Iterative Learning Control for Equations with Fractional Derivatives and Impulses

ISBN-13: 9789811682469 / Angielski / Miękka / 2022 / 256 str.

Jinrong Wang; Shengda Liu; Michal Fečkan

Opis

This book introduces iterative learning control (ILC) and its applications to the new equations such as fractional order equations, impulsive equations, delay equations, and multi-agent systems, which have not been presented in other books on conventional fields. ILC is an important branch of intelligent control, which is applicable to robotics, process control, and biological systems. The fractional version of ILC updating laws and formation control are presented in this book. ILC design for impulsive equations and inclusions are also established. The broad variety of achieved results with rigorous proofs and many numerical examples make this book unique.

This book is useful for graduate students studying ILC involving fractional derivatives and impulsive conditions as well as for researchers working in pure and applied mathematics, physics, mechanics, engineering, biology, and related disciplines.

Spis treści

1 Fractional Equations

1.1 Pulse Compensation ILC

1.2 PD-type ILC

1.3 High Order Internal Models ILC

1.4 Randomly Varying Trial Lengths ILC

2 Fractional Multi-Agent Systems

2.1 Linear Systems

2.2 Nonlinear Systems

3 Instantaneous Impulsive Equations

4.1 ODE Case

3.2 Stochastic Case

3.3 Delay Matrix Case

4 Noninstantaneous Impulsive Equations

4.1 Fixed Trial Lengths ILC

4.2 Randomly Varying Trial Lengths ILC

5 Noninstantaneous Impulsive Inclusions 

5.1 Ordinary differential inclusion without impulses

5.2 Partial differential inclusion with impulses

6. Delay Equations

6.1 Discrete Case

6.2 Continuous Case

O autorze

JinRong Wang has been Professor in the Department of Mathematics at the School of Mathematics and Statistics at Guizhou University, People’s Republic of China, since 2011. He received his master‘s degree from Guizhou University in 2006 and Ph.D. from the same university in 2009. He is interested in impulsive differential equations, fractional differential equations, delay differential equations, iterative learning controls, multi-agent systems, atmospheric Ekman flows and Antarctic Circumpolar Current. Since 2015, he has been listed in the Highly Cited Researcher in Mathematics.

Shengda Liu received the B. S. with the major of mathematics from the School of Mathematical Sciences, Harbin Normal University, Harbin, China, in 2012, and the M. S. and Ph. D. with the major of applied mathematics from the School of Mathematics and Statistics, Guizhou University, Guiyang, China, in 2016 and 2019, respectively. He is currently a post-doctoral fellow at the State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences. His current research interests include iterative learning control, fractional order equation and control theory and its application in rehabilitation robots.

Michal Fečkan has been a Professor of Mathematics at the Department of Mathematical Analysis and Numerical Mathematics in the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovak Republic since 2003. He received the master‘s degree (mathematics) from Comenius University in Bratislava in 1985 and PhD (mathematics) from the Mathematical Institute of Slovak Academy of Sciences in Bratislava, Slovak Republic in 1993. He is interested in nonlinear functional analysis, bifurcation theory, dynamical systems and fractional calculus with applications to mechanics, vibrations and economics.