Fixed-time stabilization control for port-Hamiltonian systems

Liu, Xinggui; Liao, Xiaofeng

doi:10.1007/s11071-019-04867-0

Cited by 22 publications

(26 citation statements)

References 30 publications

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“…The Port-controlled Hamiltonian (PCH) system has been studied well [ 1 – 4 ] since it was put forward [ 5 , 6 ]. In practical systems, the Hamilton function [ 7 – 9 ], as the total energy containing kinetic energy and potential energy, is a good candidate of Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation

Wang

2021

PLoS ONE

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The finite-time stabilization and finite-time H∞ control problems of Port-controlled Hamiltonian (PCH) systems with disturbances and input saturation (IS) are studied in this paper. First, by designing an appropriate output feedback, a strictly dissipative PCH system is obtained and finite-time stabilization result for nominal system is given. Second, with the help of the Hamilton function method and truncation inequality technique, a novel output feedback controller is developed to make the PCH system finite-time stable when IS occurs. Further, a finite-time H∞ controller is designed to attenuate disturbances for PCH systems with IS, and sufficient conditions are presented. Finally, a numerical example and a circuit example are given to reveal the feasibility of the obtained theoretical results.

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Section: Introductionmentioning

confidence: 99%

Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation

Wang

2021

PLoS ONE

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“…Due to the above characteristics, in the past 30 years, the PCH systems have drawn great attention in many related control designs, including Hamiltonian realization, 7 stabilization and  ∞ control, 8,9 parallel simultaneous stabilization, 10,11 stochastic feedback stabilization, 12 finite-time (or fixed-time) stabilization, and  ∞ control. 13,14 In addition, the uncertainties, such as parametric uncertainties, model uncertainties, inadequate modeling, widely exist in practical systems, which can adversely affect the performance of systems. In recent years, adaptive control strategies have been extensively applied to investigate PCH systems with parametric uncertainties.…”

Section: Introductionmentioning

confidence: 99%

“…19 It should be pointed out that the existing literatures concerning (uncertain) PCH systems mainly focused on infinite interval. And, it is well known that the precondition of the finite-time (or fixed-time) control problems in the literatures 13,14 is that the closed-loop PCH systems are stable on the infinite interval.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the Hamiltonian functions of the PCH systems, the sum of potential and kinetic energies for physical systems, can been regarded as admissible Lyapunov function candidates. Due to the above characteristics, in the past 30 years, the PCH systems have drawn great attention in many related control designs, including Hamiltonian realization, 7 stabilization and

ℋ_{\infty}

control, 8,9 parallel simultaneous stabilization, 10,11 stochastic feedback stabilization, 12 finite‐time (or fixed‐time) stabilization, and

ℋ_{\infty}

control 13,14 …”

Section: Introductionmentioning

confidence: 99%

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Finite‐time adaptive control for port‐controlled Hamiltonian systems with parametric perturbations

Wei

Wang

et al. 2022

Adaptive Control & Signal

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Summary In this article, finite‐time boundedness (FTB) and ℋ∞ control are addressed for a class of port‐controlled Hamiltonian (PCH) systems with parametric perturbations. Based on adaptive state feedback control strategies, sufficient conditions are obtained for FTB of the PCH systems with parametric perturbation and external disturbances. Furthermore, another adaptive state feedback controller is applied to compensate the parameter perturbation and attenuate the external disturbances, and finite‐time ℋ∞ control conditions are acquired for the PCH systems with parametric perturbation and external disturbances. In addition, the FTB and finite‐time ℋ∞ control conditions are also given for uncertain nonlinear systems via the Hamiltonian realization method. Finally, the numerical simulations are presented to verify the feasibility of the proposed results.

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“…For example, Zuo et al [32] summarized the latest progress in applying fixed-time cooperative control to multi-agent systems. Liu et al [33] discussed the local and global fixed-time stability respectively for a port-Hamiltonian system based on interconnected and damped distributed passive control technology, and defined the fixed-time stable area and stable boundary. In terms of spacecraft on-orbit control applications, Jiang, Shi, Chen et al [34][35][36] designed an adaptive nonsingular fixed-time sliding mode controller with the consideration of system uncertainty, external interference, actuator failure, and input saturation.…”

Section: Introductionmentioning

confidence: 99%

Safe Proximity Operation to Rotating Non-Cooperative Spacecraft with Complex Shape Using Gaussian Mixture Model-Based Fixed-Time Control

et al. 2020

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This paper studies the safety control problem for rotating spacecraft proximity maneuver in presence of complex shaped obstacles. First, considering the attitude change of the target spacecraft, a dynamic model of close-range relative motion in a body-fixed coordinate system is derived using a novel approach. Then, the Gaussian mixture model (GMM) is utilized to reconstruct the complex shape of the spacecraft, and a novel GMM-based artificial potential function (APF) is proposed to represent the collision avoidance requirement. By combining GMM-based APF with fixed-time stability methodology, a fixed-time control (FTC) is designed for close-range proximity operation to a rotating spacecraft having a complex shape. The presented GMM-FTC scheme can guarantee the convergence of relative state errors, and ensure that no collision occurs. Finally, simulation results are provided to illustrate the feasibility of the proposed control approach.

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Fixed-time stabilization control for port-Hamiltonian systems

Cited by 22 publications

References 30 publications

Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation

Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation

Finite‐time adaptive control for port‐controlled Hamiltonian systems with parametric perturbations

Safe Proximity Operation to Rotating Non-Cooperative Spacecraft with Complex Shape Using Gaussian Mixture Model-Based Fixed-Time Control

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