An adaptive learning controller for MIMO uncertain feedback linearizable nonlinear systems

Abstract

Most of available results in adaptive learning controllers (ALCs) with input learning technique have considered the single-input single-output nonlinear systems. This paper presents an ALC for MIMO uncertain feedback linearizable systems whose uncertainty is in their linear parameters. Since only an output signal is available for measurement, a high gain observer is used to estimate the unmeasurable state. The estimated state is then utilized to implement the ALC. The proposed ALC learns the input gain parameters of the state equation as well as the internal parameters. In addition, the desired input is also learned using an input learning rule to track the whole command history. In the proposed ALC, the tracking errors are bounded and the mean-square tracking error is O( ) as the task is repeated. Single-link and two-link manipulators are presented as simulation examples to confirm the feasibility and the performance of the proposed ALC.

Analysis of iterative learning control for an oscillating control system with two delays

“…With the development of the qualitative theories of differential equations, iterative learning control problems (ILC for short), proposed by Uchiyama (1978) and Arimoto and Kawamura (1984), investigated for several types of integer/fractional order linear/nonlinear differential systems. For the basic theory and experimental applications of iterative learning control, one can refer to monographs (Chen et al, 2012; Bien and Xu, 1998; Chen and Wen, 1999; Norrlöf, 2000; Xu et al, 2009) and practical applications in engineering (van de Wijdeven et al, 2009; Hou et al, 2008; Kim et al, 2015; Liu and Kong, 2013; Liu and Ruan, 2016; Ruan and Bien, 2012; Sun et al, 2010; Xu, 2011; Zhang and Li, 2014), fractional order systems (Lan and Zhou, 2012, 2013; Li et al, 2011, 2013; Liu et al, 2017; Liu and Wang, 2016), impulsive systems (Liu et al, 2015, 2016), and evolution systems (Yu and Wang, 2015; Yu et al, 2015).…”