Fuzzy optimal control for nonlinear systems with time-varying delay via sampled-data controller
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METHODOLOGIES AND APPLICATION
Fuzzy optimal control for nonlinear systems with time-varying delay via sampled-data controller Zifang Qu1,2 • Zhengdi Zhang1 • Zhenbin Du3 • Tiebiao Zhao4
Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This work is devoted to a fuzzy sampled-data optimal control problem for nonlinear systems with time-varying delay in Takagi–Sugeno fuzzy form. Based on the Lyapunov–Krasovskii functional theory, some novel stability criteria are established. A fuzzy sampled-data controller is developed to ensure that the fuzzy closed-loop sampled-data control system is asymptotically stable and the guaranteed cost performance is also minimized. It is shown that the obtained results are less conservative in the stability analysis. Two examples of the computer-simulated truck-trailer system and the continuous stirred tank reactor system are provided to show the effectiveness and the merits of the proposed design. Keywords Fuzzy system Time delay Sampled-data control Optimal control
1 Introduction Fuzzy control approach is an effective tool to deal with nonlinear control. Takagi–Sugeno (T–S) fuzzy system was first presented in (Takagi and Sugeno 1985) and often utilized to describe the nonlinear systems. Based on this system, a series of control problems have been solved, for example, stability (Cao and Frank 2001), filtering (Dong et al. 2017), guaranteed cost control (Wu et al. 2017), asynchronous dissipative control (Wu et al. 2018), and so on.
Communicated by V. Loia. & Zhengdi Zhang [email protected] & Zhenbin Du [email protected] 1
Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China
2
School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, Shandong, China
3
School of Computer and Control Engineering, Yantai University, Yantai 264005, Shandong, China
4
School of Engineering, University of California Merced, Merced, CA 95340, USA
As usual, digital computers are utilized to produce the sampled-data signals and reduce the implementation cost and time in some industrial applications. When a sampleddata controller is designed for the system stability, it leads to a so-called sampled-data control problem. Many works have been endeavored for the investigation of nonlinear systems with sampled-data mechanism represented by T–S fuzzy system, for instance (Nishikawa et al. 2000; Katayama and Ichikawa 2004; Gao and Chen 2007; Lam and Leung 2007; Lam and Ling 2008; Yang and Cai 2008; Lam and Seneviratne 2009; Kim and Lee 2009; Kim et al. 2010; Lien et al. 2010; Yoneyama 2011; Chen et al. 2011; Yoneyama 2012; Lam 2012; Zhu et al. 2012; Koo et al. 2012; Huang et al. 2013; Zhu et al. 2013; Koo et al. 2013; Ge et al. 2014; Wu et al. 2014; Jing et al. 2014; Yang et al. 2014; Jiang 2015; Li et al. 2015; Liu and Zhou 2015; Kim et al. 2015; Koo et al. 2016; Wang et al. 2016; Liu and Lee 2016; Wag et al. 2016; Wang et al. 2017; Syed Ali et al. 2017; Du et al. 201
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