Wassim Haddad - Profile on Academia.edu (original) (raw)
Papers by Wassim Haddad
Chapter Four. Impulsive Nonnegative and Compartmental Dynamical Systems
Chapter Seven. Energy-Based Control for Impulsive Port-Controlled Hamiltonian Systems
Nonlinear Dynamical Systems and Control, 2011
Contents Conventions and Notation xv Preface xxi Chapter 1. Introduction Chapter 2. Dynamical Sys... more Contents Conventions and Notation xv Preface xxi Chapter 1. Introduction Chapter 2. Dynamical Systems and Differential Equations 2.1 Introduction 2.2 Vector and Matrix Norms 2.3 Set Theory and Topology 2.4 Analysis in R n 2.5 Vector Spaces and Banach Spaces 2.6 Dynamical Systems, Flows, and Vector Fields 2.7 Nonlinear Differential Equations 2.8 Extendability of Solutions 2.9 Global Existence and Uniqueness of Solutions 2.10 Flows and Dynamical Systems 2.11 Time-Varying Nonlinear Dynamical Systems 2.12 Limit Points, Limit Sets, and Attractors 2.13 Periodic Orbits, Limit Cycles, and Poincare-Bendixson Theorems 2.14 Problems 2.15 Notes and References Chapter 3. Stability Theory for Nonlinear Dynamical. Systems 3.1 X CONTENTS 3.8 Problems 3.9 Notes and References Chapter 4. Advanced Stability Theory 4.1
One of the principal objectives of vibration isolation technology is to isolate sensitive equipme... more One of the principal objectives of vibration isolation technology is to isolate sensitive equipment from a vibrating structure or to isolate the structure from an uncertain exogenous disturbance source. In this paper, a dynamic observer-based active isolator is proposed that guarantees closed-loop asymptotic stabil- ity and disturbance decoupling between the vibrating structure and isolated structure. The proposed active isolator is applied to a uniaxial vibrational system and compared to an optimal linear-quadratic design.
Systems & Control Letters, Nov 1, 1987
A state-estimation design problem involving parametric plant uncertainties is considered. An erro... more A state-estimation design problem involving parametric plant uncertainties is considered. An error bound suggested by recent work of Petersen and Hollot is utilized for guaranteeing robust estimation. Necessary conditions which generalize the optimal projection equations for reduced-order state estimation are used to characterize the estimator which minimizes the error bound. The design equations thus effectively serve as sufficient conditions for synthesizing robust estimators. An additional feature is the presence of a static estimation gain in conjunction with the dynamic (Kalman) estimator, i.e., a nonstrictly proper estimator.
IEEE Transactions on Automatic Control, Jul 1, 1987
function K are given by (1 1) and (19), respectively, the optimal control is u= [ 2b2x:/q2Ix2(x;+... more function K are given by (1 1) and (19), respectively, the optimal control is u= [ 2b2x:/q2Ix2(x;+2x;)I 1 ' -261x1/ql [x? F,= -2G,/G.
IEEE Transactions on Automatic Control, May 1, 1993
discrete-time feedback control-design problem involving parametric uncertainty is considered. A q... more discrete-time feedback control-design problem involving parametric uncertainty is considered. A quadratic bound suggested by recent work on discrete-time state space H, theory is utilized in conjunction with the guaranteed cost approach to guarantee robust stability with a robust performance bound. The principal result involves sufficient conditions for characterizing robust fulland reduced-order controllers with a worst case H2 performance bound.
IEEE Transactions on Automatic Control, Dec 1, 1987
The optimal projection equations for reduced-order state estimation are generalized to allow for ... more The optimal projection equations for reduced-order state estimation are generalized to allow for singular (Le., colored) measurement noise. The noisy and noise-free measurements serve as inputs to dynamic and static estimators, respectively. The optimal salution is characterized by necessary conditions which involve a pair of oblique projections corresponding to reduced estimator order and singular measurement noise intensity.
In many applications of feedback control, phase information is available concerning the plant unc... more In many applications of feedback control, phase information is available concerning the plant uncertainty. For example, lightly damped flexible structures with colocated rate sensors and force actuators give rise to positive real transfer functions. Closed-loop stability is thus guaranteed by means of negative feedback with strictly positive real compensators. In this paper, the properties of positive real transfer functions are used to guarantee robust stability in the presence of positive real (but otherwise unknown) plant uncertainty. These results are then used for controller synthesis to address the problem of robust stabilization in the presence of positive real uncertainty. One of the principal motivations for these results is to utilize phase information in guaranteeing robust stability. In this sense these results go beyond the usual limitations of the small gain theorem and quadratic Lyapunov functions which may be conservative when phase information is available. The results of this paper are based upon a Riccati equation formulation of the positive real lemma and thus are in the spirit of recent Riccati-based approaches to bounded real (Hoo) control.
