Multiobjective controller design by solving a multiobjective matrix inequality problem

In this study, linear matrix inequality (LMI) approaches and multiobjective (MO) evolutionary algorithms are integrated to design controllers. An MO matrix inequality problem (MOMIP) is first defined. A hybrid MO differential evolution (HMODE) algorithm is then developed to solve the MOMIP. The hybrid algorithm combines deterministic and stochastic searching schemes. In the solving process, the deterministic part aims to exploit the structures of matrix inequalities, and the stochastic part is used to fully explore the decision variable space. Simulation results show that the HMODE algorithm can produce an approximated Pareto front (APF) and Pareto-efficient controllers that stabilize the associated controlled system. In contrast with single-objective designs using LMI approaches, the proposed MO methodology can clearly illustrate how the objectives involved affect each other, i.e., a broad perspective on optimality is provided. This facilitates the selecting process for a representative design, and particularly the design that corresponds to a nondominated vector lying in the knee region of the APF. In addition, controller gains can be readily modified to incorporate the preference or need of a system designer. W.-Y. Chiu is with the Multiobjective Control Lab, Department of Electrical Engineering, Yuan Ze University, Taoyuan 32003, Taiwan (email: [email protected]). This work was supported by the Ministry of Science and Technology of Taiwan under Grant 102-2218-E-155-004-MY3. This paper is a postprint of a paper submitted to and accepted for publication in IET Control Theory and Applications and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at IET Digital Library. doi: 10.1049/iet-cta.2014.0026 May 8, 2017 DRAFT 2