Improved robust filter synthesis combining linear matrix inequalities and heuristic algorithms

• Published in: Optimal control applications & methods Vol. 44; no. 4; pp. 1753 - 1768
• Main Authors: Souza, Ruhan Pontes Policarpo, Agulhari, Cristiano Marcos, Goedtel, Alessandro, Bugatti, Pedro Henrique
• Format: Journal Article
• Language: English
• Published: Glasgow Wiley Subscription Services, Inc 01.07.2023
• Subjects: Filter design (mathematics); genetic algorithm; Genetic algorithms; Heuristic methods; Linear matrix inequalities; linear matrix inequality; linear parameter‐varying system; Optimization; robust filtering; Robustness (mathematics); Slack variables
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2947

This article introduces an alternative and less conservative ℋ∞$$ {\mathscr{H}}_{\infty } $$ filter design procedure applied to continuous time uncertain systems. In order to provide a reduction in conservatism and an ℋ∞$$ {\mathscr{H}}_{\infty } $$ norm improvement, the proposed technique avoids the conventional convexification procedure—which uses structure restrictions and slack variables. Instead, it defines an unconstrained structure. The proposed technique consists of a hybrid procedure, combining the application of linear matrix inequalities (LMIs) with heuristic optimization algorithms (HOAs). The HOAs, specifically genetic algorithms, are used to optimize terms that could cause bilinearities, subsequently evaluated by LMIs and generating the desired filter. Numerical examples and a comparison with other methodologies are presented, testifying to the proposed method's efficacy and the performance.