A receding-horizon approach to the nonlinear $H_\infty$ control problem

L. Magni; H. Nijmeijer; A.J. van der Schaft

doi:10.1016/S0005-1098(00)00166-7

A receding-horizon approach to the nonlinear $H_\infty$ control problem

L. Magni
, H. Nijmeijer
, A.J. van der Schaft

Research output: Contribution to journal › Article › Academic › peer-review

91 Citations (Scopus)

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Abstract

The receding-horizon (RH) methodology is extended to the design of a robust controller of $H_\infty$ type for nonlinear systems. Using the nonlinear analogue of the fake $H_\infty$H algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input-output map of the closed-loop system obtained with the RH control law has a bounded $L_2$-gain. Robustness properties of the nonlinear $H_\infty$ control law in face of dynamic input uncertainty are considered.

Original language	English
Pages (from-to)	429-435
Number of pages	7
Journal	Automatica
Volume	37
Issue number	3
DOIs	https://doi.org/10.1016/S0005-1098(00)00166-7
Publication status	Published - 2001

Keywords

Non-linear control
Receding-horizon control
Robustness
HJI equation
H-infinity control
n/a OA procedure

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10.1016/S0005-1098(00)00166-7

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title = "A receding-horizon approach to the nonlinear \$H\_\textbackslash{}infty\$ control problem",

abstract = "The receding-horizon (RH) methodology is extended to the design of a robust controller of \$H\_\textbackslash{}infty\$ type for nonlinear systems. Using the nonlinear analogue of the fake \$H\_\textbackslash{}infty\$H algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input-output map of the closed-loop system obtained with the RH control law has a bounded \$L\_2\$-gain. Robustness properties of the nonlinear \$H\_\textbackslash{}infty\$ control law in face of dynamic input uncertainty are considered.",

keywords = "Non-linear control, Receding-horizon control, Robustness, HJI equation, H-infinity control, n/a OA procedure",

author = "L. Magni and H. Nijmeijer and \{van der Schaft\}, A.J.",

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T1 - A receding-horizon approach to the nonlinear $H_\infty$ control problem

AU - Magni, L.

AU - Nijmeijer, H.

AU - van der Schaft, A.J.

PY - 2001

Y1 - 2001

N2 - The receding-horizon (RH) methodology is extended to the design of a robust controller of $H_\infty$ type for nonlinear systems. Using the nonlinear analogue of the fake $H_\infty$H algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input-output map of the closed-loop system obtained with the RH control law has a bounded $L_2$-gain. Robustness properties of the nonlinear $H_\infty$ control law in face of dynamic input uncertainty are considered.

AB - The receding-horizon (RH) methodology is extended to the design of a robust controller of $H_\infty$ type for nonlinear systems. Using the nonlinear analogue of the fake $H_\infty$H algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input-output map of the closed-loop system obtained with the RH control law has a bounded $L_2$-gain. Robustness properties of the nonlinear $H_\infty$ control law in face of dynamic input uncertainty are considered.

KW - Non-linear control

KW - Receding-horizon control

KW - Robustness

KW - HJI equation

KW - H-infinity control

KW - n/a OA procedure

U2 - 10.1016/S0005-1098(00)00166-7

DO - 10.1016/S0005-1098(00)00166-7

M3 - Article

SN - 0005-1098

VL - 37

SP - 429

EP - 435

JO - Automatica

JF - Automatica

IS - 3

ER -

A receding-horizon approach to the nonlinear $H_\infty$ control problem

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Keywords

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