A Tutorial on Robust Control, Adaptive Control and Robust Adaptive Control—Application to Robotic Manipulators

Wei, Bin

doi:10.3390/inventions4030049

Cited by 6 publications

(3 citation statements)

References 39 publications

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“…The local theorem can be used to prove whether an equilibrium point is stable or asymptotically stable [1][2][3][4][5][6], whereas the global theorem can be used to prove if an equilibrium point is globally asymptotically stable and if it has been used in several applications [7][8][9][10][11][12][13][14][15][16][17]. The LaSalle theorem can also be categorized into a local version and a global version, and they are collectively called invariant set theorem [18,19]. The purpose of using the LaSalle global invariant set theorem is to further prove that an equilibrium point is globally asymptotically stable, given the fact that the Lyapunov theorem is limited somehow to proving the global stability of an equilibrium point [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

Wei

2023

Applied Sciences

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The equilibrium state of a dynamical system can be divided into the equilibrium point and limit cycle. In this paper, the stability analysis of the equilibrium point and limit cycle of dynamical systems are presented through different and all possible approaches, and those approaches are compared as well. In particular, the author presented the stability analysis of the equilibrium point through phase plane approach, Lyapunov–LaSalle energy-based approach, and linearization approach, respectively, for two-dimensional nonlinear system, while the stability analysis of the limit cycle is analyzed by using the LaSalle local invariant set theorem and Poincaré–Bendixson theorem, which is only valid in two-dimensional systems. Different case studies are used to demonstrate the stability analysis of equilibrium point and limit cycle.

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Section: Introductionmentioning

confidence: 99%

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

Wei

2023

Applied Sciences

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“…Robotic manipulators are extensively being used in different areas such as the manufacturing industry, process and mining, automatic surgery, as well as smart agriculture [1,2]. These robots considerably reduce human effort in complex task operations by adopting different controllers [3][4][5]. Despite the available control technologies in the state-of-the-art, there are still some gaps and unaddressed challenges in this domain.…”

Section: Introductionmentioning

confidence: 99%

Robust Prescribed Trajectory Tracking Control of a Robot Manipulator Using Adaptive Finite-Time Sliding Mode and Extreme Learning Machine Method

et al. 2022

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This study aims to provide a robust trajectory tracking controller which guarantees the prescribed performance of a robot manipulator, both in transient and steady-state modes, experiencing parametric uncertainties. The main core of the controller is designed based on the adaptive finite-time sliding mode control (SMC) and extreme learning machine (ELM) methods to collectively estimate the parametric model uncertainties and enhance the quality of tracking performance. Accordingly, the global estimation with a fast convergence rate is achieved while the tracking error and the impact of chattering on the control input are mitigated significantly. Following the control design, the stability of the overall control system along with the finite-time convergence rate is proved, and the effectiveness of the proposed method is investigated via extensive simulation studies. The results of simulations confirm that the prescribed transient and steady-state performances are obtained with enough accuracy, fast convergence rate, robustness, and smooth control input which are all required for practical implementation and applications.

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“…A typical controller takes in a feedback signal, containing state information, as well as a reference point and computes an actuation command. There are various ways to develop autonomous robotic control systems such as fuzzy logic [3,4], adaptive control [5,6], behavioral control theory [7,8], traditional robot control theory [2], inverse reinforcement learning [9,10], and reinforcement learning [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

On the Impact of Gravity Compensation on Reinforcement Learning in Goal-Reaching Tasks for Robotic Manipulators

2021

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Advances in machine learning technologies in recent years have facilitated developments in autonomous robotic systems. Designing these autonomous systems typically requires manually specified models of the robotic system and world when using classical control-based strategies, or time consuming and computationally expensive data-driven training when using learning-based strategies. Combination of classical control and learning-based strategies may mitigate both requirements. However, the performance of the combined control system is not obvious given that there are two separate controllers. This paper focuses on one such combination, which uses gravity-compensation together with reinforcement learning (RL). We present a study of the effects of gravity compensation on the performance of two reinforcement learning algorithms when solving reaching tasks using a simulated seven-degree-of-freedom robotic arm. The results of our study demonstrate that gravity compensation coupled with RL can reduce the training required in reaching tasks involving elevated target locations, but not all target locations.

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A Tutorial on Robust Control, Adaptive Control and Robust Adaptive Control—Application to Robotic Manipulators

Cited by 6 publications

References 39 publications

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

Robust Prescribed Trajectory Tracking Control of a Robot Manipulator Using Adaptive Finite-Time Sliding Mode and Extreme Learning Machine Method

On the Impact of Gravity Compensation on Reinforcement Learning in Goal-Reaching Tasks for Robotic Manipulators

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