Predefined-Time Robust Stabilization of Robotic Manipulators

Muñoz‐Vázquez, Aldo Jonathan; Sánchez‐Torres, Juan Diego; Jiménez‐Rodríguez, Esteban; Loukianov, Alexander G.

doi:10.1109/tmech.2019.2906289

Cited by 218 publications

(117 citation statements)

References 18 publications

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“…The proposed algorithm (19) is directly studied on a high‐order nonlinear strict‐feedback system with disturbance in (8). It can be seen that system (8) is more general than the first‐order systems, the second‐order systems, or the high‐order chain of integrators in traditional predefined‐time control studies 5‐14,17,21 The proposed algorithm (19) always takes effect on t ≥ 0.…”

Section: Predefined‐time Backstepping Controlmentioning

confidence: 99%

“…On the basis of Lyapunov‐like conditions for ensuring dynamic systems to exhibit predefined‐time stability or predefined‐time boundedness, many predefined‐time controllers were designed for various systems, for example, nonlinear second‐order systems, 6‐8 nonholonomic systems, 9 chaotic systems, 10,11 rigid spacecrafts, 12 robotic manipulators 13,14 as well as first‐order and second‐order multi‐agent systems 15,16 . However, the predefined‐time controllers derived on the basis of Lyapunov analysis 3‐14 may provide conservative estimate of upper bounds of system convergence time, especially for high‐order systems. The real convergence time may be much smaller than the estimated upper bound.…”

Section: Introductionmentioning

confidence: 99%

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Predefined‐time backstepping control for a nonlinear strict‐feedback system

Liu

Hou

et al. 2021

Intl J Robust & Nonlinear

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Two novel predefined‐time control algorithms for a nonlinear strict‐feedback system are proposed in this short communication. It is required that the upper bound of system convergence time is exactly a positive constant parameter in each algorithm, and it can be selected arbitrarily by users. Composite state tracking errors are introduced to the backstepping design process by using some novel smooth time‐varying tuning functions. In order to address the problem of explosion of complexity in the first algorithm, the second algorithm extends the predefined‐time control strategy to a dynamic surface control (DSC) case. Furthermore, the proposed predefined‐time DSC algorithm can guarantee global stability rather than semi‐global stability for the closed‐loop system compared with traditional DSC algorithms. Simulation results show the effectiveness of the two control schemes.

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Section: Predefined‐time Backstepping Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Predefined‐time backstepping control for a nonlinear strict‐feedback system

Liu

Hou

et al. 2021

Intl J Robust & Nonlinear

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“…Regarding the controller design problem for fixed‐time stability, the existing methodologies exhibit the following drawbacks. First, in methodologies like those proposed by Basin et al 32 and Tian et al, 28,29 which are based on the homogeneity property, 3 the UBST is unknown.Second, autonomous controllers derived based on Lyapunov analysis 1,16,26,34-36 may provide non‐conservative estimates of the UBST for the scalar case (see, eg, the work from Sanchez‐Torres et al 2 and Aldana‐López et al 34 ), but the estimate of the UBST becomes very conservative in high‐order systems (see, eg, section 5 in Zimenko et al 15 ). Third, in nonautonomous controllers based on time‐varying gains, 22,23,37 the origin is reached exactly at the desired time, but the time‐varying gain tends to infinity as the time approaches the desired convergence time.…”

Section: Introductionmentioning

confidence: 99%

On the design of nonautonomous fixed‐time controllers with a predefined upper bound of the settling time

