W.M. Haddad

Georgia Institute of Technology, Atlanta, Georgia, United States

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Publications (485)440.49 Total impact

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    V. Chellaboina, W.M. Haddad
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    ABSTRACT: In this paper we extend the notion of dissipative dynamical systems to formalize the concept of the nonlinear analog of strict positive realness and strict bounded realness. In particular, using exponentially weighted system storage functions with appropriate exponentially weighted supply rates we introduce the concept of exponential dissipativity. The proposed results provide a generalization to the strict positive real lemma and the strict bounded real lemma to nonlinear systems as well as a nonlinear analog to the classical passivity and small gain stability theorems for state space nonlinear feedback systems
    American Control Conference, 2000. Proceedings of the 2000; 02/2000
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    ABSTRACT: In this paper we derive guaranteed hybrid gain, sector, and disk margins for nonlinear optimal and inverse optimal hybrid regulators that minimize nonlinear-nonquadratic hybrid performance functional. Furthermore, we develop a hybrid return difference inequality to provide connections between dissipativity and optimality of nonlinear hybrid controllers. Specifically, we show that optimal hybrid controllers imply dissipativity with respect to a quadratic supply rate
    Decision and Control, 2000. Proceedings of the 39th IEEE Conference on; 02/2000
  • W.M. Haddad, V.-S. Chellaboina, J.-H. Oh
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    ABSTRACT: An output feedback control analysis framework for linear systems with input hysteresis nonlinearities is developed. By transforming the hysteresis nonlinearities into dissipative input-output dynamic operators, the dissipativity theory is used to analyze linear controllers for systems with input hysteresis nonlinearities. In particular, by representing the input hysteresis nonlinearity as a dissipative input-output dynamical operator with respect to a given supply rate, partial closed loop asymptotic stability with respect to part of the closed-loop state associated with the plant and the controller, is guaranteed in the face of an input hysteresis nonlinearity
    American Control Conference, 2000. Proceedings of the 2000; 02/2000
  • W.M. Haddad, V. Chellaboina
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    ABSTRACT: A nonlinear dynamic compensator framework for nonlinear passive systems with arbitrary input nonlinearities is proposed. For this class of systems we prove global closed-loop stability by modifying the dynamic compensator to include a suitable input nonlinearity. The proof of this result is based on 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
    American Control Conference, 2000. Proceedings of the 2000; 02/2000
  • W.M. Haddad, T. Hayakawa
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    ABSTRACT: A direct adaptive nonlinear control framework for multivariable nonlinear uncertain systems with exogenous disturbances is developed. The adaptive nonlinear controller addresses adaptive stabilization, disturbance rejection, and adaptive tracking. 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. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach
    American Control Conference, 2000. Proceedings of the 2000; 02/2000
  • W.M. Haddad, V. Chellabsina, N.A. Kablar
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    ABSTRACT: We propose an energy flow resetting control architecture as a means for achieving enhanced energy dissipation in combustion systems. The overall framework is based on a hybrid controller architecture wherein the closed-loop dynamical system is characterized by impulsive differential equations. The proposed framework is used to design high-performance hybrid controllers for suppressing thermoacoustic oscillations in combustion chambers by efficiently dissipating modal system energy
    American Control Conference, 2000. Proceedings of the 2000; 02/2000
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    V. Chellaboina, S.P. Bhat, W.M. Haddad
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    ABSTRACT: In this paper we develop an invariance principle for dynamical systems possessing left-continuous flows. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems
    American Control Conference, 2000. Proceedings of the 2000; 02/2000
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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 fixed-structure controllers and fixed-order stability multipliers which provide robust stability and performance. The robust controller synthesis technique proposed permits the treatment of fully populated real uncertain blocks which may, in addition, possess internal structure
    Decision and Control, 2000. Proceedings of the 39th IEEE Conference on; 02/2000
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    W.M. Haddad, T. Hayakawa
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    ABSTRACT: A direct adaptive nonlinear control framework for multivariable nonlinear uncertain systems with exogenous L<sub>2</sub> disturbances is developed. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system, i.e., the 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
    Decision and Control, 2000. Proceedings of the 39th IEEE Conference on; 02/2000
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    ABSTRACT: We develop an optimality-based framework for addressing the problem of nonlinear optimal robust hybrid control for nonlinear uncertain impulsive dynamical systems
    Decision and Control, 2000. Proceedings of the 39th IEEE Conference on; 02/2000
  • Source
    W.M. Haddad, V. Chellaboina
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    ABSTRACT: We develop a unified framework for a general class of dynamical systems possessing left-continuous flows; that is, left-continuous dynamical systems. These systems are shown to generalize virtually all existing notions of dynamical systems and include hybrid and impulsive dynamical systems as special cases. Furthermore, we generalize dissipativity theory to left-continuous dynamical systems. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of left-continuous systems. These results generalize the positivity and small gain theorems to the case of left-continuous, hybrid, and impulsive dynamical systems
    American Control Conference, 2000. Proceedings of the 2000; 02/2000
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    ABSTRACT: A Lyapunov-based inverse optimal adaptive control-system design problem for non-linear uncertain systems with exogenous ℒ2 disturbances is considered. Specifically, an inverse optimal adaptive non-linear control framework is developed to explicitly characterize globally stabilizing disturbance rejection adaptive controllers that minimize a nonlinear-nonquadratic performance functional for non-linear cascade and block cascade systems with parametric uncertainty. It is shown that the adaptive Lyapunov function guaranteeing closed-loop stability is a solution to the Hamilton–Jacobi–Isaacs equation for the controlled system and thus guarantees both optimality and robust stability. Additionally, the adaptive Lyapunov function is dissipative with respect to a weighted input–output energy supply rate guaranteeing closed-loop disturbance rejection. For special integrand structures of the performance functionals considered, the proposed adaptive controllers additionally guarantee robustness to multiplicative input uncertainty. In the case of linear-quadratic control it is shown that the operations of parameter estimation and controller design are coupled illustrating the breakdown of the certainty equivalence principle for the optimal adaptive control problem. Finally, the proposed framework is used to design adaptive controllers for jet engine compression systems with uncertain system dynamics. Copyright © 2000 John Wiley & Sons, Ltd.
    International Journal of Adaptive Control and Signal Processing 01/2000; 14(1):1 - 38. · 1.22 Impact Factor
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    VijaySekhar Chellaboina, Wassim M. Haddad
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    ABSTRACT: In this paper we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal regulators that minimize a nonlinear-nonquadratic performance criterion involving cross-weighting terms. Specifically, sufficient conditions that guarantee gain, sector, and disk margins are given in terms of the state, control, and cross-weighting nonlinear-nonquadratic weighting functions. The proposed results provide a generalization of the “meaningful” inverse optimal nonlinear regulator stability margins as well as the classical linear-quadratic optimal regulator gain and phase margins.
    Systems & Control Letters 01/2000; · 1.67 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 01/2000; · 0.42 Impact Factor
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    ABSTRACT: Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/57813/1/TrapDoorTAC2000.pdf
    IEEE Transactions on Automatic Control 01/2000; · 2.72 Impact Factor
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    ABSTRACT: This paper considers fixed-structure stable ℋ2-optimal controller synthesis using a multiobjective optimization technique which provides a trade-off between closed-loop performance and the degree of controller stability. The problem is presented in a decentralized static output feedback framework developed for fixed-structure dynamic controller synthesis. A quasi-Newton/continuation algorithm is used to compute solutions to the necessary conditions. To demonstrate the approach, two numerical examples are considered. The first example is a second-order spring–mass–damper system and the second example is a fourth-order two-mass system, both of which are considered in the stable stabilization literature. The results are then compared with other methods of stable compensator synthesis. Copyright © 2000 John Wiley & Sons, Ltd.
    Optimal Control Applications and Methods 01/2000; 21(3):107-124. · 1.06 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 01/2000; 73(15). · 1.01 Impact Factor
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    ABSTRACT: At first a nonlinear discrete-time system with bounded input disturbances and a nonlinear-nonquadratic performance functional is considered. The performance functional is evaluated in terms of a Lyapunov function that guarantees stability and dissipativity with respect to general supply rates. This result is then specialized to linear systems with quadratic supply rates and connections are drawn to the mixed-norm H 2 /H ∞ and mixed H 2 /positivity linear-quadratic problems. Then a nonlinear discrete-time disturbance rejection control problem is stated and transformed to an optimal control problem. Sufficient conditions are obtained that characterize an optimal nonlinear feedback controller that guarantees stability and dissipativity of the closed-loop system with respect to general supply rates. This result is specialized to the linear-quadratic case to draw connections with the mixed-norm H 2 /H ∞ linear-quadratic regulator problem and mixed H 2 /positivity control problem. At last the obtained results are specialized to discrete-time nonlinear affine systems controlled by nonlinear controllers subjected to bounded exogenous disturbances that minimize a nonlinear-nonquadratic performance criterion involving a nonlinear-nonquadratic function of the state and a linear and a quadratic function of the feedback control.
    Nonlinear Analysis 01/2000; 41(3):287-312. · 1.64 Impact Factor
  • 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 01/2000; 31:1593-1599. · 1.31 Impact Factor
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    ABSTRACT: In this paper we explore the applicability of the implicit small-gain guaranteed cost bound for controller synthesis. For flexibility in controller synthesis, we adopt the approach of fixed-structure controller design which allows consideration of arbitrary controller structures, including order, internal structure, and decentralization. A numerical example that has been addressed in the literature by means of alternative guaranteed cost bounds is presented to demonstrate the fixed-structure/implicit small-gain approach to robust controller synthesis.
    Journal of the Franklin Institute. 01/2000;

