Journal ArticleDOI
Adaptive stabilization of multi-input nonlinear systems
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In this article, a universal stabilizer for linear systems with restricted state availability is presented. The stabilizers are of a discontinuous feedback form (embedded in a set-valued map), and incorporate adaptive matrix-valued gain functions which exploit the existence of finite spectrum-unmixing sets associated with the systems under consideration.Abstract:
Universal stabilizers are presented for two classes of nonlinear systems, linear in their multiple control inputs: (I) a class of pth order controlled differential inclusions on R″ with full state available for feedback, and (II) a class of nonlinearly perturbed linear systems with restricted state availability The stabilizers are of a discontinuous feedback form (embedded in a set-valued map), and incorporate adaptive matrix-valued gain functions which exploit the existence of finite spectrum-unmixing sets associated with the systems under consideration The analysis draws on an extension, to differential inclusions, of LaSalle's invariance principle for ordinary differential equationsread more
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Journal ArticleDOI
Adding integrations, saturated controls, and stabilization for feedforward systems
Frédéric Mazenc,Laurent Praly +1 more
TL;DR: The proposed approach provides feedback laws with several degrees of freedom which can be exploited to tackle design constraints and serves as a basic tool to be used, in a recursive design, to deal with more complex systems.
Dissertation
The Order of Any Stabilizing Regulator is Sufficient a Priori Information for Adaptive Stabilization
TL;DR: In this article, it is shown that this suffices as a priori information for an adaptive stabilizing controller, which is based on a dense search through parameter space, and does not utilize high gain properties, as opposed to the universal regulators proposed before.
Journal ArticleDOI
Multivariable adaptive control
TL;DR: An overview of some fundamental theoretical aspects and technical issues of multivariable adaptive control, and a thorough presentation of various adaptive control schemes for multi-input-multi-output systems, literature reviews on adaptive control foundations and multivariables adaptive control methods, and related technical problems are presented.
Journal ArticleDOI
An Integral Invariance Principle for Differential Inclusions with Applications in Adaptive Control
TL;DR: In this paper, the Byrnes-Martin integral invariance principle for ordinary differential equations is extended to differential inclusions on {Bbb R}N. The extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a variety of nonlinear system classes.
Journal ArticleDOI
Output-feedback model-reference sliding mode control of uncertain multivariable systems
TL;DR: It is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties.
References
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Book
Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
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The stability of dynamical systems
TL;DR: In this paper, an introduction to aspects of the theory of dynamical systems based on extensions of Liapunov's direct method is presented and the main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations.
Journal ArticleDOI
Some remarks on a conjecture in parameter adaptive control
TL;DR: In this paper, it was shown that if f and g are restricted to be rational functions, the answer is no, and they gave explicit real analytic functions f and G which work.
Journal ArticleDOI
Stability theory for ordinary differential equations.
TL;DR: LaSalle stability theorems refined for ordinary differential equations, discussing classical Liapunov results on system stability were discussed in this article, where they were refined for the case of continuous systems.
Journal ArticleDOI
The Order of Any Stabilizing Regulator is Sufficient a Priori Information for Adaptive Stabilization
TL;DR: In the absence of information of such an l, it is shown how to modify the algorithm to search over the regulator structures, i.e. the controller's dimension, which yields a continuous regulator which does not utilize probing signals.