Topics in Control Theory

Knobloch, H. W.; Flockerzi, Dietrich; Isidori, Alberto

doi:10.1007/978-3-0348-8566-9

Cited by 165 publications

(83 citation statements)

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“…In this procedure a two point boundary value problem is formulated for (2. notation, so that the convergence result in [2] is somewhat weaker than ours. In our algorithm given in (2.9), the need to solve a two point boundary value problem is replaced by the minimization problem in (2.9b) and (2.9c).…”

Section: Nonlinear Systemscontrasting

confidence: 60%

“…Note that α1 α3 spans the n-dimensional stable eigenspace and α2 α4 spans the n-dimensional unstable subspace. Standard results from Algebraic Riccati Equation theory [2] show that the stable and unstable subspaces of H have the form…”

Section: Nonlinear Systemsmentioning

confidence: 99%

“…In particular one of the reviewers pointed out the need for assumption 2. Another reviewer cited the work in [2] and in [14].…”

Section: Acknowledgmentmentioning

confidence: 99%

“…They are of considerable importance in the solution of nonlinear optimal control problems [1], nonlinear H ∞ problems [2], and in various other areas.…”

Section: Introductionmentioning

confidence: 99%

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An Iterative Algorithm for Solving Hamilton--Jacobi Type Equations

Markman¹,

Katz²

2000

SIAM J. Sci. Comput.

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Abstract. Solutions of the optimal control and H∞-control problems for nonlinear affine systems can be found by solving Hamilton-Jacobi equations. However, these first order nonlinear partial differential equations can, in general, not be solved analytically. This paper studies the rate of convergence of an iterative algorithm which solves these equations numerically for points near the origin. It is shown that the procedure converges to the stabilizing solution exponentially with respect to the iteration variable. Illustrative examples are presented which confirm the theoretical rate of convergence.

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Section: Nonlinear Systemscontrasting

confidence: 60%

Section: Nonlinear Systemsmentioning

confidence: 99%

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An Iterative Algorithm for Solving Hamilton--Jacobi Type Equations

Markman¹,

Katz²

2000

SIAM J. Sci. Comput.

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“…The identification problem for some classes of chemical kinetic models just give a poor example of such situations, which can be abstracted to the problem of a class of nonlinear systems with noncomplete on-line measurable variables (Garcia and D'Atellis, 1995), (Knobloch et al, 1993). Available observations provides by a ozone sensor which supplies the current information in continuous time about the current ozone concentration in the gas phase of the reactor output.…”

Section: Precedentsmentioning

confidence: 99%

Water Treatment by Ozonation: Contaminants Concentration Estimation by Dynamical Neural Network

Chaírez

Poznyak

2005

IFAC Proceedings Volumes

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On the design of robust servomechanisms for minimum phase nonlinear systems

Khalil

2000

Int. J. Robust Nonlinear Control

127

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We consider a single‐input single‐output nonlinear system which has a well‐defined normal form with asymptotically stable zero dynamics. We study the design of a robust output feedback controller that incorporates a linear servo compensator to achieve asymptotic tracking and disturbance rejection. We determine the least amount of precise information about the plant that is needed to design the controller. Such design will be robust to plant parameters and uncertainties which are not used in the design calculations. We also study robustness of the design to errors in determining the linear servo compensator. Such errors could arise from approximating a general continuous nonlinear function by a polynomial one, or from errors in determining the frequencies of the exogenous signals. We give regional as well as semiglobal results. Copyright © 2000 John Wiley & Sons, Ltd.

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Topics in Control Theory

Cited by 165 publications

References 0 publications

An Iterative Algorithm for Solving Hamilton--Jacobi Type Equations

An Iterative Algorithm for Solving Hamilton--Jacobi Type Equations

Water Treatment by Ozonation: Contaminants Concentration Estimation by Dynamical Neural Network

On the design of robust servomechanisms for minimum phase nonlinear systems

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