Publication Stats

5k Citations
440.49 Total Impact Points

Institutions

  • 1993–2014
    • Georgia Institute of Technology
      • School of Aerospace Engineering
      Atlanta, Georgia, United States
    • Northeastern University
      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
    • Tokyo Institute of Technology
      • Department of Mechanical and Environmental Informatics
      Edo, Tōkyō, Japan
  • 2006–2008
    • Villanova University
      • Department of Mechanical Engineering
      Norristown, Pennsylvania, United States
    • University of Tennessee
      • Department of Mechanical, Aerospace and Biomedical Engineering
      Knoxville, TN, 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
  • 2000–2005
    • University of Missouri
      • Department of Mechanical and Aerospace Engineering
      Columbia, MO, United States
  • 2001–2003
    • Florida Atlantic University
      Boca Raton, Florida, United States
  • 1994–2001
    • University of Michigan
      • Department of Aerospace Engineering
      Ann Arbor, MI, United States
  • 1999
    • Florida State University
      • Department of Mechanical Engineering
      Tallahassee, FL, United States
  • 1998
    • Università della Calabria
      Rende, Calabria, Italy
  • 1994–1996
    • Stanford University
      • • Department of Mechanical Engineering
      • • Department of Aeronautics and Astronautics
      Stanford, CA, United States
  • 1989–1994
    • Massachusetts Institute of Technology
      • Department of Aeronautics and Astronautics
      Cambridge, MA, United States
  • 1987–1992
    • Harris Corporation
      Melbourne, Florida, United States