Bounded error flowpipe computation of parameterized linear systems

Ratan Lal and Pavithra Prabhakar

We consider the problem of computing a bounded error approximation of the solution over a bounded time [0, T ], of a parameterized linear system, \dot{x}(t) = Ax(t), where A is constrained by a compact polyhedron Ω. Our method consists of sampling the time domain [0, T ] as well as the parameter space Ω and constructing a continuous piecewise bilinear function which interpolates the solution of the parameterized system at these sample points. More precisely, given an \epsilon > 0, we compute a sampling interval \delta > 0, such that the piecewise bilinear function obtained from the sample points is within \epsilon of the original trajectory. We present experimental results which suggest that our method is scalable.

International Conference on Embedded Software (EMSOFT), 2015
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