Improved synthesis conditions for mixed gain-scheduling control subject to uncertain scheduling parameters

• Published in: International journal of control Vol. 90; no. 3; pp. 580 - 598
• Main Authors: Al-Jiboory, Ali Khudhair, Zhu, Guoming G.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.03.2017; Taylor & Francis Ltd
• Subjects: Algorithms; Controllers; gain-scheduling; Inequalities; linear matrix inequality; Linear parameter-varying systems; Parameter uncertainty; Parameters; robust control; Scheduling; Synthesis
• DOI: 10.1080/00207179.2016.1186843
• ISSN: 0020-7179

The vast majority of the existing work in gain-scheduling (GS) control literature assumes perfect knowledge of scheduling parameters. Generally, this assumption is not realistic since for practical control applications measurement noises are unavoidable. In this paper, novel synthesis conditions are derived to synthesise robust GS controllers with mixed performance subject to uncertain scheduling parameters. The conditions are formulated in terms of parameterised bilinear matrix inequalities (PBMIs) that depend on varying parameters inside multi-simplex domain. The conditions provide practical GS controllers independent of the derivatives of scheduling parameters. That is, the designed controllers are feasible for implementation. Since bilinear matrix inequality problems are intractable, an iterative PBMI algorithm is developed to solve the developed synthesis conditions. By the virtue of this algorithm, conservativeness reduction is achieved with few iterations. Examples are presented to illustrate the effectiveness of the developed conditions. Compared to other design methods from literature, the developed conditions achieve better performance.