Multiobjective controller design by solving a multiobjective matrix inequality problem

Wei-Yu Chiu

Multiobjective controller design by solving a multiobjective matrix inequality problem

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Author(s): Wei-Yu Chiu ¹
- Affiliations: 1: Multiobjective Control Laboratory, Department of Electrical Engineering, Yuan Ze University, Taoyuan 32003, Taiwan
Source: Volume 8, Issue 16, 06 November 2014, p. 1656 – 1665
DOI: 10.1049/iet-cta.2014.0026 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 06/09/2013, Accepted 06/06/2014, Revised 14/05/2014, Published 14/08/2014

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 stabilise 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, that is, a broad perspective on optimality is provided. This facilitates the selecting process for a representative design, and particularly the design that corresponds to a non-dominated 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.

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Multiobjective controller design by solving a multiobjective matrix inequality problem

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