The economical simulation problem

Think of a digital simulation as a computational device for which one must allocate three computational resources for computing: (a) the given inputs, (b) the outputs and (c) each state variable in the dynamics. This paper assigns these computational resources to guarantee a specified bound on response errors. We define the economical simulation problem (ESP) as designing the simulation of a stable linear system and distributing computational resources (wordlength) among the digital devices such that the computational cost (memory) is minimized without violating the required simulation accuracy. This problem is generally not convex because of the scaling constraint. By exploring the special structure of this joint optimization of the choice of the realizations and the computational resources to be applied, and under a scaling assumption, the ESP is converted to a convex problem. Numerical results are given which compare this method with existing approaches.