A novel approach to the nonlinear H&lt;sub&gt;&amp;#x0221E;&lt;/sub&gt; regulator problem

Matsuzaki, Hidenori; Eguchi, Masayoshi; Shidama, Yasunari

doi:10.1109/sice.2007.4420963

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2009

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“…This idea was originally proposed in [9], [10] in the context of nonlinear optimal regulator problems. Its extension to H ∞ control was attempted in [11], [12]. In [13], various existence conditions were also derived for the stable invariant manifold arising in generic simultaneous differential equations.…”

Section: Introductionmentioning

confidence: 99%

A Fixed-Point Theoretic Solution of the Hamilton-Jacobi Equation and Its Application to Nonlinear H∞ Control

Matsuzaki

Eguchi²,

Shidama

2009

SICE Journal of Control, Measurement, and System Integration

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This paper proposes a novel approach to the Hamilton-Jacobi equation (HJE). Through a functional analytic formulation, a stabilizing solution of the HJE is derived from a fixed-point of a nonlinear mapping on a function space. A sufficient condition for the existence of such a fixed-point is derived quantitatively. For computing the fixed-point, a numerical method based on optimization techniques is introduced. Based on these results, the nonlinear H ∞ control problem is reconsidered. Simple numerical examples show that the resulting controllers have enough performance and computed solutions can approximate their analytical counterparts almost uniformly in the entire region under consideration.

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Section: Introductionmentioning

confidence: 99%

A Fixed-Point Theoretic Solution of the Hamilton-Jacobi Equation and Its Application to Nonlinear H∞ Control

Matsuzaki

Eguchi²,

Shidama

2009

SICE Journal of Control, Measurement, and System Integration

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show abstract

A novel approach to the nonlinear H<sub>∞</sub> regulator problem

Cited by 1 publication

References 1 publication

A Fixed-Point Theoretic Solution of the Hamilton-Jacobi Equation and Its Application to Nonlinear H∞ Control

A Fixed-Point Theoretic Solution of the Hamilton-Jacobi Equation and Its Application to Nonlinear H∞ Control

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A novel approach to the nonlinear H<sub>&#x0221E;</sub> regulator problem

Cited by 1 publication

References 1 publication

A Fixed-Point Theoretic Solution of the Hamilton-Jacobi Equation and Its Application to Nonlinear H&infin; Control

A Fixed-Point Theoretic Solution of the Hamilton-Jacobi Equation and Its Application to Nonlinear H&infin; Control

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A novel approach to the nonlinear H<sub>∞</sub> regulator problem

A Fixed-Point Theoretic Solution of the Hamilton-Jacobi Equation and Its Application to Nonlinear H∞ Control

A Fixed-Point Theoretic Solution of the Hamilton-Jacobi Equation and Its Application to Nonlinear H∞ Control