Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

Wang, Yuzhen; Cheng, Daizhan; Ge, Shuzhi Sam

doi:10.1016/j.sysconle.2006.08.005

Cited by 22 publications

(19 citation statements)

References 24 publications

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“…An affirmative (constructive) answer has been given in [27], but the proposed has singularities. See also [18], [29], [35] and the discussion in Subsection 4.2.2 of [34].…”

Section: A Cyclo-passivity Of Port-hamiltonian Systemsmentioning

confidence: 99%

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Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems

Ortega

Schaft

Castaños

et al. 2008

IEEE Trans. Automat. Contr.

280

200

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Abstract-The dynamics of many physical processes can be suitably described by Port-Hamiltonian (PH) models, where the importance of the energy function, the interconnection pattern and the dissipation of the system is underscored. To regulate the behavior of PH systems it is natural to adopt a Passivity-Based Control (PBC) perspective, where the control objectives are achieved shaping the energy function and adding dissipation. In this paper we consider the PBC techniques of Control by Interconnection () and Standard PBC. In the controller is another PH system connected to the plant (through a power-preserving interconnection) to add up their energy functions, while in Standard PBC energy shaping is achieved via static state feedback. In spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems, the current version of imposes a severe restriction on the plant dissipation structure that stymies its practical application. On the other hand, Standard PBC, which is usually derived from a uninspiring and non-intuitive "passive output generation" viewpoint, is one of the most successful controller design techniques. The main objectives of this paper are: (1) To extend the method to make it more widely applicable-in particular, to overcome the aforementioned dissipation obstacle. (2) To show that various popular variants of Standard PBC can be derived proceeding from a unified perspective. (3) To establish the connections between and Standard PBC proving that the latter is obtained restricting the former to a suitable subset-providing a nice geometric interpretation to Standard PBC-and comparing the size of the set of PH plants for which they are applicable.

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“…An affirmative (constructive) answer has been given in [27], but the proposed has singularities. See also [18], [29], [35] and the discussion in Subsection 4.2.2 of [34].…”

Section: A Cyclo-passivity Of Port-hamiltonian Systemsmentioning

confidence: 99%

“…where is defined as (35) Then, for all functions , the cyclo-passivity inequality (26) with storage function (27) is satisfied.…”

Section: Sm Psmentioning

confidence: 99%

Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems

Ortega

Schaft

Castaños

et al. 2008

IEEE Trans. Automat. Contr.

280

200

View full text Add to dashboard Cite

show abstract

“…It is clear from (17) that the skew symmetricity of J implies that y T J(x)y = 0, ∀x, y ∈ R n , which means that H is a conserved quantity (first integral) of the system if R = 0. These facts motivate us to use the notion of generalized Hamiltonian systems.…”

Section: Generalized Hamiltonian Systemsmentioning

confidence: 99%

“…In [17], an effective general algorithm is presented for obtaining the approximate dissipative Hamiltonian realization and constructing local Lyapunov functions for continuous time nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Local dissipative Hamiltonian description of reversible reaction networks

Otero-Muras

Szederkényi

Alonso

et al. 2008

Systems & Control Letters

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In this letter we show that closed reversible chemical reaction networks with independent elementary reactions admit a global pseudoHamiltonian structure which is at least locally dissipative around any equilibrium point. The structure matrix of the Hamiltonian description reflects the graph topology of the reaction network and it is a smooth function of the concentrations of the chemical species in the positive orthant. The physical interpretation of the description is briefly explained and two illustrative examples are presented for global and local dissipative Hamiltonian description, respectively.

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“…Remark 4. Based on the existing dissipative Hamiltonian realization (DHR) methods [9,10] , the parameterization method given in Theorem 1 can be used for many general affine nonlinear systems. From the proof of Theorem 1, we know that the Hamiltonian function H(x) can be used to build a corresponding Lyapunov function of the system.…”

Section: Design Of a Family Of Adaptive H H H ∞ ∞ ∞ Controllers With mentioning

confidence: 99%

A family of adaptive H ∞ controllers with full information for dissipative hamiltonian systems

Hou

2011

Int. J. Autom. Comput.

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This paper investigates a parameterization method of adaptive H∞ controllers for dissipative Hamiltonian systems with disturbances and unknown parameters. The family of adaptive H∞ controllers with full information is obtained by interconnecting an adaptive H∞ controller with a generalized zero-energy-gradient (ZEG) detectable, free generalized Hamiltonian system. The present parameterization method avoids solving Hamilton-Jacobi-Issacs equations and thus the controllers obtained are easier in operation as compared to some existing ones. Simulations show the effectiveness and feasibility of the adaptive control strategy proposed in this paper.

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Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

Cited by 22 publications

References 24 publications

Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems

Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems

Local dissipative Hamiltonian description of reversible reaction networks

A family of adaptive H ∞ controllers with full information for dissipative hamiltonian systems

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