A new algorithm for approximating the state of nonlinear systems

Zimmer, Gerta

doi:10.1080/00207729308949521

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…We use the gradient descent method, see [23] and Annexe C of [26], to seek the minimum of J. The key step of this algorithm is to find the descent direction of J at the point ξ 0 , h .…”

Section: The Algorithm Of Identificationmentioning

confidence: 99%

Identification of water depth and velocity potential for water waves

Yang

Pei

2019

Systems & Control Letters

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The purpose of this paper is to investigate the identification of the water depth and the water velocity potential in a coastal region by using the linearized water wave equation (LWWE). Existence and uniqueness of the solutions to the partial differential equation LWWE are shown by using the semigroup theory. Moreover the analytical solution is found by the separation of variables method. We assume that the surface wave elevation is measurable. We like to recover the water depth and the water velocity potential from the measurement. This identification problem is shown to be well-posed by proving the parameters' identifiability by the surface elevation. Based on the classical gradient descent method we elaborate an identification algorithm to recover simultaneously both the water depth and the velocity potential. Numerical simulations are carried out to illustrate effectiveness of the algorithm. through the mathematical model of water waves and measuring the surface wave elevation.The water wave equation consists in describing the motion of the water waves occupying a domain delimited below by a fixed bottom and by a free surface above. To write down the water wave equation, let Ω t = {(x, z) ∈ R + × (−h, η(x, t)) } denote the water domain in 2-dimensional euclidian framework as illustrated in Fig.??, where R + = [0, ∞), η(x, t) is the surface elevation of water wave at position x and time t, and h the water depth. We assume that the water and the water waves satisfy the following assumptions: (A1) The water is incompressible ; (A2) There is no surface tension and the water is inviscid; (A3) The water particles do not cross the bottom and the surface; (A4) The external pressure is constant; (A5) The seabed is flat, so that h is positive constant; (A6) The water wave is irrotational. Since the irrotational assumption has been made, consequently there exists a flow potential φ = φ(x, z, t) such that the velocity field V is written by V = (φ x , φ z ) T , where φ x , φ z denote the partial derivative of φ with respect to x and to z, respectively. Thus, the mass conservation is expressed by the Laplace equationwith the boundary condition at the bottom φ z = 0, on z = −h.The Neumann condition (2) means that at the bottom of seabed, the normal component of the velocity is zero. The dynamical and kinematical boundary conditions on the free surface are

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“…We use the gradient descent method, see [23] and Annexe C of [26], to seek the minimum of J. The key step of this algorithm is to find the descent direction of J at the point ξ 0 , h .…”

Section: The Algorithm Of Identificationmentioning

confidence: 99%

Identification of water depth and velocity potential for water waves

Yang

Pei

2019

Systems & Control Letters

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“…Recently, moving horizon state estimators based on fitting of nonlinear dynamic models to online measurements have been developed (Moraal et al, 1995;Zimmer, 1993). They have good robustness properties and are easy to tune, but require more complex on-line computations compared to traditional techniques.…”

Section: State Estimation Techniquesmentioning

confidence: 99%

Indirect Measurement and Control of Moisture Content During Dehydration Performed by Frying

Trystram

Trelea²,

Raoult-Wack

et al. 1999

Drying Technology

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Frying is one of the way for performing drying of food material that permits to obtain very short duration. However the control of such operation is difficult because of the immersion of product into hot oil bath that imply difficult or impossible sensors implementation. Such problems are encoutered for Dehydration Soaking Process (DISP). In the case of Batch drying using frying of food stuffs, an original approach is presented. An indirect measurement of moisture content is performed as a combination of easy to do oil bath temperature mesasurement and an estimator.Validation is provided and performance is well established. Because of the ability of moisture content real time measurements, a control strategy is studied and put into practice. An optimal predictive controller is proprosed, able to put into practice several kind of control objectives.Results are discussed and extension of the strategy is introduced.

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Adaptive Receding Horizon State Estimation for Non Linear Processes

Boillereaux¹,

Flaus²

1995

Adaptive Systems in Control and Signal Processing 1995

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A new algorithm for approximating the state of nonlinear systems

Cited by 5 publications

References 11 publications

Identification of water depth and velocity potential for water waves

Identification of water depth and velocity potential for water waves

Indirect Measurement and Control of Moisture Content During Dehydration Performed by Frying

Adaptive Receding Horizon State Estimation for Non Linear Processes

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