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arXiv · 2111.03209

Controller Reduction for Nonlinear Systems by Generalized Differential Balancing

Yu Kawano
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Abstract

In this paper, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant input-vector fields and linear output functions. First, we study incremental properties in the GD balancing framework. Next, based on these analyses, we provide GD LQG balancing and GD $H_\infty$-balancing as controller reduction methods for nonlinear systems by focusing on linear feedback and observer gains. Especially for GD $H_\infty$-balancing, we clarify when the closed-loop system consisting of the full-order system and a reduced-order controller is exponentially stable. All provided methods for controller reduction can be relaxed to linear matrix inequalities.

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Yu Kawano. 2021-11-05. Controller Reduction for Nonlinear Systems by Generalized Differential Balancing. https://arxiv.org/abs/2111.03209

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