Stabilization analysis of time-delay Hamiltonian systems in the presence of saturation

Sun, Wei

doi:10.1016/j.amc.2011.04.044

Cited by 50 publications

(37 citation statements)

References 20 publications

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“…On account of this advantage, the Hamilton function approach has caused broad attention in the field of nonlinear controller design, as well as in practical control problems (see, e.g., [2][3][4] and the references therein). Recently, the authors obtain some results on time delay Hamiltonian systems (see, e.g., [5][6][7][8]). In [5], the stabilization problem of Hamiltonian systems with state time delay and input saturation is investigated.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the authors obtain some results on time delay Hamiltonian systems (see, e.g., [5][6][7][8]). In [5], the stabilization problem of Hamiltonian systems with state time delay and input saturation is investigated. Sufficient conditions are derived by using Lyapunov-Krasovskii functional theorem to guarantee the systems as well as the resulted closed-loop systems by output feedback asymptotically stable when input saturation effectively occurs.…”

Section: Introductionmentioning

confidence: 99%

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Observer-based robust adaptive control for uncertain stochastic Hamiltonian systems with state and input delays

Sun

Peng

2014

NAMC

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Abstract. This paper investigates the observer-based robust adaptive control problem for a class of stochastic Hamiltonian systems. The systems under consideration relate to parameter uncertainties, unknown state time-delay and input delay. The purpose is to design a delay-dependent observerbased adaptive control law such that for all admissible uncertainties, as well as stochasticity, the closed-loop error system is robustly asymptotically stable in the mean square. Several sufficient conditions are presented to ensure the rationality and validity of the proposed control laws and observers, which are derived based on Lyapunov functional method. Numerical simulations spell out to illustrate the effectiveness of the proposed theories.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observer-based robust adaptive control for uncertain stochastic Hamiltonian systems with state and input delays

Sun

Peng

2014

NAMC

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“…37 The stabilization problem was addressed for a class of Hamiltonian systems with state time-delay and input saturation in the work of Sun. 38 Considering input saturation and unknown external disturbance, an adaptive control for single input uncertain nonlinear systems was investigated in the work of Wen et al, 39 where an auxiliary design system was proposed to dispose the effect of input constraints. In the work of Chen et al, 40 involving external disturbances and input constraints, a constrained controller was designed for multi-input and multi-output nonlinear systems based on a sliding mode disturbance observer.…”

Section: Introductionmentioning

confidence: 99%

“…Input saturation has an effect on control performance, which has been investigated in the last few decades. [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] The Takagi-Sugeno fuzzy modeling approach was utilized to control the nonlinear systems with actuator saturation in the work of Cao and Lin. 37 The stabilization problem was addressed for a class of Hamiltonian systems with state time-delay and input saturation in the work of Sun.…”

Section: Introductionmentioning

confidence: 99%

Robust adaptive constrained boundary control for a suspension cable system of a helicopter

Ren

Shi

2017

Adaptive Control & Signal

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SummaryIn this article, the problems of modeling and controlling are investigated for a suspension cable system of a helicopter with input saturation, system parameter uncertainties, and external disturbances by using the boundary control method.In accordance with the Hamilton's principle, the model of the suspension cable system of a helicopter is established by using a set of partial differential and ordinary differential equations. Considering nonsymmetric saturation constraint, the auxiliary systems are designed to handle with the effect of input saturation. Considering Lyapunov's direct method and the designed auxiliary systems, two robust adaptive boundary controllers are provided by the actuators at the helicopter and the box. Under the proposed controllers, the error between the bottom payload and the target location and the vibration range are uniformly ultimately bounded. Moreover, they will converge to a small neighborhood of zero by selecting the suitable parameters. Meanwhile, to guarantee the validity of the proposed adaptive boundary control laws, some sufficient conditions are raised. Simulation results are provided to verify that the effectiveness of the designed controllers in this paper.

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“…It is known that stability is an important research topic in the mathematical field [1][2][3][4][5][6][7][8][9][10][11][12][13]. As a special class of mathematical models, neural networks are similar to the brain synapses link structure; neural networks possess multiple dynamic behaviors [14].…”

Section: Introductionmentioning

confidence: 99%

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

Yogambigai

Ali

Zhu

et al. 2018

Mathematical Problems in Engineering

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The problem of exponential Lagrange stability analysis of Markovian jump neural networks with leakage delay and mixed timevarying delays is studied in this paper. By utilizing the Lyapunov functional method, employing free-weighting matrix approach and inequality techniques in matrix form, we establish several novel stability criteria such that, for all admissible parameter uncertainties, the suggested neural network is exponentially stable in Lagrange sense. The derived criteria are expressed in terms of linear matrix inequalities (LMIs). A numerical example is provided to manifest the validity of the proposed results.

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Stabilization analysis of time-delay Hamiltonian systems in the presence of saturation

Cited by 50 publications

References 20 publications

Observer-based robust adaptive control for uncertain stochastic Hamiltonian systems with state and input delays

Observer-based robust adaptive control for uncertain stochastic Hamiltonian systems with state and input delays

Robust adaptive constrained boundary control for a suspension cable system of a helicopter

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

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