3,056 research outputs found
Investigation and Synthesis of Robust Polynomials in Uncertainty on the Basis of the Root Locus Theory
The root locus method is proposed in the chapter for searching intervals of uncertainty for coefficients of the given (source) polynomial with constant or interval coefficients under perturbations, which ensures its robust stability regardless of whether the given polynomial is Hurwitz or not. The method is based on introduction and application of the “extended root locus” notion. Polynomial adjustment is performed by setting up each one of its coefficients separately and sequentially and determining permissible values of coefficient variation intervals (intervals of uncertainty). The effect of each coefficient variation upon the polynomial root dynamics (behavior) is considered and analyzed separately, and this influence could be observed in the root locus portraits. Root locus method is thus generalized to the cases when the number of polynomial variable coefficients is arbitrary. The root locus parameter distribution diagram along the asymptotic stability bound is introduced and applied for observing the roots behavior regularities. On this basis, the stability conditions are derived, and analytical and graphic-analytical methods are worked out for calculating intervals of variation for the 4th order polynomial family parameters ensuring its robust stability. It also allows to extract Hurwitz subfamilies from the non-Hurwitz families of interval polynomials and to determine whether there exists at least one stable polynomial in the unstable polynomial family
Robust controls with structured perturbations
This final report summarizes the recent results obtained by the principal investigator and his coworkers on the robust stability and control of systems containing parametric uncertainty. The starting point is a generalization of Kharitonov's theorem obtained in 1989, and its generalization to the multilinear case, the singling out of extremal stability subsets, and other ramifications now constitutes an extensive and coherent theory of robust parametric stability that is summarized in the results contained here
Parametric Robust Control and System Identification: Unified Approach
During the period of this support, a new control system design and analysis method has been studied. This approach deals with control systems containing uncertainties that are represented in terms of its transfer function parameters. Such a representation of the control system is common and many physical parameter variations fall into this type of uncertainty. Techniques developed here are capable of providing nonconservative analysis of such control systems with parameter variations. We have also developed techniques to deal with control systems when their state space representations are given rather than transfer functions. In this case, the plant parameters will appear as entries of state space matrices. Finally, a system modeling technique to construct such systems from the raw input - output frequency domain data has been developed
Parameter Synthesis in Markov Models: A Gentle Survey
This paper surveys the analysis of parametric Markov models whose transitions
are labelled with functions over a finite set of parameters. These models are
symbolic representations of uncountable many concrete probabilistic models,
each obtained by instantiating the parameters. We consider various analysis
problems for a given logical specification : do all parameter
instantiations within a given region of parameter values satisfy ?,
which instantiations satisfy and which ones do not?, and how can all
such instantiations be characterised, either exactly or approximately? We
address theoretical complexity results and describe the main ideas underlying
state-of-the-art algorithms that established an impressive leap over the last
decade enabling the fully automated analysis of models with millions of states
and thousands of parameters
Systems Structure and Control
The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc
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