periodic coefficients. Also, general non-linear Itô-type systems are examined. A linearization procedure is applied in the non-linear case and sufficient conditions for stability are developed. Finally, a lower bound to the entropy of nonlinear systems is found. This bound provides the tools for instability results. It should be stressed that some of the results are weak because of the generality of the criterion used. However, simplicity is their virtue.

ISSN:0020-7179    

DOI:10.1080/00207178208922622

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

An algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed-loop system has specified eigenvalues. The algorithm is more efficient than many comparable techniques, and has some desirable numerical properties. It is closely related to theQRalgorithm for the eigenproblem, and extends to descriptor systems.

ISSN:0020-7179    

DOI:10.1080/00207178208922623

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

This paper arose from the need for a better understanding of the minimal-order observer problem. A deadbeat function observer is an estimator that estimates exactly a linear function of the state of a deterministic discrete-time linear system via an incomplete state observation. The minimal order of a minimal-time function observer, which exhibits the fastest deadbeat response among deadbeat function observers, was obtained and such an observer was designed. It was shown that the minimal order of a minimal-time function observer is not necessarily the same as the minimal order of a deadbeat function observer.

ISSN:0020-7179    

DOI:10.1080/00207178208922624

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor