W.M. Haddad

Georgia Institute of Technology, Atlanta, Georgia, United States

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Publications (490)499.85 Total impact

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    W.M. Haddad, V. Chellaboina
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    ABSTRACT: A nonlinear dynamic compensator framework for Hammerstein systems with passive nonlinear dynamics is proposed. For this class of systems controlled by passive nonlinear dynamic compensators we prove the global closed-loop stability by modifying the dynamic compensator to include a suitable input nonlinearity. The proof of this result is based on the dissipativity theory and shows that the nonlinear controller modification counteracts the effects of the input nonlinearity by recovering the passivity of the plant and the compensator
    IEEE Transactions on Automatic Control 11/2001; DOI:10.1109/9.956062 · 3.17 Impact Factor
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    ABSTRACT: In this paper we develop Lyapunov and invariant set stability theorems for non-linear impulsive dynamical systems. Furthermore, we generalize dissipativity theory to non-linear dynamical systems with impulsive effects. Specifically, the classical concepts of system storage functions and supply rates are extended to impulsive dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy, dissipated energy over the continuous-time system dynamics and dissipated energy over the resetting instants. Furthermore, extended Kalman‐Yakubovich‐Popov conditions in terms of the impulsive system dynamics characterizing dissipativeness via system storage functions are derived. Finally, the framework is specialized to passive and non-expansive impulsive systems to provide a generalization of the classical notions of passivity and non-expansivity for non-linear impulsive systems. These results are used in the second part of this paper to develop extensions of the small gain and positivity theorems for feedback impulsive systems as well as to develop optimal hybrid feedback controllers.
    International Journal of Control 10/2001; 74(17):1631-1658. DOI:10.1080/00207170110081705 · 1.14 Impact Factor
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    ABSTRACT: this paper, back-stepping control, has become a very popular and powerful tool in nonlinear adaptive control. A complete account for such methods can be found in [59, 73, 121]. An extension to non linearizable systems was proposed in [107]. The combination of adaptive control and feedback linearization applied to flight control can be found in [126]. In most of the classical adaptive control literature it is common to assume the unknown dynamics to have a known structure with unknown parameters entering linearly in the dynamics. The linear parameterization of unknown dynamics poses serious obstacles in adopting adaptive control algorithms in practical applications, because it is di#cult to fix the structure of the unknown nonlinearities. This fact has been the motivating factor behind the interest in on-line function approximators to estimate and learn the unknown function. The most common function approximators used in adaptive control are artificial neural network and fuzzy logic structures. On line control algorithms that do not require knowledge of the system dynamics (except its dimension and relative degree) have been made possible by employing artificial neural networks in the feedback loop [34]. The ability of neural networks to approximate uniformly continuous functions has been proven in several articles [21, 27, 38, 28, 40]. An important aspect of neural network control applications is the di#erence between approximation theory results and what is achievable in on-line adaptive schemes using such approximators. First and most importantly, in o#-line applications the neural network weights are updated based on input-output matching, 5 whereas in direct adaptive control situations the update of the network parameters is driven by a tracking error, which by it...
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    W.M. Haddad, V. Chellaboina, T. Hayakawa
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    ABSTRACT: A direct robust adaptive control framework for nonlinear uncertain systems with constant linearly parameterized uncertainty and nonlinear state-dependent uncertainty is developed. The proposed framework is Lyapunov-based and guarantees partial asymptotic robust stability of the closed-loop system; that is, asymptotic robust stability with respect to part of the closed-loop system states associated with the plant. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach
    Decision and Control, 2001. Proceedings of the 40th IEEE Conference on; 02/2001
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    ABSTRACT: A nonlinear control system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems. The switching nonlinear controller architecture is designed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria. The proposed framework provides a rigorous alternative to designing gain-scheduled feedback controllers and guarantees local and global closed-loop system stability for general nonlinear systems
    IEEE Transactions on Automatic Control 02/2001; 46(1-46):17 - 28. DOI:10.1109/9.898692 · 3.17 Impact Factor
  • N.A. Kablar, T. Hayakawa, W.M. Haddad
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    ABSTRACT: Thermoacoustic instabilities in combustion processes involve pressure and velocity limit cycling oscillations that can have adverse effects on system performance. Using a nonlinear state space model for combustion processes that captures the coupling between unsteady combustion and acoustics, a direct adaptive control framework is used to design high-performance robust controllers for suppressing thermoacoustic oscillations in the face of system parametric uncertainty
    American Control Conference, 2001. Proceedings of the 2001; 02/2001
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    ABSTRACT: The verge and foliot escapement mechanism of a mechanical clock is a classical example of a feedback regulator. In this paper we analyze the dynamics of this mechanism to understand its operation from a feedback perspective. Using impulsive differential equations and Poincare maps to model the dynamics of this closed-loop system, we determine conditions under which the system possesses a limit cycle, and we analyze the period and amplitude of the oscillations in terms of the inertias of the colliding masses and their coefficient of restitution
    American Control Conference, 2001. Proceedings of the 2001; 02/2001
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    A. Leonessa, W.M. Haddad, T. Hayakawa
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    ABSTRACT: A direct adaptive nonlinear tracking control framework for multivariable nonlinear uncertain systems with actuator amplitude and rate saturation constraints is developed. To guarantee asymptotic stability of the closed-loop tracking error dynamics in the face of amplitude and rate saturation constraints, the adaptive control signal to a given reference system is modified to effectively robustify the error dynamics to the saturation constraints. An illustrative numerical example is provided to demonstrate the efficacy of the propose approach
    American Control Conference, 2001. Proceedings of the 2001; 02/2001
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    ABSTRACT: A direct adaptive control framework for a class of nonlinear matrix second-order dynamical systems with state-dependent uncertainty is developed. The proposed framework guarantees global asymptotic stability of the closed-loop system states associated with the plant dynamics without requiring any knowledge of the system nonlinearities, other than the assumption that they axe continuous and lower bounded. Generalizations to the case where the system nonlinearities are unbounded are also considered. In the special case of matrix second-order systems having polynomial nonlinearities with unknown coefficients and unknown order, we provide a universal adaptive controller that guarantees closed-loop stability of the plant states
