Convex methods in actuator placement

Abstract

A new formulation of the actuator placement problem is presented. This formulation considers capital cost in the objective function and highlights the importance of magnitude limits on both input and output signals through variance bounding constraints on each. Thus, the proposed optimization problem is aimed at finding the set of minimum cost actuator arrays such that there exists a linear feedback for which all closed-loop signals will satisfy their magnitude limits. The original formulation of this problem results in a Mixed Integer Nonlinear Program (MINLP). However, through an LMI based transformation we exactly convert the problem into a computationally advantageous Mixed Integer Convex Program (MICP). Finally, the design method is applied to an example of actuator placement in a non-isothermal tubular reactor.