Interval methods for the implementation and verification of robust gain scheduling controllers

This paper presents a novel approach for an interval-based gain scheduling control design aiming at a guaranteed stabilization of the system dynamics over a predefined time horizon. Due to the goal of asymptotic stability, the design aims at the temporal reduction of the widths of intervals representing worst-case bounds of the system states at a specific point of time. The main idea of the control approach is the computation of feedback gains for an initial state interval with a subsequent verification step. In this step, it is examined whether the control is valid over a finitely long prediction window. If the verification fails, the gain is adjusted after computing a bounding box of states that are reachable over the complete prediction window. In such a way, controller gains can be calculated off-line so that predefined performance criteria on the closed-loop structure are satisfied. Besides using interval analysis for the underlying reachability analysis, linear matrix inequality (LMI) techniques are employed for an efficient solution of the robust and/ or optimal control design. The proposed design method is verified numerically for the control of an inverted pendulum as a prototypical benchmark application.

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