Uncertain polytopic LPV modelling of robot manipulators and trajectory tracking

Jabali, Mohammad Bagher Abolhasani; Kazemi, Mohammad Hosein

doi:10.1007/s12555-015-1432-1

Cited by 20 publications

(12 citation statements)

References 27 publications

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“…This MI reformulation is always feasible for any x due to to the inclusion of the soft constraint terms (h) . Since all of the sets in the original problem were compact, we are assured of finding positive constants μ, ν, ξ, ω, ¯ and ῡ to bound the inequalities in (18).…”

Section: S (H)mentioning

confidence: 99%

“…By requiring one to solve a nonlinear multi-parametric optimization problem online, with the current state measurement serving as the parameter, this method directly enforces a certain degree of contraction possessed by the CLF at every control step. While solving a numerical optimization problem online provides flexibility and performance guarantees, the real-time computational efforts required complicate its application in polytopic linear systems characterized by the high sampling rates frequently encountered, e.g., in fault-tolerant control of aerial vehicles [15], [16], energy-to-peak filtering [17], or robot manipulators control [18].…”

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confidence: 99%

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Neural network controllers for uncertain linear systems

Fabiani¹,

Goulart²

2022

Preprint

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We consider the design of reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems affected by polytopic uncertainty, including controllers with variable structure and those based on a minimal selection policy. We develop a systematic procedure to certify the closed-loop stability and performance of a polytopic system when a rectified linear unit (ReLU)-based approximation replaces such traditional controllers. We provide sufficient conditions to ensure stability involving the worst-case approximation error and the Lipschitz constant characterizing the error function between ReLU-based and traditional controller-based state-to-input mappings, and further provide offline, mixed-integer optimization-based methods that allow us to compute those quantities exactly.

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Section: S (H)mentioning

confidence: 99%

mentioning

confidence: 99%

Neural network controllers for uncertain linear systems

Fabiani¹,

Goulart²

2022

Preprint

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“…v 1 and v 2 are the elasticity of joints 1 and 2 (Liu, 1997;Anderson, 1985). Moreover, the constant damping coefficients t 1 and t 2 are used to denote the system damping which is concentrated at joints 1 and 2 totally (Jabali and Kazemi, 2017;Liu, 1997).…”

Section: A Two-link Robotic Manipulatormentioning

confidence: 99%

Identification of nonlinear state-space time-delay system

Liu

Zhang

Peng

et al. 2019

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Purpose This paper aims to investigate an identification strategy for the nonlinear state-space model (SSM) in the presence of an unknown output time-delay. The equations to estimate the unknown model parameters and output time-delay are derived simultaneously in the proposed strategy. Design/methodology/approach The unknown integer-valued time-delay is processed as a latent variable which is uniformly distributed in a priori known range. The estimations of the unknown time-delay and model parameters are both realized using the Expectation-Maximization (EM) algorithm, which has a good performance in dealing with latent variable issues. Moreover, the particle filter (PF) with an unknown time-delay is introduced to calculated the Q-function of the EM algorithm. Findings Although amounts of effective approaches for nonlinear SSM identification have been developed in the literature, the problem of time-delay is not considered in most of them. The time-delay is commonly existed in industrial scenario and it could cause extra difficulties for industrial process modeling. The problem of unknown output time-delay is considered in this paper, and the validity of the proposed approach is demonstrated through the numerical example and a two-link manipulator system. Originality/value The novel approach to identify the nonlinear SSM in the presence of an unknown output time-delay with EM algorithm is put forward in this work.

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“…where F 0 = 30 N , Δ F = 15 N and the fast-rate sampling period is selected as Δ t = 0 . 1 s . The phsical parameters of this manipulator system are presented by Jabali et al 37 N = 2000 fast-rate sampled data points are generated and the slow-rate sampling period is chosen as five times of the fast-rate sampling period. The random output time-delay takes an integer in range [ 0 , 4 ] and M = 400 slowly sampled outputs are collected.…”

Section: Verificationsmentioning

confidence: 99%

Linear parameter-varying systems identification with slowly sampled outputs subjected to unknown time-delays and outliers

Liu

Yang

Guo³

2018

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article proposes a robust global identification approach for nonlinear systems with slowly sampled outputs subjected to unknown time-delays. The inputs of the system are fast-rate sampled while the informative outputs are uniformly sampled at a slow rate. In practical industries, the outlier and output time-delays are commonly encountered and they are both considered in this work. To eliminate the impact brought by the outliers, the robust linear parametervarying finite impulse response observation model based on the Laplace distribution is established. The unknown timedelay is treated as a random integer at each sampling moment which follows the uniform distribution with the boundary known a priori. The proposed robust approach is derived in the expectation-maximization algorithm scheme and the formulas to iteratively update the model parameters, the scale parameter and the random output time-delays are derived, respectively. The unmeasurable noise-free fast-rate sampled outputs are estimated by simulating the identified model. A numerical example, the mass-spring-damper system and the two-link robotic manipulator are utilized to verify the effectiveness of the proposed approach.

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Uncertain polytopic LPV modelling of robot manipulators and trajectory tracking

Cited by 20 publications

References 27 publications

Neural network controllers for uncertain linear systems

Neural network controllers for uncertain linear systems

Identification of nonlinear state-space time-delay system

Linear parameter-varying systems identification with slowly sampled outputs subjected to unknown time-delays and outliers

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