Embedded-Adaptive-Observer-Based $H_\infty$ Integrated Fault Estimation and Memory Fault-Tolerant Control for Nonlinear Delayed Implicit Robotic Arm
Guangming Zhuang, Zekun Wang, Xiangpeng Xie, Jianwei Xia
Abstract
This article lays the spotlight on embedded-adaptive-observer-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> integrated fault estimation and memory fault-tolerant control for a nonlinear delayed implicit robotic arm. To tackle the nonlinearity of the system, a prototypical Takagi–Sugeno fuzzy method is deployed. An embedded adaptive proportional–integral observer program is proposed to implement <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> simultaneous estimation of the original system states, sensor faults, and actuator faults via the fault-embedded technique, embedding the sensor faults into the original system states and allowing them to be transformed into new substates. The development of a fresh fuzzy Lyapunov–Krasovskii functional with time delays, Markov jump modes, and fuzzy information creates a firm groundwork for the outcome of the fuzzy delayed implicit jump system meeting with stochastic admissibility and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance metrics. Novel observer-based memory-aware fault-tolerant controller is engineered by taking the form of linear matrix inequalities to compensate the impact of time delays, perturbations, and faults. To illustrate the validity of the method put forward, a single-link robotic arm device is offered as an example finally.