Implicit numerical integration for the simulation and control of a non-smooth system with resets

Huber, Olivier; Oza, Harshal B.

doi:10.1109/cdc.2016.7799277

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…Concerning the control community, the concept of implicit discretization of the set‐valued functions was firstly introduced for the sliding‐mode controllers. While several studies have been conducted on the implicit discretization of homogeneous systems and sliding‐mode controllers, 16,22‐25,35‐40 implicit discretization of differentiators has not been addressed extensively. Implicit time‐discretization of SMB differentiators with set‐valued functions can be traced back to 2012, 24 where some embryonic analyses may be found.…”

Section: Introductionmentioning

confidence: 99%

Time‐discretizations of differentiators: Design of implicit algorithms and comparative analysis

Mojallizadeh

Brogliato

Acary

2021

Intl J Robust & Nonlinear

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A complete review of the known differentiators and their time‐discretizations have been addressed in this study. To resolve the drawbacks of the explicit (forward Euler) discretization, which is commonly utilized in sliding‐mode‐based differentiators, implicit time discretization methods are proposed to handle the set‐valued functions. The proposed schemes are supported by some analytical results to show their crucial properties, for example, finite‐time convergence, exactness, invariant sliding‐surface, chattering elimination, insensitivity to the gains during the sliding‐phase, and the well‐posedness. The causal implementation of the proposed implicit schemes has been addressed clearly and supported by flowcharts. Semi‐implicit schemes are also presented to provide a compromise between the performance and the ease of implementation. Finally, an exhaustive comparison is made using numerical experiments among 25 different state‐of‐the‐art differentiators to evaluate the behaviors of the differentiators facing the noise and initial error. Realistic conditions are considered in the simulations to provide useful information based on practical conditions. General conclusions are that implicit discretizations can supersede explicit and semi‐implicit ones.

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Section: Introductionmentioning

confidence: 99%