Passivity based control of a class of Hamiltonian systems with nonholonomic constraints

Fujimoto, Kenji; Sakai, Satoru; Sugie, Toshiharu

doi:10.1016/j.automatica.2012.08.032

Cited by 44 publications

(29 citation statements)

References 17 publications

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“…[49][50][51][52][53][54][55][56] H(x) is called Hamiltonian function, which is the total energy in physical system, and can play the role of Lyapunov function for the system. In Definition 2, it is assumed that the Hamiltonian function has a positive quadratic form structure, which is familiar in many physical systems, such as mechanical systems, 54,55 RLC circuit, 49,56 and permanent magnet synchronous motor. 49 According to Definition 2, we know that the DHR of the nonlinear system (4) can be obtained by the compensating operation of the designed parameterized controller.…”

Section: Lemma 1 (See the Work Of Langson And Allcync 48 )mentioning

confidence: 99%

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Zhu

Hou

2018

Intl J Robust & Nonlinear

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Summary This paper considers the global feedback exponential stabilization and L2 gain disturbance attenuation problems of the switched nonlinear polynomial systems with passive and nonpassive subsystems for any given average dwell time. In the existing result, it needs that there exists at least one open loop passive subsystem in the switched nonlinear system, which is unnecessary for the switched nonlinear polynomial system in this paper because the passivity of the subsystem can be obtained according to the passivity‐based feedback dissipative Hamiltonian realization. In addition, a parameterization of controller approach–based feedback exponential stabilization method of nonlinear polynomial system is described and utilized such that the Lyapunov function of the passive subsystem possesses the required decay rate to exponentially stabilize the switched nonlinear polynomial system. Comparing with the controller designed with the existing method, the obtained controller in this paper has much simpler structure and better performance. An example simulation is provided to illustrate the effectiveness of the proposed approach.

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Section: Lemma 1 (See the Work Of Langson And Allcync 48 )mentioning

confidence: 99%

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Zhu

Hou

2018

Intl J Robust & Nonlinear

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“…In the case of mechanical pH systems with nonholonomic constraints IDA-PBC has been used in [3], [19], [11]. In this paper, we follow the Hamiltonian formulation proposed in [21] to describe NHMS with disturbances.…”

Section: Introductionmentioning

confidence: 99%

Smooth stabilisation of nonholonomic robots subject to disturbances

Donaire

Romero

Pérez

et al. 2015

2015 IEEE International Conference on Robotics and Automation (ICRA)

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In this paper, we address the problem of stabilisation of robots subject to nonholonommic constraints and external disturbances using port-Hamiltonian theory and smooth time-invariant control laws. This should be contrasted with the commonly used switched or time-varying laws. We propose a control design that provides asymptotic stability of an manifold (also called relative equilibria)-due to the Brockett condition this is the only type of stabilisation possible using smooth time-invariant control laws. The equilibrium manifold can be shaped to certain extent to satisfy specific control objectives. The proposed control law also incorporates integral action, and thus the closed-loop system is robust to unknown constant disturbances. A key step in the proposed design is a change of coordinates not only in the momentum, but also in the position vector, which differs from coordinate transformations previously proposed in the literature for the control of nonholonomic systems. The theoretical properties of the control law are verified via numerical simulation based on a robotic ground vehicle model with differential traction wheels and non co-axial centre of mass and point of contact.

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“…Please note that this portHamiltonian has the very similar form as a port-Hamiltonian system with nonholonomic constraints. 19) The difference is that the present system (12a) is canonical and consequently its state trajectory always satisfies the constraint (7).…”

Section: Port-hamiltonian Modelingmentioning

confidence: 99%

“…Namely, the result in this paper is expected to work for high dimensional systems with quaternions such as space robot systems, rendezvous control systems and so on. Also, it can be easily applied to other control purposes such as trajectory tracking control 20) and/or partial state feedback control 19) and so on.…”

Section:                           mentioning

confidence: 99%

See 1 more Smart Citation

On Port-Hamiltonian Modeling and Control of Systems with Quaternions

Fujimoto

Takeuchi

Matsumoto

2016

AEROSPACE TECHNOLOGY JAPAN

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A quaternion representation is often used to describe the attitude of a spacecraft because it does not have any singular points. However, it becomes difficult to control the attitude described by a quaternion since a quaternion has four parameters despite that the attitude has only three degrees of freedom. In this paper, we employ the concept of port-Hamiltonian modeling to control systems with quaternions to introduce a general nonlinear control system synthesis method in aerospace engineering. It is also shown that the error quaternions are also naturally described by the port-Hamiltonian framework. Furthermore, the additional design parameter achieved by the proposed method is utilized for obstacle avoidance control. A numerical example exhibits the effectiveness of the proposed method.

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Passivity based control of a class of Hamiltonian systems with nonholonomic constraints

Cited by 44 publications

References 17 publications

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Smooth stabilisation of nonholonomic robots subject to disturbances

On Port-Hamiltonian Modeling and Control of Systems with Quaternions

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Passivity based control of a class of Hamiltonian systems with nonholonomic constraints

Cited by 44 publications

References 17 publications

Robust H∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Robust H∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Smooth stabilisation of nonholonomic robots subject to disturbances

On Port-Hamiltonian Modeling and Control of Systems with Quaternions

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Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach