Algebraic Methods for Multi-Objective Optimal Design of Control Feedbacks for Linear Systems

This paper presents three novel methods for the multi-objective design of controllers with tunable parameters and fixed structure for linear systems. These techniques exploit the geometric properties of varieties and envelopes to obtain a closed-form expression of the set of candidate Pareto optimal values. The design objectives span from the regional pole placement to more general quadratic cost functionals, thus tackling a wide variety of control tasks. Examples of applications of the proposed techniques both to (possibly, non-convex) classical benchmark problems and to physical plants are given throughout the paper.