International Journal of Robust and Nonlinear Control, 1994
In a companion paper ('Explicit construction of quadratic Lyapunov functions for the small gain, ... more In a companion paper ('Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous-time theory'), Lyapunov functions were constructed in a unified framework to prove sufficiency in the small gain, positivity, circle, and Popov theorems. In this Part II, analogous results are developed for the discrete-time case. As in the continuous-time case, each result is based upon a suitable Riccati-like matrix equation that is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time-invariant system and a memoryless nonlinearity. Multivariable versions of the discrete-time circle and Popov criteria are obtained as extensions of known results. Each result is specialized to the linear uncertainty case and connections with robust stability for state-space systems is explored. Parameter-dependent Lyapunov functions In a companion paper1 Lyapunov functions were constructed in a unified framework to prove sufficiency in the small gain, positivity, circle, and Popov theorems. In this Part II, analogous results are developed for the discrete-time case. As in the continuous-time case, each result is based upon a suitable Riccati-like matrix equation that is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time-invariant system and a memoryless nonlinearity. Multivariable versions of the discrete-time circle and Popov criteria are obtained as extensions of known results.
For a given asymptotically stable linear dynamic system it is often of interest to determine whet... more For a given asymptotically stable linear dynamic system it is often of interest to determine whether stability is preserved as the system varies within a specified class of uncertainties. If, in addition, there also exist associated performance measures (such as the steady-state variances of selected state variables), it is desirable to assess the worst-case performance over a class of plant variations. These are problems of robust stability and performance analysis. In the present paper, quadratic Lyapunov bounds used to obtain a simultaneous treatment of both robust stability and performance are considered. The approach is based on the construction of modified Lyapunov equations, which provide sufficient conditions for robust stability along with robust performance bounds. In this paper, a wide variety of quadratic Lyapunov bounds are systematically developed and a unified treatment of several bounds developed previously for feedback control design is provided.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, 2005
In this paper, we study the problem of stability of linear neutral time-delay systems. Specifical... more In this paper, we study the problem of stability of linear neutral time-delay systems. Specifically, using the notion of structured phase margin, which characterizes stability margins in terms of a nominal plant transfer function in the presence of unknown structured phase perturbations, we derive several new frequency-domain sufficient conditions for stability of linear neutral time-delay systems. We provide both delay-independent as well as delay-dependent sufficient conditions for stability.
Finite settling time control of the double integrator is considered. The approach taken is to des... more Finite settling time control of the double integrator is considered. The approach taken is to design a compensator based on a virtual lossless absorber which is tuned so that, at some predetermined time, the virtual subsystem possesses all of the system's energy. At this time the controller is turned off, and the double integrator remains at rest at the origin. This strategy gives the appearance of instantaneously removing all of the system's energy as if a trap door had been sprung. A practically useful feature of the virtual trap-door absorber is that only position measurement is required. Parameters for the virtual trap-door absorber controller are chosen, and the resulting controller is compared to the classical minimal-time and minimal-energy controllers, which require measurements of both position and velocity. Index Terms-Double integrator, finite settling time control, minimal-time and minimal-energy optimal control, virtual absorber.
Chapter Five. Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems
Impulsive and Hybrid Dynamical Systems, 2006
A Fixed-Architecture Framework for Stochastic Nonlinear Controller Synthesis
2018 Annual American Control Conference (ACC), 2018
In this paper, we present a Lyapunov function-based optimization approach for designing state and... more In this paper, we present a Lyapunov function-based optimization approach for designing state and output feedback control laws for systems with polynomial nonlinearities. We use local polynomial expansions of a chosen order to approximate a higher-order nonlinear stochastic dynamical system, reformulate stochastic asymptotic stability conditions in the form of a nonlinear constrained optimization problem, and computationally determine the domain of attraction of the synthesized nonlinear controller on the original system. Finally, we illustrate the effectiveness of the proposed algorithm on two illustrative numerical examples.