    American Control Conference, 2001. Proceedings of the 2001; 02/2001
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    W.M. Haddad, V.S. Chellaboina, E. August
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    ABSTRACT: Nonnegative and compartmental dynamical systems are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering, biomedicine, and ecology. In this paper we develop several results on stability and dissipativity of discrete-time linear and nonlinear nonnegative dynamical systems. Specifically, using linear Lyapunov functions we develop necessary and sufficient conditions for Lyapunov stability and asymptotic stability for nonnegative systems. In addition, using linear storage functions and linear supply rates we develop new notions of dissipativity theory for nonnegative dynamical systems
    Decision and Control, 2001. Proceedings of the 40th IEEE Conference on; 02/2001
  • V.S. Chellaboina, W.M. Haddad
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    ABSTRACT: We present partial stability results; that is, stability with respect to part of the system's state, for nonlinear dynamical systems. Using these results we provide a rigorous unification between partial stability theory for autonomous systems and stability theory for nonlinear time-varying systems. This unification allows for time-varying stability theory to be presented as a special case of autonomous partial stability theory in a first course on nonlinear systems
    Decision and Control, 2001. Proceedings of the 40th IEEE Conference on; 02/2001
  • W.M. Haddad, V. Chellaboina, E. August
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    ABSTRACT: Nonnegative dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in biological, physiological, and ecological sciences and play a key role in the understanding of these processes. In this paper we develop several results on stability, dissipativity, and stability of feedback interconnections of linear and nonlinear nonnegative dynamical systems. Specifically, using linear Lyapunov functions we develop necessary and sufficient conditions for Lyapunov stability, semistability, and asymptotic stability for nonnegative systems. In addition, using linear storage functions and linear supply rates we develop, new notions of dissipativity theory for nonnegative dynamical systems. Finally, these results are used to develop general stability criteria for feedback
    Decision and Control, 2001. Proceedings of the 40th IEEE Conference on; 02/2001
  • Wassim M. Haddad, V. Chellaboina, Natasa A. Kablar
    International Journal of Control 01/2001; 74:1631-1658. · 1.14 Impact Factor
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    ABSTRACT: This paper uses a unifying absolute stability result for mixed uncertainty in conjunction with a quasi-Newton numerical optimization routine to obtain xed-structure controllers and xed-order stability multipliers which provide robust stability and performance. The robust controller synthesis technique proposed here permits the treatment of fully populated real uncertain blocks which may, in addition, possess internal structure. 1. Introduction The ability of the structured singular value to account for complex, real, and mixed uncertaintyprovides a powerful framework for robust stability and performance problems in both analysis and synthesis (see [1] and the numerous references therein). Since exact computation of the structured singular value is, in general, an intractable problem, the development of practically implementable bounds remains a high priority in robust control research. Recent work in this area includes upper and lower bounds for mixed uncertainty [2] as well as LMI-b...
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    ABSTRACT: In this paper we develop an optimality-based framework for addressing the problem of nonlinear optimal robust hybrid control for nonlinear uncertain impulsivedynamical systems. 1. Introduction Although the theory of impulsive dynamical systems is mature [1], robust analysis and control design techniques for nonlinear uncertain impulsive dynamical systems remain relatively undeveloped. In this paper we extend the analysis and design framework for nonlinear impulsive dynamical systems developed in [2, 3] to address robustness considerations in impulsive dynamical systems. Specifically, in [3] a unified framework for hybrid feedback optimal and inverse optimal control involving a hybrid nonlinear-nonquadratic performance functional was developed. In this paper we build on these results to develop an optimality-based framework for addressing the problem of nonlinear-nonquadratic optimal hybrid control for uncertain nonlinear impulsive dynamical systems with structured parametric uncertai...
  • Wassim M. Haddad, Tomohisa Hayakawa
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    ABSTRACT: A direct adaptive nonlinear control framework for multivariable nonlinear uncertain systems with exogenous L 2 disturbances is developed. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system# that is, asymptotic stability with respect to part of the closed-loop system states associated with the plant, as well as a nonexpansivity constraint on the closed-loop input-output map. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach. 1. Introduction In arecent paper [1], a direct adaptive control framework for adaptive stabilization, disturbance rejection, and command following of multivariable nonlinear uncertain systems with exogenous bounded amplitude disturbances was developed. In particular, a Lyapunov-based direct adaptive control framework was developed that requires a matching condition on the system disturbance and guarantees partial asymptotic stability of the closed-l...
  • Vikram Kapila, Wassim M. Haddad, Apostolos Grivas
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    ABSTRACT: In this paper we consider the problem of stabilizing continuous-time linear systems containing input nonlinearities and time delays. Specifically, a fixed-order (i.e. full and reduced-order) dynamic outputfeedback control technique is developed and sufficient conditions involving a system of modified Lyapunov-Riccati equations are presented for stabilization of systems with sector-bounded input nonlinearities and state and measurement time delays.
    International Journal of Systems Science 12/2000; 31(12):1593-1599. DOI:10.1080/00207720050217368 · 1.58 Impact Factor
  • Wassim M. Haddad, Joseph R. Corrado
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    ABSTRACT: One of the fundamental problems in feedback control design is the ability of the control system to maintain stability and performance in the face of system uncertainties. To this end, elegant multivariable robust control design frameworks such as H control, L control and mu synthesis have been developed to address the robust stability and performance control problem. An impl1icit assumption inherent in these design frameworks is that the controller will be implemented exactly. In a recent paper by Keel and Bhattacharyya, it was shown that even though such frameworks are robust with respect to system uncertainty, they are extremely fragile with respect to errors in the controller coefficients. In this paper, we extend the robust fixed-structure controller synthesis approach to develop controllers which are robust to system uncertainties and non-fragile or resilient to controller gain variations.
    International Journal of Control 10/2000; 73(15). DOI:10.1080/002071700445424 · 1.14 Impact Factor
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    ABSTRACT: In this paper we develop explicit formulas for induced convolution operator norms and their bounds. These results generalize established induced operator norms for linear dynamical systems with various classes of input–output signal pairs. Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/41865/1/498-13-3-216_00130216.pdf
    Mathematics of Control Signals and Systems 09/2000; 13(3). DOI:10.1007/PL00009868 · 1.15 Impact Factor
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    Nonlinear Analysis 07/2000; 41(3):287-312. DOI:10.1016/S0362-546X(98)00279-X · 1.61 Impact Factor

