Semi-global predefined-time stable systems

Jiménez‐Rodríguez, Esteban; Loukianov, Alexander G.; Sánchez‐Torres, Juan Diego

doi:10.1109/iceee.2017.8108875

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…This paper is a continuation of the research of the authors in predefined-time stability, in particular, it stands as an extension of the reference [16]. As a consequence, since it contains the essential definitions, this section has similar contents to others of the author reports, especially to Section II of the mentioned reference.…”

Section: Preliminariesmentioning

confidence: 82%

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Semi-Global Predefined-Time Stable Vector Systems

Jiménez‐Rodríguez

Sánchez‐Torres

Loukianov

2018

2018 IEEE Conference on Decision and Control (CDC)

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In this paper, we expose a control function which allows the semi-global predefined-time stabilization of firstorder vector systems. The predefined-time stability is a stronger class of finite-time stability that has as main advantage the settling time as a tunable parameter of the proposed function. To design that stabilizing function, we use the unit control principle jointly to the inverse incomplete gamma function. For the resulting expression, the domain of definition the inverse incomplete gamma function can be made as large as wanted with an appropriate parameter selection, and, as consequence, the attraction domain of the systems. Therefore, we say that the system exhibits semi-global predefined-time stability. As an essential feature, the parameter which defines the settling time bound and those that tune the attraction domain are independent of each other. Finally, the constructed function is used to design predefined-time stabilizing controllers which are robust against vanishing and non-vanishing perturbations.

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Section: Preliminariesmentioning

confidence: 82%

“…Due to its importance, a vector extension of the scalar semi-global predefined-time stabilizing function [16] is proposed in this paper. The constructed function involves the inverse incomplete gamma function, causing this function to be semi-global.…”

Section: Introductionmentioning

confidence: 99%

Semi-Global Predefined-Time Stable Vector Systems

Jiménez‐Rodríguez

Sánchez‐Torres

Loukianov

2018

2018 IEEE Conference on Decision and Control (CDC)

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“…Remark 3: By considering a design method of semi-global predefined-time system in [9,10,20]. A class of candidate Lyapunov function can be set as:…”

Section: A Second-order Systemmentioning

confidence: 99%

“…However, the upper bound of the settling time of traditional fixed-time is usually determined by two or more parameters, hence, a simplifying fixed-time stability system is presented in [8] to make the upper bound of settling time explicit in the system function. In addition, the improved fixed-time stability system can also obtain an upper bound of settling time without enlarging and reducing mathematically [9,10], but most of traditional fixed-time stability systems enlarged the upper bound of settling time. Especially, a note on predefined-time stability in [11] pointed that the predefined-time stability of system can be guaranteed without the exponential term.…”

Section: Introductionmentioning

confidence: 99%

On Parameter Selection of Nonsingular Predefined-time Terminal Sliding Mode With the Fixed-time Convergence Guarantee

Yan

2020

Preprint

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This paper study the parameter selection of predefined-time sliding mode and try to design a general nonsingular predefinedtime terminal sliding mode. 1). On parameter selection: Some existing predefined-time sliding modes are designed to focus on the reaching time and ignore the characterization of the equilibrium point i.e. xe = 0. In actual engineer, the system can only converge to a small neighborhood near the equilibrium point because of the existence of uncertainty i.e. xe → 0. The actual equilibrium point should be deduced by taking the limit but not directly solve the equilibrium point. Hence, the actual selection of exponential term is suggested to be not 1 to make system convergence to the equilibrium point within predefined time.2). On singularity-avoidance: Based on the exponential feature of predefined-time stability systems, a mathematic concept of switching sliding mode [1] is applied in the design of nonsingular predefined-time terminal sliding mode. However, this class of sliding mode switching method will cause a singular problem, which can be described as control input u → ∞ if the system state x → 0 and any-order time derivative of x is not 0. Hence, a non-singular selection condition for each recursive sliding mode surface is explored in this paper to realize the global finiteness of control input. In addition, an unnecessary chattering of control input will also be caused by the sliding mode switching frequency, and a novel switching condition will be applied in the controller to reduce this chattering. Simulations will be carried out to validate the effect of the novel nonsingular predefined-time sliding mode control method to some extent.

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“…Although the notion of fixed-time stability is superior to the finite-time stability notion, there is no direct relationship between the convergence time-bound and the system parameters, which is necessary for many control problems that need to satisfy hard time constraints (Sánchez-Torres et al 2018b). To cope with this shortage, the notion of predefined-time stability has been presented in Sánchez-Torres et al (2015 and Jiménez-Rodríguez et al (2017a). Using the predefined-time stability notion in the controller provides a class of fixed-time controller with convergence time-bound as an explicit parameter which can be determined as desired in advance.…”

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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Semi-global predefined-time stable systems

Cited by 7 publications

References 15 publications

Semi-Global Predefined-Time Stable Vector Systems

Semi-Global Predefined-Time Stable Vector Systems

On Parameter Selection of Nonsingular Predefined-time Terminal Sliding Mode With the Fixed-time Convergence Guarantee

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

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