Chapter 8. Finite-Time Thermodynamics
Chapter 13. Optimal Fixed-Structure Control for Nonnegative Systems
Nonnegative and Compartmental Dynamical Systems, 2010
Chapter 12. Modeling and Control for Clinical Pharmacology
Nonnegative and Compartmental Dynamical Systems, 2010
Chapter 9. Modeling and Analysis of Mass-Action Kinetics
Nonnegative and Compartmental Dynamical Systems, 2010
Mathematics, Feb 22, 2024
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Chapter Four. Impulsive Nonnegative and Compartmental Dynamical Systems
Chapter Seven. Energy-Based Control for Impulsive Port-Controlled Hamiltonian Systems
Nonlinear Dynamical Systems and Control, 2011
Contents Conventions and Notation xv Preface xxi Chapter 1. Introduction Chapter 2. Dynamical Sys... more Contents Conventions and Notation xv Preface xxi Chapter 1. Introduction Chapter 2. Dynamical Systems and Differential Equations 2.1 Introduction 2.2 Vector and Matrix Norms 2.3 Set Theory and Topology 2.4 Analysis in R n 2.5 Vector Spaces and Banach Spaces 2.6 Dynamical Systems, Flows, and Vector Fields 2.7 Nonlinear Differential Equations 2.8 Extendability of Solutions 2.9 Global Existence and Uniqueness of Solutions 2.10 Flows and Dynamical Systems 2.11 Time-Varying Nonlinear Dynamical Systems 2.12 Limit Points, Limit Sets, and Attractors 2.13 Periodic Orbits, Limit Cycles, and Poincare-Bendixson Theorems 2.14 Problems 2.15 Notes and References Chapter 3. Stability Theory for Nonlinear Dynamical. Systems 3.1 X CONTENTS 3.8 Problems 3.9 Notes and References Chapter 4. Advanced Stability Theory 4.1
One of the principal objectives of vibration isolation technology is to isolate sensitive equipme... more One of the principal objectives of vibration isolation technology is to isolate sensitive equipment from a vibrating structure or to isolate the structure from an uncertain exogenous disturbance source. In this paper, a dynamic observer-based active isolator is proposed that guarantees closed-loop asymptotic stabil- ity and disturbance decoupling between the vibrating structure and isolated structure. The proposed active isolator is applied to a uniaxial vibrational system and compared to an optimal linear-quadratic design.
Systems & Control Letters, Nov 1, 1987
A state-estimation design problem involving parametric plant uncertainties is considered. An erro... more A state-estimation design problem involving parametric plant uncertainties is considered. An error bound suggested by recent work of Petersen and Hollot is utilized for guaranteeing robust estimation. Necessary conditions which generalize the optimal projection equations for reduced-order state estimation are used to characterize the estimator which minimizes the error bound. The design equations thus effectively serve as sufficient conditions for synthesizing robust estimators. An additional feature is the presence of a static estimation gain in conjunction with the dynamic (Kalman) estimator, i.e., a nonstrictly proper estimator.
IEEE Transactions on Automatic Control, Jul 1, 1987
function K are given by (1 1) and (19), respectively, the optimal control is u= [ 2b2x:/q2Ix2(x;+... more function K are given by (1 1) and (19), respectively, the optimal control is u= [ 2b2x:/q2Ix2(x;+2x;)I 1 ' -261x1/ql [x? F,= -2G,/G.
IEEE Transactions on Automatic Control, May 1, 1993
discrete-time feedback control-design problem involving parametric uncertainty is considered. A q... more discrete-time feedback control-design problem involving parametric uncertainty is considered. A quadratic bound suggested by recent work on discrete-time state space H, theory is utilized in conjunction with the guaranteed cost approach to guarantee robust stability with a robust performance bound. The principal result involves sufficient conditions for characterizing robust fulland reduced-order controllers with a worst case H2 performance bound.
IEEE Transactions on Automatic Control, Dec 1, 1987
The optimal projection equations for reduced-order state estimation are generalized to allow for ... more The optimal projection equations for reduced-order state estimation are generalized to allow for singular (Le., colored) measurement noise. The noisy and noise-free measurements serve as inputs to dynamic and static estimators, respectively. The optimal salution is characterized by necessary conditions which involve a pair of oblique projections corresponding to reduced estimator order and singular measurement noise intensity.
In many applications of feedback control, phase information is available concerning the plant unc... more In many applications of feedback control, phase information is available concerning the plant uncertainty. For example, lightly damped flexible structures with colocated rate sensors and force actuators give rise to positive real transfer functions. Closed-loop stability is thus guaranteed by means of negative feedback with strictly positive real compensators. In this paper, the properties of positive real transfer functions are used to guarantee robust stability in the presence of positive real (but otherwise unknown) plant uncertainty. These results are then used for controller synthesis to address the problem of robust stabilization in the presence of positive real uncertainty. One of the principal motivations for these results is to utilize phase information in guaranteeing robust stability. In this sense these results go beyond the usual limitations of the small gain theorem and quadratic Lyapunov functions which may be conservative when phase information is available. The results of this paper are based upon a Riccati equation formulation of the positive real lemma and thus are in the spirit of recent Riccati-based approaches to bounded real (Hoo) control.
