Linear matrix inequalities and evolutionary optimization in multiobjective control

Abstract

The multiobjective problems of H ₂ optimal control (LQG case) and mixed H ₂/H _∞ are addressed using two different approaches: Evolutionary Algorithms and Linear Matrix Inequalities (LMIs). This study illustrates with numerical examples how both approaches can be used to find the trade-off between different signal sensitivities to noise and to find the trade-off of the mixed H ₂/H _∞ problem. For the mixed H ₂/H _∞ example, this paper shows how a Multiobjective Genetic Algorithm (MOGA) could find an improved Pareto-optimal front compared to the LMI approach.

Keywords:

• Linear matrix inequalities
• Multiobjective control
• Genetic algorithms

Acknowledgements

A. Molina-Cristóbal acknowledges the support from a Grant of the National Council of Science and Technology of Mexico (CONACYT) and the Rolls-Royce University Technology Centre (UTC) in Control and Systems Engineering, University of Sheffield.