Publication Stats

7k Citations
499.85 Total Impact Points

Institutions

  • 1993–2015
    • Georgia Institute of Technology
      • School of Aerospace Engineering
      Atlanta, Georgia, United States
    • Northeastern University
      • Department of Electrical and Computer Engineering
      Boston, Massachusetts, United States
  • 2009
    • Indian Institute of Technology Madras
      Chennai, Tamil Nādu, India
    • India Innovation Labs
      Bengalūru, Karnātaka, India
  • 2008–2009
    • Texas Tech University
      • Department of Mechanical Engineering
      Lubbock, TX, United States
  • 2006–2008
    • Villanova University
      • Department of Mechanical Engineering
      Norristown, PA, United States
    • The University of Tennessee Medical Center at Knoxville
      Knoxville, Tennessee, United States
  • 1987–2007
    • Florida Institute of Technology
      • Department of Mechanical and Aerospace Engineering
      Melbourne, Florida, United States
    • Melbourne Institute of Technology
      Melbourne, Victoria, Australia
  • 2005
    • Emory University
      • Department of Anesthesiology
      Atlanta, GA, United States
    • Japan Science and Technology Agency (JST)
      Edo, Tōkyō, Japan
  • 2000–2004
    • University of Missouri
      • Department of Mechanical and Aerospace Engineering
      Columbia, MO, United States
  • 2001–2003
    • Florida Atlantic University
      Boca Raton, Florida, United States
  • 1999
    • Florida State University
      • Department of Mechanical Engineering
      Tallahassee, FL, United States
  • 1996
    • Florida A&M University
      • Department of Mechanical Engineering
      Tallahassee, Florida, United States
  • 1994–1996
    • Stanford University
      • • Department of Mechanical Engineering
      • • Department of Aeronautics and Astronautics
      Stanford, CA, United States
    • Massachusetts Institute of Technology
      • Department of Aeronautics and Astronautics
      Cambridge, MA, United States
  • 1988–1992
    • Harris Corporation
      Melbourne, Florida, United States