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

L. Magni, Henk Nijmeijer, Arjan van der Schaft

87 Citations (Scopus)

## 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 Undefined 10.1016/S0005-1098(00)00166-7 429-435 7 Automatica 37 3 https://doi.org/10.1016/S0005-1098(00)00166-7 Published - 2001

## Keywords

• EWI-16692
• Non-linear control
• Receding-horizon control
• Robustness
• HJI equation
• H-infinity control
• IR-69077
• METIS-200876