Journal ArticleDOI
A general result on the stabilization of linear systems using bounded controls
TLDR
Two constructions of controllers that globally stabilize linear systems subject to control saturation are presented in terms of a "neural-network type" one-hidden layer architecture and a cascades of linear maps and saturations.Abstract:
We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a "neural-network type" one-hidden layer architecture, while the other one is in terms of cascades of linear maps and saturations. >read more
Citations
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Book
Stability of Time-Delay Systems
TL;DR: Preface, Notations 1.Introduction to Time-Delay Systems I.Robust Stability Analysis II.Input-output stability A.LMI and Quadratic Integral Inequalities Bibliography Index
Book ChapterDOI
Input to State Stability: Basic Concepts and Results
TL;DR: This expository presentation addresses the precise formulation of questions of robustness with respect to disturbances, formulated in the paradigm of input to state stability, with an intuitive and informal presentation of the main concepts.
Journal ArticleDOI
Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach
Murad Abu-Khalaf,Frank L. Lewis +1 more
TL;DR: It is shown that the constrained optimal control law has the largest region of asymptotic stability (RAS) and the result is a nearly optimal constrained state feedback controller that has been tuned a priori off-line.
Journal ArticleDOI
A nonlinear small gain theorem for the analysis of control systems with saturation
TL;DR: A nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation.
Journal ArticleDOI
Survey Constructive nonlinear control: a historical perspective
Petar V. Kokotovic,Murat Arcak +1 more
TL;DR: This survey describes the 'activation' of stability, optimality and uncertainty concepts into design tools and constructive procedures in nonlinear control theory and concludes with four representative applications.
References
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Book
Applied Nonlinear Control
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
Book
Mathematical Control Theory: Deterministic Finite Dimensional Systems
TL;DR: This book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects, covering a wide range of topics written in a standard theorem/proof style and develops the necessary techniques from scratch.
Journal ArticleDOI
Smooth stabilization implies coprime factorization
TL;DR: In this paper, it was shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system.
Journal ArticleDOI
Global stabilization and restricted tracking for multiple integrators with bounded controls
TL;DR: In this paper, a nonlinear combination of saturation functions of linear feedbacks is proposed to stabilize a chain of integrators of arbitrary order, where the saturation function is a linear near the origin of the input.
Journal ArticleDOI
A new design of constrained controllers for linear systems
Per-Olof Gutman,Per Hagander +1 more
TL;DR: A new method is presented to find stabilizing saturated linear state feedback controllers for linear continuous-time and discrete-time systems.
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