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Finite Approximations of Switched Homogeneous Systems for Controller Synthesis

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3 Author(s)
Danielle C. Tarraf ; Department of Electrical & Computer Engineering, Johns Hopkins University, Baltimore ; Alexandre Megretski ; Munther A. Dahleh

In this note, we demonstrate the use of a control oriented notion of finite state input/output approximation to synthesize correct-by-design controllers for hybrid plants under sensor limitations. Specifically, we consider the problem of designing stabilizing switching controllers for a pair of unstable homogeneous second order systems with binary output feedback. In addition to yielding a deterministic finite state approximate model of the hybrid plant, our approach allows one to efficiently establish a useable upper bound on the quality of approximation, and leads to a discrete optimization problem whose solution immediately provides a certified finite state controller for the plant. The resulting controller consists of a deterministic finite state observer and a corresponding full state feedback control law.

Published in:

IEEE Transactions on Automatic Control  (Volume:56 ,  Issue: 5 )