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Finite Approximations of Switched Homogeneous Systems for Controller Synthesis

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3 Author(s)
Tarraf, D.C. ; Dept. of Electr. & Comput. Eng., Johns Hopkins Univ., Baltimore, MD, USA ; Megretski, A. ; Dahleh, M.A.

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:

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