RESEARCH ARTICLE
Design proportional-integral-derivative/proportional-derivative controls for second-order time-varying switched nonlinear systems
Zhikun She,
Aijing Zhang,
Junjie Lu,
Ruiqi Hu,
Shuzhi Sam Ge,
Zhikun She
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China
Search for more papers by this authorAijing Zhang
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China
Search for more papers by this authorCorresponding Author
Junjie Lu
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China
Correspondence Junjie Lu, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China
Email: [email protected]
Search for more papers by this authorRuiqi Hu
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China
Search for more papers by this authorShuzhi Sam Ge
Department of Electrical and Computer Engineering, National University of Singapore, Singapore
Search for more papers by this authorZhikun She,
Aijing Zhang,
Junjie Lu,
Ruiqi Hu,
Shuzhi Sam Ge,
Zhikun She
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China
Search for more papers by this authorAijing Zhang
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China
Search for more papers by this authorCorresponding Author
Junjie Lu
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China
Correspondence Junjie Lu, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China
Email: [email protected]
Search for more papers by this authorRuiqi Hu
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China
Search for more papers by this authorShuzhi Sam Ge
Department of Electrical and Computer Engineering, National University of Singapore, Singapore
Search for more papers by this authorFunding information Beijing Natural Science Foundation, Z180005; China Postdoctoral Science Foundation, 2018M641182; Fundamental Research Funds for the Central Universities, FRF-TP-18-034A1; National Natural Science Foundation of China, 11422111
Summary
Based on proportional-integral-derivative (PID)/PD controls, we in the article investigate the tracking problem of a class of second-order time-varying switched nonlinear systems. To start with, for tracking a given point under arbitrary switching signals, we propose a sufficient condition about PID controller parameters, which can be implicitly described as semialgebraic sets. Successively, we consider the tracking problem under average dwell time (ADT)-based switching signals and propose an alternative sufficient condition about PID controller parameters. Especially, for tracking an equilibrium point of the system without controls, we can further simply utilize the proportional-derivative control and similarly construct corresponding semialgebraic conditions about proportional-derivative controller parameters under arbitrary switching signals and ADT-based switching signals. Finally, two examples are given to show the applicability of our theoretical results.
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