Gómez‐Gutiérrez

2020

Intl J Robust & Nonlinear

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Recently, there has been a great deal of attention in a class of finite-time stable dynamical systems, called fixed-time stable, that exhibit uniform convergence with respect to its initial condition, that is, there exists an upper bound for the settling-time (UBST) function, independent of the initial condition of the system. Of particular interest is the development of stabilizing controllers where the desired UBST can be selected a priori by the user since it allows the design of controllers to satisfy real-time constraints. Unfortunately, existing methodologies for the design of controllers for fixed-time stability exhibit the following drawbacks: on the one hand, in methods based on autonomous systems, either the UBST is unknown or its estimate is very conservative, leading to over-engineered solutions; on the other hand, in methods based on time-varying gains, the gain tends to infinity, which makes these methods unrealizable in practice. To bridge these gaps, we introduce a design methodology to stabilize a perturbed chain of integrators in a fixed-time, with the desired UBST that can be set arbitrarily tight. Our approach consists of redesigning autonomous stabilizing controllers by adding time-varying gains. However, unlike existing methods, we provide sufficient conditions such that the time-varying gain remains bounded, making our approach realizable in practice. K E Y W O R D Sfixed-time control, predefined-time control, predefined-time stabilization, prescribed-time control INTRODUCTIONRecently, there has been a great deal of attention in the control community on the analysis of a class of systems, known as fixed-time stable systems, because they exhibit finite-time convergence with an upper bound of the settling time (UBST) that is independent of the initial conditions of the system. 1-5 This effort has produced many contributions on algorithms with the fixed-time convergence property, such as multiagent coordination, 6-9 distributed resource allocation, 10 synchronization of complex networks, 11,12 stabilizing controllers, 1,13-16 state observers, 17 and online differentiation algorithms. 18,19 The fixed-time stability property is of great interest in the development of algorithms for scenarios where real-time constraints need to be satisfied. In fault detection, isolation, and recovery schemes, 20 failing to recover from the fault on time may lead to an unrecoverable mode. In missile guidance, 21 the impact time control guidance laws require stabilization in a desired time. 22,23 In hybrid dynamical systems, it is frequently required that the observer (respectively, controller) Int J Robust Nonlinear Control. 2020;30:3871-3885.wileyonlinelibrary.com/journal/rnc

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“…It can be pointed out in the work of Becerra et al (2017) that a high-order integral system has been controlled using a predefined-time SMC (PSMC) scheme. A robust controller has been designed in Munoz-Vazquez et al (2019) using PSMC scheme for manipulators. In Sánchez-Torres et al (2018a), a new PSMC scheme has been presented for a class of second-order systems.…”

Section: Introductionmentioning

confidence: 99%

Chattering-Free Trajectory Tracking Robust Predefined-Time Sliding Mode Control for a Remotely Operated Vehicle

Hosseinabadi

Abadi

Mekhilef

et al. 2020

J Control Autom Electr Syst

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This study investigates a new chattering-free robust predefined-time sliding mode control (CFRPSMC) scheme for the trajectory tracking control problem of a three-degree-of-freedom (3-DOF) remotely operated vehicle (ROV) in the presence of matched uncertainties. The advanced notion of predefined-time stability is used to provide a maximum convergence time as desired that can be set during the control design and independently of the initial conditions. Based on defining a new form of sliding surfaces, a new control law is designed to ease the undesirable chattering phenomenon without damaging the robustness properties and tracking precision. The proposed control scheme can not only solve the predefined-time tracking controller design problem, but also provide the robustness to various uncertainties. The Lyapunov stability theory is used to establish the stability analysis of the closed-loop system in both the reaching phase and the sliding phase. The performance of the proposed CFRPSMC scheme is evaluated for the 3-DOF ROV through two comparative simulation cases using Simulink/MATLAB. The comparative simulation results and analytical comparisons demonstrate the efficacy and superiority of the proposed method compared with other relevant conventional methods.

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Predefined-Time Robust Stabilization of Robotic Manipulators

Cited by 218 publications

References 18 publications

Predefined‐time backstepping control for a nonlinear strict‐feedback system

Predefined‐time backstepping control for a nonlinear strict‐feedback system

On the design of nonautonomous fixed‐time controllers with a predefined upper bound of the settling time

Chattering-Free Trajectory Tracking Robust Predefined-Time Sliding Mode Control for a Remotely Operated Vehicle

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