International Journal of Robust and Nonlinear Control, 1994
In a companion paper ('Explicit construction of quadratic Lyapunov functions for the small gain, ... more In a companion paper ('Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous-time theory'), Lyapunov functions were constructed in a unified framework to prove sufficiency in the small gain, positivity, circle, and Popov theorems. In this Part II, analogous results are developed for the discrete-time case. As in the continuous-time case, each result is based upon a suitable Riccati-like matrix equation that is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time-invariant system and a memoryless nonlinearity. Multivariable versions of the discrete-time circle and Popov criteria are obtained as extensions of known results. Each result is specialized to the linear uncertainty case and connections with robust stability for state-space systems is explored. Parameter-dependent Lyapunov functions In a companion paper1 Lyapunov functions were constructed in a unified framework to prove sufficiency in the small gain, positivity, circle, and Popov theorems. In this Part II, analogous results are developed for the discrete-time case. As in the continuous-time case, each result is based upon a suitable Riccati-like matrix equation that is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time-invariant system and a memoryless nonlinearity. Multivariable versions of the discrete-time circle and Popov criteria are obtained as extensions of known results.
For a given asymptotically stable linear dynamic system it is often of interest to determine whet... more For a given asymptotically stable linear dynamic system it is often of interest to determine whether stability is preserved as the system varies within a specified class of uncertainties. If, in addition, there also exist associated performance measures (such as the steady-state variances of selected state variables), it is desirable to assess the worst-case performance over a class of plant variations. These are problems of robust stability and performance analysis. In the present paper, quadratic Lyapunov bounds used to obtain a simultaneous treatment of both robust stability and performance are considered. The approach is based on the construction of modified Lyapunov equations, which provide sufficient conditions for robust stability along with robust performance bounds. In this paper, a wide variety of quadratic Lyapunov bounds are systematically developed and a unified treatment of several bounds developed previously for feedback control design is provided.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, 2005
In this paper, we study the problem of stability of linear neutral time-delay systems. Specifical... more In this paper, we study the problem of stability of linear neutral time-delay systems. Specifically, using the notion of structured phase margin, which characterizes stability margins in terms of a nominal plant transfer function in the presence of unknown structured phase perturbations, we derive several new frequency-domain sufficient conditions for stability of linear neutral time-delay systems. We provide both delay-independent as well as delay-dependent sufficient conditions for stability.
Finite settling time control of the double integrator is considered. The approach taken is to des... more Finite settling time control of the double integrator is considered. The approach taken is to design a compensator based on a virtual lossless absorber which is tuned so that, at some predetermined time, the virtual subsystem possesses all of the system's energy. At this time the controller is turned off, and the double integrator remains at rest at the origin. This strategy gives the appearance of instantaneously removing all of the system's energy as if a trap door had been sprung. A practically useful feature of the virtual trap-door absorber is that only position measurement is required. Parameters for the virtual trap-door absorber controller are chosen, and the resulting controller is compared to the classical minimal-time and minimal-energy controllers, which require measurements of both position and velocity. Index Terms-Double integrator, finite settling time control, minimal-time and minimal-energy optimal control, virtual absorber.
Chapter Five. Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems
Impulsive and Hybrid Dynamical Systems, 2006
A Fixed-Architecture Framework for Stochastic Nonlinear Controller Synthesis
2018 Annual American Control Conference (ACC), 2018
In this paper, we present a Lyapunov function-based optimization approach for designing state and... more In this paper, we present a Lyapunov function-based optimization approach for designing state and output feedback control laws for systems with polynomial nonlinearities. We use local polynomial expansions of a chosen order to approximate a higher-order nonlinear stochastic dynamical system, reformulate stochastic asymptotic stability conditions in the form of a nonlinear constrained optimization problem, and computationally determine the domain of attraction of the synthesized nonlinear controller on the original system. Finally, we illustrate the effectiveness of the proposed algorithm on two illustrative numerical examples.
Chapter 8. Finite-Time Thermodynamics
Chapter 13. Optimal Fixed-Structure Control for Nonnegative Systems
Nonnegative and Compartmental Dynamical Systems, 2010
Chapter 12. Modeling and Control for Clinical Pharmacology
Nonnegative and Compartmental Dynamical Systems, 2010
Chapter 9. Modeling and Analysis of Mass-Action Kinetics
Nonnegative and Compartmental Dynamical Systems, 2010
Mathematics, Feb 22, 2024
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY