Nonsmooth Optimization Method for H∞ Output Feedback Control

Qiong Wu (), Jin-He Wang, Hong-Wei Zhang (), Shuang Wang () and Li-Ping Pang ()
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Qiong Wu: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China
Jin-He Wang: School of Engineering, Huzhou University, Huzhou 313000, P. R. China
Hong-Wei Zhang: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China
Shuang Wang: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China
Li-Ping Pang: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2019, vol. 36, issue 03, 1-23

Abstract: This paper proposes a nonsmooth optimization method for H∞ output feedback control problem of linear time-invariant(LTI) systems based on bundle technique. We formulate this problem as a nonconvex and nonsmooth semi-infinite constrained optimization problem by quantifying both internal stability of closed-loop system and measurement of system performance, where H∞ norm of closed-loop transfer function and a stabilization channel is used. Our method uses progress function and bundle technique to solve the resulting problem which has a composite structure. We prove the convergence to a critical point from a feasible initial point and test some benchmarks to demonstrate the effectiveness of this method.

Keywords: H∞ synthesis; nonsmooth analysis; bundle method; composite optimization problems; semi-infinite optimization problems (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0217595919500155

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