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Hassan K. Khalil

Bio: Hassan K. Khalil is an academic researcher from Michigan State University. The author has contributed to research in topics: Nonlinear system & Nonlinear control. The author has an hindex of 57, co-authored 284 publications receiving 15992 citations. Previous affiliations of Hassan K. Khalil include Ford Motor Company & National Chiao Tung University.


Papers
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Proceedings ArticleDOI
10 Dec 2002
TL;DR: This paper shows how to introduce integral action in such a way as to recover the transient performance of ideal SMC while achieving zero steady-state error, both regional as well as global results.
Abstract: An ideal sliding mode control (SMC) can guarantee asymptotic tracking with zero steady-state error for a wide class of nonlinear systems. When implemented using continuous approximations, the controller can no longer guarantee zero steady-state error. Instead, it guarantees ultimate boundedness with an ultimate bound that is proportional to the width of the boundary layer. To reduce the steady-state error, we have to reduce the width of the boundary layer, but a too small boundary layer gets us back into chattering and excitation of high-frequency modes, which are the reasons why the ideal SMC was approximated in the first place. For constant, approximately constant, or eventually constant exogenous signals, we can achieve zero steady-state error by introducing integral action in the controller. The traditional way of introducing integral action usually leads one to deterioration of the transient response of the system. In this paper we show how to introduce integral action in such a way as to recover the transient performance of ideal SMC while achieving zero steady-state error. We give both regional as well as global results.

58 citations

Journal ArticleDOI
TL;DR: In this article, a framework for the development of a fault detection and classification algorithm based on the coefficients calculated from the discrete wavelet transform and using clustering is described, and results from testing are presented, verifying the analysis.

58 citations

Journal ArticleDOI
TL;DR: It is demonstrated that by designing the observer gain high enough, the closed-loop system recovers the performance of state feedback control with no time delay, but the gain of the observer is limited by the time delay.
Abstract: This note addresses the problem of feedback linearization for nonlinear systems with time-varying input and output delays. To solve the realization issue of future states, a high-gain-observer is constructed as a predictor. Then, the output feedback predictive control is presented. The stability of the closed-loop system is analyzed by using a Lyapunov-Krasovskii functional. It is demonstrated that by designing the observer gain high enough, the closed-loop system recovers the performance of state feedback control with no time delay. However, the gain of the observer is limited by the time delay. Finally, numerical simulations are given to illustrate the effectiveness of the proposed control.

58 citations

Journal ArticleDOI
01 Jul 1992
TL;DR: In this article, a sequential procedure is described to decompose the problem into slow and fast subproblems, and a composite compensator is formed as the parallel connection of the fast compensator with the strictly proper part of the slow compensator.
Abstract: H∞ control of linear time-invariant singularly perturbed systems is considered. A sequential procedure is described to decompose the problem into slow and fast subproblems. The fast problem is solved first. Then the slow problem is solved under a constraint on the value of the compensator at infinity. A composite compensator is formed as the parallel connection of the fast compensator with the strictly proper part of the slow compensator. The asymptotic validity of the composite compensator is established.

57 citations

Proceedings ArticleDOI
21 Jun 1989
TL;DR: In this article, the authors studied feedback control of linear time-invariant singularly perturbed systems of the form? = A 11 x + A 12 z + B 1 u + B 2 u y = C 1 x + C 2 z + Eu where Eu may be singular.
Abstract: This paper studies feedback control of linear time-invariant singularly perturbed systems of the form ? = A 11 x + A 12 z + B 1 u ? = A 21 x + A 22 z + B 2 u y = C 1 x + C 2 z + Eu. where A 22 may be singular. It is shown that, under stabilizability-detectability assumptions on the slow and fast models, the theory of feedback control of singularly perturbed systems can be extended to the case of singular A 22 . Both state and output feedback results are given.

57 citations


Cited by
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Journal ArticleDOI

[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Book
01 Jan 1994
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Abstract: Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

11,085 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a state-of-the-art survey of ANN applications in forecasting and provide a synthesis of published research in this area, insights on ANN modeling issues, and future research directions.

3,680 citations

Journal ArticleDOI
Arie Levant1
TL;DR: In this article, the authors proposed arbitrary-order robust exact differentiators with finite-time convergence, which can be used to keep accurate a given constraint and feature theoretically-infinite-frequency switching.
Abstract: Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

2,954 citations