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.

Passivity-based controller design for stablization of underwater gliders

Abstract: The problem of stabilizing steady gliding is very critical for an underwater glider, which is subject to many non-negligible disturbances from the aquatic environment. Traditional control methods like PID control, LQR control or torque control, can not provide simultaneously easy controller implementation and fast convergence speed for stabilization. In paper we propose a new nonlinear, passivity-based controller for the stablization problem. The controller is designed based on an approximation of a reduced model that is obtained through singular perturbation analysis, and consequently, it does not require full state feedback and is thus easy to implement. The local stability of the closed-loop full system is established through linearization. Simulation results are provided to demonstrate that the proposed controller achieves rapid convergence in stabilization.

Feedback control of the spatiotemporal firing patterns of neural microcircuits

Abstract: One of the fundamental objectives in systems neuroscience is to precisely control the spatiotemporal firing of cortical neurons to elicit a desired pattern of activity. In this work, we study the effects of intracortical micro-stimulation on the dynamics of a basal ganglia microcircuit model, and explore the feasibility of controlling the spatiotemporal firing patterns of the population in the presence of unobserved inputs. Results from the simulation study suggest that properly designed Multiple-Input-Multiple-Output (MIMO) feedback controller can force a subpopulation of output neurons to follow a prescribed spatiotemporal firing pattern despite the presence of unobserved inputs. The accuracy of the spike timing of the controlled neural firing with respect to the reference spike trains is in the order of tens of milliseconds. Even a simplified circuit model of Hammerstein-Wiener type can help in prescreening potential stimulation sites and analyzing the nominal stability of the closed-loop system.

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

Abstract: We give a general formulation of a number of control problems. This formulation considers a wide class of systems and any globally bounded state feedback controller that renders a certain compact set positively invariant and asymptotically attractive. We develop a converse Lyapunov theorem, and we prove that, by implementing the control law using a high-gain observer, we can recover asymptotic stability of the attractive set, its region of attraction, and trajectories.

Approximation of Nash strategies

Abstract: Near-equilibrium solutions of nonzero-sum differential games are defined. It is shown that truncated series solutions of linear quadratic games are near-equilibrium.

An algorithm for enlarging the region of attraction using trajectory reversing

Abstract: Trajectory reversing is a method commonly used for estimating the region of attraction of stabilized equilibria. Using a discrete set of points obtained by trajectory reversing, this paper presents an algorithm for estimation and mathematical representation of the region of attraction using convex hulls. Several two-dimensional examples are presented to illustrate the usefulness of the algorithm. The method provides larger estimates compared to that obtained by existing algorithms but its main advantage lies in its applicability to higher-order systems. The mathematical representation of the region of attraction is useful in applying the Impulse Manifold Method, which was developed for stabilization of equilibria of underacuated systems from configurations lying outside their region of attraction. The region of attraction of the pendubot upright equilibrium is estimated to demonstrate the applicability of our algorithm to higher-order systems and illustrate the usefulness of the Impulse Manifold Method through simulations.

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...