Robust Tracking as Constrained Optimization by Uncertain Dynamic Plant: Mirror Descent Method and ASG—Version of Integral Sliding Mode Control

A class of controlled objects is considered, the dynamics of which are determined by a vector system of ordinary differential equations with a partially known right-hand side. It is presumed that the state variables and their velocities can be measured. Designing a robust tracking controller under s...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-10, Vol.11 (19), p.4112
Main Authors: Nazin, Alexander, Alazki, Hussain, Poznyak, Alexander
Format: Article
Language:English
Subjects:
Algorithms
Constraints
Controllers
convex constrained optimization
Differential equations
Mathematical optimization
Mathematical research
Optimization
Ordinary differential equations
Process controls
Robot arms
robot manipulator
Robust control
sliding mode
Sliding mode control
State variable
subgradient descent method
Tracking control
trajectory tracking
Variables
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Summary:A class of controlled objects is considered, the dynamics of which are determined by a vector system of ordinary differential equations with a partially known right-hand side. It is presumed that the state variables and their velocities can be measured. Designing a robust tracking controller under some constraints to admissible state variables is the research goal. This construction, which extends the results for the average subgradient technique (ASG), and is an update of the subgradient descent technique (SDM) and integral sliding mode (ISM) approach, is realized by using the Legendre–Fenchel transform. A two-link robot manipulator with three revolute joints, powered by individual PMDC motors, is presented as an illustrative example of the suggested approach implementation.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11194112