Integral Sliding Mode Convex Optimization in Uncertain Lagrangian Systems Driven by PMDC Motors: Averaged Subgradient Approach

An uncertain Lagrangian dynamic controlled plant with permanent magnet dc-actuator, governed by a system of ordinary differential equations, is treated. The state variables (generalized coordinates and their velocities) are assumed to be measurable. The controller design is based on sliding mode con...

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Published in:IEEE transactions on automatic control Vol. 66; no. 9; pp. 4267 - 4273
Main Authors: Poznyak, Alexander S., Nazin, Alexander V., Alazki, Hussain
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Actuators
Algorithms
Computational geometry
Control systems design
Convergence
Convex functions
Convexity
Cost function
Differential equations
Hysteresis motors
IEEE members
Mathematical model
Optimization
Ordinary differential equations
Permanent magnets
Robot arms
sliding mode control
torque control
Upper bounds
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Abstract An uncertain Lagrangian dynamic controlled plant with permanent magnet dc-actuator, governed by a system of ordinary differential equations, is treated. The state variables (generalized coordinates and their velocities) are assumed to be measurable. The controller design is based on sliding mode concept, aimed to minimize a given convex (not obligatory strongly convex) function of the current state. The subgradient of this cost function is supposed to be measurable online. An optimization type algorithm is developed and analyzed using ideas of the averaged subgradient technique. The main results consist in proving the reachability of the "practical desired regime" (nonstationary analogue of sliding surface) from the beginning of the process and obtaining an explicit upper bound for the cost function decrement, that is, a functional convergence is proven and the rate of convergence is estimated. Numerical example, dealing with a robot manipulator of three freedom degrees illustrates the effectiveness of the suggested approach.
AbstractList An uncertain Lagrangian dynamic controlled plant with permanent magnet dc-actuator, governed by a system of ordinary differential equations, is treated. The state variables (generalized coordinates and their velocities) are assumed to be measurable. The controller design is based on sliding mode concept, aimed to minimize a given convex (not obligatory strongly convex) function of the current state. The subgradient of this cost function is supposed to be measurable online. An optimization type algorithm is developed and analyzed using ideas of the averaged subgradient technique. The main results consist in proving the reachability of the “practical desired regime” (nonstationary analogue of sliding surface) from the beginning of the process and obtaining an explicit upper bound for the cost function decrement, that is, a functional convergence is proven and the rate of convergence is estimated. Numerical example, dealing with a robot manipulator of three freedom degrees illustrates the effectiveness of the suggested approach.
Author Alazki, Hussain
Nazin, Alexander V.
Poznyak, Alexander S.
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  organization: Universidad Autónoma del Carmen (UNACAR), Playa del Carmen, México
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SubjectTerms Actuators
Algorithms
Computational geometry
Control systems design
Convergence
Convex functions
Convexity
Cost function
Differential equations
Hysteresis motors
IEEE members
Mathematical model
Optimization
Ordinary differential equations
Permanent magnets
Robot arms
sliding mode control
torque control
Upper bounds
Title Integral Sliding Mode Convex Optimization in Uncertain Lagrangian Systems Driven by PMDC Motors: Averaged Subgradient Approach
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https://www.proquest.com/docview/2565239082
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