An energy-based derivation of lyapunov functions for forced systems with application to stabilizing control

Maschke, Bernhard; Schaft, A.J. van der; Escobar, G.

doi:10.1016/s1474-6670(17)56431-9

Cited by 32 publications

(29 citation statements)

References 6 publications

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“…At the same time, it is well-known from finite-dimensional non-linear control systems [7,19,25,26,[29][30][31]33] that the (generalized) Hamiltonian formulation may be very helpful in the control design, and even more is to be expected in the distributed-parameter case. However, in extending the Hamiltonian theory as for instance exposed in [24] to distributed-parameter control systems a fundamental difficulty arises in the treatment of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In the lumped-parameter case this Hamiltonian framework has been successfully employed in the consistent (modular) modeling and simulation of complex interconnected lumped-parameter physical systems, including (actuated) multi-body systems with kinematic constraints and electro-mechanical systems [7,18,30,31], and in the design and control of such systems, exploiting the Hamiltonian and passivity structure in a crucial way [19,25,26,29,30,33]. Similar developments can be pursued in the distributed-parameter case; see already [27,32] for some initial ideas in this direction.…”

Section: Introductionmentioning

confidence: 99%

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Hamiltonian formulation of distributed-parameter systems with boundary energy flow

Schaft

Maschke

2002

Journal of Geometry and Physics

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474

393

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hamiltonian formulation of distributed-parameter systems with boundary energy flow

Schaft

Maschke

2002

Journal of Geometry and Physics

Self Cite

474

393

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“…For this class of systems, multiple approaches for control have been developed, mainly based either on continuous time approaches (i.e. sliding mode [1], passivity based control [2], stabilizing control [3],...), or on hybrid approaches (i.e. model predictive control [4], supervisory control [5],...).…”

Section: Introductionmentioning

confidence: 99%

Stabilizing control for power converters connected to transmission lines

Zainea

Schaft

Buisson

2007

2007 American Control Conference

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Abstract-This paper proposes a switching control strategy for the set-point stabilization of a power converter connected via a transmission line to a resistive load. The strategy employs a Lyapunov function that is directly based on energy considerations of the power converter, as well as of the transmission line described by the telegraph equations. The proposed stabilizing switching control still allows a certain freedom in the choice of the control law, a comparison between a maximum descent strategy and a minimum commutation strategy being discussed on a simple example.

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“…In recent years, the problem of energy-based Lyapunov functions was investigated intensively. The theory of the passivity-based control has been well-established [16], [18], [25]. Particularly, the port-controlled Hamiltonian systems were studied by [11], [15], [17].…”

mentioning

confidence: 99%

Pseudo-Hamiltonian realization and its application

Cheng

Shen

Tarn

2002

Communications in Information and Systems

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Abstract. In this paper, the problem of pseudo-Hamiltonian realization of a control system is studied. Several sufficient conditions are obtained. The stability of a dynamic system is investigated via dissipative pseudo-Hamiltonian realization, and the stabilization of a control system is also investigated via feedback dissipative pseudo-Hamiltonian realization. Some relations between the stability (asymptotical stability) with the dissipative (strict dissipative) realization are revealed. Relations between the affine dissipative control systems and the dissipative pseudo-Hamiltonian realization are also investigated. These results show that the set of pseudo-Hamiltonian systems represent a very large class of interesting dynamic systems, and this approach is a powerful tool. Particularly, a generalization of the Krasovskii's Theorem is obtained. Then the problem of L 2 disturbance attenuation of a nonlinear system via pseudo-Hamiltonian realization is investigated. It is shown that for a class of pseudo-Hamiltonian systems the disturbance attenuation problem is solvable and an estimation of the boundary of the L 2 gain is obtained. Finally the results are applied to the excitation control of power systems. The stabilization and the H∞ control problems are investigated for the singlemachine infinite bus power systems.

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An energy-based derivation of lyapunov functions for forced systems with application to stabilizing control

Cited by 32 publications

References 6 publications

Hamiltonian formulation of distributed-parameter systems with boundary energy flow

Hamiltonian formulation of distributed-parameter systems with boundary energy flow

Stabilizing control for power converters connected to transmission lines

Pseudo-Hamiltonian realization and its application

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