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arXiv · 0903.5535

Finite Approximations of Switched Homogeneous Systems for Controller Synthesis

Danielle C. Tarraf·Alexandre Megretski·Munther A. Dahleh
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Abstract

We demonstrate the use of a new, control-oriented notion of finite state approximation for a particular class of hybrid systems. Specifically, we consider the problem of designing a stabilizing binary output feedback switching controller for a pair of unstable homogeneous second order systems. The constructive approach presented in this note, in addition to yielding an explicit construction of a deterministic finite state approximate model of the hybrid plant, allows us to efficiently establish a useable upper bound on the quality of approximation, and leads to a discrete optimization problem whose solution immediately provides a certifiably correct-by-design controller for the original system. The resulting controller consists of a finite state observer for the plant and a corresponding full state feedback switching control law.

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Danielle C. Tarraf, Alexandre Megretski, Munther A. Dahleh. 2010-02-06. Finite Approximations of Switched Homogeneous Systems for Controller Synthesis. https://doi.org/10.1109/tac.2011.2108350

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