**Tuesday, 16:15 - 16:40 h, Room: H 0112**

**Eric Kerrigan**

Breaking away from double-precision floating-point in interior point solvers

**Coauthors: George A. Constantinides, Juan L. Jerez, Stefano Longo**

**Abstract:**

We will show how one can modify interior point methods for solving constrained linear quadratic control problems in computing hardware with a fixed-point number representation or with significantly less bits than in single- or double-precision floating-point. This allows one to dramatically reduce the computational resources, such as time, silicon area and power, needed to compute the optimal input sequence at each sample instant. For fixed precision, we propose a simple pre-conditioner, which can be used with iterative linear solvers such as CG or MINRES, that allows one to compute tight bounds on the ranges of the variables in the Lanczos iteration, thereby allowing one to determine the best position of the radix point. To allow one to reduce the number of bits needed, we propose the use of the delta transform of Middleton and Goodwin in order to avoid numerical errors that would occur when using the usual shift transform to discretize the continuous-time optimal control problem. We also propose a Riccati method, tailored to the delta transform, for efficiently solving the resulting KKT systems that arise within an interior point solver.

Talk 3 of the invited session Tue.3.H 0112

**"Real-time optimization III"** [...]

Cluster 16

**"Nonlinear programming"** [...]