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Singular perturbations in optimal control

Rocky Mountain Journal of Mathematics, 1976
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Modeling and Transient Stability Analysis for Type-3 Wind Turbines Using Singular Perturbation and Lyapunov Methods

IEEE transactions on industrial electronics (1982. Print), 2023
Wind turbines (WTs) are prone to transient instability during weak grid faults, which is caused by their complex interactions. However, it is a challenge to analyze the transient stability, due to high-order and strong nonlinearity.
Yumei Ma, Donghai Zhu, Ziqin Zhang, X. Zou, Jiabing Hu, Yong Kang   +5 more
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Singular Perturbation-Based Adaptive Integral Sliding Mode Control for Flexible Joint Robots

IEEE transactions on industrial electronics (1982. Print), 2023
The flexible joint robot (FJR) typically experiences parametric variations, nonlinearities, underactuation, noise propagation, and external disturbances which seriously degrade the FJR tracking.
Raja Fawad Afsar Khan, Kamal Rsetam, Z. Cao, Z. Man   +3 more
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Singular Perturbation for the Dynamic Modeling of Integrated Energy Systems

IEEE Transactions on Power Systems, 2020
An integrated energy system (IES) represents coordinated operations of constrained natural gas (NG), electric power, and thermal systems in three distinctly different time scales.
Fu Shen, P. Ju, M. Shahidehpour, Zhiyi Li, Chong Wang, Xingyu Shi   +5 more
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Full-State Tracking Control for Flexible Joint Robots With Singular Perturbation Techniques

IEEE Transactions on Control Systems Technology, 2019
This paper proposes a practical method to realize multivariable full-state tracking control for industrial robots with elastic joints. Unlike existing methods, the proposed method does not require high-order derivatives of the link states such as ...
Joonyoung Kim, E. Croft
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Nonfragile $\mathcal{H}_{\infty}$ Control for Fuzzy Markovian Jump Systems Under Fast Sampling Singular Perturbation

IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018
This paper is concerned with the nonfragile ${\mathcal {H}_{\infty }}$ control problem for discrete-time fast sampling Markovian jump singularly perturbed nonlinear systems described by the Takagi-Sugeno fuzzy model.
Hao Shen, Yunzhe Men, Zhengguang Wu, Ju H. Park   +3 more
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SINGULAR PERTURBATION AND INTERPOLATION

Mathematical Models and Methods in Applied Sciences, 1994
It is well known that the rate of convergence of the solution uε of a singular perturbed problem to the solution u of the unperturbed equation can be measured in terms of the “smoothness” of u; smoothness which, in turn, can be expressed in terms of linear interpolation theory.
BAIOCCHI C., SAVARE', GIUSEPPE
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Singular Perturbation-Based Fault-Tolerant Control of the Air-Breathing Hypersonic Vehicle

IEEE/ASME transactions on mechatronics, 2019
This article studies the fault-tolerant control issue of the air-breathing hypersonic vehicle subject to the actuator fault. Through singular perturbation modeling, the longitudinal dynamics of the vehicle can be transformed into a three-time-scale ...
Wenjing Ren, B. Jiang, Hao Yang
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Singular Perturbations of Bifurcations

SIAM Journal on Applied Mathematics, 1977
An asymptotic theory is presented to analyze perturbations of bifurcations of the solutions of nonlinear problems. The perturbations may result from imperfections, impurities, or other inhomogeneities in the corresponding physical problem. It is shown that for a wide class of problems the perturbations are singular.
Bernard J. Matkowsky, Edward L. Reiss
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Corner singularities and singular perturbations

ANNALI DELL UNIVERSITA DI FERRARA, 2001
Summary: A corner singularity expansion is developed for a singularly perturbed elliptic boundary value problem. The problem is set in a sector of the plane. In the expansion, particular attention is paid to the singular perturbation parameter. The result is used to give pointwise bounds on derivatives of the solution.
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