Stabilization of Input-Disturbed Stochastic Port-Hamiltonian Systems Via Passivity

Fang, Zhou; Gao, Chuanhou

doi:10.1109/tac.2017.2676619

Cited by 21 publications

(15 citation statements)

References 23 publications

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“…Remark The function

ϕ (x) = {false[g^{T} (x) g (x) false]}^{- 1} g^{T} (x)

could be given alternatively by

ϕ (x) = g {(x)}^{†} + [I_{n} - g {(x)}^{†} g (x)] ζ

if rank( g ( x )) < m , where (·) † denotes the Moore–Penrose generalized inverse and

ζ \in ℝ^{n}

. The condition (16) could be satisfied for many practical systems by prefeedback control technologies, stochastic generalized canonical transformations 16,17 and energy‐shaping methods 18 …”

Section: Energy‐based Output Regulation Of Sphss Via Internal Modelmentioning

confidence: 99%

“…Naturally, as an extension of deterministic port‐Hamiltonian systems, stochastic port‐Hamiltonian systems (SPHSs) described by It

\hat{o}

or Stratonovich stochastic differential equations have drawn attention recently 16‐20 . Satoh and Fujimoto 16 developed a class of coordinate transformations to preserve the stochastic port‐Hamiltonian structure, and presented a passivity‐based controller for stabilizing SPHSs in probability.…”

Section: Introductionmentioning

confidence: 99%

“…Satoh and Fujimoto 16 developed a class of coordinate transformations to preserve the stochastic port‐Hamiltonian structure, and presented a passivity‐based controller for stabilizing SPHSs in probability. Fang and Gao 17 extended SPHSs to Id‐SPHSs which emphasize the influence of the stochastic disturbances coming from both the process and the input, and designed a corresponding passivity‐based controller. Haddad et al 18 developed an energy‐based control method for SPHSs that provides a shaped energy function to preserve the Hamiltonian structure of the closed‐loop system.…”

Section: Introductionmentioning

confidence: 99%

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Energy‐based output regulation for stochastic port‐Hamiltonian systems

Wang

Chen

2020

Intl J Robust & Nonlinear

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This article investigates the output regulation for stochastic port‐Hamiltonian systems (SPHSs) subject to sinusoidal disturbances. An energy‐based regulation scheme with an internal model unit is proposed by exploiting the stochastic Hamiltonian structure, which drives the tracking error to the origin while maintaining asymptotical stability in probability of the closed‐loop system. An energy‐based robust regulation scheme as well as an alternative condition is then developed without solving Hamilton–Jacobi–Issacs inequalities. The proposed regulators preserve the stochastic Hamiltonian structure of the disturbed SPHS by coordinate transformation. Hence the output regulation problems fall into the stabilization framework for SPHSs and there is no need to solve regulator equations. These results cover the stabilization of SPHSs and the output regulation of deterministic port‐Hamiltonian systems. Simulations on an inverted pendulum show the effectiveness of the proposed methods.

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“…Remark The function

ϕ (x) = {false[g^{T} (x) g (x) false]}^{- 1} g^{T} (x)

could be given alternatively by

ϕ (x) = g {(x)}^{†} + [I_{n} - g {(x)}^{†} g (x)] ζ

if rank( g ( x )) < m , where (·) † denotes the Moore–Penrose generalized inverse and

ζ \in ℝ^{n}

. The condition (16) could be satisfied for many practical systems by prefeedback control technologies, stochastic generalized canonical transformations 16,17 and energy‐shaping methods 18 …”

Section: Energy‐based Output Regulation Of Sphss Via Internal Modelmentioning

confidence: 99%

“…Naturally, as an extension of deterministic port‐Hamiltonian systems, stochastic port‐Hamiltonian systems (SPHSs) described by It

\hat{o}

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Energy‐based output regulation for stochastic port‐Hamiltonian systems

Wang

Chen

2020

Intl J Robust & Nonlinear

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“…To control the acceleration of a mobile inverted pendulum (MIP), a nonlinear controller based on IDA-PBC is developed in [11]. In [12], an input disturbed stochastic port Hamiltonian system (Id-SPHS) is stabilized by a PBC controller. The model considers state and input disturbances.…”

Section: Introductionmentioning

confidence: 99%

Port-Hamiltonian Modeling and Control of a Micro-Channel Experimental Plant

2020

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We present a port-Hamiltonian system (PHS) model based on the interconnection between basic hydraulic elements equivalent to electrical components such as capacitors, inductors, and resistors to represent the dynamics of a water micro-channel experimental plant. We compare the fluid-structured interconnected PHS model with the data obtained from a micro-channel experimental plant. We then implement a controller using the total hydraulic-mechanical energy as a local Lyapunov function. Finally, we apply an integral action controller (IAC) to correct for modeling errors and load disturbances. The IAC is easy to design given the proposed interconnected model. INDEX TERMS Fluid-structured interconnected system, Micro-channel model identification, Local Lyapunov function, Integral Action Controller.

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“…For this reason, the current work is devoted to stabilizing in probability the CSTR systems with state and input both disturbed. By utilizing the (state, input)-disturbed stochastic port-Hamiltonian system (sidSPHS) framework (Fang & Gao, 2017), we can rewrite the (state, input)-disturbed CSTR (sidCSTR) model to be a sid-SPHS with the opposite entropy function as the Hamiltonian. A notable advantage for this rewritten version is that it can characterize both the first law and second law of thermodynamics.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of (state, input)-disturbed CSTRs through the port-Hamiltonian systems approach

Lu,

Fang,

Gao

2017

Preprint

Self Cite

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It is a universal phenomenon that the state and input of the continuous stirred tank reactor (CSTR) systems are both disturbed. This paper proposes a (state, input)-disturbed port-Hamiltonian framework that can be used to model and further designs a stochastic passivity based controller to asymptotically stabilize in probability the (state, input)-disturbed CSTR (sidCSTR) systems. The opposite entropy function and the availability function are selected as the Hamiltonian for the model and control purposes, respectively. Furthermore, the proposed (state, input)-disturbed port-Hamiltonian model can simultaneously characterize the first law and the second law of thermodynamics when the opposite entropy function acts as the Hamiltonian. A simple CSTR example illustrates how the port-Hamiltonian method is utilized for modeling and controlling sidCSTR systems.

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Stabilization of Input-Disturbed Stochastic Port-Hamiltonian Systems Via Passivity

Cited by 21 publications

References 23 publications

Energy‐based output regulation for stochastic port‐Hamiltonian systems

Energy‐based output regulation for stochastic port‐Hamiltonian systems

Port-Hamiltonian Modeling and Control of a Micro-Channel Experimental Plant

Stabilization of (state, input)-disturbed CSTRs through the port-Hamiltonian systems approach

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