A novel sliding surface design for predefined-time stabilization of Euler–Lagrange systems

Liang, Chang‐Duo; Ge, Ming‐Feng; Liu, Zhiwei; Ling, Guang; Zhao, Xiao‐Wen

doi:10.1007/s11071-021-06826-0

Cited by 49 publications

(45 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Compared with the FTSMC and FxTSMC [7][8][9][10][11][12], the tuning rules of the CPTSMC are substantially simplified. Regarding the PTSMC [15][16][17][18], the CPTSMC is much less conservative in meeting the temporal demands, as shown in Theorem 2. Furthermore, due to continuity, the CPTSMC enjoys the chattering-alleviated convergence process compared to the PTSMC [15][16][17][18][27][28][29][30] under the finite sampling frequency.…”

Section: Remarkmentioning

confidence: 99%

“…Regarding the PTSMC [15][16][17][18], the CPTSMC is much less conservative in meeting the temporal demands, as shown in Theorem 2. Furthermore, due to continuity, the CPTSMC enjoys the chattering-alleviated convergence process compared to the PTSMC [15][16][17][18][27][28][29][30] under the finite sampling frequency. Although the PTSMC laws [27,28] also exhibit weak conservativeness, some issues remain to be settled due to its aggressive convergence, such as the accuracy loss shown in Fig.…”

Section: Remarkmentioning

confidence: 99%

“…Accordingly, a CPTSMC is derived based on the novel convergent form, enabling the UBST of system states prescribed by only one parameter. Chattering is alleviated compared to the PTSMC [15][16][17][18][27][28][29][30], and conservativeness in meeting temporal demands is reduced compared to the PTSMC in [15][16][17][18]. Moreover, the boundedness of all system signals has been verified.…”

Section: Introductionmentioning

confidence: 99%

“…One is based on a kind of Lyapunov-like characterization, which guarantees the actual settling time equal to the prescribed UBST under the condition of infinite initial state errors [14]. Many PTSMC laws have been developed within this framework for Euler-Lagrange systems [15], distributed-order systems [16], under-water vehicles [17], robotic manipulators [18], and so on. Nonetheless, regarding the PTSMC [15][16][17][18], the conservativeness in estimating UBST has not been effectively reduced, and the actual convergence rate becomes unnecessarily fast for practical scenarios under small initial values.…”

Section: Introductionmentioning

confidence: 99%

“…Many PTSMC laws have been developed within this framework for Euler-Lagrange systems [15], distributed-order systems [16], under-water vehicles [17], robotic manipulators [18], and so on. Nonetheless, regarding the PTSMC [15][16][17][18], the conservativeness in estimating UBST has not been effectively reduced, and the actual convergence rate becomes unnecessarily fast for practical scenarios under small initial values. Another variety of prescribed-time control laws is based on time-varying gains and has been presented in [19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Continuous Prescribed-Time Sliding Mode Control with A Prescribed-Time ESO for Second-Order Nonlinear Systems with Mismatched Disturbance

Wang

Guan

et al. 2021

Preprint

View full text Add to dashboard Cite

This paper aims to settle the continuous prescribed-time stabilization problem of second-order nonlinear systems with mismatched disturbances. A continuous prescribed-time sliding mode control (CPTSMC) method with a prescribed-time extended state observer (PTESO) is proposed. The PTESO can precisely estimate the unknown states and disturbances, with its upper bound for the settling time (UBST) prescribed by only one parameter more tightly than existing finite-time or fixed-time ESOs. Furthermore, as a common concern for ESOs, the peaking value problem is well addressed. Then, a novel prescribed-time convergent form with little conservatism and simple tuning procedures is designed, and the internal mechanism in acquiring higher transient performance is explicitly researched. By using the estimated states and disturbances, the CPTSMC makes system states converge in a chattering-alleviated manner following the novel prescribed-time form. In addition to proving that the UBST of the whole system is tightly prescribed by only one design parameter, we show the continuity of the CPTSMC and the boundedness of all system signals, which are vital for practical applications. Ultimately, numerical simulations on the second-order system and a DC motor servo verify the efficiency of the proposed control system.

show abstract

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Continuous Prescribed-Time Sliding Mode Control with A Prescribed-Time ESO for Second-Order Nonlinear Systems with Mismatched Disturbance

Wang

Guan

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

Predefined‐time control for Euler–Lagrange systems with model uncertainties and actuator faults

Wang

Hou

Feng

et al. 2022

Asian Journal of Control

View full text Add to dashboard Cite

A novel adaptive predefined-time tracking control algorithm is proposed for the Euler-Lagrange systems (ELSs) with model uncertainties and actuator faults. Compared with traditional finite-time and fixed-time studies, the system output tracking error under the proposed predefined-time controller converges to a small neighborhood of zero in finite time, whose upper bound is exactly a design parameter in the control algorithm. For the uncertain model, radial-based function neural network (RBFNN) is utilized to approximate the continuous uncertain dynamics. To deal with the actuator faults, an adaptive control law is involved in the fault-tolerant controller. In order to achieve the predefined-time bounded, a novel predefined-time sliding mode surface is designed. It is proved that the tracking error vector trajectory of closed-loop system is semi-globally uniformly ultimately predefined-time bounded, and the upper bounds of both the system settling time and the corresponding output tracking error can be adjusted with a simple parameter. Simulation examples finally demonstrate the effectiveness of the proposed control algorithm.

show abstract

Hierarchical predefined‐time bipartite tracking of Euler–Lagrange systems over a signed graph

Zhang,

Han,

Xiao

et al. 2023

Asian Journal of Control

View full text Add to dashboard Cite

This paper addresses the hierarchical predefined‐time bipartite tracking problem in networked Euler–Lagrange systems (ELSs) over a signed graph, considering the presence of outer disturbances and dynamic uncertainties. An algorithm about the novel hierarchical predefined‐time control (HPTC) is presented here, which aims to guide the states of two opposing subgroups of the ELSs to achieve the leader's trajectory while the signs are opposite. The algorithm allows for flexibility in setting the desired settling time for the system, the upper bound of which is simple to be predetermined in advance and adjusted like other parameters.Through Lyapunov stability analysis, a sufficient criteria is established for achieving predefined‐time bipartite tracking problem. Finally, numerical simulations are conducted to illustrate the effectiveness and performance of the developed methods.

show abstract

A novel sliding surface design for predefined-time stabilization of Euler–Lagrange systems

Cited by 49 publications

References 41 publications

Continuous Prescribed-Time Sliding Mode Control with A Prescribed-Time ESO for Second-Order Nonlinear Systems with Mismatched Disturbance

Continuous Prescribed-Time Sliding Mode Control with A Prescribed-Time ESO for Second-Order Nonlinear Systems with Mismatched Disturbance

Predefined‐time control for Euler–Lagrange systems with model uncertainties and actuator faults

Hierarchical predefined‐time bipartite tracking of Euler–Lagrange systems over a signed graph

Contact Info

Product

Resources

About