Identification of distributed-parameter systems by stochastic solution of partial differential equations

Filtering equations are derived for processes described by linear partial differential equations with known homogeneous boundary conditions. Both discrete-time and continuous-time measurements are treated. As in the case of linear systems with time delays, the filtering and variance equations become partial differential equations for processes with continuous measurements. A numerical solution to the nonlinear variance equation is obtained for a particular diffusion process.

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An Efficient Computational Procedure for the Optimization of a Class of Distributed Parameter Systems

Journal of Basic Engineering ◽

10.1115/1.3571057 ◽

1969 ◽

Vol 91 (2) ◽

pp. 190-194 ◽

Cited By ~ 6

Author(s):

D. A. Wismer

Keyword(s):

Optimal Control ◽

Differential Equations ◽

Optimal Control Problem ◽

Control Problem ◽

Broad Class ◽

Distributed Parameter Systems ◽

Parabolic Partial Differential Equation ◽

Distributed Parameter ◽

Total System ◽

Partial Differential

The optimal control problem for a broad class of distributed parameter systems defined by vector parabolic partial differential equations is considered. The problem is solved by discretizing the spatial domain and then treating the (large) resultant set of ordinary differential equations as a set of independent subsystems. The subsystems are determined by decomposition of the total system into lower-dimensional problems and the necessary conditions for optimality of the overall system are then satisfied by an iterative procedure. With this treatment, the optimal control problem can be solved for larger systems (or finer spatial discretizations) than would otherwise be feasible. An example is given for a system described by a nonlinear parabolic partial differential equation in one space dimension.

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Backstepping and sliding modes for observer design of distributed parameter system

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331216661621 ◽

2016 ◽

Vol 40 (2) ◽

pp. 542-549 ◽

Cited By ~ 4

Author(s):

Abdessamad Abdelhedi ◽

Wided Saadi ◽

Driss Boutat ◽

Lasaad Sbita

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Exponential Convergence ◽

Integral Transformation ◽

Design Method ◽

Observer Design ◽

Distributed Parameter ◽

Sliding Modes ◽

Partial Differential ◽

Distributed Parameters

The observer design for partial differential equations has so far been an open problem. In this paper, an observer design for systems with distributed parameters using sliding modes theory and backstepping-like procedure in order to achieve exponential convergence is presented. Such an observer is built using the knowledge available within and throughout an integral transformation of Volterra with the output injection functions. The gains of the observer, which are attained by solving a partial differential equations system with output injection, will guarantee the exponential convergence of the observer. The design method is applied to an epidemic system to consider the sensitive population S.

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Fault Diagnosis of Distributed Parameter Systems Modeled by Linear Parabolic Partial Differential Equations With State Faults

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4037332 ◽

2017 ◽

Vol 140 (1) ◽

Cited By ~ 3

Author(s):

Hasan Ferdowsi ◽

S. Jagannathan

Keyword(s):

Fault Diagnosis ◽

Fault Detection ◽

Differential Equations ◽

Detection Threshold ◽

Distributed Parameter Systems ◽

Remaining Useful Life ◽

Distributed Parameter ◽

Parabolic Pdes ◽

Partial Differential ◽

Fault Parameters

In this paper, the problem of fault diagnosis in distributed parameter systems (DPS) is investigated. The behavior of DPS is best described by partial differential equation (PDE) models. In contrast to transforming the DPS into a finite set of ordinary differential equations (ODE) prior to the design of control or fault detection schemes by using significant approximations, thus reducing the accuracy and reliability of the overall system, in this paper, the PDE representation of the system is directly utilized to construct a fault detection observer. A fault is detected by comparing the detection residual, which is the difference between measured and estimated outputs, with a predefined detection threshold. Once the fault is detected, an adaptive approximator is activated to learn the fault function. The estimated fault parameters are then compared with their failure thresholds to provide an estimate of the remaining useful life of the system. The scheme is verified in simulations on a heat system which is described by parabolic PDEs.

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