Ian McInerney

Imperial College London

Monday, July 22, 2019, 11:00

Building 102 - SR 01-012

In this talk I will present recent work on using methods from systems theory to analyze the implementation details of the Fast Gradient Method in fixed-point representation. We begin by by exploiting the Toeplitz structure of the Hessian matrix to derive a relation between its eigenvalue distribution and the singular values of the predicted system's transfer function. This relation can then be used to bound the Hessian's condition number, and provide horizon-independent bounds on the computational complexity of the Fast Gradient Method. We additionally propose a new parametric model that exploits the Toeplitz structure to bound the round-off error experienced by the Hessian in fixed-point representation. This new model allows for horizon-independent data-type sizes for Schur-stable systems by better capturing the decay experienced by the Hessian matrix entries to provide a more accurate round-off error bound for the matrix. This approach nearly halves the number of fractional bits needed to implement an example problem, and leads to significant decreases in resource usage, computational energy and execution time for an FPGA implementation.