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Categories and Foundations of the Theory of Nonlinear Controlled Dynamical Systems: I
Differential Equations, 2002According to the introduction, ``the exposition of foundations of a particular mathematical theory begins with the definition of\dots notions.'' In the first part the author develops ``an approach that permits one to use category theory and thus introduce the above mentioned notions in a very natural manner''.
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The Nonlinear Control Theory of Complex Mechanical Systems.
1996Abstract : This report summarizes a body of research dealing with the nonlinear control theory of complex mechanical systems. The principal focus is on so-called superarticulated (or underactuated) mechanical systems and systems having a mixture of directly controlled as well as uncontrolled degrees of freedom. The two-fold goal of the research is: (1)
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Geometric Theory of Reduction of Nonlinear Control Systems
Computational Mathematics and Mathematical Physics, 2018The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).
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Singular perturbation theory in control of nonlinear systems with uncertainties
2016 24th Iranian Conference on Electrical Engineering (ICEE), 2016In this paper, a control approach is proposed for stabilization of nonlinear systems in the presence of both matched and unmatched uncertainties. By combining the time scale separation and backstepping, first, high-gain filters are designed to estimate the uncertainties, and then, a fast dynamical equation is derived which the solution is found to ...
Alireza Khayatian, Mehrnoosh Asadi
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Theory of cone methods for null controllability of nonlinear control systems
IEEE Transactions on Automatic Control, 1979Cone-valued Lyapunov functions have been used by several authors to examine the stability of nonlinear systems. However, the general problem of constructing a suitable cone given the nature of nonlinearity seems to be as difficult as that of constructing a suitable Lyapunov function.
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Decomposition and control of a class of nonlinear stochastic systems: theory and its application
Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), 2001In this paper, we design control algorithms and derive sufficient criteria for the stability and robustness of nonlinear stochastic systems. The Lyapunov stability theory is used. The results documented are verified by studying examples. In particular, a high-performance servo-system with an electric motor is examined.
Akhouri S. C. Sinha +1 more
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Factorization of nonlinear systems: toward a theory for nonlinear H/sup infinity / control
Proceedings of the 27th IEEE Conference on Decision and Control, 2003A natural approach to H/sup infinity / control for nonlinear systems, by developing a theory of factorization for a nonlinear time-invariant causal map, is presented. Whenever such factorizations exist with well-behaved frequency-response function, theta , then a substantial class of nonlinear control problems can be solved. The author reports progress
J.A. Ball, J.W. Helton
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Toward a nonequilibrium theory for nonlinear control systems
2007This paper is concerned with the development of basic concepts and constructs for a nonequilibrium theory of nonlinear control. Motivated by an example of nonstabilizability of rigid spacecraft about an equilibrium (reference attitude) but stabilizability about a revolute motion, we review recent work on the structure of those compact attractors which ...
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Output feedback control for stabilizable and incompletely observable nonlinear systems: theory
Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000This paper introduces a new approach for output feedback stabilization of SISO systems which, unlike most of the techniques found in the literature, does not use high-gain observers and control input saturation to achieve separation between the state feedback and observer designs.
Manfredi Maggiore, Kevin M. Passino
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A Résumé of the Development and Literature of Nonlinear Control-System Theory
Journal of Fluids Engineering, 1957Abstract “Es gibt nichts Praktischeres als eine gute Theorie (There is nothing more practical than a good theory)” —Boltzmann. The first section of this paper stresses the fact that nonlinear control-system theory is rooted in the theory developed earlier for the solution of other types of nonlinear systems, especially ...
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