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.

Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems

Abstract: This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.

Control of Systems With Hysteresis Via Servocompensation and Its Application to Nanopositioning

Abstract: Partly motivated by nanopositioning applications in scanning probe microscopy systems, we consider the problem of tracking periodic signals for a class of systems consisting of linear dynamics preceded by a hysteresis operator, where uncertainties exist in both the dynamics and the hysteresis. A robustified servocompensator is proposed, in combination with an approximate hysteresis inverse, to achieve high-precision tracking. The servocompensator accommodates the internal model of the reference signal and a finite number of harmonic terms. Using a Prandtl-Ishlinskii (PI) operator for modeling hysteresis, we show that the closed-loop system admits a unique and asymptotically stable periodic solution, which justifies treating the inversion error as an exogenous periodic disturbance. Consequently, the asymptotic tracking error can be made arbitrarily small as the servocompensator accommodates a sufficient number of harmonic terms. The analysis is further extended to the case where the hysteresis is modeled by a modified PI operator. Experiments on a commercial nanopositioner show that, with the proposed method, tracking can be achieved for a 200-Hz reference signal with 0.52% mean error and 1.5% peak error, for a travel range of 40 μm. The performance of the proposed method in tracking both sinusoidal and sawtooth signals does not fall off with increasing frequency as fast as the proportional-integral controller and the iterative learning controller, both adopted in this paper for comparison purposes. Further, the proposed controller shows excellent robustness to loading conditions.

Adaptive output feedback control of robot manipulators using high-gain observer

Abstract: An adaptive controller using only joint position measurement is presented for the tracking control of an n-link robot manipulator with unknown load. High-gain observers are used to estimate joint velocities. We saturate the control inputs outside a domain of interest and use an adaptive law with a parameter projection feature. Simulation results on a two-link manipulator illustrate that the proposed controller recovers the performance under state feedback.

Semiglobal stabilization of a class of nonlinear systems using output feedback

Abstract: The stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using output feedback is considered. Emphasis is placed on a class of systems that can be transformed into a global normal form with no zero dynamics. Semiglobal stabilization means that for every compact set of initial conditions, it is possible to design an output feedback controller that stabilizes the origin and includes the given compact set in the region of attraction. The system equations are allowed to depend on constant unknown parameters that do not change the vector relative degree of the system. The controller is robust with respect to these parameters. Global Lipschitz conditions are not required. >

A separation principle for the control of a class of nonlinear systems

Abstract: We extend the separation results of a previous work of ours (1999) to a case where a globally bounded state feedback controller renders a certain compact set positively invariant and asymptotically attractive. The extension covers a wide range of control tasks that arise in adaptive control, servomechanisms, and practical stabilization. It is shown that by implementing the control law using a high-gain observer, we can recover the performance of the state feedback controller.

I and i

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 …

Linear Matrix Inequalities in System and Control Theory

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.

Higher-order sliding modes, differentiation and output-feedback control

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...