Disturbance‐observer‐based‐control and
 L
 2
 −
 L
 ∞
 resilient control for Markovian jump non‐linear systems with multiple disturbances and its application to single robot arm system

Li, Yankai; Sun, Haibin; Zong, Guangdeng; Hou, Linlin

doi:10.1049/iet-cta.2015.0430

Cited by 54 publications

(47 citation statements)

References 31 publications

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“…Example In this example, we consider the single link robot arm system in the work of Li et al

\overset{θ}{true} false(t false) = - \frac{M_{i} g L}{J_{i}} \sin ((), θ false(t false)) - \frac{D}{J_{i}} \overset{θ}{true} false(t false) + \frac{1}{J_{i}} ([], u false(t false) + d_{1} false(t false)) + \frac{1}{J_{i}} d_{2} false(t false),

where θ ( t ) is the angel position of the robot arm; u ( t ) is the control input; d 1 ( t ) is the bias failure of the actuator; d 2 ( t ) is the exogenous disturbance. M i is the mass of the payload, g is the acceleration of gravity, L is the length of the arm, J i is the moment of inertia, and D is the viscous friction.…”

Section: Numerical Examplementioning

confidence: 99%

Mixed passive / H_∞ hybrid control for delayed Markovian jump system with actuator constraints and fault alarm

et al. 2018

Intl J Robust & Nonlinear

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Summary In this paper, mixed passive / H∞ hybrid controllers are designed for a delayed Markovian jump system with actuator constraints and alarm signal. The actuator constraints include the unknown actuator bias failure and the actuator partial failure, and the controllers are switched by using alarm signals. First, a sufficient condition for mixed passive / H∞ performance of the closed‐loop system is constructed, and robust controllers and fault‐tolerant controllers are designed, respectively. Then, mixed passive / H∞ observers are presented to ensure that the actuator bias failure is well estimated. Next, an alarm system is proposed by designing multiple thresholds to avoid false alarm, and this system is used to invoke suitable controllers and determine whether to remove the estimated value of actuator bias failure. Finally, two numerical examples are given to illustrate the effectiveness of the method.

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“…Example In this example, we consider the single link robot arm system in the work of Li et al

\overset{θ}{true} false(t false) = - \frac{M_{i} g L}{J_{i}} \sin ((), θ false(t false)) - \frac{D}{J_{i}} \overset{θ}{true} false(t false) + \frac{1}{J_{i}} ([], u false(t false) + d_{1} false(t false)) + \frac{1}{J_{i}} d_{2} false(t false),

Section: Numerical Examplementioning

confidence: 99%

Mixed passive / H_∞ hybrid control for delayed Markovian jump system with actuator constraints and fault alarm

et al. 2018

Intl J Robust & Nonlinear

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“…Example A single‐link robot arm is considered, in which the dynamic equation is given as follows:

\overset{θ}{true} false(t false) = - \frac{M g L}{J} \sin ((), θ false(t false)) - \frac{D}{J} \overset{θ}{true} false(t false) - \frac{D^{*}}{J} \overset{θ}{true} ((), t - τ false(t false)) + \frac{1}{J} ((), u false(t false) + ω false(t false)),

where θ ( t ), u ( t ), and ω ( t ) are the angle position of the arm, the control input, and the perturbation input, respectively. M ,

sans-serifg

, L , J , and D are the mass of the payload, the acceleration of gravity, the length of the arm, the moment of inertia, and the viscous friction, respectively.…”

Section: Numerical Examplementioning

confidence: 99%

“…A single-link robot arm is considered, [46][47][48] in which the dynamic equation is given as follows:…”

Section: Examplementioning

confidence: 99%

Observer‐based H_∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

Shu

Huang

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper addresses the observer‐based H∞ control of Markovian jump systems with interval time‐varying delays and incomplete transition rates. To reduce the conservatism of proposed results, a modified Lyapunov‐Krasovskii functional is constructed, where an improved delay partitioning method is used by partitioning the delay interval into multiple segments with a geometric sequence. Moreover, the Jensen‐based integral inequality and the reciprocally convex technique are used to tackle the time‐varying delays. Some less conservative stochastic stability criteria are derived in the framework of linear matrix inequalities. Then, the observer‐based H∞ controller is designed. Finally, three numerical examples are given to demonstrate the merit and effectiveness of the proposed method.

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“…Example A single‐link robot arm from the work of Li et al is given as

\overset{θ}{true} false(t false) = - \frac{M G L}{J} \sin (() θ (t)) - \frac{D false(t false)}{J} \overset{θ}{true} false(t false) + A_{d} x (() t - τ (t)) + \frac{1}{J} (() u (t) + d (t)),

where θ( t ), u ( t ), and d ( t ) are the angle position of the arm, the control input, and the unknown disturbance input. M , J , G , L , and D ( t ) are the mass of the payload, the moment of inertia, the acceleration of gravity, the length of the arm, and the viscous friction.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…This paper will study the issue of control for MJSs with time delay and disturbance uncertainties via DOBC. First, the literatures mainly investigated the MJSs without time delay, whereas the model in this paper includes time delay. Second, the designed controller in the works of Yao and Guo, Yao et al, and Li et al is mode‐dependent, whereas the mode‐dependent controller and the mode‐independent controller are designed in this paper.…”

Section: Introductionmentioning

confidence: 99%

Disturbance‐observer–based control for Markov jump systems with time‐varying delay

Gao

2017

Optim Control Appl Methods

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Summary This paper deals with disturbance‐observer–based control for Markov jump systems with time‐varying delay. A disturbance observer is constructed to estimate the disturbance generated by an exogenous dynamic system. Meantime, a control scheme is proposed to guarantee the corresponding system to be stochastically stable and achieve the purpose of suppressing the corresponding disturbance. By constructing the stochastic Lyapunov‐Krasovskii functional, the desired observer and the controller are designed to ensure stochastic stability of the closed‐loop system. Finally, the simulation results illustrate the effectiveness of the proposed schemes.

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Disturbance‐observer‐based‐control and L ₂ − L _∞ resilient control for Markovian jump non‐linear systems with multiple disturbances and its application to single robot arm system

Cited by 54 publications

References 31 publications

Mixed passive / H_∞ hybrid control for delayed Markovian jump system with actuator constraints and fault alarm

Mixed passive / H_∞ hybrid control for delayed Markovian jump system with actuator constraints and fault alarm

Observer‐based H_∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

Disturbance‐observer–based control for Markov jump systems with time‐varying delay

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Disturbance‐observer‐based‐control and L 2 − L ∞ resilient control for Markovian jump non‐linear systems with multiple disturbances and its application to single robot arm system

Cited by 54 publications

References 31 publications

Mixed passive / H∞ hybrid control for delayed Markovian jump system with actuator constraints and fault alarm

Mixed passive / H∞ hybrid control for delayed Markovian jump system with actuator constraints and fault alarm

Observer‐based H∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

Disturbance‐observer–based control for Markov jump systems with time‐varying delay

Contact Info

Product

Resources

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Disturbance‐observer‐based‐control and L ₂ − L _∞ resilient control for Markovian jump non‐linear systems with multiple disturbances and its application to single robot arm system

Mixed passive / H_∞ hybrid control for delayed Markovian jump system with actuator constraints and fault alarm

Mixed passive / H_∞ hybrid control for delayed Markovian jump system with actuator constraints and fault alarm

Observer‐based H_∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates